🚦 Dijkstra's Algorithm Explained – A Beginner's Guide

📚 Introduction

Hey, algorithm explorers! 🧭

Today, we’re diving into a classic in the world of graph theory — Dijkstra's Algorithm. Whether you're navigating road maps, network packets, or game AI, this algorithm plays a pivotal role in finding the shortest path from a source node to all other nodes in a graph. Let’s unpack it, step by step.

---

🧠 Problem Summary

You are given:

• A graph represented with nodes and weighted edges (non-negative).
• A source node from which we want to compute the shortest path to every other node.

Your goal:

Find the minimum distance from the source to each node using Dijkstra’s algorithm.

This algorithm works for graphs with non-negative weights only.

---

🧩 Intuition

The core idea is greedy:

1. Start at the source node with distance 0.
2. Repeatedly pick the node with the smallest known distance that hasn't been visited.
3. Update the distances of its neighbors.
4. Repeat until all nodes are processed.

Think of it like expanding a ripple outward from the source node, always touching the closest unvisited node.

---

🛠️ Approach

We use:

• A priority queue (min-heap) to efficiently fetch the next closest node.
• A distance array to store the shortest known distance to each node.

At each step, we process the node with the smallest tentative distance and relax its neighbors.

---

🧮 C++ Code

#include <vector>
#include <queue>
using namespace std;

vector<int> dijkstra(int n, vector<vector<pair<int, int>>>& graph, int start) {
    vector<int> dist(n, INT_MAX);
    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<>> pq;
    dist[start] = 0;
    pq.emplace(0, start);

    while (!pq.empty()) {
        auto [d, u] = pq.top(); pq.pop();
        if (d > dist[u]) continue;

        for (auto [v, w] : graph[u]) {
            if (dist[u] + w < dist[v]) {
                dist[v] = dist[u] + w;
                pq.emplace(dist[v], v);
            }
        }
    }
    return dist;
}

---

💻 JavaScript Code

function dijkstra(n, graph, start) {
    const dist = Array(n).fill(Infinity);
    dist[start] = 0;
    const pq = [[0, start]];

    while (pq.length) {
        pq.sort((a, b) => a[0] - b[0]);
        const [d, u] = pq.shift();

        if (d > dist[u]) continue;

        for (const [v, w] of graph[u]) {
            if (dist[u] + w < dist[v]) {
                dist[v] = dist[u] + w;
                pq.push([dist[v], v]);
            }
        }
    }

    return dist;
}

---

🐍 Python Code

def dijkstra(n, graph, start):
    import heapq
    dist = [float('inf')] * n
    dist[start] = 0
    pq = [(0, start)]

    while pq:
        d, u = heapq.heappop(pq)
        if d > dist[u]:
            continue

        for v, w in graph[u]:
            if dist[u] + w < dist[v]:
                dist[v] = dist[u] + w
                heapq.heappush(pq, (dist[v], v))

    return dist

---

📝 Key Notes

• Graph should be adjacency list: graph[u] = [(v1, w1), (v2, w2), ...]
• Time Complexity: O((V + E) log V) with a min-heap
• Only works with non-negative edge weights

---

✅ Final Thoughts

Dijkstra’s algorithm is a cornerstone in graph algorithms — fast, efficient, and foundational. Whether you're building GPS navigation systems or solving competitive programming problems, mastering this will serve you well.

Drop a ❤️ if you learned something new, and stay tuned for more algorithm deep dives!

Happy coding! 🚀

Comments

[Ravavyr]

Curious.
"Think of it like expanding a ripple outward from the source node, always touching the closest unvisited node."

Is there a visualization of this somewhere?
Also, what are real world scenarios where this is useful? [the article mentions GPS and some others, but can someone elaborate on some?]

[Om Shree]

Great questions! 🌊

For visualizing the "ripple" analogy, I'd recommend searching for “Dijkstra algorithm animation” on YouTube, there are some excellent step-by-step grid visualizations that show how the algorithm expands outward.

As for real-world use cases: beyond GPS, Dijkstra is used in network routing (e.g., OSPF protocol), game AI pathfinding, robot motion planning, and even social network analysis (like finding the shortest chain of connections). Basically, anytime you're looking for a cost-optimal path through a weighted system, Dijkstra fits in.

Happy to dive deeper if you're curious about a specific domain! 🚀

[Ravavyr]

Thank you for that, i thought i had heard of Dijkstra algorithm before, and when you mentioned Game pathfinding it hit me.

Cool, yea, as a web developer I don't really deal with complex algorithms often, or at least nothing that hasn't been abstracted a few levels so i just call a function and it "magically" does it.

I do wonder how often engineers have to actually write this kind of logic even for network software. It would seem this kinda logic would have been abstracted for everyone by now.

But it's still cool to learn about it :) thanks again!

[Om Shree]

Thanks for the kind words, Ravavyr! I'm glad I could help spark some memories of the Dijkstra algorithm. You're right, many developers might not need to implement it directly, but understanding the underlying logic can be beneficial. If you have any more questions or topics you'd like to explore, feel free to ask!

[Nevo David]

pretty cool seeing the breakdown in all three languages, gotta say i always wondered if there’s a clever shortcut or tweak folks use when dealing with huge graphs

[Om Shree]

Thanks! Glad you liked the breakdown! 😊

When dealing with huge graphs, people often use optimizations like A* search (adds heuristics for faster pathfinding), Bidirectional Dijkstra (search from both ends), or even preprocessing-based techniques like Contraction Hierarchies for road networks. For sparse graphs, using Fibonacci heaps can theoretically improve performance too, though in practice binary heaps are faster due to lower overhead.

Appreciate the thoughtful comment, happy to dive deeper anytime! 🚀

[Nathan Tarbert]

very cool, i love how you broke down the logic and showed the code in three languages makes me want to pick up a new one honestly
you ever find yourself mixing up the details when switching between python and c++

[Om Shree]

Thanks a lot! 🙌 Glad you enjoyed the breakdown. And yes, switching between Python and C++ definitely trips me up sometimes, especially with things like zero-based indexing quirks, default data structures, or forgetting to manage memory in C++. But it’s also a great way to stay sharp across languages. Would totally encourage giving a new one a shot! 🚀

[Dotallio]

Awesome breakdown, especially with the code in all three languages! Have you tried tweaking your approach for graphs with negative weights or do you always switch to Bellman-Ford for that?

[Om Shree]

Great question — and thank you! 🙌

For graphs with negative weights, I usually switch to Bellman-Ford, since Dijkstra assumes all edge weights are non-negative. That said, if the graph has only a few negative edges and no negative cycles, some folks do experiment with hybrid strategies, but they're tricky and rarely more efficient than Bellman-Ford or even Johnson’s algorithm (for all-pairs shortest paths).

Glad you enjoyed the breakdown, always up for algorithm talk! ⚙️📚