Dijkstra's Algorithm: A History and How It Works

Amsterdam, 1956. Edsger W. Dijkstra is out shopping with his girlfriend. They get tired, find a café terrace, order coffee. By the time the cups are empty, Dijkstra has worked out the logic of what will become one of the most widely deployed algorithms in computing history—powering everything from GPS navigation to network routing to the social graph behind platforms serving billions of users.

Twenty minutes. No pencil. No paper.

That origin story anchors a recent freeCodeCamp video developed by educator Estefania Garcia (@codingwithestefania), which walks through Dijkstra's algorithm from its historical roots through a full Python implementation. It's a well-constructed piece of CS education, and the story it tells—about how the algorithm came to be and what makes it work—is worth sitting with, even if you already know how a min-heap operates.

The Problem Dijkstra Was Actually Trying to Solve

Context matters here. In 1956, Dijkstra was a programmer at the Mathematical Center in Amsterdam. The center was preparing to debut the ARMAC computer—a pioneering Dutch machine—and Dijkstra wanted a demonstration problem. His criteria were specific: challenging enough to show what the computer could do, general enough that non-specialists could follow it.

He landed on shortest-path routing. The original framing was concrete—how do you get from Rotterdam to Groningen most efficiently?—but Dijkstra immediately pushed toward generalization. Why solve one instance when you can solve all of them? That pivot, from a specific city-pair to an abstract graph problem, is the real intellectual move. The algorithm was formally published three years later, in 1959, under the modest title A Note on Two Problems in Connection with Graphs.

What's striking about the origin story isn't just the speed. It's the working method. Dijkstra later wrote that he designed the algorithm entirely in his head, and that this constraint was a feature, not a bug. As the video relays: "one of the advantages of designing without pencil and paper is that you're almost forced to avoid all avoidable complexities."

There's something worth sitting with there. Dijkstra was an advocate for intellectual simplicity in programming—programming as a rigorous, almost philosophical discipline. Whether designing mentally actually forces better abstraction, or whether that's just a good story told in retrospect, is genuinely hard to disentangle. But the algorithm itself is elegant enough that the claim doesn't feel implausible.

What the Algorithm Actually Does

The video's pedagogical approach is solid: start with vocabulary, build up through a worked example, then show the code. Let's track the same path.

A graph is a data structure made of nodes (the things) and edges (the connections between things). In Dijkstra's original framing, nodes are cities and edges are roads. But the abstraction travels: nodes can be routers in a network, users in a social platform, warehouses in a supply chain, tiles in a video game map. The edges carry weights—numerical values representing cost, distance, time, or whatever quantity you're optimizing against. A graph with weighted edges is, unsurprisingly, a weighted graph.

Dijkstra's algorithm operates on these. Its goal: find the path from a source node to every other node in the graph with the lowest total weight.

Here's the mechanical heart of it. The algorithm starts by setting the distance from the source to itself as zero, and the distance to every other node as infinity (a placeholder for "we don't know yet"). It then visits nodes one at a time, always choosing the unvisited node with the currently lowest recorded distance from the source. For each visited node, it checks all unvisited neighbors: if traveling through the current node to a neighbor would be cheaper than the best-known path to that neighbor, it updates the record.

Walk through the four-node example from the video: starting at node A, you reach node B (distance: 2) and node C (distance: 6). Next you visit B—the closest unvisited node—and discover you can reach D via A→B for a total cost of 7. Then you visit C (distance 6, still the next-cheapest), check D via A→C, and find that route costs 14—worse than 7. So you keep 7. D is last; nothing updates. Final answer: A→B→D at cost 7.

The algorithm classifies as greedy—it always takes the locally optimal step (visit the closest unvisited node) without backtracking. The video puts it plainly: "it chooses the best possible option in each step... the path that looks best whenever it has to make a decision." Greedy algorithms don't always produce globally optimal results, but for this specific problem—non-negative edge weights, single-source shortest paths—Dijkstra's greedy approach is provably correct. That's the elegant part: the local optimum and the global optimum align.

The Code: Where Theory Meets Implementation

The freeCodeCamp video walks through a Python implementation that translates the conceptual steps into working code. A few design decisions worth noting.

The graph is represented as an adjacency list using nested Python dictionaries. The outer dictionary keys are nodes; the values are dictionaries mapping each neighbor to the edge weight. Clean, readable, scales reasonably well for sparse graphs.

The key data structure in the implementation is a priority queue (min-heap via Python's heapq module). This is where the practical computer science lives. Without it, you'd need to scan all unvisited nodes to find the minimum-distance one at each step—O(n) per iteration, which compounds painfully on large graphs. The min-heap keeps the minimum-distance unvisited node at the top, making retrieval O(log n). For dense graphs or performance-critical applications, more sophisticated heap implementations (like Fibonacci heaps) can push this further, but for learning purposes, heapq is the right choice.

The implementation tracks two dictionaries: distances (the best-known cost to each node) and previous_nodes (which node precedes each node on the optimal path). Once the main loop completes, a separate backtracking function walks the previous_nodes chain from destination to source and reverses it—giving you the actual path sequence, not just the cost.

Path reconstruction is often glossed over in algorithm explainers, so it's worth the attention the video gives it. Knowing the shortest distance to a destination is useful. Knowing which route achieves that distance is what actually gets you there.

The Legacy Question

Dijkstra went on to receive the Turing Award in 1972—computing's equivalent of the Nobel—and the field honors him with the annual Edsger W. Dijkstra Prize in Distributed Computing. His influence on how practitioners think about software correctness and structured programming runs well beyond any single algorithm.

But the shortest-path algorithm is probably his most democratized contribution. It's embedded in infrastructure most people use daily without knowing it exists. When your maps app reroutes you around traffic, when a packet finds its way across a network, when a game's AI navigates around obstacles—Dijkstra's logic is likely somewhere in the chain.

The freeCodeCamp video frames this with appropriate wonder, and the wonder is earned. But it's also worth noting the things the algorithm doesn't do. Dijkstra's algorithm requires non-negative edge weights; negative weights break the greedy logic (Bellman-Ford handles those). It finds shortest paths from a single source to all other nodes; all-pairs shortest paths need a different approach (Floyd-Warshall). And "shortest" depends entirely on what you're weighting—the algorithm optimizes for whatever cost metric you assign, which means the humans setting up the graph still have to make the hard choices about what "best" means.

An algorithm this foundational tends to get treated as a solved, closed artifact of history. The video is right that Dijkstra's core insight—abstract the physical world into a weighted graph, greedily minimize—has proven remarkably durable. But every time a system deploys it, someone decided what the nodes are, what the edges connect, and what the weights represent. Those decisions are where the real complexity lives, and they don't show up in the pseudocode.

The 20 minutes Dijkstra spent at that café table produced something that genuinely works. What it works on is always a choice somebody makes.

— Dev Kapoor, Open Source & Developer Communities Correspondent, Buzzrag