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    <title>DEV Community: Piyush Chauhan</title>
    <description>The latest articles on DEV Community by Piyush Chauhan (@frorning).</description>
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      <title>Integration Is the Product: Platform Engineering for Fast Frontend Teams</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 12 Sep 2026 13:26:14 +0000</pubDate>
      <link>https://dev.to/frorning/integration-is-the-product-platform-engineering-for-fast-frontend-teams-1df8</link>
      <guid>https://dev.to/frorning/integration-is-the-product-platform-engineering-for-fast-frontend-teams-1df8</guid>
      <description>&lt;p&gt;&lt;em&gt;How local composition, exact artifacts, and versioned releases turn a dependency queue into continuous feedback.&lt;/em&gt;&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.us-east-2.amazonaws.com%2Fuploads%2Farticles%2Fpdmfwsn02t6q7w3ap3kd.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.us-east-2.amazonaws.com%2Fuploads%2Farticles%2Fpdmfwsn02t6q7w3ap3kd.png" alt="A visual overview of the four feedback loops: local workbench, real product shell, PR preview, and versioned release." width="800" height="336"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;strong&gt;The useful measure of team autonomy is not “can it publish?” It is “how quickly can the team see its exact change running in a realistic product?”&lt;/strong&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;A frontend package can compile, test, and publish successfully—and still break when the product shell owns routing, authentication, server-side rendering (SSR), hydration, global styles, middleware, or a singleton dependency such as React.&lt;/p&gt;

&lt;p&gt;I learned this through a familiar local loop:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;build package → pnpm pack → edit the shell's package.json → install → run → discover → repeat
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;That loop proves the product boundary matters. It is also a warning: integration has become manual, temporary state leaks into committed files, and every cross-team change waits for the central application to catch up.&lt;/p&gt;

&lt;p&gt;The answer is not “never integrate” or “put everything in a monorepo.” The answer is to make integration a &lt;strong&gt;self-service product capability&lt;/strong&gt;: composable locally, verified as an artifact, previewable in a pinned product, and promotable as an immutable release.&lt;/p&gt;

&lt;h2&gt;
  
  
  The model in one picture
&lt;/h2&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.us-east-2.amazonaws.com%2Fuploads%2Farticles%2Ft8xr2428kx3qceib0git.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.us-east-2.amazonaws.com%2Fuploads%2Farticles%2Ft8xr2428kx3qceib0git.png" alt="Four feedback loops progress from a fast local workbench to a real shell, an exact-artifact preview, and an immutable release." width="800" height="345"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;Each loop answers a different question. Do not make the slowest one the default.&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Loop&lt;/th&gt;
&lt;th&gt;Question it answers&lt;/th&gt;
&lt;th&gt;Default use&lt;/th&gt;
&lt;th&gt;Evidence it produces&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;1. Domain workbench&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Does the domain feature behave correctly?&lt;/td&gt;
&lt;td&gt;Daily implementation&lt;/td&gt;
&lt;td&gt;Fast, deterministic UI and contract feedback&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;2. Local product composition&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Does my source work in the real shell?&lt;/td&gt;
&lt;td&gt;Host-boundary changes&lt;/td&gt;
&lt;td&gt;Routing, auth, SSR, hydration, styling feedback&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;3. PR product preview&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Does the artifact I intend to ship work in a clean product?&lt;/td&gt;
&lt;td&gt;Before merge&lt;/td&gt;
&lt;td&gt;A reviewable URL using exact candidate bytes&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;4. Versioned release&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Is this selected composition healthy under shared and production conditions?&lt;/td&gt;
&lt;td&gt;Promotion&lt;/td&gt;
&lt;td&gt;Canary and operational evidence&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;The important design rule:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;strong&gt;A failure found in an outer loop should improve the cheapest inner loop that can catch it next time.&lt;/strong&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;Some failures—real traffic, irreversible migrations, external side effects—belong in the outer loop. Pretending every risk can move left makes local feedback less trustworthy, not more.&lt;/p&gt;

&lt;h2&gt;
  
  
  A concrete example: the Booking module
&lt;/h2&gt;

&lt;p&gt;Assume a &lt;strong&gt;Booking&lt;/strong&gt; frontend module mounted in a product shell. It calls Hotel APIs, participates in auth and routing, emits booking events, and server-renders UI.&lt;/p&gt;

&lt;p&gt;Here are the four boundaries where its “green” isolated build can still fail:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;┌──────────────────┐    ┌────────────────────────┐
│ Booking package  │───▶│ Product shell          │
│ exports, assets, │    │ routing, auth, SSR,    │
│ peer dependencies│    │ hydration, CSS         │
└────────┬─────────┘    └──────────┬─────────────┘
         │                         │
         ▼                         ▼
┌──────────────────┐    ┌────────────────────────┐
│ Domain contracts │    │ Environment and data   │
│ Hotel API/events │    │ pinned versions, known │
│ errors, timing   │    │ scenarios, replayable  │
└──────────────────┘    └────────────────────────┘
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  1. Build and artifact boundary
&lt;/h3&gt;

&lt;p&gt;Local linking can succeed while the published tarball omits types, CSS, assets, compiled files, or an export-map entry. It can also hide bad peer-dependency resolution.&lt;/p&gt;

&lt;p&gt;A particularly expensive frontend failure is a duplicate singleton: Booking bundles React or framework context while the shell expects to own it. Hooks, contexts, or hydration then fail only in the composed application.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Design consequence:&lt;/strong&gt; support fast local source overrides &lt;em&gt;and&lt;/em&gt; install the packed artifact into a clean shell in CI. Neither replaces the other.&lt;/p&gt;

&lt;h3&gt;
  
  
  2. Platform and runtime boundary
&lt;/h3&gt;

&lt;p&gt;A mini-shell is valuable, but it is not the product. The real shell may resolve auth asynchronously, evaluate flags on the server, enforce CSP, select locale, apply global CSS, and hydrate browser markup.&lt;/p&gt;

&lt;p&gt;A synchronous fake user can hide a lifecycle race. A &lt;code&gt;window&lt;/code&gt; access can pass locally and fail during SSR. A global selector can quietly override the product header.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Design consequence:&lt;/strong&gt; teams need an easy route into the real shell before release—not a handoff to another team.&lt;/p&gt;

&lt;h3&gt;
  
  
  3. Domain contract boundary
&lt;/h3&gt;

&lt;p&gt;Types alone are not contracts. A Hotel response can make a field optional; an event can be duplicated; a shared package can preserve its type while changing runtime behavior.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Design consequence:&lt;/strong&gt; contracts need examples for absence, errors, timeout, compatibility, and delivery semantics. Providers own valid fakes; consumers own the assumptions they make.&lt;/p&gt;

&lt;h3&gt;
  
  
  4. Environment and data boundary
&lt;/h3&gt;

&lt;p&gt;A shared environment called &lt;code&gt;dev&lt;/code&gt; is usually a location, not a reproducible state. It may contain yesterday’s Hotel build, today’s Payment candidate, mutable test accounts, and an unannounced shell change.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Design consequence:&lt;/strong&gt; pin composition and provide named, deterministic data scenarios. A passing result should be attributable; a failure should be replayable.&lt;/p&gt;

&lt;h2&gt;
  
  
  The paved road: two local modes, one composition contract
&lt;/h2&gt;

&lt;p&gt;The productive workflow is not “fake everything” versus “run the whole company.” It offers two intentionally different local modes.&lt;/p&gt;

&lt;h3&gt;
  
  
  Mode A: domain workbench
&lt;/h3&gt;

&lt;p&gt;The workbench mounts local Booking with the production rendering mode, design system, route contract, and named auth, flag, and locale scenarios. Hotel and Payment provide provider-owned fakes; inexpensive, behaviorally important infrastructure can run locally.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;platform dev
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Use it for focused work. It should be fast, deterministic, usable offline where practical, and let an engineer select success, absence, timeout, error, and authorization states in one command.&lt;/p&gt;

&lt;h3&gt;
  
  
  Mode B: real-shell composition
&lt;/h3&gt;

&lt;p&gt;The real product shell runs with released dependencies while the developer substitutes only local Booking source and gets HMR.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;platform dev &lt;span class="nt"&gt;--composition&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;integration-stable
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Use it when the change touches routing, auth lifecycle, SSR/hydration, global CSS, middleware, or framework ownership. It removes the &lt;code&gt;pnpm pack&lt;/code&gt; / edit-manifest / reinstall loop without claiming to prove the tarball.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.us-east-2.amazonaws.com%2Fuploads%2Farticles%2F0dbd3cgh7mnvvye9bfxa.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.us-east-2.amazonaws.com%2Fuploads%2Farticles%2F0dbd3cgh7mnvvye9bfxa.png" alt="A resolved composition makes every local override, remote dependency, and scenario visible." width="800" height="400"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;Both modes resolve the same &lt;strong&gt;composition contract&lt;/strong&gt;. The interface can be a CLI, package-manager feature, dev server, container stack, or managed environment; the durable part is the input and output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight yaml"&gt;&lt;code&gt;&lt;span class="na"&gt;composition&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;integration-stable@sha256:8f1e...&lt;/span&gt;
&lt;span class="na"&gt;shell&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;product-shell@13.2.1&lt;/span&gt;
&lt;span class="na"&gt;modules&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
  &lt;span class="na"&gt;booking&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="na"&gt;mode&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;local-source&lt;/span&gt;
    &lt;span class="na"&gt;path&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;../booking&lt;/span&gt;
    &lt;span class="na"&gt;watch&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;
  &lt;span class="na"&gt;hotel&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="na"&gt;mode&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;integration-stable&lt;/span&gt;
    &lt;span class="na"&gt;version&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;5.8.2&lt;/span&gt;
  &lt;span class="na"&gt;payment&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="na"&gt;mode&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;fake&lt;/span&gt;
    &lt;span class="na"&gt;scenario&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;authorized&lt;/span&gt;
&lt;span class="na"&gt;scenarios&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
  &lt;span class="na"&gt;auth&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;signed-in-customer&lt;/span&gt;
  &lt;span class="na"&gt;locale&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;en-GB&lt;/span&gt;
&lt;span class="na"&gt;data&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
  &lt;span class="na"&gt;booking&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;local-isolated&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;A good &lt;code&gt;platform dev&lt;/code&gt; command does four things before it starts:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Resolves peer, shell-API, rendering-mode, and contract compatibility.&lt;/li&gt;
&lt;li&gt;Leaves the application’s normal &lt;code&gt;package.json&lt;/code&gt; and lockfile untouched.&lt;/li&gt;
&lt;li&gt;Watches &lt;strong&gt;only&lt;/strong&gt; explicit local overrides; released components remain immutable.&lt;/li&gt;
&lt;li&gt;Prints the resolved versions, modes, paths, scenario IDs, and manifest digest.&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;That last point matters. “Works on my machine” is useful only when “it” has an identity another developer or CI job can reproduce.&lt;/p&gt;

&lt;p&gt;Useful companion commands are straightforward:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;platform preview  &lt;span class="c"&gt;# create or show this change's pinned preview&lt;/span&gt;
platform trace    &lt;span class="c"&gt;# inspect correlated diagnostics&lt;/span&gt;
platform doctor   &lt;span class="c"&gt;# explain peers, credentials, ports, versions, dependencies&lt;/span&gt;
platform reset    &lt;span class="c"&gt;# remove generated state; never normal project files&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  Let contracts unblock implementation—not conversation
&lt;/h2&gt;

&lt;p&gt;Composition accelerates feedback after code exists. Contracts solve the earlier scheduling problem: &lt;strong&gt;how can Booking start when Hotel is not finished?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;The teams still need to agree on meaning. The goal is to turn that agreement into a versioned candidate someone can consume immediately.&lt;/p&gt;

&lt;p&gt;For a cancellable reservation hold, the sequence is:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Agree on the smallest useful contract.&lt;/strong&gt; Request, response, errors, idempotency, timeout expectations, and representative examples.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Publish a provider-owned candidate.&lt;/strong&gt; Hotel ships the contract plus valid fixtures, fake adapter, or mock server under an immutable candidate ID.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Implement the consumer against it.&lt;/strong&gt; Booking exercises success, absence, timeout/error, and compatibility scenarios in the workbench.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Verify the provider against the same agreement.&lt;/strong&gt; Hotel’s CI verifies the implementation. Consumer-driven contracts can run concrete consumer expectations before merge; &lt;a href="https://docs.pact.io/" rel="noopener noreferrer"&gt;Pact&lt;/a&gt; is one option.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Compose both candidates.&lt;/strong&gt; The preview pins Booking and Hotel candidates for product-level review.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Keep a declared compatibility window.&lt;/strong&gt; Support current and previous versions unless an exception is explicit and time-bounded.
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;semantic decision
        │
        ▼
provider contract candidate ──────▶ consumer implementation
        │                                      │
        └──── provider verification ◀──────────┘
                         │
                         ▼
               pinned combined preview
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This separates a necessary &lt;strong&gt;semantic dependency&lt;/strong&gt; from an avoidable &lt;strong&gt;implementation dependency&lt;/strong&gt;. Contract verification does not prove assembled-product behavior, so the combined preview remains necessary.&lt;/p&gt;

&lt;h2&gt;
  
  
  Test the bytes you will release
&lt;/h2&gt;

&lt;p&gt;Source composition is for speed. Artifact verification is for release confidence.&lt;/p&gt;

&lt;p&gt;Before merge, CI should:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;build once → pack once → attach commit and provenance → clean install into pinned shell → test → preview
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;For a Node package, &lt;a href="https://pnpm.io/cli/pack" rel="noopener noreferrer"&gt;&lt;code&gt;pnpm pack&lt;/code&gt;&lt;/a&gt; produces the tarball under test. The clean shell install should verify exports, included files, types, assets, lifecycle behavior, package metadata, SSR/hydration where relevant, and only the critical product journeys affected by the module.&lt;/p&gt;

&lt;p&gt;The artifact that passes is the artifact that moves forward. Rebuilding for staging or production invalidates prior evidence.&lt;/p&gt;

&lt;p&gt;The shell owns singleton dependencies such as React, framework runtimes, and shared contexts. Modules declare supported ranges through &lt;code&gt;peerDependencies&lt;/code&gt; rather than bundling private copies. A compatibility manifest adds constraints package resolution cannot express—such as supported shell APIs, rendering modes, or contract generations—and fails an invalid composition with an explanation before it runs.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://slsa.dev/spec/v1.2/provenance" rel="noopener noreferrer"&gt;Provenance&lt;/a&gt; answers a different question: which source revision and CI build produced these tested bytes? It complements, rather than replaces, compatibility testing.&lt;/p&gt;

&lt;h2&gt;
  
  
  Preview a product, not an isolated copy of the company
&lt;/h2&gt;

&lt;p&gt;A PR preview should be a &lt;strong&gt;hybrid composition&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;dedicate the changed Booking candidate and shell where needed;&lt;/li&gt;
&lt;li&gt;reuse known-stable Hotel, Payment, and other remote services;&lt;/li&gt;
&lt;li&gt;pin every reused version;&lt;/li&gt;
&lt;li&gt;expose the final composition and artifact IDs in the preview.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;This gives QA, design, and product a reviewable URL without creating a full company clone for every pull request. It catches artifact omissions, clean-install failures, selected cross-domain behavior, and visual product issues. It still has bounded data, traffic, scale, and external integrations—so it is strong evidence, not a production guarantee.&lt;/p&gt;

&lt;h2&gt;
  
  
  GitOps gives promotion a memory
&lt;/h2&gt;

&lt;p&gt;A composition is already declarative, so GitOps is useful connective tissue between verified bytes and running environments. It does not “solve integration”; it records, applies, and reconciles a selected product state.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight yaml"&gt;&lt;code&gt;&lt;span class="na"&gt;composition&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;booking-canary-2026-09-12&lt;/span&gt;
&lt;span class="na"&gt;shell&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;product-shell@13.2.1&lt;/span&gt;
&lt;span class="na"&gt;components&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
  &lt;span class="na"&gt;booking&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="na"&gt;artifact&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;registry.example/booking@sha256:4d8c...&lt;/span&gt;
    &lt;span class="na"&gt;version&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;7.5.0&lt;/span&gt;
    &lt;span class="na"&gt;sourceCommit&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;91ac...&lt;/span&gt;
    &lt;span class="na"&gt;buildProvenance&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;attestations/booking/4d8c...&lt;/span&gt;
  &lt;span class="na"&gt;hotel&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="na"&gt;artifact&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;registry.example/hotel@sha256:70be...&lt;/span&gt;
    &lt;span class="na"&gt;version&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;5.8.2&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;candidate artifact → composition-manifest PR → verification + preview
    → merge → reconciled environment → canary → manifest revert if unhealthy
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This aligns with the &lt;a href="https://opengitops.dev/#principles" rel="noopener noreferrer"&gt;OpenGitOps principles&lt;/a&gt;: desired state is declarative, versioned and immutable, automatically pulled, and continuously reconciled.&lt;/p&gt;

&lt;p&gt;Keep environment semantics distinct:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Environment&lt;/th&gt;
&lt;th&gt;Purpose&lt;/th&gt;
&lt;th&gt;What may change it?&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;integration-latest&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Early compatibility signal from accepted updates&lt;/td&gt;
&lt;td&gt;Accepted component updates&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;integration-stable&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Dependable baseline for local hybrid development&lt;/td&gt;
&lt;td&gt;Deliberate known-compatible promotion&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;staging / release candidate&lt;/td&gt;
&lt;td&gt;Release evidence&lt;/td&gt;
&lt;td&gt;Deliberately selected manifest only&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;production&lt;/td&gt;
&lt;td&gt;Real customer and traffic evidence&lt;/td&gt;
&lt;td&gt;Canary promotion of a reviewed manifest&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;Routine deployments must not mutate staging. Otherwise it becomes contested shared workspace exactly when it needs to represent a release candidate.&lt;/p&gt;

&lt;p&gt;A manifest revert restores the prior artifact digest. It cannot reverse destructive migrations or external side effects, so every module still needs a forward- and backward-compatible migration strategy.&lt;/p&gt;

&lt;h2&gt;
  
  
  Make failure attributable in one screen
&lt;/h2&gt;

&lt;p&gt;Pinning versions is necessary but incomplete. Reproducibility also needs data and diagnostics.&lt;/p&gt;

&lt;p&gt;A provisioned Booking scenario should have a &lt;code&gt;testRunId&lt;/code&gt;, TTL, and cleanup policy. Records across Booking, Hotel, and Payment carry that identifier where permitted. Stable fixtures are immutable or automatically reset; tests needing mutation receive isolated data.&lt;/p&gt;

&lt;p&gt;Requests and events should propagate trace and request IDs plus:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;module version · product composition ID · contract version · testRunId
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;a href="https://opentelemetry.io/docs/concepts/signals/traces/" rel="noopener noreferrer"&gt;OpenTelemetry&lt;/a&gt; provides the trace and context-propagation model. Adding composition context makes a trace actionable integration evidence.&lt;/p&gt;

&lt;p&gt;A failed Booking request should answer:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Which Booking artifact and product composition handled it?&lt;/li&gt;
&lt;li&gt;Which Hotel contract and service version were selected?&lt;/li&gt;
&lt;li&gt;Which test scenario supplied the data?&lt;/li&gt;
&lt;li&gt;Where did time or failure enter the trace?&lt;/li&gt;
&lt;li&gt;Which team owns the failing capability and what changed last?&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Ownership then follows the boundary: Booking triages a failure in its artifact; Hotel owns a published-contract violation; the platform team owns a composition engine rejection of a valid declared configuration. A bare failure routed to a team channel recreates the integration queue.&lt;/p&gt;

&lt;h2&gt;
  
  
  Start small: improve one developer journey
&lt;/h2&gt;

&lt;p&gt;Do not begin by building a universal portal. Begin with the most painful edit-to-integrated-feedback loop and give it a measurable exit condition.&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Stage&lt;/th&gt;
&lt;th&gt;Deliverable&lt;/th&gt;
&lt;th&gt;Exit condition&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;1. Make composition explicit&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Pinned shell/module versions, clean artifact install&lt;/td&gt;
&lt;td&gt;Any authorized engineer can reproduce a candidate from clean state without editing &lt;code&gt;package.json&lt;/code&gt;.&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;2. Shorten local feedback&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Workbench, named scenarios, real-shell local overrides&lt;/td&gt;
&lt;td&gt;One command reaches a usable shell while the normal lockfile remains unchanged.&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;3. Move compatibility before merge&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Candidate contracts, packed-artifact CI, hybrid preview&lt;/td&gt;
&lt;td&gt;CI installs exact candidates into a clean pinned composition and reviewers can identify every changed/reused component.&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;4. Close the production loop&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;GitOps manifests, canary, trace metadata, ownership routing&lt;/td&gt;
&lt;td&gt;The PR-tested artifact reaches canary/production unchanged and a safe revert restores the prior compatible version.&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;Measure the wait, not the tooling:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;median edit-to-feedback time, separately for workbench and real shell;&lt;/li&gt;
&lt;li&gt;percentage of PRs verified with the exact artifact later promoted;&lt;/li&gt;
&lt;li&gt;local composition startup &lt;strong&gt;success&lt;/strong&gt; rate, not just process starts;&lt;/li&gt;
&lt;li&gt;preview request-to-ready and recovery time;&lt;/li&gt;
&lt;li&gt;failures found before versus after merge, classified by boundary;&lt;/li&gt;
&lt;li&gt;dependency-update lead time and blocked days caused by cross-team dependencies;&lt;/li&gt;
&lt;li&gt;deployment failure/recovery outcomes and observed developer task success.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;a href="https://dora.dev/guides/dora-metrics/" rel="noopener noreferrer"&gt;DORA’s delivery metrics&lt;/a&gt; are useful alongside these leading indicators. Do not turn them into a cross-team leaderboard: trends for one product journey reveal more than a blended organizational number.&lt;/p&gt;

&lt;h2&gt;
  
  
  Integration is the platform product
&lt;/h2&gt;

&lt;p&gt;A weak platform makes teams publishable, then centralizes the moment of truth. A healthy platform makes the product boundary continuously available to the team changing it.&lt;/p&gt;

&lt;p&gt;For Booking, that means one connected path:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;local source in real shell
  → exact packed candidate in clean CI
  → pinned PR preview
  → reviewed composition manifest
  → canary with traceable identity
  → manifest revert when healthy evidence disappears
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Packages, separate repositories, and independent releases can all support this model. The decisive capability is faster, self-service feedback at progressively realistic levels—not the repository topology or a portal.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Integration is not the gate after development. Integration is the product the platform team provides.&lt;/strong&gt;&lt;/p&gt;

&lt;h2&gt;
  
  
  References
&lt;/h2&gt;

&lt;ol&gt;
&lt;li&gt;&lt;a href="https://github.com/cncf/tag-app-delivery/blob/main/platforms-whitepaper/latest/index.md" rel="noopener noreferrer"&gt;CNCF Platforms White Paper&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://dora.dev/capabilities/platform-engineering/" rel="noopener noreferrer"&gt;DORA: Platform engineering capability&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://dora.dev/guides/dora-metrics/" rel="noopener noreferrer"&gt;DORA: Software delivery performance metrics&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://opengitops.dev/#principles" rel="noopener noreferrer"&gt;OpenGitOps principles v1.0.0&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://docs.pact.io/" rel="noopener noreferrer"&gt;Pact introduction&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://pnpm.io/cli/pack" rel="noopener noreferrer"&gt;pnpm &lt;code&gt;pack&lt;/code&gt; documentation&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://slsa.dev/spec/v1.2/provenance" rel="noopener noreferrer"&gt;SLSA provenance&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://opentelemetry.io/docs/concepts/signals/traces/" rel="noopener noreferrer"&gt;OpenTelemetry trace concepts&lt;/a&gt;&lt;/li&gt;
&lt;/ol&gt;

</description>
      <category>platformengineering</category>
      <category>frontend</category>
      <category>architecture</category>
      <category>devops</category>
    </item>
    <item>
      <title>Graph Coloring: A Simple Implementation with JavaScript</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Tue, 08 Sep 2026 17:04:14 +0000</pubDate>
      <link>https://dev.to/frorning/graph-coloring-a-simple-implementation-with-javascript-4jdo</link>
      <guid>https://dev.to/frorning/graph-coloring-a-simple-implementation-with-javascript-4jdo</guid>
      <description>&lt;h2&gt;
  
  
  Introduction
&lt;/h2&gt;

&lt;p&gt;Graph coloring is a fundamental problem in computer science and graph theory, often used to solve various real-world problems such as scheduling tasks, register allocation in compilers, and solving map coloring puzzles. In this article, we will explore how to implement a simple graph coloring algorithm using JavaScript.&lt;/p&gt;

&lt;h2&gt;
  
  
  What is Graph Coloring?
&lt;/h2&gt;

&lt;p&gt;Graph coloring involves assigning colors to the vertices of a graph such that no two adjacent vertices share the same color. The goal is to use the minimum number of colors required to achieve this condition.&lt;/p&gt;

&lt;h3&gt;
  
  
  Example: Map Coloring
&lt;/h3&gt;

&lt;p&gt;A classic example is map coloring, where countries (vertices) are colored so that no two adjacent countries have the same color. This ensures that maps can be visually distinguished and avoids confusion between neighboring regions.&lt;/p&gt;

&lt;h2&gt;
  
  
  Implementation in JavaScript
&lt;/h2&gt;

&lt;p&gt;We will implement a graph coloring algorithm using JavaScript objects to represent the graph structure and perform depth-first search (DFS) for coloring.&lt;/p&gt;

&lt;h3&gt;
  
  
  Step-by-Step Guide
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Graph Representation&lt;/strong&gt;:

&lt;ul&gt;
&lt;li&gt;We will use an adjacency list representation of the graph.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Color Assignment&lt;/strong&gt;:

&lt;ul&gt;
&lt;li&gt;We will use DFS to assign colors while ensuring no two adjacent vertices share the same color.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Conflict Detection&lt;/strong&gt;:

&lt;ul&gt;
&lt;li&gt;We will detect conflicts and return false if a valid coloring cannot be achieved.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  JavaScript Code
&lt;/h3&gt;

&lt;p&gt;Here's the complete implementation:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Function to perform the graph coloring using DFS&lt;/span&gt;
&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// If the vertex is already colored, return true&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="kc"&gt;undefined&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Initialize with a default color&lt;/span&gt;
    &lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="nx"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Conflict found&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Conflict found&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// Assign the next available color&lt;/span&gt;
    &lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Function to perform graph coloring on the entire graph&lt;/span&gt;
&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;graphColoring&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;colorMap&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;

    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;vertex&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="nb"&gt;Object&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;keys&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;vertex&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Conflict found&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Coloring scheme:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;colorMap&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Example usage:&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;graph&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;A&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;B&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;C&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="na"&gt;B&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;A&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;D&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="na"&gt;C&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;A&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;D&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;E&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="na"&gt;D&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;B&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;C&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;E&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="na"&gt;E&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;C&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;D&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;

&lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;graphColoring&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Graph is colored successfully!&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Conflict found in graph coloring.&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Explanation
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;dfs Function&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;This function performs a depth-first search to assign colors.&lt;/li&gt;
&lt;li&gt;If the vertex has already been assigned a color, it returns true.&lt;/li&gt;
&lt;li&gt;It initializes the color map for unvisited vertices and recursively assigns the next available color while checking for conflicts.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;graphColoring Function&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Initializes &lt;code&gt;visited&lt;/code&gt; and &lt;code&gt;colorMap&lt;/code&gt; arrays.&lt;/li&gt;
&lt;li&gt;Iterates over all vertices in the graph and calls &lt;code&gt;dfs&lt;/code&gt; for unvisited vertices.&lt;/li&gt;
&lt;li&gt;If a conflict is found during the DFS, it returns false; otherwise, it prints the color map.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Example Graph
&lt;/h3&gt;

&lt;p&gt;Let's consider the example graph:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Vertices&lt;/strong&gt;: A, B, C, D, E&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Edges&lt;/strong&gt;: A-B, A-C, B-D, C-D, C-E, D-E&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The output will be a valid coloring scheme for this graph if one exists.&lt;/p&gt;

&lt;h2&gt;
  
  
  Conclusion
&lt;/h2&gt;

&lt;p&gt;In this article, we explored how to implement a simple graph coloring algorithm using JavaScript. By representing the graph as an adjacency list and performing depth-first search, we can efficiently assign colors while ensuring no two adjacent vertices share the same color.&lt;/p&gt;

</description>
      <category>javascript</category>
      <category>programming</category>
      <category>beginners</category>
      <category>algorithms</category>
    </item>
    <item>
      <title>Navigating Python Development: A Step-by-Step Guide to Using Poetry</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Tue, 08 Sep 2026 17:03:46 +0000</pubDate>
      <link>https://dev.to/frorning/navigating-python-development-a-step-by-step-guide-to-using-poetry-14n3</link>
      <guid>https://dev.to/frorning/navigating-python-development-a-step-by-step-guide-to-using-poetry-14n3</guid>
      <description>&lt;h3&gt;
  
  
  What is Poetry?
&lt;/h3&gt;

&lt;p&gt;Poetry is an opinionated package management system for Python projects. It helps you:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Set up your project&lt;/strong&gt; with all the necessary files.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Manage dependencies&lt;/strong&gt; easily.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Isolate environments&lt;/strong&gt; to ensure that different projects have separate dependencies.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Resolve dependency conflicts&lt;/strong&gt; automatically.&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Why Use Poetry?
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Simplifies Project Setup&lt;/strong&gt;: Automatically generates &lt;code&gt;pyproject.toml&lt;/code&gt; and &lt;code&gt;poetry.lock&lt;/code&gt; files, making it easier to share your project with others.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Environment Management&lt;/strong&gt;: Creates isolated virtual environments for each project, which helps avoid version conflicts.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Dependency Resolution&lt;/strong&gt;: Automatically handles dependencies and their versions, reducing the risk of issues related to dependency mismatches.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Installing Poetry
&lt;/h3&gt;

&lt;p&gt;You can install Poetry using pip:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;pip &lt;span class="nb"&gt;install &lt;/span&gt;poetry
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Creating a New Project with Poetry
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;Open your terminal or command prompt.&lt;/li&gt;
&lt;li&gt;Navigate to the directory where you want to create your project.&lt;/li&gt;
&lt;li&gt;Run the following command to create a new Python project:
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   poetry new my_project
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This will create a new directory named &lt;code&gt;my_project&lt;/code&gt; with the following structure:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;my_project/
├── pyproject.toml
└── src/
    └── my_project/
        ├── __init__.py
        └── main.py
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Managing Dependencies
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Add a Dependency&lt;/strong&gt;: You can add dependencies to your project using the &lt;code&gt;add&lt;/code&gt; command:
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   poetry add requests
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;List Installed Dependencies&lt;/strong&gt;: To see all installed dependencies, use:
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   poetry show
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Update a Dependency&lt;/strong&gt;: To update an existing dependency, use:
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   poetry update requests
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Remove a Dependency&lt;/strong&gt;: To remove a dependency, use:
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   poetry remove requests
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Managing Environments
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Activate the Environment&lt;/strong&gt;: Run the following command to activate your project's virtual environment:
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   poetry shell
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Deactivate the Environment&lt;/strong&gt;: Simply type &lt;code&gt;exit&lt;/code&gt; in the activated shell.&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Running Scripts
&lt;/h3&gt;

&lt;p&gt;You can run scripts from within a Poetry-managed environment by using the &lt;code&gt;poetry run&lt;/code&gt; command:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;poetry run python src/my_project/main.py
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This runs &lt;code&gt;main.py&lt;/code&gt; with the virtual environment's Python interpreter.&lt;/p&gt;

&lt;h3&gt;
  
  
  Summary
&lt;/h3&gt;

&lt;p&gt;Poetry is a powerful tool for managing Python projects. It simplifies dependency management, ensures isolated environments, and helps resolve version &lt;br&gt;
conflicts. By following these steps, you can effectively use Poetry to manage your Python projects.&lt;/p&gt;

</description>
      <category>python</category>
      <category>poetry</category>
      <category>beginners</category>
      <category>tutorial</category>
    </item>
    <item>
      <title>The browser only talks to one server — composing Marko, React, and Riot into one hotel page</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Mon, 07 Sep 2026 12:32:03 +0000</pubDate>
      <link>https://dev.to/frorning/the-browser-only-talks-to-one-server-composing-marko-react-and-riot-into-one-hotel-page-3355</link>
      <guid>https://dev.to/frorning/the-browser-only-talks-to-one-server-composing-marko-react-and-riot-into-one-hotel-page-3355</guid>
      <description>&lt;p&gt;You open a hotel page. It looks like one product: a search grid, a featured stay, local highlights, reviews, a sticky trip summary.&lt;/p&gt;

&lt;p&gt;Under the hood it is &lt;strong&gt;eight HTTP servers and three UI runtimes&lt;/strong&gt;.&lt;/p&gt;

&lt;p&gt;That is the experiment behind &lt;strong&gt;HarborStay&lt;/strong&gt;, a demo booking app I built to answer a stubborn question:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;Can independent teams ship independent UI, in independent frameworks, and still give the browser a single, paint-ready HTML page?&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;The punchline: &lt;strong&gt;yes — if the shell never imports a component.&lt;/strong&gt; It only fetches HTML.&lt;/p&gt;

&lt;h2&gt;
  
  
  The one rule
&lt;/h2&gt;

&lt;p&gt;The browser never talks to a fragment.&lt;/p&gt;

&lt;p&gt;It talks to the &lt;strong&gt;composer&lt;/strong&gt; on port &lt;code&gt;3100&lt;/code&gt;. The composer owns routes, layout, and the booking flow. Everything else is a fragment server that returns a chunk of HTML.&lt;br&gt;
&lt;/p&gt;

&lt;pre data-lang="mermaid"&gt;&lt;code&gt;flowchart LR
  Browser["Browser"] --&amp;gt; Composer["Composer :3100"]

  subgraph fragments["Fragment servers"]
    Nav["Navigation Marko :3101"]
    Search["Hotel search Marko :3102"]
    Details["Hotel details Marko :3103"]
    Reviews["Reviews Marko :3104"]
    Recs["Recommendations Marko :3105"]
    Highlights["Local highlights React :3106"]
    Disco["Experiences discovery Riot :3107"]
    Itin["Experiences itinerary Riot :3108"]
  end

  Composer --&amp;gt; Nav
  Composer --&amp;gt; Search
  Composer --&amp;gt; Details
  Composer --&amp;gt; Reviews
  Composer --&amp;gt; Recs
  Composer --&amp;gt; Highlights
  Composer --&amp;gt; Disco
  Composer --&amp;gt; Itin
  Composer --&amp;gt; CDN["CDN :3200"]&lt;/code&gt;&lt;/pre&gt;



&lt;p&gt;This is the opposite of the usual microfrontend story (Module Federation, shared React, a host that &lt;code&gt;import()&lt;/code&gt;s widgets). HarborStay is &lt;strong&gt;HTML composition&lt;/strong&gt;. The shell does not know whether a fragment was rendered by Marko, React, or a hand-rolled Riot string. It only knows a URL.&lt;/p&gt;

&lt;p&gt;That one constraint buys a lot:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Fragment teams can pick a runtime without asking the shell.&lt;/li&gt;
&lt;li&gt;A fragment outage becomes a fallback box, not a blank page.&lt;/li&gt;
&lt;li&gt;You can deploy search without redeploying reviews.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;It also forces honesty. If two fragments need to share a Redux store, the architecture is already leaking.&lt;/p&gt;

&lt;h2&gt;
  
  
  What the user actually sees
&lt;/h2&gt;

&lt;p&gt;HarborStay models a small premium catalog: &lt;strong&gt;Harbor View Lodge&lt;/strong&gt; in Lisbon, &lt;strong&gt;Copper Hill Suites&lt;/strong&gt; in Seville, &lt;strong&gt;Sunset Terrace House&lt;/strong&gt; in Barcelona, &lt;strong&gt;Moss &amp;amp; Lantern&lt;/strong&gt; in Copenhagen.&lt;/p&gt;

&lt;p&gt;Routes the composer owns:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Route&lt;/th&gt;
&lt;th&gt;What you get&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;code&gt;/&lt;/code&gt; and &lt;code&gt;/hotel/:hotelId&lt;/code&gt;
&lt;/td&gt;
&lt;td&gt;Streaming stays page&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;/experiences/:hotelId&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Neighborhood explorer + day plan&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;/booking/confirm/:hotelId&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Confirmation (I got &lt;code&gt;HS-470455&lt;/code&gt; for Moss &amp;amp; Lantern)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;On &lt;code&gt;/hotel/moss-lantern&lt;/code&gt; the page is not “a React tree.” It is a &lt;strong&gt;layout of slots&lt;/strong&gt;:&lt;br&gt;
&lt;/p&gt;

&lt;pre data-lang="mermaid"&gt;&lt;code&gt;flowchart TB
  subgraph page["One HTML page from the composer"]
    Topbar["Topbar: HarborStay + Stays / Experiences"]
    subgraph main["Main column"]
      Search["Search island: Where to next?"]
      Details["Details island: Featured stay"]
      Highlights["Highlights island: What to do in Copenhagen"]
      Reviews["Reviews island: What travelers say"]
      Recs["Recommendations island: More stays nearby"]
    end
    Sidebar["Sticky trip summary + Book this stay"]
  end&lt;/code&gt;&lt;/pre&gt;



&lt;p&gt;Click &lt;strong&gt;Luxury&lt;/strong&gt; on the search chips and the grid collapses to Harbor View Lodge and Moss &amp;amp; Lantern. The reviews below do not re-fetch. They never heard about the filter. That is not a bug — that is the point.&lt;/p&gt;


&lt;div class="crayons-card c-embed"&gt;

  &lt;br&gt;
&lt;strong&gt;Island rule:&lt;/strong&gt; each fragment owns its own interactivity. Search filters are Marko state. Highlight selection is React state. Experience categories are Riot state. The composer does not have a global store.&lt;br&gt;

&lt;/div&gt;


&lt;h2&gt;
  
  
  A tiny protocol instead of a shared SDK
&lt;/h2&gt;

&lt;p&gt;Every fragment speaks &lt;code&gt;harborstay-fragment/v1&lt;/code&gt;.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight http"&gt;&lt;code&gt;&lt;span class="err"&gt;GET /?hotelId=moss-lantern
GET /manifest
GET /assets/&amp;lt;name&amp;gt;.css
GET /assets/&amp;lt;name&amp;gt;.js
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;And a few provenance headers:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight http"&gt;&lt;code&gt;&lt;span class="err"&gt;X-Fragment-Name: search
X-Fragment-Hotel-Id: moss-lantern
X-Fragment-Protocol: harborstay-fragment/v1
X-Fragment-Css: http://localhost:3200/assets/search.css
X-Fragment-Js:  http://localhost:3200/assets/search.js
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;The composer reads the HTML body. Asset URLs are informational. In this demo, CSS and JS are served from a tiny CDN app on &lt;code&gt;:3200&lt;/code&gt; that copies fragment assets on startup.&lt;/p&gt;

&lt;p&gt;That split is the real-world shape: &lt;strong&gt;SSR lives with the team that owns the UI. Bytes live on a CDN.&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Assets belong to the fragment that created them, not to the shell:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;apps/hotel-search/src/assets/search.css
apps/hotel-search/src/build-client.js   → cdn/public/assets/search.js
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;If search wants a new filter chip, reviews does not rebuild.&lt;/p&gt;
&lt;h2&gt;
  
  
  Three runtimes, one HTML contract
&lt;/h2&gt;

&lt;p&gt;This is the part people assume is impossible.&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Runtime&lt;/th&gt;
&lt;th&gt;Fragments&lt;/th&gt;
&lt;th&gt;Server render&lt;/th&gt;
&lt;th&gt;Client&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Marko&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;navigation, search, details, reviews, recommendations&lt;/td&gt;
&lt;td&gt;
&lt;code&gt;@marko/compiler&lt;/code&gt; → &lt;code&gt;template.render().toString()&lt;/code&gt;
&lt;/td&gt;
&lt;td&gt;Marko DOM runtime mounts into a root&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;React 19&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;local highlights&lt;/td&gt;
&lt;td&gt;
&lt;code&gt;react-dom/server&lt;/code&gt; &lt;code&gt;renderToStaticMarkup&lt;/code&gt;
&lt;/td&gt;
&lt;td&gt;&lt;code&gt;hydrateRoot&lt;/code&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Riot&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;experiences discovery + itinerary&lt;/td&gt;
&lt;td&gt;hand-written &lt;code&gt;renderSsrMarkup()&lt;/code&gt;
&lt;/td&gt;
&lt;td&gt;
&lt;code&gt;riot.component()&lt;/code&gt; after clearing the SSR root&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;The composer does not care. All three return strings.&lt;br&gt;
&lt;/p&gt;
&lt;pre data-lang="mermaid"&gt;&lt;code&gt;flowchart TB
  subgraph marko["Marko :3102"]
    M1["hotel-search.marko"] --&amp;gt; M2["HTML string"]
  end
  subgraph react["React :3106"]
    R1["HighlightsView.jsx"] --&amp;gt; R2["HTML string"]
  end
  subgraph riot["Riot :3107"]
    T1["renderSsrMarkup()"] --&amp;gt; T2["HTML string"]
  end
  M2 --&amp;gt; Composer["Composer stitches slots"]
  R2 --&amp;gt; Composer
  T2 --&amp;gt; Composer
  Composer --&amp;gt; Browser["Browser paints HTML before any island JS"]&lt;/code&gt;&lt;/pre&gt;



&lt;p&gt;Why SSR in a microfrontend at all?&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;The first paint does not wait for JavaScript.&lt;/li&gt;
&lt;li&gt;HTML is the only lingua franca three frameworks share.&lt;/li&gt;
&lt;li&gt;If &lt;code&gt;experiences-discovery.js&lt;/code&gt; fails, the user still sees the cards.&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;That last one is Islands architecture in the small: &lt;strong&gt;static HTML with pockets of JS&lt;/strong&gt;, not a SPA that hydrates the entire document.&lt;/p&gt;
&lt;h2&gt;
  
  
  How data crosses the SSR/client gap
&lt;/h2&gt;

&lt;p&gt;Every interactive fragment embeds props as JSON, not &lt;code&gt;data-&lt;/code&gt; attributes:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight html"&gt;&lt;code&gt;&lt;span class="nt"&gt;&amp;lt;script &lt;/span&gt;&lt;span class="na"&gt;type=&lt;/span&gt;&lt;span class="s"&gt;"application/json"&lt;/span&gt; &lt;span class="na"&gt;id=&lt;/span&gt;&lt;span class="s"&gt;"hotel-search-fragment-data"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;hotels&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;:[...],&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;hotelId&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;moss-lantern&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/script&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;div&lt;/span&gt; &lt;span class="na"&gt;id=&lt;/span&gt;&lt;span class="s"&gt;"hotel-search-fragment-root"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="c"&gt;&amp;lt;!-- SSR HTML --&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/div&amp;gt;&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;The client bundle reads that script and mounts. Before embedding, fragment servers escape &lt;code&gt;&amp;lt;&lt;/code&gt; as &lt;code&gt;\u003c&lt;/code&gt; so a hotel description cannot break out of the script tag.&lt;/p&gt;

&lt;p&gt;&lt;code&gt;data-hotels='[{...}]'&lt;/code&gt; looks simpler. It is worse: large JSON in attributes bloats the DOM, needs ugly escaping, and is visible to everything that walks the tree.&lt;/p&gt;
&lt;h2&gt;
  
  
  Hydration is not one word
&lt;/h2&gt;

&lt;p&gt;Walking the live app made this concrete.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Marko search&lt;/strong&gt; hydrates into &lt;code&gt;#hotel-search-fragment-root&lt;/code&gt;. Luxury / Value / Top rated re-render the grid without a navigation. The client template must match the server template or you get a flash.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;React highlights&lt;/strong&gt; hydrates with &lt;code&gt;hydrateRoot&lt;/code&gt;. On Moss &amp;amp; Lantern you get &lt;em&gt;Garden loop&lt;/em&gt;, &lt;em&gt;Sauna ritual&lt;/em&gt;, &lt;em&gt;Harbor market&lt;/em&gt;. Click a card and only that island updates.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Riot cannot hydrate&lt;/strong&gt; the way React does. There is no reconcile-existing-DOM API in this setup, so the client &lt;strong&gt;wipes the SSR HTML and remounts&lt;/strong&gt;:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="nx"&gt;mountNode&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;innerHTML&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;''&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="nf"&gt;component&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;DiscoveryTag&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="nx"&gt;mountNode&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;props&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;You still get a fast first paint. You also get a tiny risk of visual flash if the Riot template and &lt;code&gt;renderSsrMarkup()&lt;/code&gt; drift. Keep class names, element types, and copy identical.&lt;/p&gt;

&lt;p&gt;On &lt;code&gt;/experiences/moss-lantern&lt;/code&gt; I clicked &lt;strong&gt;Food&lt;/strong&gt;: three cards became one tasting session. I clicked &lt;strong&gt;Day 2&lt;/strong&gt;: breakfast / walk / dinner became scenic run / museum / sunset lounge. Two Riot islands, two state machines, zero shared store.&lt;br&gt;
&lt;/p&gt;
&lt;pre data-lang="mermaid"&gt;&lt;code&gt;sequenceDiagram
  participant U as User
  participant D as Discovery Riot
  participant I as Itinerary Riot
  U-&amp;gt;&amp;gt;D: Click Food
  D-&amp;gt;&amp;gt;D: state.activeCategory = Food
  Note over I: Itinerary does not care
  U-&amp;gt;&amp;gt;I: Click Day 2
  I-&amp;gt;&amp;gt;I: state.selectedDay = 2
  Note over D: Discovery does not care&lt;/code&gt;&lt;/pre&gt;


&lt;h2&gt;
  
  
  Streaming: do not wait for the slowest fragment
&lt;/h2&gt;

&lt;p&gt;The stays page does not &lt;code&gt;await Promise.all&lt;/code&gt; then send one blob.&lt;/p&gt;

&lt;p&gt;&lt;code&gt;streamPage()&lt;/code&gt; is an &lt;code&gt;async function*&lt;/code&gt; . It yields the &lt;code&gt;&amp;lt;head&amp;gt;&lt;/code&gt; and shell immediately, then races fragment promises and flushes HTML as each one finishes.&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="k"&gt;yield&lt;/span&gt; &lt;span class="nx"&gt;headPrefix&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;pending&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Map&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
  &lt;span class="nx"&gt;fragmentOrder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;name&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nf"&gt;safeRenderFragment&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;hotelId&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;delay&lt;/span&gt;&lt;span class="p"&gt;)])&lt;/span&gt;
&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pending&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;await&lt;/span&gt; &lt;span class="nb"&gt;Promise&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;race&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;pending&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;entries&lt;/span&gt;&lt;span class="p"&gt;()].&lt;/span&gt;&lt;span class="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;(([&lt;/span&gt;&lt;span class="nx"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;promise&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;
      &lt;span class="nx"&gt;promise&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;fragment&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="nx"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;fragment&lt;/span&gt; &lt;span class="p"&gt;}))&lt;/span&gt;
    &lt;span class="p"&gt;)&lt;/span&gt;
  &lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="nx"&gt;pending&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;delete&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;next&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;name&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="k"&gt;yield&lt;/span&gt; &lt;span class="nx"&gt;next&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;fragment&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;html&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;Fastify wraps that in &lt;code&gt;Readable.from(...)&lt;/code&gt;. The response header &lt;code&gt;x-ssr-stream: true&lt;/code&gt; is a breadcrumb that this is a streamed document.&lt;br&gt;
&lt;/p&gt;
&lt;pre data-lang="mermaid"&gt;&lt;code&gt;gantt
  title Streaming vs waiting for everyone
  dateFormat  X
  axisFormat  %s ms
  section Buffered
  Wait for slowest fragment     :a1, 0, 860
  First paint                   :a2, 860, 50
  section Streamed
  Head + shell                  :b1, 0, 40
  Search HTML                   :b2, 160, 40
  Recommendations HTML          :b3, 300, 40
  Details HTML                  :b4, 540, 40
  Reviews HTML                  :b5, 860, 40&lt;/code&gt;&lt;/pre&gt;



&lt;p&gt;The demo even fakes latency so you can &lt;em&gt;see&lt;/em&gt; streaming:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;FRAGMENT_STREAM_DELAY_MS&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="na"&gt;search&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;160&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;recommendations&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;300&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;details&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;540&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;reviews&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;860&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;In production you delete those delays. Keep the race. First Contentful Paint becomes “when the shell arrives,” not “when reviews finally woke up.” Skeletons (&lt;code&gt;.loading-fragment&lt;/code&gt;) hold layout so later chunks do not shove the page around.&lt;/p&gt;

&lt;p&gt;If a fragment is restarting, &lt;code&gt;safeRenderFragment&lt;/code&gt; catches the error and yields:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;code&gt;reviews fragment is warming up.&lt;/code&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;Independent deploys stop being theoretical.&lt;/p&gt;
&lt;h2&gt;
  
  
  JavaScript budget is a route problem
&lt;/h2&gt;

&lt;p&gt;A composed page can accidentally ship four frameworks to every visitor. HarborStay avoids that with &lt;strong&gt;page splits&lt;/strong&gt;, not heroics.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;pnpm dev:home&lt;/code&gt; runs composer + CDN + stays fragments.&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;pnpm dev:experiences&lt;/code&gt; runs composer + CDN + the two Riot apps.&lt;/li&gt;
&lt;li&gt;The stays page builder never emits &lt;code&gt;experiences-discovery.js&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;The experiences page never emits &lt;code&gt;search.js&lt;/code&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;That is the cheapest performance win in the repo. Intersection Observer hydration, click-to-hydrate, and &lt;code&gt;requestIdleCallback&lt;/code&gt; are next — the docs already sketch them — but route-level omission beats all of them.&lt;br&gt;
&lt;/p&gt;
&lt;pre data-lang="mermaid"&gt;&lt;code&gt;flowchart LR
  StayPage["/hotel/:id"] --&amp;gt; StayJS["search.js + highlights.js"]
  ExpPage["/experiences/:id"] --&amp;gt; ExpJS["discovery.js + itinerary.js"]
  StayPage -.-&amp;gt; NoRiot["Riot bundles not referenced"]
  ExpPage -.-&amp;gt; NoMarko["Search bundle not referenced"]&lt;/code&gt;&lt;/pre&gt;


&lt;h2&gt;
  
  
  State: URL, local, or an event — pick one
&lt;/h2&gt;

&lt;p&gt;Shared mutable global state is how microfrontends become a distributed monolith.&lt;/p&gt;

&lt;p&gt;HarborStay’s rules:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Ephemeral UI state stays in the island.&lt;/strong&gt; Filter chips, selected highlight, active day.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Shareable state lives in the URL.&lt;/strong&gt; &lt;code&gt;/hotel/moss-lantern&lt;/code&gt; is the source of truth for “which stay.” Full page reload is intentional in this demo.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Cross-fragment talk is an event, not a store import.&lt;/strong&gt;
&lt;/li&gt;
&lt;/ol&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;dispatchEvent&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;CustomEvent&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;harborstay:hotel-selected&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="na"&gt;bubbles&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;detail&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;hotelId&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;moss-lantern&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
&lt;span class="p"&gt;}));&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;Do not do this:&lt;br&gt;
&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;store&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;@harborstay/store&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// two bundles = two stores&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;Two IIFE bundles that “import the same store” get two closures. They will not share state. They will gaslight you.&lt;/p&gt;

&lt;p&gt;&lt;code&gt;BroadcastChannel&lt;/code&gt; is the right tool only when tabs or iframes must stay in sync. &lt;code&gt;localStorage&lt;/code&gt; is for values that must survive a round trip. Neither belongs in the first version.&lt;/p&gt;
&lt;h2&gt;
  
  
  How this would ship
&lt;/h2&gt;

&lt;p&gt;Each fragment is a Node HTTP server. DNS for users points at the composer. Fragments live on internal hostnames. Static assets go to a real CDN.&lt;br&gt;
&lt;/p&gt;
&lt;pre data-lang="mermaid"&gt;&lt;code&gt;flowchart TB
  User["User"] --&amp;gt; LB["Load balancer / CDN"]
  LB --&amp;gt; Composer["Composer"]
  Composer --&amp;gt; F1["mfe-hotel-search"]
  Composer --&amp;gt; F2["mfe-reviews"]
  Composer --&amp;gt; F3["mfe-local-highlights"]
  Composer --&amp;gt; F4["other fragments"]
  Assets["cdn.example.com"] -.-&amp;gt; User&lt;/code&gt;&lt;/pre&gt;



&lt;p&gt;Rolling deploy order:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Publish content-hashed assets.&lt;/li&gt;
&lt;li&gt;Roll fragment servers (any order — fallbacks cover restarts).&lt;/li&gt;
&lt;li&gt;Roll the composer last.&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;Turborepo is the monorepo glue: &lt;code&gt;pnpm dev:home&lt;/code&gt; fans out with persistent &lt;code&gt;dev&lt;/code&gt; tasks, and &lt;code&gt;turbo run build&lt;/code&gt; only rebuilds what changed.&lt;/p&gt;

&lt;p&gt;This is a &lt;strong&gt;demo&lt;/strong&gt;, not a production platform. The goal is a shape you can reason about: one contract, many runtimes, progressive HTML.&lt;/p&gt;
&lt;h2&gt;
  
  
  What I would do next
&lt;/h2&gt;

&lt;p&gt;The interesting unfinished work is not “add another framework.” It is:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Soft navigation&lt;/strong&gt; — &lt;code&gt;history.pushState&lt;/code&gt; + swap only the fragments that changed.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;True streaming inside fragments&lt;/strong&gt; — Marko &lt;code&gt;template.stream()&lt;/code&gt;, React &lt;code&gt;renderToPipeableStream&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Riot hydrate()&lt;/strong&gt; when the API is stable, so we stop wiping SSR DOM.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Edge composer&lt;/strong&gt; — the generator already looks like a Web Streams mental model.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;SWR cache&lt;/strong&gt; of fragment HTML at the composer for anonymous hotel pages.&lt;/li&gt;
&lt;/ul&gt;
&lt;h2&gt;
  
  
  Run it
&lt;/h2&gt;


&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;pnpm &lt;span class="nb"&gt;install
&lt;/span&gt;pnpm dev:home          &lt;span class="c"&gt;# stays flow&lt;/span&gt;
pnpm dev:experiences   &lt;span class="c"&gt;# experiences flow&lt;/span&gt;
pnpm dev:all           &lt;span class="c"&gt;# everything&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;


&lt;p&gt;Then open &lt;code&gt;http://localhost:3100&lt;/code&gt;.&lt;/p&gt;

&lt;p&gt;If you want a mental model to steal, steal this one:&lt;/p&gt;


&lt;div class="crayons-card c-embed"&gt;

  &lt;br&gt;
&lt;strong&gt;Compose HTML, not components. Hydrate islands, not pages. Keep state with the team that owns the UI. Let the slowest fragment arrive last without blocking the first paint.&lt;/strong&gt;&lt;br&gt;

&lt;/div&gt;



&lt;p&gt;The user still sees one hotel page. The architecture is allowed to be many rooms behind one door.&lt;/p&gt;

&lt;p&gt;GITHUB: &lt;a href="https://github.com/piyushchauhan2011/marko-mfe" rel="noopener noreferrer"&gt;https://github.com/piyushchauhan2011/marko-mfe&lt;/a&gt;&lt;/p&gt;

</description>
      <category>microfrontends</category>
      <category>ssr</category>
      <category>webperf</category>
      <category>architecture</category>
    </item>
    <item>
      <title>Why Your JavaScript Sums Are Wrong (And How to Fix Them)</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Wed, 05 Aug 2026 07:24:22 +0000</pubDate>
      <link>https://dev.to/frorning/why-your-javascript-sums-are-wrong-and-how-to-fix-them-55cp</link>
      <guid>https://dev.to/frorning/why-your-javascript-sums-are-wrong-and-how-to-fix-them-55cp</guid>
      <description>&lt;p&gt;You know that &lt;code&gt;Array.prototype.reduce&lt;/code&gt; you've used a thousand times to sum numbers? It's lying to you.&lt;/p&gt;

&lt;h2&gt;
  
  
  1. A One-Liner That Should Work
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;nums&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;from&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;length&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1000&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;a&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;        &lt;span class="c1"&gt;// 99.9999999999986&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;sum&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// false (!)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;A thousand tenths should equal one hundred. But in JavaScript — and in virtually every other mainstream language — it doesn't. Not exactly.&lt;/p&gt;

&lt;p&gt;If you've ever shrugged off a &lt;code&gt;0.0000000000001&lt;/code&gt; discrepancy, this article is for you. Because at scale, that "tiny" error isn't tiny at all.&lt;/p&gt;




&lt;h2&gt;
  
  
  2. The Problem: Why Floats Betray Us
&lt;/h2&gt;

&lt;p&gt;JavaScript uses &lt;a href="https://en.wikipedia.org/wiki/IEEE_754" rel="noopener noreferrer"&gt;IEEE 754 double-precision floating-point&lt;/a&gt; for all numbers. In plain English: your numbers are stored as binary fractions, and most decimal fractions (like &lt;code&gt;0.1&lt;/code&gt;) have no exact binary representation.&lt;/p&gt;

&lt;p&gt;When you add &lt;code&gt;0.1 + 0.2&lt;/code&gt;, the computer isn't adding "one-tenth plus two-tenths." It's adding the closest binary approximations it can store. The result? &lt;code&gt;0.30000000000000004&lt;/code&gt;.&lt;/p&gt;

&lt;p&gt;Now multiply that imperfection across a thousand, a million, or a billion additions. The error doesn't stay small — it &lt;strong&gt;accumulates&lt;/strong&gt;.&lt;/p&gt;

&lt;h3&gt;
  
  
  The Core Issue
&lt;/h3&gt;

&lt;p&gt;When you sum left-to-right with a running total, you eventually reach a point where the running total is huge and the next number is tiny. In floating-point arithmetic, adding a tiny number to a huge number often results in &lt;strong&gt;no change at all&lt;/strong&gt; — the tiny number gets "swallowed."&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;em&gt;Imagine pouring water into a bucket with a small hole. Each pour loses a few drops. After 1,000 pours, you're missing a puddle.&lt;/em&gt;&lt;/p&gt;
&lt;/blockquote&gt;




&lt;h2&gt;
  
  
  3. The Fix: Kahan Summation
&lt;/h2&gt;

&lt;p&gt;In 1965, William Kahan published an algorithm that tracks and recovers the low-order bits lost in each addition. The trick? A &lt;strong&gt;compensation variable&lt;/strong&gt; that remembers what got rounded away.&lt;/p&gt;

&lt;h3&gt;
  
  
  The Intuition
&lt;/h3&gt;

&lt;p&gt;Instead of just keeping a running total, Kahan summation keeps two values:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;code&gt;sum&lt;/code&gt; — the best approximation so far&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;c&lt;/code&gt; (compensation) — the error that was discarded in the last step&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;Before each new addition, the compensation from the previous step is added back in. After the addition, the new error is computed and stored for the next iteration.&lt;/p&gt;

&lt;h3&gt;
  
  
  The Algorithm
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Input: x
       │
       ▼
    x + c  ◄── compensation from last step
       │
       ▼
   t = sum + (x + c)
       │
       ▼
   c = (t - sum) - (x + c)  ← the "recovered" error
       │
       ▼
   sum = t
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  JavaScript Implementation
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;kahanSum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// compensation for lost low-order bits&lt;/span&gt;

  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// subtract previous error&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;sum&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;         &lt;span class="c1"&gt;// tentative sum&lt;/span&gt;
    &lt;span class="nx"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;t&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;         &lt;span class="c1"&gt;// new error: (what we added) - (what we meant to add)&lt;/span&gt;
    &lt;span class="nx"&gt;sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;t&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Line-by-Line Breakdown
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Line&lt;/th&gt;
&lt;th&gt;What It Does&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;y = numbers[i] - c&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Add back the error from the previous step&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;t = sum + y&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Perform the actual addition&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;c = (t - sum) - y&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Calculate what got lost in rounding&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;sum = t&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Commit the new sum&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;The magic is in &lt;code&gt;(t - sum) - y&lt;/code&gt;. Because of how floating-point subtraction works, this expression recovers the bits that were rounded away during &lt;code&gt;sum + y&lt;/code&gt;.&lt;/p&gt;




&lt;h2&gt;
  
  
  4. Live Comparison: Naive vs. Kahan
&lt;/h2&gt;

&lt;p&gt;Let's run both algorithms on the same pathological dataset:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// 10 million copies of 0.0001&lt;/span&gt;
&lt;span class="c1"&gt;// True answer: exactly 1000&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;nums&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;from&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;length&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="nx"&gt;_000_000&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="mf"&gt;0.0001&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;time&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;naive&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;naive&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;a&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;timeEnd&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;naive&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;time&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;kahan&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;kahan&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;kahanSum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;timeEnd&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;kahan&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Naive: &lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;naive&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;  &lt;span class="c1"&gt;// 999.9998999965879&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Kahan: &lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;kahan&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;  &lt;span class="c1"&gt;// 1000.0000000000001&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;The naive sum is off by &lt;code&gt;0.0001&lt;/code&gt;&lt;/strong&gt;. That might not sound like much, but in financial systems processing millions of transactions, "small" errors compound into real money.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Kahan's error?&lt;/strong&gt; &lt;code&gt;1.1e-13&lt;/code&gt; — effectively zero for all practical purposes.&lt;/p&gt;




&lt;h2&gt;
  
  
  5. The Middle Ground: Pairwise Summation
&lt;/h2&gt;

&lt;p&gt;Before we crown Kahan the winner, there's a third contender that often gets overlooked: &lt;strong&gt;pairwise summation&lt;/strong&gt; (also called cascade summation).&lt;/p&gt;

&lt;p&gt;The idea is beautifully simple: instead of accumulating left-to-right, recursively split the array in half, sum each half, then add the two results. This ensures you're always adding numbers of roughly the same magnitude.&lt;/p&gt;

&lt;h3&gt;
  
  
  The Intuition
&lt;/h3&gt;

&lt;p&gt;Imagine balancing a scale. Naive summation keeps piling weights on one side until the running total dwarfs every new addition. Pairwise summation weighs equal-sized groups against each other at every step.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;[1, 2, 3, 4, 5, 6, 7, 8]
    /              \
[1,2,3,4]      [5,6,7,8]
  /    \          /    \
[1,2] [3,4]    [5,6] [7,8]
 |     |        |     |
 3     7        11    15
   \   /          \  /
    10             26
         \        /
           36
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Recursive Implementation
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;pairwiseSum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;len&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;end&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;len&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;len&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;mid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;start&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;floor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;len&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;pairwiseSum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;mid&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;pairwiseSum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;mid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;end&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;⚠️ &lt;strong&gt;Caution:&lt;/strong&gt; For very large arrays (&amp;gt; ~10,000 items), the recursive version will blow the call stack. Here's a stack-safe iterative version:&lt;/p&gt;

&lt;p&gt;🔧 Stack-safe iterative version&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;pairwiseSumIterative&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;queue&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;slice&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;

  &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="nx"&gt;gt&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[];&lt;/span&gt;
    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="nx"&gt;lt&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="nx"&gt;next&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="nx"&gt;queue&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  6. The Heavyweight: decimal.js
&lt;/h2&gt;

&lt;p&gt;Sometimes you need &lt;strong&gt;exact&lt;/strong&gt; decimal arithmetic, not just "less error." That's where &lt;code&gt;decimal.js&lt;/code&gt; comes in. It represents numbers as strings internally and performs arbitrary-precision math.&lt;/p&gt;

&lt;h3&gt;
  
  
  Installation
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;npm &lt;span class="nb"&gt;install &lt;/span&gt;decimal.js
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Usage
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;Decimal&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;require&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;decimal.js&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;decimalSum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;numbers&lt;/span&gt;
    &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;sum&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;plus&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Decimal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toString&lt;/span&gt;&lt;span class="p"&gt;())),&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Decimal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toNumber&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;blockquote&gt;
&lt;p&gt;💡 &lt;strong&gt;Pro tip:&lt;/strong&gt; Always pass numbers through &lt;code&gt;.toString()&lt;/code&gt; before constructing a &lt;code&gt;Decimal&lt;/code&gt;. &lt;code&gt;new Decimal(0.1)&lt;/code&gt; still inherits floating-point imprecision because &lt;code&gt;0.1&lt;/code&gt; is already corrupted by the time it reaches the constructor.&lt;/p&gt;
&lt;/blockquote&gt;




&lt;h2&gt;
  
  
  7. The Showdown: Four-Way Comparison
&lt;/h2&gt;

&lt;p&gt;Let's put them all to the test with a pathological dataset:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// 10 million copies of 0.0001&lt;/span&gt;
&lt;span class="c1"&gt;// True answer: exactly 1000&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;nums&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;from&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;length&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="nx"&gt;_000_000&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="mf"&gt;0.0001&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Method&lt;/th&gt;
&lt;th&gt;Result&lt;/th&gt;
&lt;th&gt;Error&lt;/th&gt;
&lt;th&gt;Relative Speed&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Naive &lt;code&gt;reduce&lt;/code&gt;&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;&lt;code&gt;999.9998999965879&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;&lt;code&gt;~1.0e-4&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;1.0x (baseline)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Pairwise&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;&lt;code&gt;999.9999999999123&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;&lt;code&gt;~8.8e-11&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;~1.5x slower&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Kahan&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;&lt;code&gt;1000.0000000000001&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;&lt;code&gt;~1.1e-13&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;~3.5x slower&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;decimal.js&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;
&lt;code&gt;1000&lt;/code&gt; (exact)&lt;/td&gt;
&lt;td&gt;&lt;code&gt;0&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;~40-80x slower&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  What the Numbers Tell Us
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Naive&lt;/strong&gt; is fast but wrong at scale. The error is small in absolute terms, but in financial systems, "small" errors compound into real money.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pairwise&lt;/strong&gt; dramatically reduces error with minimal overhead. Its error grows logarithmically &lt;code&gt;O(log n)&lt;/code&gt; instead of linearly.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Kahan&lt;/strong&gt; achieves near-constant error &lt;code&gt;O(ε)&lt;/code&gt; — the gold standard for floating-point summation.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;decimal.js&lt;/strong&gt; is exact but slow. It's not really a summation algorithm; it's a different number system entirely.&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  8. The Decision Framework
&lt;/h2&gt;

&lt;p&gt;Here's a quick cheat sheet for choosing the right tool:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Scenario&lt;/th&gt;
&lt;th&gt;Recommendation&lt;/th&gt;
&lt;th&gt;Why&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Small arrays (&amp;lt; 1,000 items)&lt;/td&gt;
&lt;td&gt;&lt;strong&gt;Naive &lt;code&gt;reduce&lt;/code&gt;&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Error is negligible; don't over-engineer&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Large arrays, need speed, "good enough" accuracy&lt;/td&gt;
&lt;td&gt;&lt;strong&gt;Pairwise&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Logarithmic error growth, parallelizable&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Financial/scientific computing, must minimize error&lt;/td&gt;
&lt;td&gt;&lt;strong&gt;Kahan&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Constant error bound, no extra dependencies&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Accounting, currency, must be &lt;strong&gt;exact&lt;/strong&gt;
&lt;/td&gt;
&lt;td&gt;&lt;strong&gt;decimal.js&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Arbitrary precision eliminates rounding entirely&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;GPU/Web Worker parallel processing&lt;/td&gt;
&lt;td&gt;&lt;strong&gt;Pairwise&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Perfectly parallelizable; Kahan is inherently sequential&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  The Trade-off Triangle
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;        Speed
         /\
        /  \
       /    \
      /      \
     /   ⚠️   \
    /__________\
 Accuracy    Simplicity
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;You can pick &lt;strong&gt;two&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Fast + Simple&lt;/strong&gt; → Naive&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Fast + Accurate&lt;/strong&gt; → Pairwise&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Accurate + Simple&lt;/strong&gt; → Kahan&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Exact&lt;/strong&gt; → decimal.js (sacrifices speed)&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  9. When NOT to Use Kahan
&lt;/h2&gt;

&lt;p&gt;Kahan summation is great, but it's not always the right call:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Integers only&lt;/strong&gt; — If your array contains only integers representable in 53 bits, naive summation is exact until you exceed &lt;code&gt;Number.MAX_SAFE_INTEGER&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Already using a decimal library&lt;/strong&gt; — If you've bought into &lt;code&gt;decimal.js&lt;/code&gt; or &lt;code&gt;big.js&lt;/code&gt;, you don't need Kahan; you're already exact.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Real-time graphics/animation&lt;/strong&gt; — A 3-4x slowdown for a pixel-perfect particle position is rarely worth it.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Very small datasets&lt;/strong&gt; — The error on &lt;code&gt;[0.1, 0.2, 0.3]&lt;/code&gt; is &lt;code&gt;5.55e-17&lt;/code&gt;. Your users don't care.&lt;/li&gt;
&lt;/ol&gt;




&lt;h2&gt;
  
  
  10. One-Liners for Your Toolkit
&lt;/h2&gt;

&lt;p&gt;For the copy-paste engineers:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Kahan (functional, but slightly slower due to array destructuring)&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;kahanSum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;(([&lt;/span&gt;&lt;span class="nx"&gt;s&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;c&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;s&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;t&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

&lt;span class="c1"&gt;// Pairwise (iterative, stack-safe)&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;pairwiseSum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;q&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
  &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[];&lt;/span&gt;
    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;q&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;q&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="nx"&gt;q&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;q&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Conclusion
&lt;/h2&gt;

&lt;p&gt;Floating-point summation is one of those problems that seems trivial until it isn't. The good news: JavaScript gives you options.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Reach for &lt;strong&gt;pairwise summation&lt;/strong&gt; when you need a quick accuracy boost without a performance cliff.&lt;/li&gt;
&lt;li&gt;Reach for &lt;strong&gt;Kahan summation&lt;/strong&gt; when precision is paramount and you're working with raw floats.&lt;/li&gt;
&lt;li&gt;Reach for &lt;strong&gt;decimal.js&lt;/strong&gt; when you're dealing with money, tax calculations, or anything where "close enough" isn't in your vocabulary.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;And sometimes? Just use &lt;code&gt;reduce&lt;/code&gt;. Not every array needs a PhD.&lt;/p&gt;




&lt;p&gt;&lt;em&gt;What's your go-to strategy for numerical accuracy in JavaScript? Drop your war stories in the comments below.&lt;/em&gt; 👇&lt;/p&gt;

</description>
      <category>javascript</category>
      <category>algorithms</category>
      <category>programming</category>
      <category>webdev</category>
    </item>
    <item>
      <title>Backtracking Unveiled: Mastering Depth-First Search and Pruning Techniques</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 22 Feb 2025 09:04:27 +0000</pubDate>
      <link>https://dev.to/frorning/backtracking-unveiled-mastering-depth-first-search-and-pruning-techniques-251c</link>
      <guid>https://dev.to/frorning/backtracking-unveiled-mastering-depth-first-search-and-pruning-techniques-251c</guid>
      <description>&lt;p&gt;Backtracking is a systematic way to iterate through all possible configurations of a problem. It is often used to solve problems where a sequence of decisions must be made, and each decision leads to a new set of possibilities. Backtracking uses &lt;strong&gt;depth-first search (DFS)&lt;/strong&gt; to explore the state space, and it employs &lt;strong&gt;pruning functions&lt;/strong&gt; to eliminate invalid or suboptimal paths early in the search process.&lt;/p&gt;




&lt;h3&gt;
  
  
  Components of Backtracking Problems
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: The starting point of the problem.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target/Goal State&lt;/strong&gt;: The desired solution.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Intermediate States&lt;/strong&gt;: States generated while moving from the initial state to the target state.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Path&lt;/strong&gt;: The sequence of states from the initial state to the target state.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Rules or actions that transform one state into another.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: A heuristic to eliminate invalid or suboptimal states early.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  Backtracking Algorithm
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;Start with the initial state.&lt;/li&gt;
&lt;li&gt;Use DFS to explore all possible states.&lt;/li&gt;
&lt;li&gt;If a state is invalid (based on the pruning function), backtrack and try another path.&lt;/li&gt;
&lt;li&gt;If a state is the goal state, return the solution.&lt;/li&gt;
&lt;li&gt;Repeat until all possible states are explored or a solution is found.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  Example Problems Solved Using Backtracking
&lt;/h3&gt;

&lt;h4&gt;
  
  
  1. &lt;strong&gt;3-Digit Lock Problem&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: "111"&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target State&lt;/strong&gt;: The correct combination (e.g., "352")&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Increment each digit by 1 (from 1 to 9).&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: If a digit is correct (e.g., produces a "click"), fix it and move to the next digit.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Implementation:
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;findLockCombination&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;combination&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;combination&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Found combination:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;combination&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;index&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newCombination&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;combination&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;slice&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;combination&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;slice&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newCombination&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Click at position&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;with digit&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
                &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newCombination&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;111&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;targetCombination&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;352&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="nf"&gt;findLockCombination&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;targetCombination&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h4&gt;
  
  
  2. &lt;strong&gt;Monks and Demons Problem&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: 3 monks, 3 demons, and the boat on the left shore.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target State&lt;/strong&gt;: All monks and demons on the right shore.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Move 1 or 2 people in the boat.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: Ensure that monks are never outnumbered by demons on either shore.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Implementation:
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;solveMonksAndDemons&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;initialState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;left&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="na"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="na"&gt;boat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Set&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;

    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;return &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
            &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
            &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;JSON&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;stringify&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;has&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Solution found:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;moves&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="p"&gt;];&lt;/span&gt;

        &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="nx"&gt;moves&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
                &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt;
                &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;right&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                    &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
                    &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
                &lt;span class="p"&gt;};&lt;/span&gt;
                &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                    &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;right&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
                    &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;right&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
                &lt;span class="p"&gt;};&lt;/span&gt;
                &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                    &lt;span class="na"&gt;left&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                    &lt;span class="na"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                    &lt;span class="na"&gt;boat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;right&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                &lt;span class="p"&gt;};&lt;/span&gt;

                &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
                &lt;span class="p"&gt;}&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;initialState&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="nf"&gt;solveMonksAndDemons&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h4&gt;
  
  
  3. &lt;strong&gt;Farmer, Goat, Cabbage, and Wolf Problem&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: Farmer, goat, cabbage, and wolf on the left shore.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target State&lt;/strong&gt;: All on the right shore.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Farmer can take one item (goat, cabbage, or wolf) in the boat.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: Ensure the goat is not left alone with the cabbage, and the wolf is not left alone with the goat.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Implementation:
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;solveFarmerProblem&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;initialState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;left&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;goat&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;cabbage&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;wolf&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="na"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[],&lt;/span&gt;
    &lt;span class="na"&gt;boat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="p"&gt;};&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Set&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;

  &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;unsafe&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;
      &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;goat&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
        &lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;cabbage&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
        &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt;
      &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;wolf&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
        &lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;goat&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
        &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;unsafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="nf"&gt;unsafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;stateKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;JSON&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;stringify&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Solution found:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;stateKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;has&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;fromShore&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Possible moves: Farmer alone or Farmer + one item&lt;/span&gt;
    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;fromShore&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
        &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="nx"&gt;newLeft&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;filter&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
          &lt;span class="nx"&gt;newRight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
          &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="nx"&gt;newRight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;filter&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
          &lt;span class="nx"&gt;newLeft&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
          &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="na"&gt;left&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
          &lt;span class="na"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
          &lt;span class="na"&gt;boat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;right&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="p"&gt;};&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
      &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;initialState&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="nf"&gt;solveFarmerProblem&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h4&gt;
  
  
  4. &lt;strong&gt;Water Jug Problem&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: Both jugs are empty.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target State&lt;/strong&gt;: 2 gallons in the 4-gallon jug.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Fill, empty, or pour water between jugs.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: Avoid revisiting states.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Implementation:
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;solveWaterJug&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;initialState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Set&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;

    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;,&lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;has&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;jug4&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Solution found:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;moves&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Fill jug4&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Fill jug3&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Empty jug4&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Empty jug3&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;)),&lt;/span&gt; &lt;span class="na"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Pour jug4 to jug3&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="na"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Pour jug3 to jug4&lt;/span&gt;
        &lt;span class="p"&gt;];&lt;/span&gt;

        &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="nx"&gt;moves&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;initialState&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="nf"&gt;solveWaterJug&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  Key Points:
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;Backtracking is a &lt;strong&gt;systematic way&lt;/strong&gt; to explore all possible solutions.&lt;/li&gt;
&lt;li&gt;It uses &lt;strong&gt;depth-first search&lt;/strong&gt; and &lt;strong&gt;pruning functions&lt;/strong&gt; to eliminate invalid paths.&lt;/li&gt;
&lt;li&gt;It is useful for solving &lt;strong&gt;NP-hard problems&lt;/strong&gt; like puzzles, constraint satisfaction problems, and combinatorial optimization.&lt;/li&gt;
&lt;/ol&gt;

</description>
      <category>javascript</category>
      <category>algorithms</category>
      <category>programming</category>
      <category>beginners</category>
    </item>
    <item>
      <title>A* Search Algorithm and Iterative Deepening A* in JavaScript</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 08 Feb 2025 05:44:55 +0000</pubDate>
      <link>https://dev.to/frorning/a-search-algorithm-and-iterative-deepening-a-in-javascript-4c0o</link>
      <guid>https://dev.to/frorning/a-search-algorithm-and-iterative-deepening-a-in-javascript-4c0o</guid>
      <description>&lt;h3&gt;
  
  
  &lt;strong&gt;1. Introduction&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Search algorithms play a crucial role in solving problems across computer science, robotics, game development, and beyond. Among them, heuristic-based search algorithms stand out for their ability to efficiently find solutions by leveraging additional knowledge about the problem domain. This article delves into two such algorithms: the widely used A* search algorithm and its memory-efficient counterpart, Iterative Deepening A* (IDA*).&lt;/p&gt;

&lt;p&gt;By the end of this article, you will:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Understand the core principles of A* and IDA*.&lt;/li&gt;
&lt;li&gt;Learn how these algorithms work through code implementations in JavaScript.&lt;/li&gt;
&lt;li&gt;Explore their mathematical underpinnings and use cases.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;2. Understanding A* Search Algorithm&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  What is A*?
&lt;/h4&gt;

&lt;p&gt;A* is a best-first search algorithm that aims to find the shortest path from a start node to a goal node. It uses an evaluation function:&lt;/p&gt;

&lt;p&gt;

&lt;/p&gt;
&lt;div class="katex-element"&gt;
  &lt;span class="katex-display"&gt;&lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;=&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;+&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/div&gt;


&lt;p&gt;Where:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
: The cost of the path from the start node to the current node 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;li&gt;
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
: A heuristic estimate of the cost to reach the goal node from 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The algorithm prioritizes nodes with the smallest 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 value, making it both optimal and complete, provided the heuristic 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 is admissible (never overestimates the true cost).&lt;/p&gt;
&lt;h4&gt;
  
  
  Properties of A*
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Completeness&lt;/strong&gt;: Guaranteed to find a solution if one exists.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Optimality&lt;/strong&gt;: Finds the shortest path with an admissible heuristic.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Admissibility and Consistency&lt;/strong&gt;: Ensures the heuristic is reliable for optimal solutions.&lt;/li&gt;
&lt;/ul&gt;
&lt;h4&gt;
  
  
  &lt;a href="https://en.wikipedia.org/wiki/A*_search_algorithm#Pseudocode" rel="noopener noreferrer"&gt;Wikipedia Pseudocode for A*&lt;/a&gt;
&lt;/h4&gt;


&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;function reconstruct_path(cameFrom, current)
    total_path := {current}
    while current in cameFrom.Keys:
        current := cameFrom[current]
        total_path.prepend(current)
    return total_path

// A* finds a path from start to goal.
// h is the heuristic function. h(n) estimates the cost to reach goal from node n.
function A_Star(start, goal, h)
    // The set of discovered nodes that may need to be (re-)expanded.
    // Initially, only the start node is known.
    // This is usually implemented as a min-heap or priority queue rather than a hash-set.
    openSet := {start}

    // For node n, cameFrom[n] is the node immediately preceding it on the cheapest path from the start
    // to n currently known.
    cameFrom := an empty map

    // For node n, gScore[n] is the currently known cost of the cheapest path from start to n.
    gScore := map with default value of Infinity
    gScore[start] := 0

    // For node n, fScore[n] := gScore[n] + h(n). fScore[n] represents our current best guess as to
    // how cheap a path could be from start to finish if it goes through n.
    fScore := map with default value of Infinity
    fScore[start] := h(start)

    while openSet is not empty
        // This operation can occur in O(Log(N)) time if openSet is a min-heap or a priority queue
        current := the node in openSet having the lowest fScore[] value
        if current = goal
            return reconstruct_path(cameFrom, current)

        openSet.Remove(current)
        for each neighbor of current
            // d(current,neighbor) is the weight of the edge from current to neighbor
            // tentative_gScore is the distance from start to the neighbor through current
            tentative_gScore := gScore[current] + d(current, neighbor)
            if tentative_gScore &amp;lt; gScore[neighbor]
                // This path to neighbor is better than any previous one. Record it!
                cameFrom[neighbor] := current
                gScore[neighbor] := tentative_gScore
                fScore[neighbor] := tentative_gScore + h(neighbor)
                if neighbor not in openSet
                    openSet.add(neighbor)

    // Open set is empty but goal was never reached
    return failure
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;3. Implementing A* in JavaScript&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Below is a JavaScript implementation of A* for a grid-based shortest path problem:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;assert&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;require&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;assert&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="kd"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;PriorityQueue&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nf"&gt;constructor&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[];&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="nf"&gt;enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;priority&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;priority&lt;/span&gt; &lt;span class="p"&gt;});&lt;/span&gt;
    &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;priority&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;priority&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="nf"&gt;dequeue&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;shift&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="nf"&gt;isEmpty&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;aStar&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;openSet&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;PriorityQueue&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
  &lt;span class="nx"&gt;openSet&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;gScore&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;from&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;length&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;rows&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nc"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;fill&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;Infinity&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
  &lt;span class="nx"&gt;gScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]][&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;fScore&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;from&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;length&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;rows&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nc"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;fill&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;Infinity&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
  &lt;span class="nx"&gt;fScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]][&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

  &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;openSet&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isEmpty&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;openSet&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;dequeue&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;reconstructPath&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
      &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
      &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
      &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
      &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

      &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;nx&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;ny&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;ny&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;tentative_gScore&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;gScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;y&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;tentative_gScore&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;gScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
          &lt;span class="nx"&gt;gScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;tentative_gScore&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
          &lt;span class="nx"&gt;fScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;tentative_gScore&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

          &lt;span class="nx"&gt;openSet&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;fScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
      &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="nx"&gt;x1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;y1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;y2&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;x1&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;y1&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;y2&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;reconstructPath&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
  &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;unshift&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Test A* Algorithm&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
&lt;span class="p"&gt;];&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;aStar&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Found Path:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;notStrictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isArray&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// Test for no path&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;blockedGrid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;noPathResult&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;aStar&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="nx"&gt;blockedGrid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;noPathResult&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  &lt;strong&gt;4. Mathematical Proofs and Analysis&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Proof of Optimality
&lt;/h4&gt;

&lt;p&gt;A* guarantees the shortest path if the heuristic 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 is admissible and consistent.&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Admissibility&lt;/strong&gt;: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 never overestimates the true cost to the goal. This ensures that A* will not bypass the optimal path.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Consistency&lt;/strong&gt;: For every pair of nodes 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 and 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, the heuristic satisfies:

&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;≤&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;c&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;+&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;

where 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;c&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 is the cost of transitioning from 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
. This property ensures that the 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 values along a path are non-decreasing.&lt;/li&gt;
&lt;/ol&gt;

&lt;h4&gt;
  
  
  Time and Space Complexity
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Time Complexity&lt;/strong&gt;: In the worst case, A* explores all nodes with 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 less than the cost of the optimal solution. This can grow exponentially with the branching factor 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;b&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 and the depth 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;d&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 of the solution: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;b&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mathnormal mtight"&gt;d&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Space Complexity&lt;/strong&gt;: A* stores all explored nodes in memory, leading to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;b&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mathnormal mtight"&gt;d&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 space usage.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;5. Limitations of A&lt;/strong&gt;*
&lt;/h3&gt;

&lt;p&gt;While A* is highly efficient for many problems, it has significant limitations:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Memory Requirements&lt;/strong&gt;: Storing all explored nodes can become infeasible for large graphs.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Performance&lt;/strong&gt;: On graphs with high branching factors or inaccurate heuristics, A* may perform poorly.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;6. Iterative Deepening A* (IDA*)&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Why IDA*?
&lt;/h4&gt;

&lt;p&gt;IDA* addresses A*'s memory limitations by combining the benefits of A*'s heuristic-guided search with the memory efficiency of depth-first search. Instead of maintaining a priority queue, IDA* performs iterative depth-first searches with increasing 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
-cost thresholds.&lt;/p&gt;

&lt;h4&gt;
  
  
  How It Works
&lt;/h4&gt;

&lt;ol&gt;
&lt;li&gt;Initialize the threshold to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;s&lt;/span&gt;&lt;span class="mord mathnormal"&gt;t&lt;/span&gt;&lt;span class="mord mathnormal"&gt;a&lt;/span&gt;&lt;span class="mord mathnormal"&gt;r&lt;/span&gt;&lt;span class="mord mathnormal"&gt;t&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;li&gt;Perform a depth-first search, pruning paths with 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;&amp;gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 threshold.&lt;/li&gt;
&lt;li&gt;If no solution is found, increase the threshold to the smallest 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 value that exceeded the current threshold.&lt;/li&gt;
&lt;li&gt;Repeat until the goal is reached.&lt;/li&gt;
&lt;/ol&gt;

&lt;h4&gt;
  
  
  &lt;a href="https://en.wikipedia.org/wiki/Iterative_deepening_A*#Pseudocode" rel="noopener noreferrer"&gt;Wikipedia Pseudocode for IDA*&lt;/a&gt;
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;path              current search path (acts like a stack)
node              current node (last node in current path)
g                 the cost to reach current node
f                 estimated cost of the cheapest path (root..node..goal)
h(node)           estimated cost of the cheapest path (node..goal)
cost(node, succ)  step cost function
is_goal(node)     goal test
successors(node)  node expanding function, expand nodes ordered by g + h(node)
ida_star(root)    return either NOT_FOUND or a pair with the best path and its cost

procedure ida_star(root)
    bound := h(root)
    path := [root]
    loop
        t := search(path, 0, bound)
        if t = FOUND then return (path, bound)
        if t = ∞ then return NOT_FOUND
        bound := t
    end loop
end procedure

function search(path, g, bound)
    node := path.last
    f := g + h(node)
    if f &amp;gt; bound then return f
    if is_goal(node) then return FOUND
    min := ∞
    for succ in successors(node) do
        if succ not in path then
            path.push(succ)
            t := search(path, g + cost(node, succ), bound)
            if t = FOUND then return FOUND
            if t &amp;lt; min then min := t
            path.pop()
        end if
    end for
    return min
end function
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  &lt;strong&gt;7. Implementing IDA* in JavaScript&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;idaStar&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;threshold&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

  &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
      &lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Set&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;found&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;reconstructPath&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;threshold&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="kc"&gt;Infinity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="nx"&gt;threshold&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;f&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;g&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;f&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;f&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;found&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;found&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;

  &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toString&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;
  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;minThreshold&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="kc"&gt;Infinity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
    &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
      &lt;span class="nx"&gt;nx&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="nx"&gt;nx&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="nx"&gt;ny&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="nx"&gt;ny&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;has&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toString&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;
    &lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;g&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;visited&lt;/span&gt;
      &lt;span class="p"&gt;);&lt;/span&gt;
      &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;found&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
      &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;threshold&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;minThreshold&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="nx"&gt;minThreshold&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;delete&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toString&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;minThreshold&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;found&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
&lt;span class="p"&gt;];&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;pathIdaStar&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;idaStar&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;IDA* Found Path:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;pathIdaStar&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;notStrictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pathIdaStar&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isArray&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pathIdaStar&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;blockedGrid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
&lt;span class="p"&gt;];&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;noPathResultIdaStar&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;idaStar&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="nx"&gt;blockedGrid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;noPathResultIdaStar&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  &lt;strong&gt;8. Comparing A* and IDA&lt;/strong&gt;*
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Feature&lt;/th&gt;
&lt;th&gt;A*&lt;/th&gt;
&lt;th&gt;IDA*&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Memory Usage&lt;/td&gt;
&lt;td&gt;High (stores all nodes)&lt;/td&gt;
&lt;td&gt;Low (depth-first search)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Speed&lt;/td&gt;
&lt;td&gt;Faster for smaller graphs&lt;/td&gt;
&lt;td&gt;Slower due to iterative nature&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Implementation Complexity&lt;/td&gt;
&lt;td&gt;Moderate&lt;/td&gt;
&lt;td&gt;Higher&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Suitability for Large Graphs&lt;/td&gt;
&lt;td&gt;Limited&lt;/td&gt;
&lt;td&gt;More suitable&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;9. Use Cases&lt;/strong&gt;
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Game Development&lt;/strong&gt;: Pathfinding for characters and AI in games (e.g., NPC movement).&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Robotics&lt;/strong&gt;: Navigation for autonomous robots in real-world environments.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Network Routing&lt;/strong&gt;: Finding the shortest paths in network graphs.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Puzzle Solving&lt;/strong&gt;: Solving puzzles like the 8-puzzle or 15-puzzle efficiently.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;10. Common Pitfalls and Best Practices&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;When implementing and applying A* or IDA*, it’s essential to avoid common mistakes and adopt best practices to ensure optimal performance.&lt;/p&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;1. Choosing Heuristics Wisely&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Admissibility&lt;/strong&gt;: Ensure that the heuristic never overestimates the cost to reach the goal. This guarantees that A* will find the optimal solution.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Consistency (Monotonicity)&lt;/strong&gt;: Verify that the heuristic satisfies the triangle inequality: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;≤&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;c&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;+&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
. This ensures that the algorithm’s 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 values are non-decreasing.&lt;/li&gt;
&lt;li&gt;Common heuristics include:

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Manhattan Distance&lt;/strong&gt;: Suitable for grid-based problems where movement is restricted to horizontal or vertical directions.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Euclidean Distance&lt;/strong&gt;: Best for problems allowing diagonal or free movement in a continuous space.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Domain-Specific Heuristics&lt;/strong&gt;: Tailor heuristics based on specific problem knowledge to improve performance.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;/ul&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;2. Balancing 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 and 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;Assign appropriate weights to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 (path cost so far) and 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 (estimated cost to goal).&lt;/li&gt;
&lt;li&gt;Overemphasizing 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 might lead to suboptimal solutions or longer paths.&lt;/li&gt;
&lt;li&gt;Relying heavily on 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 might degrade performance, as the algorithm explores more nodes unnecessarily.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;3. Debugging and Visualization Techniques&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Visualization&lt;/strong&gt;: Tools like heatmaps or animations of the search process can help debug and optimize the algorithm.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Logging&lt;/strong&gt;: Track 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, and 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 values for each node to identify anomalies.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Unit Testing&lt;/strong&gt;: Validate heuristic functions and graph structures with simple test cases to ensure correctness.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Benchmarking&lt;/strong&gt;: Test the implementation on different datasets to measure performance and identify bottlenecks.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;11. Advanced Topics&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;1. Variants of A&lt;/strong&gt;*
&lt;/h4&gt;

&lt;p&gt;A* has inspired several variants tailored to specific scenarios or performance needs:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Weighted A&lt;/strong&gt;*:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Modifies the evaluation function to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;=&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;+&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;w&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;⋅&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, where 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;w&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 (weight) adjusts the heuristic's influence.&lt;/li&gt;
&lt;li&gt;Used to trade optimality for speed by biasing the search toward the goal.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;

&lt;p&gt;&lt;strong&gt;Memory-Bounded A&lt;/strong&gt;*:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Examples include &lt;a href="https://en.wikipedia.org/wiki/SMA*" rel="noopener noreferrer"&gt;Simplified Memory-Bounded A* (SMA*)&lt;/a&gt; and &lt;a href="http://ai-maker.atrilla.net/the-recursive-best-first-search-algorithm/" rel="noopener noreferrer"&gt;Recursive Best-First Search (RBFS)&lt;/a&gt;.&lt;/li&gt;
&lt;li&gt;These variants limit memory usage by discarding or revisiting nodes as needed.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;

&lt;p&gt;&lt;strong&gt;&lt;a href="https://aaai.org/papers/079-aaai96-079-hierarchical-a-searching-abstraction-hierarchies-efficiently/" rel="noopener noreferrer"&gt;Hierarchical A*&lt;/a&gt;&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Splits large graphs into smaller subgraphs, solves each independently, and combines results.&lt;/li&gt;
&lt;li&gt;Ideal for complex environments like city navigation.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;/ul&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;2. Integration with Machine Learning&lt;/strong&gt;
&lt;/h4&gt;

&lt;p&gt;Machine learning can enhance A* by dynamically adjusting heuristics or guiding the search process:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Dynamic Heuristics&lt;/strong&gt;: Use neural networks or reinforcement learning to predict better heuristic values for each state.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Adaptive Pathfinding&lt;/strong&gt;: Train models to optimize paths based on historical data or changing environments.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Hybrid Models&lt;/strong&gt;: Combine A* with ML-driven approaches for problems like real-time strategy games or robotics.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;3. Parallelizing A&lt;/strong&gt;* for Performance Optimization
&lt;/h4&gt;

&lt;p&gt;Parallelization can significantly speed up A* for large graphs:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Parallel Open Set&lt;/strong&gt;: Divide the open set among multiple threads or processes, each exploring a subset of nodes.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Distributed Search&lt;/strong&gt;: Use distributed systems to partition the graph and execute search concurrently.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;GPU Acceleration&lt;/strong&gt;: Leverage GPUs for massive parallelism, especially for heuristic computations and large-scale graph traversal.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;12. Conclusion&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;The A* search algorithm and Iterative Deepening A* are powerful tools for solving pathfinding and graph traversal problems. While A* excels in speed and guarantees optimality with sufficient memory, IDA* offers a memory-efficient alternative for large graphs. By understanding their principles, properties, and implementations, you can leverage these algorithms to tackle a wide range of computational problems effectively.&lt;/p&gt;

</description>
      <category>algorithms</category>
      <category>ai</category>
      <category>javascript</category>
      <category>node</category>
    </item>
    <item>
      <title>How I Use AI, Sticky Notes, and Pomodoro to Stay Productive as a Software Engineer</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Fri, 24 Jan 2025 15:43:44 +0000</pubDate>
      <link>https://dev.to/frorning/how-i-use-ai-sticky-notes-and-pomodoro-to-stay-productive-as-a-software-engineer-3kl3</link>
      <guid>https://dev.to/frorning/how-i-use-ai-sticky-notes-and-pomodoro-to-stay-productive-as-a-software-engineer-3kl3</guid>
      <description>&lt;p&gt;As a software engineer juggling frontend and backend tasks, I’ve found that staying organized and focused is key to delivering quality work without burning out. Over time, I’ve developed a workflow that combines &lt;strong&gt;AI assistance&lt;/strong&gt;, &lt;strong&gt;sticky notes&lt;/strong&gt;, and the &lt;strong&gt;Pomodoro Technique&lt;/strong&gt; to break down tasks, track progress, and maintain my sanity. In this article, I’ll share my process and how you can adapt it to your own workflow.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;The Problem: Overwhelming Tasks and Context Switching&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;When working on a new feature or story, I often start with a vague set of requirements. Breaking these down into actionable steps can be overwhelming, especially when I’m still figuring out the details. Add in the constant context switching between frontend and backend work, and it’s easy to lose track of what’s done and what’s left.&lt;/p&gt;

&lt;p&gt;To tackle this, I needed a system that:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Helps me break down tasks into manageable chunks.&lt;/li&gt;
&lt;li&gt;Keeps me aware of my progress.&lt;/li&gt;
&lt;li&gt;Allows me to adapt as I learn more about the problem.&lt;/li&gt;
&lt;li&gt;Ensures I stay focused and hydrated (because, let’s be honest, we all forget to drink water sometimes).&lt;/li&gt;
&lt;/ol&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;My Workflow: AI, Sticky Notes, and Pomodoro&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;Here’s how I’ve structured my workflow to address these challenges:&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;1. Generate an Initial To-Do List with AI&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;When I start a new subtask, I use &lt;strong&gt;AI tools&lt;/strong&gt; (like Perplexity.ai or Continue.dev with Codellama) to generate an initial to-do list based on the requirements. For example, if I’m working on a user login feature, I might ask:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;em&gt;"Generate a to-do list for implementing a user login feature with email and password authentication. Include frontend and backend tasks."&lt;/em&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;The AI might suggest:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Set up login API endpoint.&lt;/li&gt;
&lt;li&gt;Create frontend login form.&lt;/li&gt;
&lt;li&gt;Add input validation for email and password.&lt;/li&gt;
&lt;li&gt;Implement error handling for invalid credentials.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;This gives me a solid starting point with 2–5 high-level tasks.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;2. Create a Feature Branch&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Once I have my initial to-do list, I create a feature branch for the subtask. For example:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;git checkout &lt;span class="nt"&gt;-b&lt;/span&gt; feature/user-login
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This keeps my work isolated and makes it easier to manage changes.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;3. Work Incrementally and Extend the To-Do List&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;I start by tackling the first task on my list. As I work, I often uncover additional subtasks or edge cases. This is where AI comes in again. I’ll share my current progress and ask for suggestions:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;em&gt;"I’m working on implementing the login API. Here’s what I’ve done so far: [details]. What additional tasks should I consider?"&lt;/em&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;The AI might suggest:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Add rate limiting to prevent brute force attacks.&lt;/li&gt;
&lt;li&gt;Log failed login attempts for security monitoring.&lt;/li&gt;
&lt;li&gt;Write unit tests for the login functionality.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;I add these tasks to my to-do list and continue working incrementally.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;4. Track Progress with Sticky Notes&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;I’m a big fan of &lt;strong&gt;sticky notes&lt;/strong&gt; for tracking progress. Whether physical or digital, they give me a visual representation of what’s done and what’s left.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Physical Sticky Notes&lt;/strong&gt;: I place them on my desk or monitor, moving completed tasks to a "Done" section.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Digital Tools&lt;/strong&gt;: If I’m working remotely, I use tools like &lt;strong&gt;Trello&lt;/strong&gt;, &lt;strong&gt;Notion&lt;/strong&gt;, or &lt;strong&gt;Todoist&lt;/strong&gt; to manage my to-do list.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Crossing off tasks gives me a sense of accomplishment and keeps me motivated.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;5. Stay Focused with the Pomodoro Technique&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;To maintain focus, I use the &lt;strong&gt;Pomodoro Technique&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Work for 25 minutes, then take a 5-minute break.&lt;/li&gt;
&lt;li&gt;After four Pomodoros, take a longer break (15–30 minutes).&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;I assign specific to-do items to each Pomodoro session. For example:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Pomodoro 1&lt;/strong&gt;: Set up login API endpoint.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pomodoro 2&lt;/strong&gt;: Add input validation for email and password.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;During breaks, I make sure to hydrate, stretch, or take a short walk. &lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;6. Create a Pull Request and Request Review&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Once all tasks are completed, I create a &lt;strong&gt;pull request (PR)&lt;/strong&gt; for my feature branch. I write a detailed PR description summarizing:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;What was implemented.&lt;/li&gt;
&lt;li&gt;Any challenges faced.&lt;/li&gt;
&lt;li&gt;Testing performed.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;I then request a review from my team and iterate based on feedback.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Tools I Use&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;Here are some tools and methods that have been invaluable in my workflow:&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;AI Tools&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Perplexity.ai&lt;/strong&gt;: For generating initial to-do lists and brainstorming solutions.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Continue.dev&lt;/strong&gt;: For seamless integration with my IDE and local development environment.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Local AI Models&lt;/strong&gt;: I use &lt;strong&gt;Qwen2.5-Coder 7B&lt;/strong&gt; and &lt;strong&gt;CodeLlama 7B&lt;/strong&gt; for code completion, debugging, and extending my to-do lists as I work. Running these models locally ensures privacy and customization.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Task Management&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Trello&lt;/strong&gt;: For visual task tracking with boards, lists, and cards.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Notion&lt;/strong&gt;: For documenting requirements, progress, and reference materials.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;JIRA&lt;/strong&gt;: For aligning my tasks with team-wide project management and sprint planning.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Pomodoro Timers&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Manual iPhone Timer&lt;/strong&gt;: I use the built-in timer on my iPhone for Pomodoro sessions. It’s simple and effective.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Paper Checklist&lt;/strong&gt;: I keep a handwritten checklist on paper to track tasks for each Pomodoro session. There’s something satisfying about physically crossing off completed tasks.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Hydration Tracking&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Manual iPhone Timer&lt;/strong&gt;: I set recurring reminders to drink water throughout the day.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Paper Drawing&lt;/strong&gt;: I draw circles on paper and color them in to track my hydration progress. Each circle represents a glass of water, and filling them in gives me a visual sense of accomplishment.&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Why This Works for Me&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;This workflow works because it:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Breaks down complex tasks&lt;/strong&gt; into manageable chunks.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Adapts to new information&lt;/strong&gt; as I learn more about the problem.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Keeps me focused&lt;/strong&gt; with the Pomodoro Technique.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Provides a visual representation of progress&lt;/strong&gt; with sticky notes.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Ensures I stay hydrated and energized&lt;/strong&gt; throughout the day.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;Example Workflow in Action&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;Scenario&lt;/strong&gt;: Implementing a User Login Feature
&lt;/h4&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Initial To-Do List (AI-Generated)&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Set up login API endpoint.&lt;/li&gt;
&lt;li&gt;Create frontend login form.&lt;/li&gt;
&lt;li&gt;Add input validation for email and password.&lt;/li&gt;
&lt;li&gt;Implement error handling for invalid credentials.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Feature Branch&lt;/strong&gt;: &lt;code&gt;feature/user-login&lt;/code&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Incremental Work&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Start with "Set up login API endpoint."&lt;/li&gt;
&lt;li&gt;Commit: &lt;code&gt;git commit -m "Add login API endpoint with email/password validation"&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Ask AI: &lt;em&gt;"What else should I consider for the login API?"&lt;/em&gt;
&lt;/li&gt;
&lt;li&gt;AI suggests: Add rate limiting, log failed attempts, and write unit tests.&lt;/li&gt;
&lt;li&gt;Add these tasks to your to-do list.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Sticky Notes&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Move "Set up login API endpoint" to "Done."&lt;/li&gt;
&lt;li&gt;Add new tasks: "Add rate limiting," "Log failed attempts," "Write unit tests."&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Pomodoro Sessions&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Session 1: Work on "Add rate limiting."&lt;/li&gt;
&lt;li&gt;Session 2: Work on "Log failed attempts."&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;PR and Review&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Create PR with title &lt;em&gt;"feat: implement user login"&lt;/em&gt; and description: &lt;em&gt;"Implemented user login feature with email/password authentication. Added rate limiting and logging for security. Unit tests included."&lt;/em&gt;
&lt;/li&gt;
&lt;li&gt;Request review and iterate based on feedback.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;Key Benefits of This Workflow&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Clarity&lt;/strong&gt;: Breaking tasks into smaller chunks makes complex work manageable.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Focus&lt;/strong&gt;: Pomodoro sessions and sticky notes help maintain focus and track progress.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Adaptability&lt;/strong&gt;: AI assistance allows you to dynamically adjust your plan as you learn more.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Wellness&lt;/strong&gt;: Regular breaks and hydration keep you energized and productive.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;By formalizing and refining this workflow, you can enhance your productivity, reduce stress, and deliver high-quality work consistently.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Try It Out!&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;If you’re feeling overwhelmed by your tasks or struggling to stay focused, give this workflow a try. Start small—use AI to generate a to-do list, create a feature branch, and work incrementally. Experiment with sticky notes and the Pomodoro Technique to see what works best for you.&lt;/p&gt;

&lt;p&gt;I’d love to hear how you stay productive in your day-to-day work. Share your tips and tools in the comments below!&lt;/p&gt;




&lt;p&gt;&lt;strong&gt;Happy coding!&lt;/strong&gt; 🚀&lt;/p&gt;

</description>
      <category>chatgpt</category>
      <category>productivity</category>
      <category>git</category>
      <category>tooling</category>
    </item>
    <item>
      <title>Introduction to WebAssembly (WASM)</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Fri, 10 Jan 2025 16:21:06 +0000</pubDate>
      <link>https://dev.to/frorning/introduction-to-webassembly-wasm-4g35</link>
      <guid>https://dev.to/frorning/introduction-to-webassembly-wasm-4g35</guid>
      <description>&lt;p&gt;WebAssembly (WASM) is a binary instruction format for a stack-based virtual machine, designed as a portable target for high-performance applications. In this article, we'll explore how to compile a simple C program to WebAssembly, load it into a web browser, and interact with it using JavaScript. We'll also explore some useful tools and commands for working with WASM outside the dev container environment.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Setting Up the Development Environment&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;Create the necessary folder structure and files for your WebAssembly project.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Create Project Folder&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;Begin by creating a new directory for your project. Inside this folder, you'll add the necessary files and configurations.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="nb"&gt;mkdir &lt;/span&gt;wasm-web-example
&lt;span class="nb"&gt;cd &lt;/span&gt;wasm-web-example
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Set Up Dev Container&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;In the &lt;code&gt;wasm-web-example&lt;/code&gt; directory, create the &lt;code&gt;.devcontainer&lt;/code&gt; folder to store the dev container configuration files. These files will set up a container with Emscripten installed to compile C code into WebAssembly.&lt;/p&gt;

&lt;p&gt;Inside the &lt;code&gt;.devcontainer&lt;/code&gt; folder, create the following files:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;devcontainer.json&lt;/strong&gt;: 
The &lt;code&gt;devcontainer.json&lt;/code&gt; file configures VSCode to use the Docker container with the necessary extensions and environment settings.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight json"&gt;&lt;code&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"name"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"Emscripten DevContainer"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"build"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"dockerfile"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"Dockerfile"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"customizations"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"vscode"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="nl"&gt;"settings"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="nl"&gt;"terminal.integrated.shell.linux"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"/bin/bash"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="nl"&gt;"C_Cpp.default.configurationProvider"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"ms-vscode.cmake-tools"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="nl"&gt;"C_Cpp.default.intelliSenseMode"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"gcc-x64"&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="nl"&gt;"extensions"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="s2"&gt;"ms-vscode.cpptools"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="s2"&gt;"ms-vscode.cmake-tools"&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"postCreateCommand"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"emcc --version"&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Dockerfile&lt;/strong&gt;: 
The &lt;code&gt;Dockerfile&lt;/code&gt; will set up the Emscripten environment. Here's the content for that file:
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight docker"&gt;&lt;code&gt;&lt;span class="c"&gt;# Use the official Emscripten image&lt;/span&gt;
&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="s"&gt; emscripten/emsdk:3.1.74&lt;/span&gt;

&lt;span class="c"&gt;# Set the working directory&lt;/span&gt;
&lt;span class="k"&gt;WORKDIR&lt;/span&gt;&lt;span class="s"&gt; /workspace&lt;/span&gt;

&lt;span class="c"&gt;# Copy the source code into the container&lt;/span&gt;
&lt;span class="k"&gt;COPY&lt;/span&gt;&lt;span class="s"&gt; . .&lt;/span&gt;

&lt;span class="c"&gt;# Install any additional packages if necessary (optional)&lt;/span&gt;
&lt;span class="c"&gt;# Ensure to clean up cache to minimize image size&lt;/span&gt;
&lt;span class="k"&gt;RUN &lt;/span&gt;apt-get update &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="se"&gt;\
&lt;/span&gt;    apt-get &lt;span class="nb"&gt;install&lt;/span&gt; &lt;span class="nt"&gt;-y&lt;/span&gt; build-essential &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="se"&gt;\
&lt;/span&gt;    apt-get clean &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="se"&gt;\
&lt;/span&gt;    &lt;span class="nb"&gt;rm&lt;/span&gt; &lt;span class="nt"&gt;-rf&lt;/span&gt; /var/lib/apt/lists/&lt;span class="k"&gt;*&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Create VSCode Settings&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;In the root of your project, create a &lt;code&gt;.vscode&lt;/code&gt; folder with the following files:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;c_cpp_properties.json&lt;/strong&gt;:
This file configures the C++ IntelliSense and include paths for your project.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight json"&gt;&lt;code&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"configurations"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"name"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"Linux"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"includePath"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="s2"&gt;"${workspaceFolder}/**"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="s2"&gt;"/emsdk/upstream/emscripten/system/include"&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"defines"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[],&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"compilerPath"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"/usr/bin/gcc"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"cStandard"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"c17"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"cppStandard"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"gnu++17"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"configurationProvider"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"ms-vscode.cmake-tools"&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"version"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;settings.json&lt;/strong&gt;: 
This file includes specific VSCode settings for language associations.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight json"&gt;&lt;code&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"files.associations"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"emscripten.h"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"c"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[javascript]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.typescript-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[typescript]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.typescript-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[jsonc]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.json-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[json]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.json-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[html]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.html-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Create C, JavaScript, and HTML Files&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;Now, create the following files for your project:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;test.c&lt;/strong&gt;:
This C file contains the simple function that will be compiled to WebAssembly.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// test.c&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;test.html&lt;/strong&gt;:
This HTML file will load the WebAssembly module using JavaScript.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight html"&gt;&lt;code&gt;&lt;span class="cp"&gt;&amp;lt;!DOCTYPE html&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;html&lt;/span&gt; &lt;span class="na"&gt;lang=&lt;/span&gt;&lt;span class="s"&gt;"en"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;head&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;meta&lt;/span&gt; &lt;span class="na"&gt;charset=&lt;/span&gt;&lt;span class="s"&gt;"UTF-8"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;meta&lt;/span&gt; &lt;span class="na"&gt;name=&lt;/span&gt;&lt;span class="s"&gt;"viewport"&lt;/span&gt; &lt;span class="na"&gt;content=&lt;/span&gt;&lt;span class="s"&gt;"width=device-width, initial-scale=1.0"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;title&amp;gt;&lt;/span&gt;WebAssembly Example&lt;span class="nt"&gt;&amp;lt;/title&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/head&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;body&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;h1&amp;gt;&lt;/span&gt;WebAssembly Example&lt;span class="nt"&gt;&amp;lt;/h1&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;div&lt;/span&gt; &lt;span class="na"&gt;id=&lt;/span&gt;&lt;span class="s"&gt;"output"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&amp;lt;/div&amp;gt;&lt;/span&gt;

  &lt;span class="nt"&gt;&amp;lt;script &lt;/span&gt;&lt;span class="na"&gt;src=&lt;/span&gt;&lt;span class="s"&gt;"test.js"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&amp;lt;/script&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/body&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;/html&amp;gt;&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;test.js&lt;/strong&gt;:
This JavaScript file will fetch the WebAssembly module and call the exported function.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// test.js&lt;/span&gt;
&lt;span class="c1"&gt;// Path to the .wasm file&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;wasmFile&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;test.wasm&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Load the WebAssembly module&lt;/span&gt;
&lt;span class="nf"&gt;fetch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;wasmFile&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;ok&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Error&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;`Failed to load &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;wasmFile&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;statusText&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;arrayBuffer&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
  &lt;span class="p"&gt;})&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;bytes&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;WebAssembly&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;instantiate&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;bytes&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(({&lt;/span&gt; &lt;span class="nx"&gt;instance&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// Access exported functions&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;instance&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;exports&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt;

    &lt;span class="c1"&gt;// Example: Call a function exported from the WebAssembly module&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;wasmExports&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;add&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// Example function call&lt;/span&gt;
      &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s2"&gt;`Result from WebAssembly: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;No "add" function found in the WebAssembly module.&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="p"&gt;})&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;catch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;error&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;error&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Error loading or running the WebAssembly module:&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;error&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Error loading WebAssembly module.&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;});&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Now that you've set up all the necessary files and configurations, you can move on to compiling and interacting with WebAssembly.&lt;/p&gt;

&lt;p&gt;The project structure looks like following now:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;➜  wasm-web-example: tree &lt;span class="nb"&gt;.&lt;/span&gt; &lt;span class="nt"&gt;-a&lt;/span&gt;
&lt;span class="nb"&gt;.&lt;/span&gt;
├── .devcontainer
│&amp;nbsp;&amp;nbsp; ├── Dockerfile
│&amp;nbsp;&amp;nbsp; └── devcontainer.json
├── .vscode
│&amp;nbsp;&amp;nbsp; ├── c_cpp_properties.json
│&amp;nbsp;&amp;nbsp; └── settings.json
├── test.c
├── test.html
├── test.js
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  &lt;strong&gt;Compiling C Code to WebAssembly Using Emscripten&lt;/strong&gt;
&lt;/h2&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Basic C Program&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;The file &lt;code&gt;test.c&lt;/code&gt; contains a simple function &lt;code&gt;add&lt;/code&gt; that adds two integers. We will compile this C function into WebAssembly using Emscripten.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// test.c&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Emscripten Command&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;Inside the dev container, open the terminal (use &lt;code&gt;cmd+j&lt;/code&gt; in VSCode) and run the following Emscripten command to compile the C code to WebAssembly:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;emcc test.c &lt;span class="nt"&gt;-O3&lt;/span&gt; &lt;span class="nt"&gt;-s&lt;/span&gt; STANDALONE_WASM &lt;span class="nt"&gt;-s&lt;/span&gt; &lt;span class="nv"&gt;EXPORTED_FUNCTIONS&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s1"&gt;'["_add"]'&lt;/span&gt; &lt;span class="nt"&gt;--no-entry&lt;/span&gt; &lt;span class="nt"&gt;-o&lt;/span&gt; test.wasm
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F9u8ybcwjwinz7cgytqct.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F9u8ybcwjwinz7cgytqct.png" alt="Webassembly Example Devcontainer" width="800" height="234"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;h3&gt;
  
  
  Breakdown of the Command
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;emcc&lt;/code&gt;&lt;/strong&gt;: This is the Emscripten C/C++ compiler command. It compiles C/C++ source files into WebAssembly or asm.js.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;test.c&lt;/code&gt;&lt;/strong&gt;: This specifies the input C source file that you want to compile.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;-O3&lt;/code&gt;&lt;/strong&gt;: This flag enables aggressive optimizations during the compilation process. The &lt;code&gt;-O3&lt;/code&gt; optimization level is typically used for performance-critical applications, as it applies various optimization techniques that can significantly improve runtime performance.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;-s STANDALONE_WASM&lt;/code&gt;&lt;/strong&gt;: This option instructs Emscripten to generate a standalone WebAssembly module. A standalone WASM module does not depend on any JavaScript glue code and can be executed independently in environments that support WebAssembly.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;-s EXPORTED_FUNCTIONS='["_add"]'&lt;/code&gt;&lt;/strong&gt;: This flag specifies which functions from the C code should be exported and made available for calling from JavaScript. In this case, the function named &lt;code&gt;_add&lt;/code&gt; will be accessible in the resulting WASM module.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;--no-entry&lt;/code&gt;&lt;/strong&gt;: This option tells the compiler that there is no entry point (like a &lt;code&gt;main()&lt;/code&gt; function) in the program. This is useful for libraries or modules that are intended to be used by other code rather than executed directly.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;-o test.wasm&lt;/code&gt;&lt;/strong&gt;: This specifies the output file name for the compiled WebAssembly module. In this case, it will create a file named &lt;code&gt;test.wasm&lt;/code&gt;.&lt;/p&gt;&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;This command will generate &lt;code&gt;test.wasm&lt;/code&gt;, the WebAssembly binary, and ensure that the &lt;code&gt;add&lt;/code&gt; function is exported for use in JavaScript.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Loading and Interacting with WebAssembly in the Browser&lt;/strong&gt;
&lt;/h2&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;HTML Setup&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;The file &lt;code&gt;test.html&lt;/code&gt; contains a simple HTML page that loads the WebAssembly binary using JavaScript. The JavaScript code in &lt;code&gt;test.js&lt;/code&gt; fetches the &lt;code&gt;.wasm&lt;/code&gt; file and instantiates it.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight html"&gt;&lt;code&gt;&lt;span class="c"&gt;&amp;lt;!-- test.html --&amp;gt;&lt;/span&gt;
&lt;span class="cp"&gt;&amp;lt;!DOCTYPE html&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;html&lt;/span&gt; &lt;span class="na"&gt;lang=&lt;/span&gt;&lt;span class="s"&gt;"en"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;head&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;meta&lt;/span&gt; &lt;span class="na"&gt;charset=&lt;/span&gt;&lt;span class="s"&gt;"UTF-8"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;meta&lt;/span&gt; &lt;span class="na"&gt;name=&lt;/span&gt;&lt;span class="s"&gt;"viewport"&lt;/span&gt; &lt;span class="na"&gt;content=&lt;/span&gt;&lt;span class="s"&gt;"width=device-width, initial-scale=1.0"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;title&amp;gt;&lt;/span&gt;WebAssembly Example&lt;span class="nt"&gt;&amp;lt;/title&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/head&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;body&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;h1&amp;gt;&lt;/span&gt;WebAssembly Example&lt;span class="nt"&gt;&amp;lt;/h1&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;div&lt;/span&gt; &lt;span class="na"&gt;id=&lt;/span&gt;&lt;span class="s"&gt;"output"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&amp;lt;/div&amp;gt;&lt;/span&gt;

  &lt;span class="nt"&gt;&amp;lt;script &lt;/span&gt;&lt;span class="na"&gt;src=&lt;/span&gt;&lt;span class="s"&gt;"test.js"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&amp;lt;/script&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/body&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;/html&amp;gt;&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;JavaScript Setup&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;The JavaScript file &lt;code&gt;test.js&lt;/code&gt; loads the &lt;code&gt;test.wasm&lt;/code&gt; file and calls the exported &lt;code&gt;add&lt;/code&gt; function:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// test.js&lt;/span&gt;
&lt;span class="c1"&gt;// Path to the .wasm file&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;wasmFile&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;test.wasm&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Load the WebAssembly module&lt;/span&gt;
&lt;span class="nf"&gt;fetch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;wasmFile&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;ok&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Error&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;`Failed to load &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;wasmFile&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;statusText&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;arrayBuffer&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
  &lt;span class="p"&gt;})&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;bytes&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;WebAssembly&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;instantiate&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;bytes&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(({&lt;/span&gt; &lt;span class="nx"&gt;instance&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// Access exported functions&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;instance&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;exports&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt;

    &lt;span class="c1"&gt;// Example: Call a function exported from the WebAssembly module&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;wasmExports&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;add&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// Example function call&lt;/span&gt;
      &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s2"&gt;`Result from WebAssembly: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;No "add" function found in the WebAssembly module.&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="p"&gt;})&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;catch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;error&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;error&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Error loading or running the WebAssembly module:&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;error&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Error loading WebAssembly module.&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;});&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This will display the result of the &lt;code&gt;add&lt;/code&gt; function in the HTML page when the module is loaded successfully.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Using External Tools on macOS&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;Outside the dev container, there are several useful commands you can run to work with WebAssembly on your Mac.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Install &lt;code&gt;wabt&lt;/code&gt;&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;&lt;code&gt;wabt&lt;/code&gt; (WebAssembly Binary Toolkit) provides utilities for working with WebAssembly, including converting &lt;code&gt;.wasm&lt;/code&gt; files to the human-readable WAT (WebAssembly Text) format. Install it via Homebrew:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;brew &lt;span class="nb"&gt;install &lt;/span&gt;wabt
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Convert WASM to WAT&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;Once &lt;code&gt;wabt&lt;/code&gt; is installed, you can use the &lt;code&gt;wasm2wat&lt;/code&gt; tool to convert your WebAssembly binary (&lt;code&gt;test.wasm&lt;/code&gt;) to the WAT format:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;wasm2wat test.wasm
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This will output a text representation of the WebAssembly module that you can read and inspect.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;(module
  (type (;0;) (func))
  (type (;1;) (func (param i32 i32) (result i32)))
  (type (;2;) (func (param i32)))
  (type (;3;) (func (result i32)))
  (func (;0;) (type 0)
    nop)
  (func (;1;) (type 1) (param i32 i32) (result i32)
    local.get 0
    local.get 1
    i32.add)
  (func (;2;) (type 2) (param i32)
    local.get 0
    global.set 0)
  (func (;3;) (type 3) (result i32)
    global.get 0)
  (table (;0;) 2 2 funcref)
  (memory (;0;) 258 258)
  (global (;0;) (mut i32) (i32.const 66560))
  (export "memory" (memory 0))
  (export "add" (func 1))
  (export "_initialize" (func 0))
  (export "__indirect_function_table" (table 0))
  (export "_emscripten_stack_restore" (func 2))
  (export "emscripten_stack_get_current" (func 3))
  (elem (;0;) (i32.const 1) func 0))
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Serve the HTML Page&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;To view the HTML page that interacts with the WebAssembly module, you can use Python’s simple HTTP server:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;python &lt;span class="nt"&gt;-m&lt;/span&gt; http.server
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This command will start a local web server on &lt;code&gt;http://localhost:8000&lt;/code&gt;, where you can open &lt;code&gt;index.html&lt;/code&gt; in your browser to see the WebAssembly module in action.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fsk8amzwwxy9if5hkboy6.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fsk8amzwwxy9if5hkboy6.png" alt="Webassembly Example Output" width="800" height="179"&gt;&lt;/a&gt;&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;Conclusion&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;By following the steps outlined in this article, you can set up a development environment to compile C code to WebAssembly, interact with it using JavaScript, and convert the resulting WebAssembly binary to the WAT format for inspection. The use of external tools like &lt;code&gt;wabt&lt;/code&gt; and Python’s HTTP server makes it easier to manage and explore WebAssembly modules on your macOS system.&lt;/p&gt;

</description>
      <category>javascript</category>
      <category>webassembly</category>
      <category>vscode</category>
      <category>docker</category>
    </item>
    <item>
      <title>Functional Programming in Go with IBM fp-go: Error Handling Made Explicit</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Fri, 27 Dec 2024 14:43:19 +0000</pubDate>
      <link>https://dev.to/frorning/functional-programming-in-go-with-ibm-fp-go-error-handling-made-explicit-9of</link>
      <guid>https://dev.to/frorning/functional-programming-in-go-with-ibm-fp-go-error-handling-made-explicit-9of</guid>
      <description>&lt;p&gt;Functional programming (FP) principles are gaining popularity in modern software development due to their emphasis on immutability, composability, and explicitness. While Go is traditionally an imperative language, the &lt;strong&gt;fp-go&lt;/strong&gt; library, developed by IBM, introduces FP abstractions such as &lt;code&gt;Option&lt;/code&gt;, &lt;code&gt;Either&lt;/code&gt;, &lt;code&gt;Fold&lt;/code&gt;, and utilities for functional composition. In this article, we will explore how to use &lt;strong&gt;fp-go&lt;/strong&gt; to handle errors explicitly, define function signatures with multiple error types, and build a real-world CRUD API example demonstrating these concepts.&lt;/p&gt;

&lt;h2&gt;
  
  
  Why Functional Error Handling?
&lt;/h2&gt;

&lt;p&gt;Error handling is crucial for building reliable software. Traditional Go error handling relies on returning &lt;code&gt;error&lt;/code&gt; values, which can be unintentionally ignored or mishandled. Functional error handling introduces abstractions like:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;&lt;code&gt;Option&lt;/code&gt;&lt;/strong&gt;: Represents optional values, akin to &lt;code&gt;Some&lt;/code&gt; and &lt;code&gt;None&lt;/code&gt; in other FP languages.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;&lt;code&gt;Either&lt;/code&gt;&lt;/strong&gt;: Encapsulates a value that can either be a &lt;code&gt;Right&lt;/code&gt; (success) or &lt;code&gt;Left&lt;/code&gt; (failure), making error propagation explicit.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Tagged Unions&lt;/strong&gt;: Allow function signatures to clearly define possible error types.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Composition&lt;/strong&gt;: Enables chaining operations while handling errors naturally.&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;Let’s dive into these concepts and see how &lt;strong&gt;fp-go&lt;/strong&gt; facilitates them in Go.&lt;/p&gt;




&lt;h2&gt;
  
  
  Getting Started with fp-go
&lt;/h2&gt;

&lt;p&gt;First, add &lt;strong&gt;fp-go&lt;/strong&gt; to your Go project:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;go get github.com/IBM/fp-go
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Import the necessary modules:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="n"&gt;either&lt;/span&gt; &lt;span class="s"&gt;"github.com/IBM/fp-go/either"&lt;/span&gt;
    &lt;span class="n"&gt;option&lt;/span&gt; &lt;span class="s"&gt;"github.com/IBM/fp-go/option"&lt;/span&gt;
&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  &lt;code&gt;Option&lt;/code&gt;: Handling Optional Values
&lt;/h2&gt;

&lt;p&gt;&lt;code&gt;Option&lt;/code&gt; represents a value that may or may not exist. It is either &lt;code&gt;Some(value)&lt;/code&gt; or &lt;code&gt;None&lt;/code&gt;.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Example: Parsing an Integer&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;parseInt&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;option&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Option&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;strconv&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Atoi&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="no"&gt;nil&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;option&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;None&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]()&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;option&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Some&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;opt&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;parseInt&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"42"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;option&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Println&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"No value"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Parsed value: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;opt&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Key Takeaways:
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;Option&lt;/code&gt; eliminates &lt;code&gt;nil&lt;/code&gt; values.&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;Fold&lt;/code&gt; is used to handle both cases (&lt;code&gt;Some&lt;/code&gt; or &lt;code&gt;None&lt;/code&gt;).&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  &lt;code&gt;Either&lt;/code&gt;: Handling Errors Explicitly
&lt;/h2&gt;

&lt;p&gt;&lt;code&gt;Either&lt;/code&gt; represents a computation that can result in two possibilities:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;&lt;code&gt;Left&lt;/code&gt;&lt;/strong&gt;: Represents an error.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;&lt;code&gt;Right&lt;/code&gt;&lt;/strong&gt;: Represents a successful result.&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Example: Safe Division&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;MathError&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Code&lt;/span&gt;    &lt;span class="kt"&gt;string&lt;/span&gt;
    &lt;span class="n"&gt;Message&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;safeDivide&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MathError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MathError&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"DIV_BY_ZERO"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"Cannot divide by zero"&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;safeDivide&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="n"&gt;MathError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Error [%s]: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Result: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Key Takeaways:
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;Either&lt;/code&gt; separates success and failure paths.&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;Fold&lt;/code&gt; simplifies handling both cases in one place.&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Function Signatures with Multiple Error Types
&lt;/h2&gt;

&lt;p&gt;Real-world applications often need to handle multiple types of errors. By using tagged unions, we can define explicit error types.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Example: Tagged Union for Errors&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Tag&lt;/span&gt;     &lt;span class="kt"&gt;string&lt;/span&gt;
    &lt;span class="n"&gt;Message&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="n"&gt;MathErrorTag&lt;/span&gt;    &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"MathError"&lt;/span&gt;
    &lt;span class="n"&gt;DatabaseErrorTag&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"DatabaseError"&lt;/span&gt;
&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;NewMathError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;msg&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Tag&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;MathErrorTag&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;msg&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;NewDatabaseError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;msg&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Tag&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;DatabaseErrorTag&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;msg&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;process&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;NewMathError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Division by zero"&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;process&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Error [%s]: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Tag&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Processed result: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Benefits:
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;Tagged unions make errors self-documenting.&lt;/li&gt;
&lt;li&gt;Explicit types reduce ambiguity in error handling.&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Real-World Example: CRUD API
&lt;/h2&gt;

&lt;p&gt;Let’s implement a simple CRUD API with explicit error handling using &lt;code&gt;Either&lt;/code&gt;.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Model and Error Definitions&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;ID&lt;/span&gt;    &lt;span class="kt"&gt;int&lt;/span&gt;
    &lt;span class="n"&gt;Name&lt;/span&gt;  &lt;span class="kt"&gt;string&lt;/span&gt;
    &lt;span class="n"&gt;Email&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Code&lt;/span&gt;    &lt;span class="kt"&gt;string&lt;/span&gt;
    &lt;span class="n"&gt;Message&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="n"&gt;NotFoundError&lt;/span&gt;    &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"NOT_FOUND"&lt;/span&gt;
    &lt;span class="n"&gt;ValidationError&lt;/span&gt;  &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"VALIDATION_ERROR"&lt;/span&gt;
    &lt;span class="n"&gt;DatabaseError&lt;/span&gt;    &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"DATABASE_ERROR"&lt;/span&gt;
&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;NewAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;message&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Repository Layer&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;var&lt;/span&gt; &lt;span class="n"&gt;users&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;map&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;ID&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Name&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"Alice"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Email&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"alice@example.com"&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;getUserByID&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;exists&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;users&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;exists&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;NewAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;NotFoundError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"User not found"&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Service Layer&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;validateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Name&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s"&gt;""&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Email&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s"&gt;""&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;NewAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ValidationError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"Name and email are required"&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;createUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;validation&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;validateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Chain&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;validUser&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ID&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;users&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="m"&gt;1&lt;/span&gt;
            &lt;span class="n"&gt;users&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ID&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;user&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;validation&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Controller&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;handleGetUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;getUserByID&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Error [%s]: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"User: %+v&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;handleCreateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;createUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Error [%s]: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;newUser&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Created user: %+v&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;newUser&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;handleGetUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;handleCreateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Name&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"Bob"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Email&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"bob@example.com"&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt;
    &lt;span class="n"&gt;handleGetUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Conclusion
&lt;/h2&gt;

&lt;p&gt;Using &lt;strong&gt;fp-go&lt;/strong&gt; in Go, we can:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Model errors explicitly using &lt;code&gt;Either&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;Represent optional values with &lt;code&gt;Option&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;Handle multiple error types via tagged unions.&lt;/li&gt;
&lt;li&gt;Build maintainable and composable APIs.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;These patterns make your Go code more robust, readable, and functional. Whether you’re building a CRUD API or complex business logic, &lt;strong&gt;fp-go&lt;/strong&gt; empowers you to handle errors cleanly and consistently.&lt;/p&gt;

</description>
      <category>go</category>
      <category>functional</category>
      <category>programming</category>
      <category>webdev</category>
    </item>
    <item>
      <title>Mastering Trampolining: A Deep Dive into Recursive Optimization</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Wed, 25 Dec 2024 17:02:44 +0000</pubDate>
      <link>https://dev.to/frorning/mastering-trampolining-a-deep-dive-into-recursive-optimization-45nc</link>
      <guid>https://dev.to/frorning/mastering-trampolining-a-deep-dive-into-recursive-optimization-45nc</guid>
      <description>&lt;h2&gt;
  
  
  Mastering Trampolining: A Deep Dive into Recursive Optimization
&lt;/h2&gt;

&lt;p&gt;In the world of programming, recursion is a powerful tool that allows functions to call themselves to solve complex problems. However, deep recursion can lead to stack overflow errors, especially in languages that do not optimize recursive calls. Enter &lt;strong&gt;trampolining&lt;/strong&gt;, a technique that transforms recursive calls into an iterative process, allowing for infinite recursion without the risk of exhausting the call stack. In this article, we will explore trampolining in detail, providing implementations in multiple programming languages, including Java, C++, JavaScript, and Go. &lt;/p&gt;

&lt;h3&gt;
  
  
  Understanding Trampolining
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;What is Trampolining?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Trampolining is a method used to optimize recursive functions by converting them into iterations. Instead of a function calling itself directly, it returns another function (or "thunk") to be executed later. This allows the program to manage function calls without piling them up on the call stack.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Why Use Trampolining?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Using trampolining has several benefits:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Improved Performance&lt;/strong&gt;: It enhances the execution speed of your code by converting recursive calls into iterations.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Preventing Stack Overflow&lt;/strong&gt;: By avoiding deep recursion, it prevents stack overflow errors, especially in functions that call themselves repeatedly.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  How Trampolining Works
&lt;/h3&gt;

&lt;p&gt;The basic principle of trampolining involves converting recursive calls into iterations. Instead of a function calling itself directly, it returns another function to be executed. This process continues until a final value is produced.&lt;/p&gt;

&lt;h4&gt;
  
  
  Example Code
&lt;/h4&gt;

&lt;p&gt;To illustrate how trampolining works, let's look at an example in JavaScript.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Before Trampolining:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;After Trampolining:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;fn&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kd"&gt;function&lt;/span&gt;&lt;span class="p"&gt;(...&lt;/span&gt;&lt;span class="nx"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;fn&lt;/span&gt;&lt;span class="p"&gt;(...&lt;/span&gt;&lt;span class="nx"&gt;args&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;typeof&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;function&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;result&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;acc&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return &lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;trampolinedFactorial&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;trampolinedFactorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt; &lt;span class="c1"&gt;// Output: 120&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Technical Explanation
&lt;/h3&gt;

&lt;p&gt;Trampolining leverages continuations and tail-call optimization. Continuations allow the function to pause and resume, while tail-call optimization ensures that the function doesn’t add new frames to the call stack.&lt;/p&gt;

&lt;h4&gt;
  
  
  Preparing Your Functions
&lt;/h4&gt;

&lt;p&gt;Not all functions need trampolining. Identify functions that involve deep recursion or are likely to cause stack overflow.&lt;/p&gt;

&lt;h4&gt;
  
  
  Refactoring for Trampolining
&lt;/h4&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Identify the Recursive Function&lt;/strong&gt;: Find the function that repeatedly calls itself.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Modify the Function&lt;/strong&gt;: Change it to return another function instead of making a direct recursive call.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Wrap with a Trampoline&lt;/strong&gt;: Use a trampoline function to execute the modified function iteratively.&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Common Pitfalls and How to Avoid Them
&lt;/h3&gt;

&lt;p&gt;Common pitfalls include infinite loops and performance overhead. Ensure your base case is correct to avoid infinite loops, and test and optimize performance as needed.&lt;/p&gt;

&lt;h3&gt;
  
  
  Advanced Trampolining Techniques
&lt;/h3&gt;

&lt;p&gt;Trampolining can be further enhanced with techniques like memoization and lazy evaluation. These techniques can help improve performance further by caching results or delaying computations until necessary.&lt;/p&gt;

&lt;h3&gt;
  
  
  Real-World Applications
&lt;/h3&gt;

&lt;p&gt;Many large-scale applications use trampolining to handle recursive tasks efficiently. Examples include:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Parsing Complex Data Structures&lt;/strong&gt;: For instance, when dealing with nested JSON objects or XML.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Functional Programming Paradigms&lt;/strong&gt;: Languages like Scala and Haskell often utilize trampolining for efficient recursion.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Implementing Trampolining in Other Languages
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Java Implementation
&lt;/h4&gt;

&lt;p&gt;In Java, trampolining can be implemented using interfaces or functional programming constructs available in Java 8 and later.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight java"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;java.util.function.Supplier&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;

&lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;TrampolineExample&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;

    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="no"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="no"&gt;T&lt;/span&gt; &lt;span class="nf"&gt;trampoline&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="no"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;supplier&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="no"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;supplier&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="no"&gt;T&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;get&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="k"&gt;instanceof&lt;/span&gt; &lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="no"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;)&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
                &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;String&lt;/span&gt;&lt;span class="o"&gt;[]&lt;/span&gt; &lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;number&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;trampoline&lt;/span&gt;&lt;span class="o"&gt;(()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;number&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;));&lt;/span&gt;
        &lt;span class="nc"&gt;System&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;out&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;println&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Factorial of "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;number&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="s"&gt;" is: "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// Output: 120&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  C++ Implementation
&lt;/h4&gt;

&lt;p&gt;In C++, trampolining can be achieved using &lt;code&gt;std::function&lt;/code&gt; and lambda expressions.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;iostream&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;functional&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;function&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;function&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;func&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;nullptr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;function&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;]()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;]()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;number&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;number&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;cout&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="s"&gt;"Factorial of "&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;number&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="s"&gt;" is: "&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;endl&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Output: 120&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Go Implementation with Generics
&lt;/h4&gt;

&lt;p&gt;Go provides an elegant way to implement trampolining using generics introduced in Go 1.18.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;package&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;

&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="s"&gt;"fmt"&lt;/span&gt;
&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c"&gt;// Define the thunk type for generic functions&lt;/span&gt;
&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="n"&gt;any&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="c"&gt;// Trampoline function that executes the supplied thunk&lt;/span&gt;
&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="n"&gt;any&lt;/span&gt;&lt;span class="p"&gt;](&lt;/span&gt;&lt;span class="n"&gt;fn&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;fn&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="no"&gt;nil&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="c"&gt;// Final result&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;fn&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="c"&gt;// Continue with the next thunk&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c"&gt;// Fibonacci function using trampolining with generics&lt;/span&gt;
&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="no"&gt;nil&lt;/span&gt; &lt;span class="c"&gt;// Return final accumulated value&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="m"&gt;1&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;curr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="no"&gt;nil&lt;/span&gt; &lt;span class="c"&gt;// Return final accumulated value&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;// Return next step as a thunk&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="m"&gt;10&lt;/span&gt; &lt;span class="c"&gt;// fib(10) == 55&lt;/span&gt;
    &lt;span class="n"&gt;fibThunk&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;fib&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;// Initialize with starting values&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fibThunk&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Fibonacci(%d) = %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;// Output: 55&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Conclusion
&lt;/h3&gt;

&lt;p&gt;Trampolining is a powerful technique for optimizing recursive functions across various programming languages. It improves performance and prevents stack overflow errors by transforming recursive calls into an iterative process. By mastering this technique and implementing it in your codebase—whether in JavaScript, Java, C++, or Go—you can enhance the robustness and efficiency of your applications.&lt;/p&gt;

&lt;p&gt;As you explore more complex algorithms and data structures in your programming journey, consider incorporating trampolining where appropriate. This approach not only helps manage recursion effectively but also encourages cleaner and more maintainable code.&lt;/p&gt;

&lt;p&gt;Happy coding!&lt;/p&gt;

&lt;p&gt;Citations:&lt;br&gt;
[1] &lt;a href="https://rdinnager.github.io/trampoline/" rel="noopener noreferrer"&gt;https://rdinnager.github.io/trampoline/&lt;/a&gt;&lt;br&gt;
[2] &lt;a href="https://www.geeksforgeeks.org/es6-trampoline-function/" rel="noopener noreferrer"&gt;https://www.geeksforgeeks.org/es6-trampoline-function/&lt;/a&gt;&lt;br&gt;
[3] &lt;a href="https://gcc.gnu.org/onlinedocs/gccint/Trampolines.html" rel="noopener noreferrer"&gt;https://gcc.gnu.org/onlinedocs/gccint/Trampolines.html&lt;/a&gt;&lt;/p&gt;

</description>
      <category>javascript</category>
      <category>java</category>
      <category>go</category>
      <category>cpp</category>
    </item>
    <item>
      <title>Mastering Quick Sort: A Fundamental Algorithm in Computer Science</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Wed, 25 Dec 2024 13:46:12 +0000</pubDate>
      <link>https://dev.to/frorning/mastering-quick-sort-a-fundamental-algorithm-in-computer-science-15bi</link>
      <guid>https://dev.to/frorning/mastering-quick-sort-a-fundamental-algorithm-in-computer-science-15bi</guid>
      <description>&lt;h2&gt;
  
  
  Introduction to Quick Sort
&lt;/h2&gt;

&lt;p&gt;In the vast world of algorithms and data structures, Quick Sort stands as one of the most elegant and efficient sorting methods. Its simplicity and effectiveness make it a favorite among developers and researchers alike. Whether you're working on optimizing code or just curious about how modern computing systems handle large datasets, understanding Quick Sort is invaluable.&lt;/p&gt;

&lt;h2&gt;
  
  
  The Essence of Quick Sort
&lt;/h2&gt;

&lt;p&gt;Quick Sort is based on the divide-and-conquer strategy, which involves breaking down a complex problem into smaller sub-problems that are easier to solve. &lt;br&gt;
In the context of sorting algorithms, this means dividing an array or list of elements into two parts, such that the left part contains elements less than a chosen pivot and the right part contains elements greater than the pivot.&lt;/p&gt;
&lt;h3&gt;
  
  
  How It Works
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Choose a Pivot&lt;/strong&gt;: Select an element from the array as the pivot.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Partitioning&lt;/strong&gt;: Rearrange the array so that all elements with values less than the pivot come before it, while all elements with values greater than the pivot come after it. The pivot is now in its final position.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Recursively Apply to Sub-arrays&lt;/strong&gt;: Repeat the process for both sub-arrays formed by partitioning.&lt;/li&gt;
&lt;/ol&gt;
&lt;h2&gt;
  
  
  Implementing Quick Sort
&lt;/h2&gt;

&lt;p&gt;Here’s a basic Python implementation of Quick Sort:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;quick_sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;
    &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;pivot&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;//&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;pivot&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="n"&gt;middle&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;pivot&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;pivot&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;quick_sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;middle&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;quick_sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Example usage
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;quick_sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This implementation is straightforward and leverages list comprehensions for simplicity. However, it's important to note that in practice, the choice of pivot can significantly impact performance.&lt;/p&gt;

&lt;h2&gt;
  
  
  Performance Analysis
&lt;/h2&gt;

&lt;p&gt;The efficiency of Quick Sort varies based on the chosen pivot:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Average Case&lt;/strong&gt;: 

&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mord mathnormal"&gt;l&lt;/span&gt;&lt;span class="mord mathnormal"&gt;o&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, where n is the number of elements.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Best Case&lt;/strong&gt;: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mord mathnormal"&gt;l&lt;/span&gt;&lt;span class="mord mathnormal"&gt;o&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Worst Case&lt;/strong&gt;: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;2&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, which occurs when the smallest or largest element is always chosen as the pivot.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The worst-case scenario can be mitigated by choosing a good pivot, such as the median-of-three method (choosing the median of the first, middle, and last elements).&lt;/p&gt;

&lt;h2&gt;
  
  
  Applications
&lt;/h2&gt;

&lt;p&gt;Quick Sort is widely used in real-world applications due to its efficiency. It's particularly useful for:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Sorting Large Datasets&lt;/strong&gt;: Quick Sort handles large datasets well, making it suitable for big data processing.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Memory Usage&lt;/strong&gt;: It uses 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;l&lt;/span&gt;&lt;span class="mord mathnormal"&gt;o&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 extra space if implemented with recursion.&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Practical Examples
&lt;/h2&gt;

&lt;p&gt;Imagine you have a dataset of millions of records that need to be sorted. By leveraging the quick sort algorithm, you can efficiently manage and sort this data in a way that minimizes memory usage and processing time.&lt;/p&gt;

&lt;h3&gt;
  
  
  Example: Sorting Financial Data
&lt;/h3&gt;

&lt;p&gt;In a financial application, where transactions are processed in real-time, Quick Sort can help quickly process and analyze large volumes of transaction data to identify trends or anomalies.&lt;/p&gt;

&lt;h2&gt;
  
  
  Conclusion
&lt;/h2&gt;

&lt;p&gt;Quick Sort is an essential algorithm for any programmer or computer scientist. Its elegance lies not only in its simplicity but also in its ability to handle complex datasets efficiently. Whether you're optimizing code, analyzing algorithms, or just curious about the underlying principles, mastering Quick Sort provides a solid foundation in computational thinking and problem-solving.&lt;/p&gt;

</description>
      <category>python</category>
      <category>algorithms</category>
      <category>programming</category>
      <category>beginners</category>
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