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    <title>DEV Community: Om Shree</title>
    <description>The latest articles on DEV Community by Om Shree (@om_shree_0709).</description>
    <link>https://dev.to/om_shree_0709</link>
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      <title>DEV Community: Om Shree</title>
      <link>https://dev.to/om_shree_0709</link>
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    <language>en</language>
    <item>
      <title>Anthropic Just Paid $400M for a Team of 10. Here's Why That Makes Sense.</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Sat, 04 Apr 2026 06:10:18 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/anthropic-just-paid-400m-for-a-team-of-10-heres-why-that-makes-sense-3oi6</link>
      <guid>https://dev.to/om_shree_0709/anthropic-just-paid-400m-for-a-team-of-10-heres-why-that-makes-sense-3oi6</guid>
      <description>&lt;p&gt;Eight months. That's how long Coefficient Bio existed before Anthropic bought it for $400 million in stock.&lt;/p&gt;

&lt;p&gt;No public product. No disclosed revenue. No conventional traction metrics. Just a small team of fewer than 10 people, most of them former Genentech computational biology researchers, and one very large claim: they were building artificial superintelligence for science.&lt;/p&gt;

&lt;p&gt;Anthropic paid up anyway. And if you look at what they've been building in healthcare and life sciences over the past year, this acquisition is less of a surprise and more of a logical endpoint.&lt;/p&gt;




&lt;h2&gt;
  
  
  Who Is Coefficient Bio?
&lt;/h2&gt;

&lt;p&gt;Coefficient Bio was founded roughly eight months ago by Samuel Stanton and Nathan C. Frey. Both came from Prescient Design, Genentech's computational drug discovery unit. Frey led a group there working on biological foundation models and novel machine learning approaches to biomolecule design.&lt;/p&gt;

&lt;p&gt;The startup was backed by Dimension, a VC firm that reportedly ended up with a 38,513% IRR on the deal. That number tells you what Dimension thought of the team they were backing.&lt;/p&gt;

&lt;p&gt;Coefficient was building biology-specific AI models from scratch. The ambition, per internal materials, was nothing less than artificial superintelligence for science. That's a big claim for an eight-month-old company. But when your founding team comes from one of the best computational biology units in the world, people tend to take it seriously.&lt;/p&gt;




&lt;h2&gt;
  
  
  What Anthropic Is Actually Buying
&lt;/h2&gt;

&lt;p&gt;This is not a product acquisition. There was no product.&lt;/p&gt;

&lt;p&gt;What Anthropic is buying is domain expertise that is genuinely hard to replicate: protein design, biomolecule modelling, biological foundation models. These are not skills you find by posting a job listing. They come from years of doing specialized research at places like Genentech.&lt;/p&gt;

&lt;p&gt;The Coefficient Bio team will join Anthropic's Health Care Life Sciences group, led by Eric Kauderer-Abrams. He joined in mid-2025 with an explicit mandate: make Claude the dominant AI model in biology. At the JP Morgan Healthcare Conference in January, he laid out a three-part roadmap to get Claude collaborating across every stage of R&amp;amp;D, from early fundamental research through clinical translation.&lt;/p&gt;

&lt;p&gt;The Coefficient Bio team is the domain fuel for that roadmap.&lt;/p&gt;




&lt;h2&gt;
  
  
  Where This Fits in Anthropic's Healthcare Strategy
&lt;/h2&gt;

&lt;p&gt;Anthropic has been building in healthcare and life sciences for about a year. Claude for Life Sciences launched in October 2025, focused on preclinical research. Claude for Healthcare followed in January 2026 with HIPAA-ready infrastructure, connectors to clinical databases like CMS Coverage and PubMed, and tools for prior authorization, care coordination, and regulatory submissions.&lt;/p&gt;

&lt;p&gt;Partners like Sanofi, Novo Nordisk, Genmab, and Banner Health are already using Claude in real workflows. Banner built an internal assistant called BannerWise, which had processed over 1,400 clinical notes by end-2025. The underlying model has improved too. On Protocol QA, a benchmark that tests understanding of laboratory protocols, Sonnet 4.5 scored 0.83 against a human baseline of 0.79.&lt;/p&gt;

&lt;p&gt;Claude for Life Sciences was the general-purpose layer. Coefficient Bio's team brings the specialized depth that a general-purpose layer cannot fake. That distinction matters more in biology than in almost any other domain, because the consequences of getting it wrong are measured in years of wasted research.&lt;/p&gt;




&lt;h2&gt;
  
  
  The $400M Price Tag: Justified?
&lt;/h2&gt;

&lt;p&gt;At $400 million for fewer than 10 people, the math looks strange on first glance.&lt;/p&gt;

&lt;p&gt;But consider the context. Anthropic closed a $30 billion Series G in February 2026, valuing the company at $380 billion post-money. The Coefficient Bio acquisition represents roughly 0.1% dilution. It is not even a rounding error at that scale.&lt;/p&gt;

&lt;p&gt;The cost of not having this expertise could be far higher. Drug discovery is a trillion-dollar market. The race between AI labs to own the scientific decision layer in biotech is real and accelerating. OpenAI launched ChatGPT Health in January 2026. Google DeepMind has been investing in AlphaFold follow-ons for years. The window to establish deep domain credibility in computational biology is not unlimited.&lt;/p&gt;

&lt;p&gt;One fair counterpoint: Coefficient was eight months old. A $400M valuation for a company with no product and no revenue could reflect frontier-lab equity inflation as much as genuine asset quality. That's worth acknowledging.&lt;/p&gt;

&lt;p&gt;But Anthropic is not buying a product. They're buying a founding team with rare credentials before anyone else does. That's a talent acquisition at acqui-hire prices, just at a much larger scale than typical.&lt;/p&gt;




&lt;h2&gt;
  
  
  What This Means for Drug Discovery
&lt;/h2&gt;

&lt;p&gt;The expertise Coefficient Bio brings, specifically protein design and biomolecule modelling, sits at the heart of modern drug discovery.&lt;/p&gt;

&lt;p&gt;Drug discovery is slow and expensive. A typical drug takes 10 to 15 years from discovery to approval and costs over a billion dollars on average. A large portion of that timeline is spent on early-stage research: understanding target proteins, designing molecules that interact with them predictably, and filtering dead ends before expensive clinical trials begin.&lt;/p&gt;

&lt;p&gt;AI-driven approaches to protein design have already changed parts of this process. DeepMind's AlphaFold changed how researchers approach structure prediction. What Coefficient Bio was working on goes further: using foundation models to understand biomolecules not just structurally but functionally, and to generate candidate molecules with specific properties.&lt;/p&gt;

&lt;p&gt;If Anthropic can integrate this into Claude's existing life sciences infrastructure, the potential output is a model that takes on genuinely hard scientific problems, not just documentation or literature review.&lt;/p&gt;

&lt;p&gt;Kauderer-Abrams put it plainly at JP Morgan: the goal is to get Claude to a point where it can take on increasingly large chunks of the R&amp;amp;D process autonomously. Coefficient Bio is a step toward making that real.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Broader Pattern
&lt;/h2&gt;

&lt;p&gt;Coefficient Bio is not Anthropic's first acquisition. They previously acquired Bun, a JavaScript runtime, and Vercept, an AI agent computer-use startup. Each deal extended a specific capability rather than added headcount for its own sake.&lt;/p&gt;

&lt;p&gt;The healthcare bet is larger and longer-term. It is one of the most regulated, high-stakes, and high-value industries on the planet. Getting AI into this space in a way that researchers and clinicians actually trust requires more than a good base model. It requires deep domain knowledge, rigorous safety standards, and integrations into the workflows that scientists and doctors use every day.&lt;/p&gt;

&lt;p&gt;Anthropic has been assembling all three. The Coefficient Bio acquisition adds the one thing you cannot build quickly: genuine biological expertise from people who have already done it at the frontier.&lt;/p&gt;




&lt;h2&gt;
  
  
  Final Thought
&lt;/h2&gt;

&lt;p&gt;A $400 million acquisition of an eight-month-old startup sounds irrational until you understand the market Anthropic is trying to win.&lt;/p&gt;

&lt;p&gt;This is not a side bet on drug discovery. It is about positioning Claude as the default reasoning layer for biology. The Coefficient Bio team has the credentials to help build that. And the timing, coming months after Claude for Life Sciences, Claude for Healthcare, and the build-out of a dedicated life sciences division, shows this is a strategy, not a one-off move.&lt;/p&gt;

&lt;p&gt;Whether the price was right is something only time will answer. But the direction makes sense.&lt;/p&gt;

</description>
      <category>ai</category>
      <category>claude</category>
      <category>productivity</category>
      <category>discuss</category>
    </item>
    <item>
      <title>Microsoft's AI Agents Now Have Rules. Here's Why That Took So Long.</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Fri, 03 Apr 2026 17:25:26 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/microsofts-ai-agents-now-have-rules-heres-why-that-took-so-long-9do</link>
      <guid>https://dev.to/om_shree_0709/microsofts-ai-agents-now-have-rules-heres-why-that-took-so-long-9do</guid>
      <description>&lt;p&gt;Building an AI agent in 2025 takes an afternoon. Controlling what that agent does once it's running, that part has been nobody's problem. Until now.&lt;/p&gt;

&lt;p&gt;Microsoft just open-sourced the Agent Governance Toolkit, a middleware layer that sits between your AI agents and everything they can touch. Every tool call gets evaluated against a policy before it runs. No rewriting your existing agents. No switching frameworks. Just a security kernel dropped into whatever stack you're already using.&lt;/p&gt;

&lt;p&gt;This is not a flashy release. There's no demo video with a robot arm. But if you're building anything serious with agents, this is probably more important than the last three model releases you got excited about.&lt;/p&gt;




&lt;h2&gt;
  
  
  How We Got Here
&lt;/h2&gt;

&lt;p&gt;In December 2025, OWASP published the first-ever risk list specifically for autonomous AI agents. Ten risks. All of them serious. Goal hijacking, tool misuse, memory poisoning, rogue agents, identity abuse, the list reads like a threat model for a system nobody had actually finished securing yet.&lt;/p&gt;

&lt;p&gt;That's because nobody had.&lt;/p&gt;

&lt;p&gt;Frameworks like LangChain and CrewAI made it genuinely easy to spin up agents that call APIs, read files, browse the web, and take actions on your behalf. That was the point. The problem is what those frameworks didn't ship: any real mechanism for controlling what agents are allowed to do at runtime.&lt;/p&gt;

&lt;p&gt;You could set instructions in a system prompt. You could wrap tool calls in try/catch. You could pray. But there was no standard way to say "this agent can read files but cannot delete them" and have that enforced at the execution level, not just hoped for at the prompt level.&lt;/p&gt;

&lt;p&gt;That gap is what the toolkit closes.&lt;/p&gt;




&lt;h2&gt;
  
  
  What It Actually Does
&lt;/h2&gt;

&lt;p&gt;The Agent Governance Toolkit is middleware. It doesn't replace LangChain or CrewAI or the OpenAI Agents SDK. It wraps them. Every time an agent tries to call a tool, read a file, hit an API, write to a database, that call passes through the governance layer first.&lt;/p&gt;

&lt;p&gt;The governance layer checks it against a policy. If the call is permitted, it goes through. If it isn't, it gets blocked, logged, and flagged. The whole check happens in under 0.1 milliseconds. You won't notice the latency. Your agents will notice the rules.&lt;/p&gt;

&lt;p&gt;Here's what that looks like in practice:&lt;/p&gt;

&lt;p&gt;You define policies. Things like: this agent can only read from these directories, cannot make external API calls after 6pm, cannot delete records, cannot exceed 1,000 tool calls per session. These aren't system prompt instructions that a sufficiently confused model might ignore. They're enforced at the infrastructure level.&lt;/p&gt;

&lt;p&gt;Every blocked or allowed action gets logged. That audit trail is not optional, it's baked in. Which matters a lot more than it might seem right now, and we'll get to why.&lt;/p&gt;

&lt;p&gt;The toolkit works with LangChain, CrewAI, and the OpenAI Agents SDK out of the box. It's available in Python, TypeScript, .NET, Go, and Rust. The GitHub repo has over 9,500 adversarial tests covering tamper detection, policy bypass attempts, and trust score recovery. That's not a toy project. Someone spent real time on this.&lt;/p&gt;




&lt;h2&gt;
  
  
  Microsoft Ran the Experiment So You Don't Have To
&lt;/h2&gt;

&lt;p&gt;Here's the part of this story that doesn't get enough attention.&lt;/p&gt;

&lt;p&gt;Microsoft's own engineering team ran 11 agents against live production code. Not a sandbox. Live production code. And they deliberately ran those agents without governance in place first, to see what would happen.&lt;/p&gt;

&lt;p&gt;What happened: agents tried to delete files. They blew past token limits. They spammed tool calls in loops. Not because the models were broken or the prompts were bad. Because without hard constraints at the infrastructure level, agents will take the path of least resistance to completing their objective, and that path sometimes runs straight through your production database.&lt;/p&gt;

&lt;p&gt;This isn't a hypothetical risk. This is what Microsoft's own team documented running their own agents on their own systems. The toolkit is the direct result of that experiment.&lt;/p&gt;

&lt;p&gt;There's something worth sitting with here. These are not junior developers running toy demos. This is a team at one of the largest software companies in the world, running agents against real systems, watching them go off the rails without guardrails. If it happened to them in a controlled experiment, it's happening to people right now in production who don't know it yet.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Compliance Clock Is Already Running
&lt;/h2&gt;

&lt;p&gt;Here's the part that makes this urgent rather than just interesting.&lt;/p&gt;

&lt;p&gt;The EU AI Act's provisions for high-risk AI systems come into full force in August 2026. That's not far away. And among the requirements: audit trails, explainability, and demonstrable policy enforcement for automated systems that make consequential decisions.&lt;/p&gt;

&lt;p&gt;If you're deploying agents in a regulated industry, finance, healthcare, legal, HR, you don't get to scramble on this in July 2026. Compliance infrastructure takes time to design, implement, test, and document. The organizations that start now will have audit trails and policy enforcement that actually reflect months of real-world operation. The ones that start later will have something they assembled in a panic.&lt;/p&gt;

&lt;p&gt;The Agent Governance Toolkit is not a compliance silver bullet. But it gives you the audit trail and policy enforcement layer that forms the foundation of any reasonable compliance story. That's not nothing. That's actually a significant part of what regulators will want to see.&lt;/p&gt;




&lt;h2&gt;
  
  
  Why Open Source Matters Here
&lt;/h2&gt;

&lt;p&gt;Microsoft could have shipped this as a managed cloud service. They didn't. They put it on GitHub under an open source license, in five languages, with nearly ten thousand adversarial tests.&lt;/p&gt;

&lt;p&gt;That's a deliberate choice, and it's the right one.&lt;/p&gt;

&lt;p&gt;Governance infrastructure needs to be auditable. If the tool enforcing your agent policies is a black box sitting in someone else's cloud, you have a governance layer that you cannot fully inspect, verify, or trust. An open source toolkit that you can read, modify, and run yourself is a governance layer you can actually reason about.&lt;/p&gt;

&lt;p&gt;It also means the community can extend it. Policies that work for a customer service agent are different from policies that work for a code-generation agent or a financial research agent. Open source means organizations can build domain-specific policy sets, share them, and improve on each other's work. That's how security tooling actually matures.&lt;/p&gt;

&lt;p&gt;The 9,500+ adversarial tests are particularly significant. Adversarial testing for AI systems is hard. It requires thinking carefully about how a sufficiently motivated agent, or a sufficiently clever attacker manipulating an agent, might try to bypass the controls you've put in place. That test suite is itself a body of knowledge about how agent governance can fail. Making it public means everyone benefits from that knowledge, not just Microsoft's internal teams.&lt;/p&gt;




&lt;h2&gt;
  
  
  What This Doesn't Solve
&lt;/h2&gt;

&lt;p&gt;Let's be honest about the limits.&lt;/p&gt;

&lt;p&gt;The toolkit enforces policies that you define. If you define bad policies, it enforces bad policies. If you forget to cover an edge case, that edge case is uncovered. Garbage in, garbage out, the governance layer doesn't make you smarter about what rules your agents should follow. It just makes sure they actually follow the rules you set.&lt;/p&gt;

&lt;p&gt;It also doesn't solve the problem of goal hijacking through prompt injection. If an attacker can manipulate the input to your agent in a way that changes the goal the agent is pursuing, the governance layer will dutifully enforce policies on behalf of the wrong goal. That's a separate problem, and it's a hard one. The OWASP list includes it for a reason.&lt;/p&gt;

&lt;p&gt;And it doesn't replace good agent design. If your agent architecture is fundamentally unsafe, if it's set up to take irreversible actions without confirmation, or to operate with more permissions than it actually needs, a governance layer adds safety margin but doesn't fix the underlying design.&lt;/p&gt;

&lt;p&gt;Think of it like seatbelts. They save lives. They don't make reckless driving safe.&lt;/p&gt;




&lt;h2&gt;
  
  
  What You Should Do With This
&lt;/h2&gt;

&lt;p&gt;If you're building agents and you haven't thought carefully about runtime governance, now is the time. Not when the EU AI Act hits. Not when something goes wrong in production. Now.&lt;/p&gt;

&lt;p&gt;The toolkit is at github.com/microsoft/agent-governance-toolkit. Read the documentation. Look at the adversarial test suite, even if you don't use the toolkit, that test suite will teach you something about how agents fail. Think about what policies actually make sense for the specific agents you're running. What can they touch? What can't they? What should require a human in the loop?&lt;/p&gt;

&lt;p&gt;If you're in a regulated industry, bring your compliance team into the conversation now. Show them the audit logging capabilities. Start building the documentation trail that proves your agents operate within defined policies. August 2026 will come faster than you think.&lt;/p&gt;

&lt;p&gt;And if you're a developer who's been spinning up agents because it's easy and fun, which it is, take an afternoon and think about what happens when one of those agents does something you didn't intend. What's your blast radius? What would you wish you had in place?&lt;/p&gt;

&lt;p&gt;The toolkit is free. The time to implement it is now. The cost of not having it shows up later, usually at the worst possible moment.&lt;/p&gt;




&lt;p&gt;Building AI agents got easy. Governing them is the work we're all just starting.&lt;/p&gt;




&lt;p&gt;&lt;em&gt;Follow Us on &lt;a href="https://www.linkedin.com/company/shreesozo/" rel="noopener noreferrer"&gt;LinkedIn&lt;/a&gt; and &lt;a href="https://youtu.be/YMj2Ly6uQSw?si=jSOPYesh1Us6y9u5" rel="noopener noreferrer"&gt;YouTube&lt;/a&gt; for more on Agentic AI, MCP, and what's actually happening in the AI infrastructure space.&lt;/em&gt;&lt;/p&gt;

</description>
      <category>ai</category>
      <category>programming</category>
      <category>opensource</category>
      <category>beginners</category>
    </item>
    <item>
      <title>Google Gemma 4: Everything Developers Need to Know</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Fri, 03 Apr 2026 00:45:57 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/google-gemma-4-everything-developers-need-to-know-3daf</link>
      <guid>https://dev.to/om_shree_0709/google-gemma-4-everything-developers-need-to-know-3daf</guid>
      <description>&lt;p&gt;Google dropped Gemma 4 on April 2, 2026, A full generational jump in what open models can do at their parameter range and the first time in the Gemma family's history that one ships under Apache 2.0, meaning commercial use without permission-seeking.&lt;/p&gt;

&lt;p&gt;Some context: since Gemma's first generation, developers have downloaded the models over 400 million times and built more than 100,000 variants.&lt;/p&gt;




&lt;h2&gt;
  
  
  Four Models, One Family
&lt;/h2&gt;

&lt;p&gt;Gemma 4 is a family of four, each aimed at a different point in the hardware spectrum.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;E2B&lt;/strong&gt; : Effective 2 billion active parameters. Runs on smartphones, Raspberry Pi, Jetson Orin Nano. 128K context window. Handles images, video, and audio. Built for battery and memory efficiency.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;E4B&lt;/strong&gt; : Effective 4 billion active parameters. Same hardware targets, higher reasoning quality. About 3x slower than E2B, but noticeably more capable. Also supports images, video, and audio. Up to 4x faster than prior versions, 60% less battery.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;26B MoE&lt;/strong&gt; : 26 billion total parameters, but only 3.8 billion activate during inference. Context window up to 256K tokens. Ranked 6th among all open models on the Arena AI Text Leaderboard. Quantized versions run on consumer GPUs.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;31B Dense&lt;/strong&gt; : The flagship. Full dense architecture. 256K context. Currently ranked 3rd among open models on Arena AI. Fits unquantized on a single 80 GB H100; quantized versions run on consumer hardware. The obvious fine-tuning base.&lt;/p&gt;

&lt;p&gt;One thing to notice: E2B and E4B both handle audio input natively. The 26B and 31B do not. If speech recognition is part of your application, the edge models are your only option in this family.&lt;/p&gt;




&lt;h2&gt;
  
  
  Benchmarks: The Numbers That Matter
&lt;/h2&gt;

&lt;p&gt;Google says Gemma 4 outperforms models 20 times its size. Sounds like marketing. Third-party data from Artificial Analysis makes it harder to wave away.&lt;/p&gt;

&lt;p&gt;On GPQA Diamond (scientific reasoning), the 31B scores 85.7% in reasoning mode. Second-best among open models under 40 billion parameters, just behind Qwen3.5 27B at 85.8%. The efficiency angle is also worth noting: the 31B generates roughly 1.2 million output tokens in that evaluation, versus 1.5 million for Qwen3.5 27B. Less compute for roughly equal quality.&lt;/p&gt;

&lt;p&gt;The 26B MoE scores 79.2% on GPQA Diamond, putting it ahead of OpenAI's gpt-oss-120B at 76.2%. That is a 94-billion-parameter gap between those two models.&lt;/p&gt;

&lt;p&gt;The agentic tool use numbers are where it gets genuinely interesting. On τ2-bench (Retail), the 31B scores 86.4% and the 26B scores 85.5%. Gemma 3 27B scored 6.6% on the same benchmark. Whatever changed in how these models handle multi-step tool use, it was not incremental.&lt;/p&gt;

&lt;p&gt;Math and coding follow a similar pattern. On AIME 2026, the 31B and 26B reach 89.2% and 88.3%, versus Gemma 3 27B's 20.8%. On LiveCodeBench v6, the 31B scores 80.0% and the 26B scores 77.1%. Gemma 3 27B was at 29.1%.&lt;/p&gt;

&lt;p&gt;The edge models are more modest. E4B hits 52.0% on LiveCodeBench and 58.6% on GPQA Diamond. Reasonable for a model designed to fit on a phone.&lt;/p&gt;




&lt;h2&gt;
  
  
  Architecture: What Actually Changed
&lt;/h2&gt;

&lt;p&gt;Gemma 4 comes from the same research stack as Gemini 3, Google's closed model family. The reasoning and math benchmark jumps suggest the knowledge transfer from that training actually worked, not just a talking point.&lt;/p&gt;

&lt;p&gt;The MoE design in the 26B model is worth understanding. The total parameter count is 26 billion, but only 3.8 billion activate on any given forward pass. In practice, this gets you near-31B quality at a fraction of the inference cost. Token generation should be faster than the dense model, with some trade-off in raw quality.&lt;/p&gt;

&lt;p&gt;Both the 26B and 31B support function calling, structured JSON output, and system instructions natively. Gemma 3 was awkward for agentic use. Gemma 4 was built for it from day one.&lt;/p&gt;

&lt;p&gt;The models also cover over 140 languages, which opens up a wider range of deployment contexts without additional localization work.&lt;/p&gt;




&lt;h2&gt;
  
  
  On-Device Deployment: What "Completely Offline" Actually Means
&lt;/h2&gt;

&lt;p&gt;The E2B and E4B models run fully offline on Android, Raspberry Pi, and NVIDIA Jetson Orin Nano. Google worked with Qualcomm Technologies and MediaTek on hardware optimization. Android developers can start prototyping agentic flows through the AICore Developer Preview now, and code written for Gemma 4 will be forward-compatible with Gemini Nano 4 devices coming later this year.&lt;/p&gt;

&lt;p&gt;Why does running offline matter? Three things: latency (no network round trip), privacy (data stays on device), and reliability (no API dependency). For healthcare apps, legal review tools, or anything touching sensitive user data, local inference is not just a nice-to-have.&lt;/p&gt;

&lt;p&gt;One caveat: the AICore Developer Preview is still a preview. Tool calling, structured output, and thinking mode through the Prompt API are coming during the preview period, not available at launch. If you are building for production Android deployment today, check what is actually ready before you commit to an architecture.&lt;/p&gt;




&lt;h2&gt;
  
  
  Where to Get It and What Runs It
&lt;/h2&gt;

&lt;p&gt;Gemma 4 is on Hugging Face, Kaggle, and Ollama now. Google AI Studio has the 31B and 26B. Google AI Edge Gallery covers the E4B and E2B.&lt;/p&gt;

&lt;p&gt;Framework support at launch is broad: Hugging Face Transformers, TRL, Transformers.js, Candle, vLLM, llama.cpp, MLX, Ollama, NVIDIA NIM and NeMo, LM Studio, Unsloth, SGLang, Keras, and more. You can train on Google Colab, Vertex AI, or a consumer gaming GPU.&lt;/p&gt;

&lt;p&gt;For production, the options are Vertex AI, Cloud Run, GKE, or TPU-accelerated serving. NVIDIA hardware from Jetson Orin Nano to Blackwell GPUs is supported. AMD GPUs work via ROCm.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Apache 2.0 License: Why It Actually Matters
&lt;/h2&gt;

&lt;p&gt;Every previous Gemma release shipped under a Google proprietary license. Gemma 4 is the first to go Apache 2.0.&lt;/p&gt;

&lt;p&gt;What that means concretely: you can build and sell products with Gemma 4, modify it, fine-tune it, redistribute it, and deploy it, all without negotiating Google's terms. For startups and solo developers, that is one less legal headache when taking something to market.&lt;/p&gt;




&lt;h2&gt;
  
  
  What to Use It For (And What to Watch)
&lt;/h2&gt;

&lt;p&gt;The jump in agentic tool use is the most significant thing about this release. If you are building multi-step reasoning pipelines, function calling workflows, or autonomous agents, Gemma 4 is a different category of model than Gemma 3 was.&lt;/p&gt;

&lt;p&gt;The 31B dense model, with its strong scores across reasoning, coding, and science benchmarks, is a solid starting point for fine-tuning on domain-specific data. Familiar tooling (Hugging Face, Unsloth, Colab, Vertex AI) means the fine-tuning workflow will not surprise you.&lt;/p&gt;

&lt;p&gt;The honest caveat: benchmarks are controlled. τ2-bench numbers are encouraging, but whether the agentic improvements hold up when tool schemas are messy and information is partial - that is something the community will figure out over the next few weeks. Worth watching.&lt;/p&gt;




&lt;h2&gt;
  
  
  Getting Started
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Pull with Ollama&lt;/span&gt;
ollama pull gemma4:31b
ollama pull gemma4:26b-moe

&lt;span class="c"&gt;# Or grab from Hugging Face&lt;/span&gt;
pip &lt;span class="nb"&gt;install &lt;/span&gt;transformers
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Google AI Studio has the 31B and 26B available directly in browser - no local setup needed to start experimenting.&lt;/p&gt;

&lt;p&gt;For Android, the AICore Developer Preview requires opt-in, after which you can trigger model download directly to a supported test device.&lt;/p&gt;

&lt;p&gt;There is also a Gemma 4 Good Challenge on Kaggle if you learn better by building toward a concrete problem.&lt;/p&gt;

</description>
      <category>ai</category>
      <category>programming</category>
      <category>python</category>
      <category>googlecloud</category>
    </item>
    <item>
      <title>Anthropic Claude Code Source Code Leaked: What Happened, Why It Matters, and What Comes Next</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Thu, 02 Apr 2026 14:55:32 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/anthropic-claude-code-source-code-leaked-what-happened-why-it-matters-and-what-comes-next-53cc</link>
      <guid>https://dev.to/om_shree_0709/anthropic-claude-code-source-code-leaked-what-happened-why-it-matters-and-what-comes-next-53cc</guid>
      <description>&lt;p&gt;The timing could not have been worse. On March 31, 2026, one of the most closely watched AI companies in the world accidentally published the source code of its most popular product, and the internet noticed within minutes.&lt;/p&gt;




&lt;h2&gt;
  
  
  Introduction
&lt;/h2&gt;

&lt;p&gt;On March 31, 2026, Anthropic accidentally published the entire source code of Claude Code, its flagship AI coding agent, inside an npm package. Nobody hacked their servers. Nobody broke in. A missing .npmignore entry shipped a 59.8 MB source map containing 512,000 lines of unobfuscated TypeScript across roughly 1,900 files.&lt;/p&gt;

&lt;p&gt;Within hours, the code was mirrored, analyzed, rewritten in Python and Rust, and studied by tens of thousands of developers worldwide. GitHub repositories went up faster than Anthropic's legal team could file takedown requests. And right in the middle of all of it, Anthropic was quietly talking to Goldman Sachs, JPMorgan, and Morgan Stanley about a $60 billion IPO.&lt;/p&gt;

&lt;p&gt;This was not just an embarrassing technical mistake. It was a full-scale IP exposure event, arriving at possibly the worst moment in the company's five-year history.&lt;/p&gt;




&lt;h2&gt;
  
  
  What Is Claude Code?
&lt;/h2&gt;

&lt;p&gt;Before getting into the leak itself, it's worth understanding what exactly got exposed.&lt;/p&gt;

&lt;p&gt;Claude Code is Anthropic's terminal-based AI coding tool. It runs in your command line, reads your codebase, writes and edits files, runs commands, manages git workflows, and handles entire development tasks through natural language. It is, by most accounts, one of the most capable AI coding agents currently available, and one of Anthropic's fastest-growing products by enterprise adoption.&lt;/p&gt;

&lt;p&gt;Claude Code is perhaps Anthropic's most popular product and has seen soaring adoption rates from large enterprises. At least some of Claude Code's capabilities come not from the underlying large language model but from the software "harness" that sits around the underlying AI model, the layer that instructs it how to use other software tools and provides important guardrails and instructions that govern its behavior.&lt;/p&gt;

&lt;p&gt;That harness, the thing competitors would have paid a fortune to understand, was now sitting in a public zip file on Anthropic's own R2 storage bucket.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Full Timeline: How It Happened, Hour by Hour
&lt;/h2&gt;

&lt;h3&gt;
  
  
  March 11, 2026
&lt;/h3&gt;

&lt;p&gt;A known bug in the Bun JavaScript runtime (issue #28001) is filed. It reports that source maps are being served in production builds even when the documentation says they should not be. The bug sits open.&lt;/p&gt;

&lt;p&gt;Nobody catches it. Nobody flags it to the Claude Code release team.&lt;/p&gt;

&lt;h3&gt;
  
  
  Late 2025
&lt;/h3&gt;

&lt;p&gt;Anthropic acquired Bun in late 2025, and Claude Code is built on top of it. Bun generates source maps by default unless you explicitly turn them off.&lt;/p&gt;

&lt;h3&gt;
  
  
  ~00:21 UTC, March 31, 2026
&lt;/h3&gt;

&lt;p&gt;Malicious axios versions (1.14.1 and 0.30.4) appear on npm with an embedded Remote Access Trojan. This is unrelated to Anthropic, but the timing is catastrophic.&lt;/p&gt;

&lt;h3&gt;
  
  
  ~04:00 UTC, March 31, 2026
&lt;/h3&gt;

&lt;p&gt;Claude Code v2.1.88 is pushed to npm. The 59.8 MB source map ships with it. The R2 bucket containing all source code is live and publicly accessible.&lt;/p&gt;

&lt;p&gt;The release team does not realize anything is wrong.&lt;/p&gt;

&lt;h3&gt;
  
  
  04:23 UTC, March 31, 2026
&lt;/h3&gt;

&lt;p&gt;Chaofan Shou (@Fried_rice), an intern at Solayer Labs, broadcasts the discovery on X. The post included a direct download link to a hosted archive, acting as a digital flare. Within hours, the ~512,000-line TypeScript codebase was mirrored across GitHub and analyzed by thousands of developers.&lt;/p&gt;

&lt;p&gt;The post immediately stirred the AI community, attracting nearly 10 million views and 1,500 comments.&lt;/p&gt;

&lt;h3&gt;
  
  
  Next few hours
&lt;/h3&gt;

&lt;p&gt;GitHub repositories start appearing. Some are direct mirrors. Others are rewrites. Some are just the code, labeled plainly as leaked. Anthropic scrambles to pull the package from npm.&lt;/p&gt;

&lt;h3&gt;
  
  
  April 1, 2026
&lt;/h3&gt;

&lt;p&gt;A repository called claw-code, born as a mirror that later became a complete rewrite of the Claude Code app, first in Python, later in Rust, crosses 100,000 stars on GitHub.&lt;/p&gt;

&lt;p&gt;Claw-code hit 50,000 stars in approximately two hours after publication, reaching over 55,800 stars and 58,200 forks by April 1. The repository's own description calls it the fastest repo in history to surpass 50K stars.&lt;/p&gt;

&lt;p&gt;Anthropic begins filing DMCA takedown notices. GitHub repositories containing leaked code start going down. Some repositories have already been disabled, suggesting Anthropic is actively trying to contain the damage.&lt;/p&gt;




&lt;h2&gt;
  
  
  Why Did This Happen? The Technical Explanation
&lt;/h2&gt;

&lt;p&gt;The cause was mundane. When you publish a JavaScript/TypeScript package to npm, the build toolchain often generates source map files (.map files). These files exist so that when something crashes in production, the stack trace can point you to the actual line of code in the original file, not some unintelligible line 1, column 48293 of a minified bundle.&lt;/p&gt;

&lt;p&gt;The problem: someone on the release team failed to add *.map to .npmignore or configure the files field in package.json to exclude debugging artifacts.&lt;/p&gt;

&lt;p&gt;It gets worse. There is an entire system in Claude Code called "Undercover Mode" specifically designed to prevent Anthropic's internal information from leaking. They built a whole subsystem to stop their AI from accidentally revealing internal codenames in git commits, and then shipped the entire source in a .map file, likely by Claude itself.&lt;/p&gt;

&lt;p&gt;And worse still: the Bun bug that caused this had been known for 20 days. Nobody caught it. Anthropic's own acquired toolchain contributed to exposing Anthropic's own product.&lt;/p&gt;

&lt;p&gt;This was not a sophisticated attack. This was a checklist item that got missed.&lt;/p&gt;




&lt;h2&gt;
  
  
  What the Code Actually Revealed
&lt;/h2&gt;

&lt;h3&gt;
  
  
  KAIROS: The Always-On Agent
&lt;/h3&gt;

&lt;p&gt;Referenced over 150 times in the source, KAIROS is an unreleased autonomous daemon mode where Claude operates as a persistent, always-on background agent. It receives periodic  prompts to decide whether to act proactively, maintains append-only daily log files, and subscribes to GitHub webhooks.&lt;/p&gt;

&lt;p&gt;While current AI tools are largely reactive, KAIROS allows Claude Code to operate as an always-on background agent that handles background sessions and employs a process called autoDream. In this mode, the agent performs memory consolidation while the user is idle. The autoDream logic merges disparate observations, removes logical contradictions, and converts vague insights into absolute facts.&lt;/p&gt;

&lt;h3&gt;
  
  
  Undercover Mode
&lt;/h3&gt;

&lt;p&gt;This one got the most attention. The most controversial discovery was undercover.ts, roughly 90 lines, which injects a system prompt instructing Claude to never mention that it is an AI and to strip all Co-Authored-By attribution when contributing to external repositories.&lt;/p&gt;

&lt;p&gt;The system prompt discovered in the leak explicitly warns the model: "You are operating UNDERCOVER... Your commit messages MUST NOT contain ANY Anthropic-internal information. Do not blow your cover."&lt;/p&gt;

&lt;p&gt;The reaction from the developer community was divided. Some thought this was a reasonable enterprise feature. Others found it unsettling, an AI silently contributing to public open-source projects without attribution.&lt;/p&gt;

&lt;h3&gt;
  
  
  Internal Model Roadmap
&lt;/h3&gt;

&lt;p&gt;The source exposed internal codenames: Capybara maps to Claude 4.6, Fennec to Opus 4.6, and Numbat to an unreleased model. Internal benchmarks revealed that Capybara v8 has a 29-30% false claims rate, a regression from 16.7% in v4.&lt;/p&gt;

&lt;p&gt;That last number is worth sitting with. A nearly 30% false claims rate from a model Anthropic is actively shipping to enterprise customers.&lt;/p&gt;

&lt;h3&gt;
  
  
  The Architecture
&lt;/h3&gt;

&lt;p&gt;Beyond the controversial features, developers were genuinely impressed by the engineering. Claude Code uses a modular system prompt with cache-aware boundaries, approximately 40 tools in a plugin architecture, a 46,000-line query engine, and React + Ink terminal rendering using game-engine techniques. Multi-agent orchestration fits in a prompt rather than a framework, which one commenter noted makes LangChain and LangGraph look like solutions in search of a problem.&lt;/p&gt;

&lt;h3&gt;
  
  
  A Waste Problem Nobody Knew About
&lt;/h3&gt;

&lt;p&gt;A bug fix comment revealed 250,000 wasted API calls per day from autocompact failures. The fix was three lines: MAX_CONSECUTIVE_AUTOCOMPACT_FAILURES = 3. After 3 consecutive compaction failures, it just stops trying.&lt;/p&gt;

&lt;p&gt;And perhaps the most mocked discovery: the codebase included a frustration detection regex matching swear words, widely mocked as the world's most expensive company using regex for sentiment analysis.&lt;/p&gt;




&lt;h2&gt;
  
  
  This Was Not the First Time
&lt;/h2&gt;

&lt;p&gt;This is the part that makes Anthropic's situation look considerably worse.&lt;/p&gt;

&lt;p&gt;In February 2025, an early version of Claude Code accidentally exposed its original code in a similar breach. The exposure showed how the tool worked behind the scenes as well as how it connected to Anthropic's internal systems. Anthropic later removed the software and took the public code down.&lt;/p&gt;

&lt;p&gt;So this is not a first offense. A nearly identical thing happened fourteen months earlier, and the lesson apparently did not make it into the release process for v2.1.88.&lt;/p&gt;

&lt;p&gt;The leak also came just days after Fortune reported that the company had inadvertently made close to 3,000 files publicly available, including a draft blog post that detailed a powerful upcoming model that presents unprecedented cybersecurity risks. The model is known internally as both "Mythos" and "Capybara."&lt;/p&gt;

&lt;p&gt;Three separate leaks in weeks. Each one independently embarrassing. Together, they start looking like a systemic issue with how Anthropic handles internal information.&lt;/p&gt;




&lt;h2&gt;
  
  
  The IPO Problem
&lt;/h2&gt;

&lt;p&gt;Here is where timing becomes genuinely painful.&lt;/p&gt;

&lt;p&gt;Anthropic is discussing an initial public offering as soon as the fourth quarter of 2026, with bankers expecting the AI company to raise more than $60 billion. That figure could make it the second-biggest IPO deal in history after SpaceX.&lt;/p&gt;

&lt;p&gt;Anthropic closed a $30 billion funding round at a $380 billion valuation in February 2026, while OpenAI closed a $120 billion funding round at an $850 billion valuation in March 2026.&lt;/p&gt;

&lt;p&gt;Monthly visits to claude.ai surged from 16 million in January 2025 to 220 million in January 2026, a 13-fold increase in twelve months.&lt;/p&gt;

&lt;p&gt;The company is estimated to be operating at around a $14 billion annualized revenue run rate in early 2026, with projections suggesting it could move closer to $18-20 billion as enterprise demand continues to grow.&lt;/p&gt;

&lt;p&gt;The fundamentals are strong. The momentum is real. And then this happens.&lt;/p&gt;

&lt;p&gt;For Anthropic, a company currently riding a meteoric rise with a reported $19 billion annualized revenue run rate as of March 2026, the leak is more than a security lapse; it is a strategic hemorrhage of intellectual property. The timing is particularly critical given the commercial velocity of the product.&lt;/p&gt;

&lt;p&gt;Public markets have a long memory for things like this. When Anthropic eventually files its S-1, this incident will be in the risk factors section. Institutional investors will ask questions about internal controls. The SEC will scrutinize the company's operational governance alongside the already-complicated question of how Anthropic accounts for cloud computing credits as revenue.&lt;/p&gt;

&lt;p&gt;Bank of America put Anthropic's potential cloud payments at up to $6.4 billion to hyperscale providers in 2026. Whether the SEC requires Anthropic to harmonize its accounting treatment with OpenAI ahead of listing remains a consequential open question.&lt;/p&gt;

&lt;p&gt;The leak adds another complication to an already complicated story that prospective public shareholders will have to evaluate.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Legal Situation: Can Anthropic Put the Genie Back?
&lt;/h2&gt;

&lt;p&gt;Probably not.&lt;/p&gt;

&lt;p&gt;While Anthropic's DMCA takedown requests target direct mirrors on major platforms, they're unlikely to reach decentralized code-sharing platforms. It's also to be seen how the company's legal actions will fare against code rewrites.&lt;/p&gt;

&lt;p&gt;The clean-room rewrite approach is the interesting wrinkle here. Gergely Orosz (The Pragmatic Engineer) observed that Anthropic faces a dilemma: a Python rewrite constitutes a new creative work potentially outside DMCA scope.&lt;/p&gt;

&lt;p&gt;There is also a copyright question nobody has a clean answer to. Anthropic's own CEO has implied that significant portions of Claude Code were written by Claude. The DC Circuit upheld in March 2025 that AI-generated work doesn't carry automatic copyright. If Anthropic's copyright claim over Claude-authored code is legally murky, the entire takedown strategy weakens.&lt;/p&gt;

&lt;p&gt;And then there are torrents. As one analysis bluntly noted: 512,000 lines of Claude Code are permanently in the wild, regardless of what any court decides.&lt;/p&gt;




&lt;h2&gt;
  
  
  What This Means for Competitors
&lt;/h2&gt;

&lt;p&gt;For every company building AI coding tools, Cursor, Cognition, GitHub Copilot, Sourcegraph, and dozens of others, the leak is an unexpected gift.&lt;/p&gt;

&lt;p&gt;The leaked source is now the most detailed public documentation of how to build a production-grade AI agent harness that exists.&lt;/p&gt;

&lt;p&gt;The specific architecture decisions: how Claude Code handles context window management, how its multi-agent orchestration works, how it structures tool definitions, how it renders a terminal UI using React and Ink, all of this is now readable by any engineer who wants to understand it.&lt;/p&gt;

&lt;p&gt;Competitors will study this. They already are.&lt;/p&gt;




&lt;h2&gt;
  
  
  Future Possibilities: What Happens Next
&lt;/h2&gt;

&lt;p&gt;A few things seem likely.&lt;/p&gt;

&lt;p&gt;Anthropic rebuilds its release process. After two nearly identical incidents fourteen months apart, the company almost certainly needs to overhaul how it packages and ships npm releases. Whether that means better toolchain auditing, a dedicated security review step for package releases, or moving entirely away from npm is unclear. But something has to change.&lt;/p&gt;

&lt;p&gt;KAIROS ships eventually. The autonomous background agent mode described in the leak is too interesting and too developed to stay unreleased. The community has now seen it. The pressure to ship it, or to explain why it won't ship, will only grow.&lt;/p&gt;

&lt;p&gt;The IPO narrative gets more complicated. Anthropic is not alone in its IPO ambitions. OpenAI is also targeting public markets before the end of 2026, with the Wall Street Journal reporting it hopes to list ahead of its rival. The race to go public before your main competitor is already stressful. Add three separate leaks in six weeks, a complicated revenue recognition question, and a product that is both your strongest asset and now partially open-sourced by accident, and you have an S-1 that will require some very careful writing.&lt;/p&gt;

&lt;p&gt;The clean-room rewrites survive. The Anthropic-inspired open-source tools that emerged from this leak, claw-code and its descendants, will likely continue to exist in some form. Whether they grow into real competitors depends on how much developer energy follows the initial GitHub star count. It often does not. But the architecture documentation is real, and that does not go away.&lt;/p&gt;




&lt;h2&gt;
  
  
  Anthropic's Official Response
&lt;/h2&gt;

&lt;p&gt;When reached for comment, Anthropic confirmed that "some internal source code" had been leaked within a "Claude Code release." A spokesperson said: "No sensitive customer data or credentials were involved or exposed. This was a release packaging issue caused by human error, not a security breach."&lt;/p&gt;

&lt;p&gt;That is accurate as far as it goes. No customer data was exposed. No model weights leaked. Nobody's API keys are compromised (assuming you were not one of the users who installed between 00:21 and 03:29 UTC and also pulled in the malicious axios version, that's a separate and more serious problem).&lt;/p&gt;

&lt;p&gt;But calling it a "release packaging issue caused by human error" understates what happened. This was the second time the same category of mistake exposed Claude Code source code. The code contained unreleased product roadmap information, internal model benchmark data showing a regression in false claims rate, and a feature instructing the AI to hide its identity in public repositories. That is not a routine packaging slip.&lt;/p&gt;




&lt;h2&gt;
  
  
  What You Should Do If You Use Claude Code
&lt;/h2&gt;

&lt;p&gt;If you installed or updated Claude Code via npm on March 31, 2026, between 00:21 and 03:29 UTC, you may have inadvertently pulled in a malicious version of axios (1.14.1 or 0.30.4) that contains a Remote Access Trojan. You should immediately search your project lockfiles for these specific versions or the dependency plain-crypto-js. If found, treat the host machine as fully compromised, rotate all secrets, and perform a clean OS reinstallation.&lt;/p&gt;

&lt;p&gt;Anthropic has designated the Native Installer (curl -fsSL &lt;a href="https://claude.ai/install.sh" rel="noopener noreferrer"&gt;https://claude.ai/install.sh&lt;/a&gt; | bash) as the recommended method going forward, because it uses a standalone binary that does not rely on the volatile npm dependency chain.&lt;/p&gt;




&lt;h2&gt;
  
  
  Final Thoughts
&lt;/h2&gt;

&lt;p&gt;There is something almost poetic about the fact that Anthropic built an "Undercover Mode" to prevent internal information from leaking into git commits, and then accidentally published the entire source code of their most popular product through a missing line in a config file.&lt;/p&gt;

&lt;p&gt;The company is not in existential trouble. The fundamentals are too strong, the revenue too real, the enterprise relationships too established. The IPO will likely still happen. Investors will still line up.&lt;/p&gt;

&lt;p&gt;But the pattern of leaks, three in rapid succession, two of them involving the same product, suggests something about how Anthropic's operational processes are keeping pace with its technical ambitions. Building fast is one thing. Shipping responsibly is another. Right now, Anthropic is better at one than the other, and the public market investors they are courting will have opinions about that.&lt;/p&gt;

&lt;p&gt;The genie is out of the bottle. 512,000 lines of it. And it is not going back in.&lt;/p&gt;




&lt;p&gt;&lt;em&gt;Follow us for daily coverage of what's actually happening in MCP and agentic AI.&lt;/em&gt;&lt;/p&gt;

</description>
      <category>ai</category>
      <category>programming</category>
      <category>opensource</category>
      <category>architecture</category>
    </item>
    <item>
      <title>FDB Just Launched the First MCP Server for Medication Decisions</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Wed, 01 Apr 2026 17:14:44 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/fdb-just-launched-the-first-mcp-server-for-medication-decisions-48n1</link>
      <guid>https://dev.to/om_shree_0709/fdb-just-launched-the-first-mcp-server-for-medication-decisions-48n1</guid>
      <description>&lt;h1&gt;
  
  
  April 1st, 2026 | MCP &amp;amp; Agentic AI
&lt;/h1&gt;




&lt;p&gt;Every week, a new AI tool promises to "transform healthcare." Most of them are polished wrappers around a general-purpose LLM with a medical disclaimer buried in the footer.&lt;/p&gt;

&lt;p&gt;FDB's MedProof MCP™ is not that.&lt;/p&gt;

&lt;p&gt;On March 31, 2026, First Databank (FDB) announced the general availability of FDB MedProof MCP™ - the first Model Context Protocol server built specifically for AI agent-driven medication decisions.&lt;/p&gt;

&lt;p&gt;Not a chatbot.&lt;br&gt;&lt;br&gt;
Not a demo.&lt;br&gt;&lt;br&gt;
Production infrastructure, live today, already running inside platforms that touch over 100 million patients.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Problem Nobody Was Solving Correctly
&lt;/h2&gt;

&lt;p&gt;Here's a number worth sitting with:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;Pharmacists spend 30–40% of every shift manually checking medication orders.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;That's nearly half a working day, every day, spent on verification tasks that are mind-numbing and high-stakes at the same time.&lt;/p&gt;

&lt;p&gt;Physicians aren't doing much better.&lt;/p&gt;

&lt;p&gt;After every patient encounter, they're manually re-entering prescription data into EMRs - transcribing what was just discussed verbally into structured codified orders.&lt;/p&gt;

&lt;p&gt;By hand. In 2026.&lt;/p&gt;

&lt;p&gt;The frustrating part?&lt;/p&gt;

&lt;p&gt;Healthcare has had "AI" in it for years. But most of that AI couldn't actually &lt;em&gt;do&lt;/em&gt; anything inside clinical workflows.&lt;/p&gt;

&lt;p&gt;It could flag things.&lt;br&gt;&lt;br&gt;
It could suggest things.&lt;/p&gt;

&lt;p&gt;But the moment a decision needed grounding in real drug knowledge - dosages, contraindications, formulary status, patient context - the AI hit a wall.&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;The wall wasn't intelligence.&lt;br&gt;&lt;br&gt;
It was infrastructure.&lt;/p&gt;
&lt;/blockquote&gt;




&lt;h2&gt;
  
  
  What MCP Changes (For Those New to It)
&lt;/h2&gt;

&lt;p&gt;Model Context Protocol (MCP) is an open standard that defines how AI agents connect to external tools, data sources, and services.&lt;/p&gt;

&lt;p&gt;Think of it as USB-C for AI: one plug that any agent can use to talk to any capable system, without a custom integration built from scratch every time.&lt;/p&gt;

&lt;p&gt;Before MCP, if a healthcare company wanted to plug an LLM into their drug knowledge database, they'd build a bespoke API integration. Then another one for the next agent. Then maintain both. Then rebuild when the AI layer changed.&lt;/p&gt;

&lt;p&gt;It was fragile, slow, and expensive in a domain that can't afford fragile.&lt;/p&gt;

&lt;p&gt;MCP collapses that complexity.&lt;/p&gt;

&lt;p&gt;One server.&lt;br&gt;&lt;br&gt;
Any compliant agent can connect.&lt;br&gt;&lt;br&gt;
The drug knowledge is current, patient-specific, and accessible - without the integration work that used to take months to get right.&lt;/p&gt;

&lt;p&gt;FDB saw this coming early. They first piloted their MCP server in October 2025. The response was strong enough that by March 2026, they had a generally available product, now formally named FDB MedProof MCP™.&lt;/p&gt;




&lt;h2&gt;
  
  
  What FDB MedProof MCP Actually Does
&lt;/h2&gt;

&lt;p&gt;FDB isn't a startup. They're the company whose drug knowledge already sits inside the majority of US hospitals, pharmacies, and physician practices.&lt;/p&gt;

&lt;p&gt;When their data flags a dangerous interaction, clinicians act on it. That credibility took decades to build.&lt;/p&gt;

&lt;p&gt;MedProof MCP puts that same intelligence in reach of AI agents - in patient-specific context, across every major EHR.&lt;/p&gt;

&lt;p&gt;The server supports a few key workflows:&lt;/p&gt;

&lt;h3&gt;
  
  
  Prescription Automation
&lt;/h3&gt;

&lt;p&gt;An agent listens to a doctor-patient conversation via ambient audio, pulls the relevant medication intent, and pre-populates a structured prescription order inside the EMR.&lt;/p&gt;

&lt;p&gt;The physician reviews, confirms, or adjusts.&lt;/p&gt;

&lt;p&gt;No re-typing, no transcription step.&lt;/p&gt;




&lt;h3&gt;
  
  
  Pharmacy Order Verification
&lt;/h3&gt;

&lt;p&gt;Instead of a pharmacist manually pulling up charts to verify every single order, an agent runs the checks and surfaces only the cases that genuinely need a human call.&lt;/p&gt;




&lt;h3&gt;
  
  
  Medication Reconciliation
&lt;/h3&gt;

&lt;p&gt;Building an accurate list of a patient's current medications across fragmented records is one of those tasks that sounds simple and takes forever.&lt;/p&gt;

&lt;p&gt;Agents handle it as part of standard workflow.&lt;/p&gt;




&lt;h3&gt;
  
  
  Ambient Listening
&lt;/h3&gt;

&lt;p&gt;Medication insights surface during clinical conversations in real time, so the physician gets the relevant context while still in the room - not after they've moved to the next patient.&lt;/p&gt;




&lt;p&gt;All of this runs through one connection point.&lt;/p&gt;

&lt;p&gt;Developers don't rebuild drug knowledge access from scratch for every new agent they ship.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Three Products to Know
&lt;/h2&gt;

&lt;p&gt;FDB is shipping three things under this umbrella:&lt;/p&gt;

&lt;h3&gt;
  
  
  FDB MedProof MCP™
&lt;/h3&gt;

&lt;p&gt;The infrastructure layer.&lt;/p&gt;

&lt;p&gt;Connects AI agents to FDB's drug knowledge database across Epic, athenahealth, eClinicalWorks, MEDITECH, Oracle Health/Cerner, and others.&lt;/p&gt;

&lt;p&gt;This is what everything else sits on top of, including third-party tools.&lt;/p&gt;




&lt;h3&gt;
  
  
  FDB Script Agent™
&lt;/h3&gt;

&lt;p&gt;A prescription automation agent for ambulatory settings.&lt;/p&gt;

&lt;p&gt;Doctor speaks, prescription gets structured and queued.&lt;/p&gt;

&lt;p&gt;The physician reviews it, not types it.&lt;/p&gt;




&lt;h3&gt;
  
  
  FDB VerifyAssist™
&lt;/h3&gt;

&lt;p&gt;An inpatient pharmacy verification assistant.&lt;/p&gt;

&lt;p&gt;Runs drug checks at the right moment, cutting out the chart-digging that currently eats up so much pharmacist time.&lt;/p&gt;




&lt;p&gt;Each integrates via MCP or traditional API, so health tech teams can adopt at whatever layer makes sense for their current stack.&lt;/p&gt;




&lt;h2&gt;
  
  
  Real Adoption, Not Vaporware
&lt;/h2&gt;

&lt;p&gt;The most credible signal is who's already building on it.&lt;/p&gt;

&lt;p&gt;Artera - a patient communications platform serving over 1,000 healthcare organizations and more than 100 million patients a year - is one of the early adopters.&lt;/p&gt;

&lt;p&gt;Their platform handles billions of messages across major EHR systems, and they're already using MedProof MCP as a foundation for agentic workflows.&lt;/p&gt;

&lt;p&gt;Zach Wood, Chief Product and Strategy Officer at Artera, described it as "a critical unlock" - not because it brought new drug knowledge, but because it made that knowledge reliably accessible to agents in a way that wasn't possible before.&lt;/p&gt;

&lt;p&gt;Secure, consistent, and fast enough to actually prototype on.&lt;/p&gt;

&lt;p&gt;That last part matters more than it sounds.&lt;/p&gt;

&lt;p&gt;In healthcare, compliance cycles are long and trust is earned slowly. If teams can go from idea to validated prototype in weeks instead of months, that changes what's worth building.&lt;/p&gt;




&lt;h2&gt;
  
  
  Why This Is Bigger Than One Launch
&lt;/h2&gt;

&lt;p&gt;FDB's move here is worth thinking through carefully.&lt;/p&gt;

&lt;p&gt;For decades, their model was to license drug knowledge to health IT vendors via SDKs and APIs. That worked well when software was built once and updated slowly.&lt;/p&gt;

&lt;p&gt;The AI era broke that model.&lt;/p&gt;

&lt;p&gt;Agents are dynamic - they spin up, query external systems, and act, all inside a single workflow.&lt;/p&gt;

&lt;p&gt;Static API integrations weren't designed for that rhythm.&lt;/p&gt;

&lt;p&gt;By building a native MCP server, FDB is repositioning from data supplier to something closer to core infrastructure.&lt;/p&gt;

&lt;p&gt;They're not just the source of drug knowledge anymore.&lt;/p&gt;

&lt;p&gt;They're the layer that any healthcare AI agent needs to plug into to work safely.&lt;/p&gt;

&lt;p&gt;That's a different business.&lt;/p&gt;

&lt;p&gt;And a different kind of defensibility.&lt;/p&gt;

&lt;p&gt;Virginia Halsey, SVP of Strategy and Product at FDB, described this as moving "beyond data delivery to more intelligent, workflow-integrated solutions."&lt;/p&gt;

&lt;p&gt;The translation: we're not selling data exports anymore, we're becoming the plumbing.&lt;/p&gt;




&lt;h2&gt;
  
  
  What This Probably Means Going Forward
&lt;/h2&gt;

&lt;p&gt;A few things seem worth watching as MedProof MCP settles in:&lt;/p&gt;

&lt;p&gt;The infrastructure layer is starting to separate clearly from the application layer.&lt;/p&gt;

&lt;p&gt;There will be specialized MCP servers for drug knowledge, clinical records, lab data, billing.&lt;/p&gt;

&lt;p&gt;AI agents will connect across all of them.&lt;/p&gt;

&lt;p&gt;The companies that own those infrastructure positions will have real leverage over anything built on top - which means this isn't just a product launch, it's a land grab.&lt;/p&gt;

&lt;p&gt;Safety is becoming a genuine differentiator, not just a checkbox.&lt;/p&gt;

&lt;p&gt;The healthcare AI market has a long list of products that failed because clinicians didn't trust them.&lt;/p&gt;

&lt;p&gt;FDB's argument is that grounding agents in validated drug knowledge - instead of letting an LLM guess at interactions from training data - is what earns that trust.&lt;/p&gt;

&lt;p&gt;It's a reasonable argument, and one that's harder to replicate than it sounds.&lt;/p&gt;

&lt;p&gt;If MCP is getting production traction in healthcare - the hardest possible domain for this stuff - finance and legal and insurance will follow.&lt;/p&gt;

&lt;p&gt;Not because they want to copy healthcare, but because the same infrastructure problem exists everywhere regulated.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Bottom Line
&lt;/h2&gt;

&lt;p&gt;FDB MedProof MCP™ is what it looks like when a legacy data company actually understands what agentic AI requires - and builds for it instead of bolting a chat interface onto an existing product.&lt;/p&gt;

&lt;p&gt;Pharmacists get time back.&lt;/p&gt;

&lt;p&gt;Physicians stop re-entering what they already said out loud.&lt;/p&gt;

&lt;p&gt;Developers get a foundation that doesn't require rebuilding every time the AI layer shifts.&lt;/p&gt;

&lt;p&gt;David Delaney, President of FDB, put it plainly:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;em&gt;"This is how AI stops being a promise and starts being infrastructure."&lt;/em&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;Hard to argue with that.&lt;/p&gt;

&lt;p&gt;The interesting question now is who builds what on top of it.&lt;/p&gt;




&lt;p&gt;&lt;em&gt;Follow us for daily coverage of what's actually happening in MCP and agentic AI.&lt;/em&gt;&lt;/p&gt;

</description>
      <category>ai</category>
      <category>programming</category>
      <category>python</category>
      <category>mcp</category>
    </item>
    <item>
      <title>💥 Beginner-Friendly Guide 'Check if Binary String Has at Most One Segment of Ones' - Problem 1784 (C++, Python, JavaScript)</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Fri, 06 Mar 2026 13:03:35 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/beginner-friendly-guide-check-if-binary-string-has-at-most-one-segment-of-ones-problem-1784-74g</link>
      <guid>https://dev.to/om_shree_0709/beginner-friendly-guide-check-if-binary-string-has-at-most-one-segment-of-ones-problem-1784-74g</guid>
      <description>&lt;p&gt;Binary strings often appear simple, but they are the foundation of how data is stored and processed in every computer. Mastering how to traverse these strings and identify patterns is a fundamental skill for any aspiring software engineer.&lt;/p&gt;

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

&lt;p&gt;&lt;strong&gt;You're given:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;A binary string $s$ consisting only of characters '0' and '1'.&lt;/li&gt;
&lt;li&gt;The guarantee that $s$ does not have leading zeros, meaning it always starts with '1'.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Your goal:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Return &lt;code&gt;true&lt;/code&gt; if the string contains at most one contiguous segment of ones.&lt;/li&gt;
&lt;li&gt;Return &lt;code&gt;false&lt;/code&gt; if there are multiple separated segments of ones.&lt;/li&gt;
&lt;/ul&gt;




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

&lt;p&gt;The problem states that the string always starts with a '1'. If there is only one segment of ones, all the '1's must be clustered at the beginning or stay together without being interrupted by a '0'.&lt;/p&gt;

&lt;p&gt;If we ever see a '0' followed immediately by a '1' (the pattern "01"), it means a new segment of ones has started after a gap. Since we are only allowed one segment, the presence of the substring "01" is the "smoking gun" that tells us the condition has been violated.&lt;/p&gt;




&lt;h3&gt;
  
  
  Walkthrough: Understanding the Examples
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Example 1: s = "1001"&lt;/strong&gt;&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;We start at the beginning. We see "1".&lt;/li&gt;
&lt;li&gt;We move to the next characters and see "00".&lt;/li&gt;
&lt;li&gt;Suddenly, we see a "1" following a "0". This forms the pattern "01".&lt;/li&gt;
&lt;li&gt;Because a new segment of ones started after a zero, we return &lt;code&gt;false&lt;/code&gt;.&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;&lt;strong&gt;Example 2: s = "110"&lt;/strong&gt;&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;We start with "11".&lt;/li&gt;
&lt;li&gt;We see a "0" at the end.&lt;/li&gt;
&lt;li&gt;We never encounter a "1" appearing after that "0".&lt;/li&gt;
&lt;li&gt;Since there is no "01" pattern, there is only one segment. We return &lt;code&gt;true&lt;/code&gt;.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  C++ Solution
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;public:&lt;/span&gt;
    &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;checkOnesSegment&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;string&lt;/span&gt; &lt;span class="n"&gt;s&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 "01" is not found, s.find returns string::npos&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;find&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"01"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;string&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;npos&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;h3&gt;
  
  
  Python Solution
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;checkOnesSegment&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="nb"&gt;bool&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="c1"&gt;# The 'in' operator returns True if the substring exists
&lt;/span&gt;        &lt;span class="c1"&gt;# We want True if it does NOT exist
&lt;/span&gt;        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;01&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt; &lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  JavaScript Solution
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="cm"&gt;/**
 * @param {string} s
 * @return {boolean}
 */&lt;/span&gt;
&lt;span class="kd"&gt;var&lt;/span&gt; &lt;span class="nx"&gt;checkOnesSegment&lt;/span&gt; &lt;span class="o"&gt;=&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;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// includes() returns true if the pattern is found&lt;/span&gt;
    &lt;span class="c1"&gt;// We negate it because we want true if the segment is contiguous&lt;/span&gt;
    &lt;span class="k"&gt;return&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="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;01&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;
  
  
  Key Takeaways
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Pattern Recognition:&lt;/strong&gt; Sometimes a complex-sounding problem (counting contiguous segments) can be simplified into searching for a specific sub-pattern.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;String Searching:&lt;/strong&gt; Understanding built-in string methods like &lt;code&gt;find&lt;/code&gt;, &lt;code&gt;includes&lt;/code&gt;, or &lt;code&gt;in&lt;/code&gt; can lead to highly efficient and readable $O(n)$ solutions.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Constraints Matter:&lt;/strong&gt; The fact that there are no leading zeros ($s[0]$ is always '1') is the key piece of information that allows the "01" check to work perfectly.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Final Thoughts
&lt;/h3&gt;

&lt;p&gt;This problem is a fantastic example of how software engineers optimize code. While you could write a complex loop with multiple counters and state variables, identifying the "01" pattern allows for a "one-liner" solution. This type of logic is frequently used in &lt;strong&gt;data validation&lt;/strong&gt; and &lt;strong&gt;stream processing&lt;/strong&gt;, where you need to ensure data packets follow a specific format without overhead.&lt;/p&gt;

</description>
      <category>programming</category>
      <category>cpp</category>
      <category>python</category>
      <category>javascript</category>
    </item>
    <item>
      <title>💡 Beginner-Friendly Guide 'Minimum Changes To Make Alternating Binary String' - Problem 1758 (C++, Python, JavaScript)</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Thu, 05 Mar 2026 04:41:49 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/beginner-friendly-guide-minimum-changes-to-make-alternating-binary-string-problem-1758-c-2beh</link>
      <guid>https://dev.to/om_shree_0709/beginner-friendly-guide-minimum-changes-to-make-alternating-binary-string-problem-1758-c-2beh</guid>
      <description>&lt;p&gt;Binary strings can often feel like a puzzle where every piece must fit a strict alternating sequence. This problem challenges us to find the most efficient way to transform a messy string of zeros and ones into a perfect "0101..." or "1010..." pattern. By understanding the underlying symmetry of binary strings, we can solve this with a single pass through the data.&lt;/p&gt;

&lt;h3&gt;
  
  
  You're given:
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;A string &lt;code&gt;s&lt;/code&gt; consisting only of the characters '0' and '1'.&lt;/li&gt;
&lt;li&gt;A single operation: changing any '0' to '1' or vice versa.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Your goal:
&lt;/h3&gt;

&lt;p&gt;Find the &lt;strong&gt;minimum&lt;/strong&gt; number of operations needed to make the string alternating, meaning no two adjacent characters are the same.&lt;/p&gt;




&lt;h3&gt;
  
  
  Intuition: The Power of Two Patterns
&lt;/h3&gt;

&lt;p&gt;There are only two possible ways a binary string can be alternating:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Starting with '0': &lt;code&gt;010101...&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Starting with '1': &lt;code&gt;101010...&lt;/code&gt;
&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;At first, you might think we need to calculate the cost for both patterns separately. However, there is a clever mathematical shortcut. If it takes $x$ operations to transform a string of length $n$ into Pattern 1, then it will take exactly $n - x$ operations to transform it into Pattern 2.&lt;/p&gt;

&lt;p&gt;Why? Because Pattern 2 is just the exact opposite (inverse) of Pattern 1. Every character that was "correct" for Pattern 1 is "wrong" for Pattern 2, and vice versa. Therefore, we only need to count the changes for one pattern and then compare that count against the remaining length of the string.&lt;/p&gt;




&lt;h3&gt;
  
  
  Walkthrough: Understanding the Examples
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Example 1: s = "0100"&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Target Pattern 1:&lt;/strong&gt; &lt;code&gt;0101&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Compare index by index:&lt;/li&gt;
&lt;li&gt;Index 0: '0' vs '0' (Match)&lt;/li&gt;
&lt;li&gt;Index 1: '1' vs '1' (Match)&lt;/li&gt;
&lt;li&gt;Index 2: '0' vs '0' (Match)&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Index 3: '0' vs '1' (&lt;strong&gt;Mismatch!&lt;/strong&gt;)&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Total operations for Pattern 1: 1.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Total operations for Pattern 2: $4 - 1 = 3$.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Result:&lt;/strong&gt; 1 (The minimum of 1 and 3).&lt;/p&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Example 3: s = "1111"&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Target Pattern 1 (0101):&lt;/strong&gt;&lt;/li&gt;
&lt;li&gt;Index 0: '1' vs '0' (Mismatch)&lt;/li&gt;
&lt;li&gt;Index 1: '1' vs '1' (Match)&lt;/li&gt;
&lt;li&gt;Index 2: '1' vs '0' (Mismatch)&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Index 3: '1' vs '1' (Match)&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Total operations for Pattern 1: 2.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Total operations for Pattern 2: $4 - 2 = 2$.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Result:&lt;/strong&gt; 2.&lt;/p&gt;&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Code Blocks
&lt;/h3&gt;

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



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;public:&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;minOperations&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;string&lt;/span&gt; &lt;span class="n"&gt;s&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;operationsForPattern1&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="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="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;

        &lt;span class="c1"&gt;// We compare the string against the pattern "010101..."&lt;/span&gt;
        &lt;span class="k"&gt;for&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;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="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="c1"&gt;// Even index should be '0', odd index should be '1'&lt;/span&gt;
            &lt;span class="c1"&gt;// (i % 2) gives 0 for even, 1 for odd&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;s&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="sc"&gt;'0'&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&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="n"&gt;operationsForPattern1&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="p"&gt;}&lt;/span&gt;

        &lt;span class="c1"&gt;// The cost for "101010..." is (n - operationsForPattern1)&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;operationsForPattern1&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;operationsForPattern1&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;h4&gt;
  
  
  Python
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;minOperations&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;operations_for_pattern1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;
        &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&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;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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="c1"&gt;# Check if current character matches the "0101..." pattern
&lt;/span&gt;            &lt;span class="c1"&gt;# i % 2 is 0 at even indices and 1 at odd indices
&lt;/span&gt;            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="nf"&gt;int&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&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="n"&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="n"&gt;operations_for_pattern1&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;

        &lt;span class="c1"&gt;# Return the smaller of the two possible transformation costs
&lt;/span&gt;        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;operations_for_pattern1&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;operations_for_pattern1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  JavaScript
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="cm"&gt;/**
 * @param {string} s
 * @return {number}
 */&lt;/span&gt;
&lt;span class="kd"&gt;var&lt;/span&gt; &lt;span class="nx"&gt;minOperations&lt;/span&gt; &lt;span class="o"&gt;=&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;s&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;operationsForPattern1&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;n&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="nx"&gt;length&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;n&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="c1"&gt;// We check against pattern where even indices are '0' and odd are '1'&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;parseInt&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;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;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;operationsForPattern1&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="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// Pattern 2 cost is simply the remaining characters&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;min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;operationsForPattern1&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;operationsForPattern1&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;strong&gt;Parity Logic:&lt;/strong&gt; Using the modulo operator &lt;code&gt;% 2&lt;/code&gt; is a standard way to handle alternating patterns based on index position.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Complementary Counting:&lt;/strong&gt; Recognizing that the cost of one binary pattern is $n - x$ relative to its inverse pattern saves significant computation time.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Linear Complexity:&lt;/strong&gt; This solution runs in $O(n)$ time and uses $O(1)$ extra space, making it highly efficient for large inputs.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Final Thoughts
&lt;/h3&gt;

&lt;p&gt;This problem is a fantastic introduction to "Greedy" thinking and pattern recognition. In real-world software engineering, similar logic is used in &lt;strong&gt;Error Detection and Correction&lt;/strong&gt; algorithms (like parity bits in data transmission) and &lt;strong&gt;UI/UX design&lt;/strong&gt; for rendering alternating row colors in data tables. Mastering these simple string manipulations builds the foundation for more complex dynamic programming tasks you might encounter in technical interviews.&lt;/p&gt;

</description>
      <category>programming</category>
      <category>cpp</category>
      <category>python</category>
      <category>javascript</category>
    </item>
    <item>
      <title>🎯 Beginner-Friendly Guide 'Special Positions in a Binary Matrix' - Problem 1582 (C++, Python, JavaScript)</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Wed, 04 Mar 2026 05:11:11 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/beginner-friendly-guide-special-positions-in-a-binary-matrix-problem-1582-c-python-10ei</link>
      <guid>https://dev.to/om_shree_0709/beginner-friendly-guide-special-positions-in-a-binary-matrix-problem-1582-c-python-10ei</guid>
      <description>&lt;p&gt;Scanning a grid for specific patterns is a fundamental skill in both competitive programming and real-world image processing. This problem challenges you to identify unique elements that stand out as the sole occupants of their respective rows and columns.&lt;/p&gt;

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

&lt;p&gt;&lt;strong&gt;You're given:&lt;/strong&gt;&lt;br&gt;
A 2D grid called a matrix, consisting of $m$ rows and $n$ columns, filled only with 0s and 1s.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Your goal:&lt;/strong&gt;&lt;br&gt;
Return the number of "special positions" in the matrix. A position $(i, j)$ is considered special if the value at that coordinate is 1, and all other elements in row $i$ and column $j$ are 0.&lt;/p&gt;




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

&lt;p&gt;To determine if a 1 is "special," we need to know how many other 1s exist in its specific row and its specific column. If the count of 1s in row $i$ is exactly 1, and the count of 1s in column $j$ is also exactly 1, then the 1 located at $(i, j)$ must be the only one there.&lt;/p&gt;

&lt;p&gt;Instead of re-scanning the entire row and column for every single 1 we encounter, which would be inefficient, we can perform a "pre-computation" step. We use two auxiliary arrays to store the frequency of 1s for every row and every column. Once we have these counts, a second pass through the matrix allows us to verify each 1 in $O(1)$ constant time.&lt;/p&gt;




&lt;h3&gt;
  
  
  Walkthrough: Understanding the Examples
&lt;/h3&gt;

&lt;p&gt;Consider a matrix like this:&lt;br&gt;
&lt;code&gt;[[1, 0, 0], [0, 0, 1], [1, 0, 0]]&lt;/code&gt;&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;&lt;strong&gt;Counting Phase:&lt;/strong&gt;&lt;/li&gt;
&lt;li&gt;Row counts: Row 0 has one 1. Row 1 has one 1. Row 2 has one 1. Result: &lt;code&gt;rowOnes = [1, 1, 1]&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Column counts: Column 0 has two 1s. Column 1 has zero 1s. Column 2 has one 1. Result: &lt;code&gt;colOnes = [2, 0, 1]&lt;/code&gt;.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Verification Phase:&lt;/strong&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Check &lt;code&gt;mat[0][0]&lt;/code&gt;: It is a 1. Its row count is 1, but its column count is 2. &lt;strong&gt;Not special.&lt;/strong&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Check &lt;code&gt;mat[1][2]&lt;/code&gt;: It is a 1. Its row count is 1 and its column count is 1. &lt;strong&gt;Special!&lt;/strong&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Check &lt;code&gt;mat[2][0]&lt;/code&gt;: It is a 1. Its row count is 1, but its column count is 2. &lt;strong&gt;Not special.&lt;/strong&gt;&lt;/p&gt;&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;The total count of special positions is 1.&lt;/p&gt;




&lt;h3&gt;
  
  
  Code Blocks
&lt;/h3&gt;

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



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;public:&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;numSpecial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&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="o"&gt;&amp;gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;mat&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;m&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;mat&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
        &lt;span class="k"&gt;const&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="n"&gt;mat&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="n"&gt;size&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;ans&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="n"&gt;vector&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="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;rowOnes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;m&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="n"&gt;vector&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="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;colOnes&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="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

        &lt;span class="c1"&gt;// Step 1: Pre-compute the number of 1s in each row and column&lt;/span&gt;
        &lt;span class="k"&gt;for&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;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="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;m&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;i&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&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="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;j&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;mat&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;j&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="n"&gt;rowOnes&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
                    &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;colOnes&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&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="c1"&gt;// Step 2: Identify positions that meet the special criteria&lt;/span&gt;
        &lt;span class="k"&gt;for&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;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="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;m&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;i&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&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="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;j&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;mat&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;j&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="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;rowOnes&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&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="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;colOnes&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&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="n"&gt;ans&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="n"&gt;ans&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;h4&gt;
  
  
  Python
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;numSpecial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;mat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;list&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;list&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&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="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;m&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="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;mat&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;mat&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="n"&gt;row_ones&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="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;m&lt;/span&gt;
        &lt;span class="n"&gt;col_ones&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="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;
        &lt;span class="n"&gt;ans&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;

        &lt;span class="c1"&gt;# Step 1: Count 1s in rows and columns
&lt;/span&gt;        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;m&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;mat&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;c&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="n"&gt;row_ones&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;r&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="n"&gt;col_ones&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;c&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="c1"&gt;# Step 2: Check for special 1s
&lt;/span&gt;        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;m&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;mat&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;c&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="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;row_ones&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;r&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="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;col_ones&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;c&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="n"&gt;ans&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;

        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ans&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  JavaScript
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="cm"&gt;/**
 * @param {number[][]} mat
 * @return {number}
 */&lt;/span&gt;
&lt;span class="kd"&gt;var&lt;/span&gt; &lt;span class="nx"&gt;numSpecial&lt;/span&gt; &lt;span class="o"&gt;=&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;mat&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;m&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;mat&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;n&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;mat&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;rowOnes&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;Array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;m&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="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;colOnes&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;Array&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;fill&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;let&lt;/span&gt; &lt;span class="nx"&gt;ans&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;// Step 1: Accumulate counts&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;m&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="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;j&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;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&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;j&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;mat&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="nx"&gt;j&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="nx"&gt;rowOnes&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;colOnes&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;j&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="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// Step 2: Evaluate special conditions&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;m&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="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;j&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;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&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;j&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;mat&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="nx"&gt;j&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="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;rowOnes&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="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;colOnes&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;j&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="nx"&gt;ans&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="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;ans&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;strong&gt;Space-Time Tradeoff:&lt;/strong&gt; By using $O(m + n)$ extra space for our count arrays, we avoid a nested scan that would result in a much higher time complexity.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Frequency Arrays:&lt;/strong&gt; Using arrays to "remember" counts is a powerful pattern that simplifies complex conditional logic.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Matrix Traversal:&lt;/strong&gt; This problem reinforces how to navigate 2D data structures using nested loops efficiently.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Final Thoughts
&lt;/h3&gt;

&lt;p&gt;This problem is an excellent introduction to optimization. In real-world software engineering, this logic is mirrored in &lt;strong&gt;database indexing&lt;/strong&gt; or &lt;strong&gt;spreadsheet software&lt;/strong&gt;, where we need to quickly identify unique records across different dimensions. In a search engine, you might use similar techniques to find unique keywords that only appear once in a specific document and nowhere else in a cluster. Mastering the ability to pre-calculate metadata about your data will make your algorithms significantly faster.&lt;/p&gt;

</description>
      <category>programming</category>
      <category>cpp</category>
      <category>python</category>
      <category>javascript</category>
    </item>
    <item>
      <title>🧬 Beginner-Friendly Guide 'Find Kth Bit in Nth Binary String' - Problem 1545 (C++, Python, JavaScript)</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Tue, 03 Mar 2026 01:10:59 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/beginner-friendly-guide-find-kth-bit-in-nth-binary-string-problem-1545-c-python-21cg</link>
      <guid>https://dev.to/om_shree_0709/beginner-friendly-guide-find-kth-bit-in-nth-binary-string-problem-1545-c-python-21cg</guid>
      <description>&lt;p&gt;Generating massive binary strings can quickly exhaust your computer's memory. This problem challenges you to find a specific character within a complex, growing sequence without actually building the entire string. By leveraging the symmetrical properties of the sequence, we can use a "divide and conquer" strategy to pinpoint our answer.&lt;/p&gt;




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

&lt;p&gt;&lt;strong&gt;You're given:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;An integer $n$, representing the $n^{th}$ generation of a binary string $S_n$.&lt;/li&gt;
&lt;li&gt;An integer $k$, representing the 1-indexed position of the bit you need to find.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Your goal:&lt;/strong&gt;&lt;br&gt;
Return the value of the $k^{th}$ bit in $S_n$ as a character ('0' or '1').&lt;/p&gt;




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

&lt;p&gt;The structure of $S_n$ follows a very specific pattern: $S_n = S_{n-1} + "1" + \text{reverse}(\text{invert}(S_{n-1}))$.&lt;/p&gt;

&lt;p&gt;If we look closely at the length of these strings, $S_n$ has a length of $2^n - 1$. This means there is always a "middle" bit at position $2^{n-1}$. This middle bit is always '1' (except for the base case $S_1 = "0"$).&lt;/p&gt;

&lt;p&gt;Because the second half of the string is just a transformed version of the first half, we don't need to generate it. We can use recursion to "look back" at previous versions of the string:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Base Case:&lt;/strong&gt; If $n = 1$, the bit is always '0'.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Middle Case:&lt;/strong&gt; If $k$ is exactly at the middle position, the bit is '1'.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Left Side:&lt;/strong&gt; If $k$ is less than the middle, the bit is the same as the $k^{th}$ bit in $S_{n-1}$.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Right Side:&lt;/strong&gt; If $k$ is greater than the middle, the bit is the &lt;strong&gt;inverted&lt;/strong&gt; version of a bit in $S_{n-1}$. Because the right side is reversed, the $k^{th}$ bit in $S_n$ corresponds to the bit at position $(\text{Total Length} + 1 - k)$ in $S_{n-1}$.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  Walkthrough: Understanding the Examples
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Example: $n = 3, k = 1$&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;$S_3$ length is 7. Middle is 4.&lt;/li&gt;
&lt;li&gt;$k=1$ is less than the middle (4).&lt;/li&gt;
&lt;li&gt;We look for the $1^{st}$ bit in $S_2$.&lt;/li&gt;
&lt;li&gt;$S_2$ length is 3. Middle is 2.&lt;/li&gt;
&lt;li&gt;$k=1$ is less than the middle (2).&lt;/li&gt;
&lt;li&gt;We look for the $1^{st}$ bit in $S_1$.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Base Case:&lt;/strong&gt; $n=1$ returns '0'.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Example: $n = 4, k = 11$&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;$S_4$ length is 15. Middle is 8.&lt;/li&gt;
&lt;li&gt;$k=11$ is greater than 8.&lt;/li&gt;
&lt;li&gt;The corresponding position in $S_3$ is $16 - 11 = 5$.&lt;/li&gt;
&lt;li&gt;We find the $5^{th}$ bit of $S_3$ and &lt;strong&gt;invert&lt;/strong&gt; it.&lt;/li&gt;
&lt;li&gt;In $S_3$, middle is 4. $k=5$ is greater than 4.&lt;/li&gt;
&lt;li&gt;Corresponding position in $S_2$ is $8 - 5 = 3$.&lt;/li&gt;
&lt;li&gt;We find the $3^{rd}$ bit of $S_2$ and &lt;strong&gt;invert&lt;/strong&gt; the result again.&lt;/li&gt;
&lt;li&gt;In $S_2$, middle is 2. $k=3$ is greater than 2.&lt;/li&gt;
&lt;li&gt;Corresponding position in $S_1$ is $4 - 3 = 1$.&lt;/li&gt;
&lt;li&gt;$S_1$ at $k=1$ is '0'.&lt;/li&gt;
&lt;li&gt;Following the chain of inversions: '0' $\rightarrow$ '1' $\rightarrow$ '0' $\rightarrow$ '1'. Final result is '1'.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Code Blocks
&lt;/h3&gt;

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



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
 &lt;span class="nl"&gt;public:&lt;/span&gt;
  &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;findKthBit&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;k&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;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="sc"&gt;'0'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// The middle index is 2^(n-1)&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;midIndex&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;&amp;lt;&amp;lt;&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="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;k&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;midIndex&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="sc"&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="n"&gt;k&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;midIndex&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;findKthBit&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;k&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// If k is in the right half, find the bit in the reflected position&lt;/span&gt;
    &lt;span class="c1"&gt;// and invert it (0 becomes 1, 1 becomes 0)&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;findKthBit&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;midIndex&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'0'&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="sc"&gt;'1'&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="sc"&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Python
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;findKthBit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&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="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&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="nb"&gt;str&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="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="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;0&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;

        &lt;span class="c1"&gt;# Calculate middle index using bit shift for 2^(n-1)
&lt;/span&gt;        &lt;span class="n"&gt;mid_index&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;&amp;lt;&amp;lt;&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="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;mid_index&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;1&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;
        &lt;span class="k"&gt;elif&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;mid_index&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;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;findKthBit&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;k&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="c1"&gt;# Mirror the position and invert the result
&lt;/span&gt;            &lt;span class="n"&gt;res&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;findKthBit&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;mid_index&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;1&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;res&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;0&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;0&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  JavaScript
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="cm"&gt;/**
 * @param {number} n
 * @param {number} k
 * @return {character}
 */&lt;/span&gt;
&lt;span class="kd"&gt;var&lt;/span&gt; &lt;span class="nx"&gt;findKthBit&lt;/span&gt; &lt;span class="o"&gt;=&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;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;k&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;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="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;0&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;midIndex&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;pow&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;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="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;k&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;midIndex&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="s1"&gt;1&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="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;k&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;midIndex&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;findKthBit&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;k&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="c1"&gt;// Mirror position: (Total Length + 1) - k&lt;/span&gt;
        &lt;span class="c1"&gt;// Total Length is (midIndex * 2) - 1&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;reflectedBit&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;findKthBit&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;midIndex&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;k&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;reflectedBit&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;0&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;1&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;0&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






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

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Recursive Symmetry:&lt;/strong&gt; Many string generation problems can be solved by recognizing how the current state relates to the previous state without building the full data structure.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Divide and Conquer:&lt;/strong&gt; By halving the search space at each step, we achieve a time complexity of $O(n)$, which is much better than the $O(2^n)$ required to build the string.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Bit Manipulation:&lt;/strong&gt; Using &lt;code&gt;1 &amp;lt;&amp;lt; (n - 1)&lt;/code&gt; is a fast and efficient way to calculate powers of 2 in many programming languages.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Final Thoughts
&lt;/h3&gt;

&lt;p&gt;This problem is a classic example of why understanding recursion is vital for technical interviews. In a real-world system, such as a file compression utility or a data recovery algorithm, you might need to extract specific pieces of data from a pattern-based stream. Generating the entire stream would crash your system if the "n" was large, but using these mathematical properties allows your code to stay lightweight and fast.&lt;/p&gt;

</description>
      <category>programming</category>
      <category>cpp</category>
      <category>python</category>
      <category>javascript</category>
    </item>
    <item>
      <title>🧱 Beginner-Friendly Guide 'Minimum Swaps to Arrange a Binary Grid' - Problem 1536 (C++, Python, JavaScript)</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Mon, 02 Mar 2026 17:14:46 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/beginner-friendly-guide-minimum-swaps-to-arrange-a-binary-grid-problem-1536-c-python-5amj</link>
      <guid>https://dev.to/om_shree_0709/beginner-friendly-guide-minimum-swaps-to-arrange-a-binary-grid-problem-1536-c-python-5amj</guid>
      <description>&lt;p&gt;Sorting a grid might seem like a complex task, but it often boils down to identifying a single critical property of each row. In this challenge, we explore how to transform a matrix through greedy swaps to satisfy a specific geometric constraint.&lt;br&gt;
You're given:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;An n \times n binary grid consisting of 0s and 1s.&lt;/li&gt;
&lt;li&gt;The ability to swap any two adjacent rows.
Your goal:&lt;/li&gt;
&lt;li&gt;Find the minimum number of swaps needed so that all cells above the main diagonal are zeros.&lt;/li&gt;
&lt;li&gt;Return -1 if it is impossible to reach this state.
Intuition: The Power of Suffix Zeros
To make a grid "valid," the first row must have at least n - 1 zeros at the end. The second row needs at least n - 2 zeros, and so on. The last row doesn't require any trailing zeros.
Instead of moving the whole grid, we can simplify each row into a single number: the count of consecutive zeros starting from the right (suffix zeros).
The strategy is Greedy:&lt;/li&gt;
&lt;li&gt;For the current row i, determine how many suffix zeros are required (n - 1 - i).&lt;/li&gt;
&lt;li&gt;Search downward from the current row to find the first row that satisfies this requirement.&lt;/li&gt;
&lt;li&gt;Once found, "bubble" that row up to the current position using adjacent swaps. This is similar to a single pass of Bubble Sort.&lt;/li&gt;
&lt;li&gt;If no such row exists in the remaining options, the task is impossible.
Walkthrough: Understanding the Examples
Example 1: grid = &lt;a href="https://dev.ton%20=%203"&gt;[0,0,1],[1,1,0],[1,0,0]&lt;/a&gt;
&lt;/li&gt;
&lt;li&gt;Step 0 (Pre-calculation):

&lt;ul&gt;
&lt;li&gt;Row 0: [0,0,1] has 0 suffix zeros.&lt;/li&gt;
&lt;li&gt;Row 1: [1,1,0] has 1 suffix zero.&lt;/li&gt;
&lt;li&gt;Row 2: [1,0,0] has 2 suffix zeros.&lt;/li&gt;
&lt;li&gt;suffixZeros array: [0, 1, 2]&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;Step 1 (Row i = 0): Needs 3 - 1 - 0 = 2 zeros. The first row with \ge 2 zeros is at index 2. Swap index 2 with 1, then index 1 with 0. (2 swaps). Array becomes [2, 0, 1].&lt;/li&gt;

&lt;li&gt;Step 2 (Row i = 1): Needs 3 - 1 - 1 = 1 zero. The first row from index 1 onwards with \ge 1 zero is at index 2. Swap index 2 with 1. (1 swap). Array becomes [2, 1, 0].&lt;/li&gt;

&lt;li&gt;

&lt;p&gt;Total Swaps: 2 + 1 = 3.&lt;br&gt;
Code Blocks&lt;br&gt;
C++&lt;br&gt;
class Solution {&lt;br&gt;
public:&lt;br&gt;
int minSwaps(vector&amp;gt;&amp;amp; grid) {&lt;br&gt;
const int n = grid.size();&lt;br&gt;
int ans = 0;&lt;br&gt;
vector suffixZeros;&lt;/p&gt;

&lt;p&gt;// Pre-calculate suffix zeros for each row&lt;br&gt;
for (const vector&amp;amp; row : grid) {&lt;br&gt;
  int count = 0;&lt;br&gt;
  for (int j = n - 1; j &amp;gt;= 0 &amp;amp;&amp;amp; row[j] == 0; --j) {&lt;br&gt;
    count++;&lt;br&gt;
  }&lt;br&gt;
  suffixZeros.push_back(count);&lt;br&gt;
}&lt;/p&gt;

&lt;p&gt;for (int i = 0; i &amp;lt; n; ++i) {&lt;br&gt;
  const int neededZeros = n - 1 - i;&lt;br&gt;
  int foundIdx = -1;&lt;/p&gt;

&lt;p&gt;// Find the first row that satisfies the requirement&lt;br&gt;
  for (int j = i; j &amp;lt; n; ++j) {&lt;br&gt;
    if (suffixZeros[j] &amp;gt;= neededZeros) {&lt;br&gt;
      foundIdx = j;&lt;br&gt;
      break;&lt;br&gt;
    }&lt;br&gt;
  }&lt;/p&gt;

&lt;p&gt;if (foundIdx == -1) return -1;&lt;/p&gt;

&lt;p&gt;// Simulate the swaps and accumulate the cost&lt;br&gt;
  for (int k = foundIdx; k &amp;gt; i; --k) {&lt;br&gt;
    swap(suffixZeros[k], suffixZeros[k - 1]);&lt;br&gt;
  }&lt;br&gt;
  ans += (foundIdx - i);&lt;br&gt;
}&lt;/p&gt;

&lt;p&gt;return ans;&lt;br&gt;
}&lt;br&gt;
};&lt;/p&gt;


&lt;/li&gt;

&lt;/ul&gt;

&lt;p&gt;Python&lt;br&gt;
class Solution:&lt;br&gt;
    def minSwaps(self, grid: list[list[int]]) -&amp;gt; int:&lt;br&gt;
        n = len(grid)&lt;br&gt;
        suffix_zeros = []&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;    # Pre-calculate suffix zeros for each row
    for row in grid:
        count = 0
        for j in range(n - 1, -1, -1):
            if row[j] == 0:
                count += 1
            else:
                break
        suffix_zeros.append(count)

    ans = 0
    for i in range(n):
        needed_zeros = n - 1 - i
        found_idx = -1

        # Find the first row meeting the criteria
        for j in range(i, n):
            if suffix_zeros[j] &amp;gt;= needed_zeros:
                found_idx = j
                break

        if found_idx == -1:
            return -1

        # Move the row to current position i
        # Using pop and insert simulates the adjacent swaps efficiently
        row_to_move = suffix_zeros.pop(found_idx)
        suffix_zeros.insert(i, row_to_move)
        ans += (found_idx - i)

    return ans
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;

&lt;p&gt;JavaScript&lt;br&gt;
/**&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;a class="mentioned-user" href="https://dev.to/param"&gt;@param&lt;/a&gt; {number[][]} grid&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;@return {number}&lt;br&gt;
*/&lt;br&gt;
var minSwaps = function(grid) {&lt;br&gt;
const n = grid.length;&lt;br&gt;
const suffixZeros = [];&lt;/p&gt;

&lt;p&gt;// Pre-calculate suffix zeros for each row&lt;br&gt;
for (const row of grid) {&lt;br&gt;
    let count = 0;&lt;br&gt;
    for (let j = n - 1; j &amp;gt;= 0; j--) {&lt;br&gt;
        if (row[j] === 0) {&lt;br&gt;
            count++;&lt;br&gt;
        } else {&lt;br&gt;
            break;&lt;br&gt;
        }&lt;br&gt;
    }&lt;br&gt;
    suffixZeros.push (count);&lt;br&gt;
}&lt;/p&gt;

&lt;p&gt;let ans = 0;&lt;br&gt;
for (let i = 0; i &amp;lt; n; i++) {&lt;br&gt;
    const neededZeros = n - 1 - i;&lt;br&gt;
    let foundIdx = -1;&lt;/p&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;for (let j = i; j &amp;lt; n; j++) {
    if (suffixZeros[j] &amp;gt;= neededZeros) {
        foundIdx = j;
        break;
    }
}

if (foundIdx === -1) return -1;

// Move the required value to the current position
const val = suffixZeros.splice(foundIdx, 1)[0];
suffixZeros.splice(i, 0, val);
ans += (foundIdx - i);
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;}&lt;/p&gt;

&lt;p&gt;return ans;&lt;br&gt;
};&lt;/p&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Key Takeaways&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Greedy Strategy: Choosing the first available row that meets the criteria is optimal because it leaves the most flexible options for subsequent rows.&lt;/li&gt;
&lt;li&gt;Data Reduction: Reducing a complex 2D grid into a 1D array of counts makes the problem much easier to reason about.&lt;/li&gt;
&lt;li&gt;Simulation Cost: The number of swaps needed to move an element from index j to index i is exactly j - i.
Final Thoughts
This problem is a classic example of how to handle constraints in a grid by focusing on the properties of rows rather than the individual cells. In real-world software engineering, this kind of logic is frequently applied in resource scheduling or data packet ordering, where you need to arrange items to meet specific priority thresholds with minimal overhead. Mastering greedy simulations is a key step toward passing technical interviews for roles in systems optimization.&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>programming</category>
      <category>cpp</category>
      <category>python</category>
      <category>javascript</category>
    </item>
    <item>
      <title>🍢 Beginner-Friendly Guide 'Partitioning Into Minimum Number Of Deci-Binary Numbers' - Problem 1689 (C++, Python, JavaScript)</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Sun, 01 Mar 2026 02:52:23 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/beginner-friendly-guide-partitioning-into-minimum-number-of-deci-binary-numbers-problem-1689-6e8</link>
      <guid>https://dev.to/om_shree_0709/beginner-friendly-guide-partitioning-into-minimum-number-of-deci-binary-numbers-problem-1689-6e8</guid>
      <description>&lt;p&gt;At first glance, this problem looks like a complex mathematical challenge involving partitions and sums. However, once you peek under the hood, you will find it is actually a clever logic puzzle that tests your ability to identify the "bottleneck" in a system.&lt;/p&gt;

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

&lt;p&gt;&lt;strong&gt;You're given:&lt;/strong&gt;&lt;br&gt;
A string $n$ representing a very large positive integer.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Your goal:&lt;/strong&gt;&lt;br&gt;
Find the minimum number of "deci-binary" numbers (numbers consisting only of digits 0 and 1) that sum up to $n$.&lt;/p&gt;




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

&lt;p&gt;To solve this, we need to think about how addition works digit by digit. A deci-binary number can only contribute a value of 0 or 1 to any specific decimal place.&lt;/p&gt;

&lt;p&gt;If you have a digit 7 in the units place, you need at least 7 separate deci-binary numbers to provide enough 1s to sum up to that 7. Even if other digits in the number are smaller, like 2 or 3, they can be satisfied by using 0s in those specific positions for some of the deci-binary numbers.&lt;/p&gt;

&lt;p&gt;Therefore, the "limiting factor" is simply the largest digit present in the string. If the string contains a 9, you need 9 deci-binary numbers. If the largest digit is 3, you only need 3. The logic is as simple as finding the maximum character in the string.&lt;/p&gt;




&lt;h3&gt;
  
  
  Walkthrough: Understanding the Examples
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Example 1: $n = 32$&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;The digits are 3 and 2.&lt;/li&gt;
&lt;li&gt;To get the 3 in the tens place, we need at least three 1s (10 + 10 + 10).&lt;/li&gt;
&lt;li&gt;To get the 2 in the units place, we only need two 1s.&lt;/li&gt;
&lt;li&gt;We can use: $11 + 11 + 10 = 32$.&lt;/li&gt;
&lt;li&gt;Total numbers used: 3 (which is the maximum digit).&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Example 2: $n = 82734$&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;The digits are 8, 2, 7, 3, and 4.&lt;/li&gt;
&lt;li&gt;The largest digit is 8.&lt;/li&gt;
&lt;li&gt;To satisfy the 8, we must have 8 separate numbers. All other positions (2, 7, 3, 4) can be formed using 8 or fewer 1s.&lt;/li&gt;
&lt;li&gt;Result: 8.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Code Blocks
&lt;/h3&gt;

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



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;public:&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;minPartitions&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;string&lt;/span&gt; &lt;span class="n"&gt;n&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;maxi&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="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="c1"&gt;// Convert character to integer and track the maximum&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;maxi&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="sc"&gt;'0'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;maxi&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="sc"&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="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;maxi&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;h4&gt;
  
  
  Python
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;minPartitions&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&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="nb"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="c1"&gt;# The result is simply the maximum digit in the string
&lt;/span&gt;        &lt;span class="c1"&gt;# We convert the characters to integers to find the max
&lt;/span&gt;        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;int&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="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  JavaScript
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="cm"&gt;/**
 * @param {string} n
 * @return {number}
 */&lt;/span&gt;
&lt;span class="kd"&gt;var&lt;/span&gt; &lt;span class="nx"&gt;minPartitions&lt;/span&gt; &lt;span class="o"&gt;=&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;n&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;maxi&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;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;n&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="c1"&gt;// Find the highest digit in the string&lt;/span&gt;
        &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;digit&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;Number&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;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="nx"&gt;digit&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;maxi&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;maxi&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;digit&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="c1"&gt;// Optimization: if we find a 9, we can stop early&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;maxi&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;9&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;9&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;maxi&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;strong&gt;Greedy Logic:&lt;/strong&gt; Often, the most extreme value in a dataset (the maximum) dictates the requirements for the entire set.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;String Manipulation:&lt;/strong&gt; When dealing with massive numbers that exceed standard integer limits ($10^{100000}$), treating the number as a string is the only way to process it.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Complexity:&lt;/strong&gt; This solution runs in $O(n)$ time where $n$ is the length of the string, and $O(1)$ extra space, making it highly efficient.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Final Thoughts
&lt;/h3&gt;

&lt;p&gt;This problem is a classic "Aha!" moment in technical interviews. It looks like a dynamic programming or partition problem, but it is actually a test of observation. In real-world software engineering, this mirrors &lt;strong&gt;resource allocation&lt;/strong&gt;. If you are building a system to process parallel tasks, your total execution time is often limited by the single longest task in the queue, just as our sum was limited by the largest digit.&lt;/p&gt;

</description>
      <category>programming</category>
      <category>cpp</category>
      <category>python</category>
      <category>javascript</category>
    </item>
    <item>
      <title>🔗 Beginner-Friendly Guide 'Concatenation of Consecutive Binary Numbers' - Problem 1680 (C++, Python, JavaScript)</title>
      <dc:creator>Om Shree</dc:creator>
      <pubDate>Sat, 28 Feb 2026 00:09:24 +0000</pubDate>
      <link>https://dev.to/om_shree_0709/beginner-friendly-guide-concatenation-of-consecutive-binary-numbers-problem-1680-c-3ch9</link>
      <guid>https://dev.to/om_shree_0709/beginner-friendly-guide-concatenation-of-consecutive-binary-numbers-problem-1680-c-3ch9</guid>
      <description>&lt;p&gt;Ever wondered how computers handle massive strings of data by simply stitching bits together? This problem challenges you to simulate that exact process by joining the binary forms of consecutive numbers into one giant value. It is a fantastic exercise in bitwise manipulation and understanding how large numbers are stored in memory.&lt;/p&gt;




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

&lt;p&gt;&lt;strong&gt;You're given:&lt;/strong&gt;&lt;br&gt;
An integer $n$, representing a range of numbers starting from 1 up to $n$.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Your goal:&lt;/strong&gt;&lt;br&gt;
Concatenate the binary representations of every number in that range in order. You must then convert that resulting binary string back into a decimal integer, returning the result modulo $10^9 + 7$.&lt;/p&gt;




&lt;h3&gt;
  
  
  Intuition: The Art of Shifting
&lt;/h3&gt;

&lt;p&gt;To solve this without actually creating a massive string (which would be slow and memory-heavy), we use bitwise math. Think of it like a conveyor belt. When you want to add a new number to the end of your current binary sequence, you first need to make exactly enough "room" for it.&lt;/p&gt;

&lt;p&gt;For every number $i$ from 1 to $n$, we follow these steps:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Find the bit length:&lt;/strong&gt; Determine how many bits are needed to represent the current number $i$. For example, the number 2 is &lt;code&gt;10&lt;/code&gt; in binary, which needs 2 bits.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Shift the result:&lt;/strong&gt; Shift our existing total to the left by that many bits. This effectively adds zeros to the end of our current number, creating a "slot" for the new value.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Merge with OR:&lt;/strong&gt; Use the bitwise OR operator to place the bits of $i$ into that new slot.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Keep it small:&lt;/strong&gt; Since the number grows incredibly fast, we apply the modulo $10^9 + 7$ at every single step to prevent integer overflow.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  Walkthrough: Understanding the Examples
&lt;/h3&gt;

&lt;p&gt;Let's look at $n = 3$:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Step 1 ($i = 1$):&lt;/strong&gt; Binary is &lt;code&gt;1&lt;/code&gt;. Result becomes &lt;code&gt;1&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Step 2 ($i = 2$):&lt;/strong&gt; Binary is &lt;code&gt;10&lt;/code&gt; (2 bits). We shift our current result (&lt;code&gt;1&lt;/code&gt;) left by 2 positions to get &lt;code&gt;100&lt;/code&gt;. We then OR it with &lt;code&gt;10&lt;/code&gt; to get &lt;code&gt;110&lt;/code&gt;. Decimal value: 6.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Step 3 ($i = 3$):&lt;/strong&gt; Binary is &lt;code&gt;11&lt;/code&gt; (2 bits). We shift our current result (&lt;code&gt;110&lt;/code&gt;) left by 2 positions to get &lt;code&gt;11000&lt;/code&gt;. We then OR it with &lt;code&gt;11&lt;/code&gt; to get &lt;code&gt;11011&lt;/code&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The final binary &lt;code&gt;11011&lt;/code&gt; converts to 27 in decimal.&lt;/p&gt;




&lt;h3&gt;
  
  
  C++ Solution
&lt;/h3&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;bit&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;public:&lt;/span&gt;
    &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;mod&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;1e9&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;7&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;concatenatedBinary&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="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;long&lt;/span&gt; &lt;span class="n"&gt;result&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&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="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="c1"&gt;// std::bit_width calculates the number of bits required for i&lt;/span&gt;
            &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;width&lt;/span&gt; &lt;span class="o"&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;bit_width&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="kt"&gt;unsigned&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;i&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="p"&gt;((&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;width&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;mod&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="kt"&gt;int&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="p"&gt;};&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Python Solution
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;concatenatedBinary&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&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="nb"&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="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;mod&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="mi"&gt;9&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;7&lt;/span&gt;
        &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;

        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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;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="c1"&gt;# bit_length() gives the number of bits required for the integer
&lt;/span&gt;            &lt;span class="n"&gt;width&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;bit_length&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
            &lt;span class="c1"&gt;# Shift result left by width and add the current number i
&lt;/span&gt;            &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&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;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;width&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;mod&lt;/span&gt;

        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  JavaScript Solution
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="cm"&gt;/**
 * @param {number} n
 * @return {number}
 */&lt;/span&gt;
&lt;span class="kd"&gt;var&lt;/span&gt; &lt;span class="nx"&gt;concatenatedBinary&lt;/span&gt; &lt;span class="o"&gt;=&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;n&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;mod&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1000000007&lt;/span&gt;&lt;span class="nx"&gt;n&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="mi"&gt;0&lt;/span&gt;&lt;span class="nx"&gt;n&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="nx"&gt;n&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="c1"&gt;// Find bit length by converting to binary string&lt;/span&gt;
        &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;width&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;BigInt&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="nf"&gt;toString&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;length&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="c1"&gt;// Using BigInt to handle large numbers before modulo&lt;/span&gt;
        &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&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;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;width&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="nc"&gt;BigInt&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;mod&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="nc"&gt;Number&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="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;strong&gt;Bitwise Shifting:&lt;/strong&gt; Shifting left by $k$ bits is mathematically equivalent to multiplying a number by $2^k$.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Modulo Arithmetic:&lt;/strong&gt; When working with large numbers, applying modulo at each step of an addition or multiplication keeps the values within the safe limits of your data type.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Efficiency:&lt;/strong&gt; Calculating bit width and using bitwise operations is significantly faster than performing string concatenation and converting back to an integer.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  Final Thoughts
&lt;/h3&gt;

&lt;p&gt;This problem is a classic example of how "low-level" thinking can lead to high-performance solutions. In the real world, these concepts are vital for &lt;strong&gt;data compression&lt;/strong&gt; and &lt;strong&gt;network protocols&lt;/strong&gt;, where information is often packed into the smallest possible bit-space to save bandwidth. Mastering bitwise logic makes you a much more versatile developer, especially when working close to the hardware or optimizing high-traffic systems.&lt;/p&gt;

</description>
      <category>programming</category>
      <category>cpp</category>
      <category>python</category>
      <category>javascript</category>
    </item>
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