Learning Experience

Dijkstra's Algorithm

Find the shortest distance from one start node to every other node in a weighted graph, by always finalizing the nearest unvisited node next and relaxing its edges.

Computer ScienceAdvanced9 min readalgorithmsgraphsshortest-path

Before you start

Prerequisite

Graph Traversal (BFS & DFS)

Two ways to visit every reachable node in a graph — breadth-first spreads outward level by level, depth-first commits to one path and backtracks.

Prerequisite

Heaps & Priority Queues

A complete binary tree, stored flat in an array, that keeps the smallest (or largest) element one O(log n) extraction away — the standard way to build a priority queue.

Your learning journey

Every module Axiom offers for dijkstra's algorithm — work through them in order, or jump to what you need.

0 of 5 complete0%

TopicLiveUp next

Explains single-source shortest path, why BFS isn't enough for weighted graphs, relaxation, and complexity.

VisualizerLive

Animates extract-min and edge relaxation on a live weighted graph, with a real-time distance row.

QuizLive

Checks that the 'extraction is final' guarantee and its dependence on non-negative weights is understood.

AI TutorLive

Answers follow-up questions and adapts the explanation to the learner's level.

Cheat SheetLive

One-glance recall of the extract-min/relax loop, complexity, and the non-negative-weights requirement.

Ask the AI tutor about Dijkstra's Algorithm

Answers follow-up questions and adapts the explanation to the learner's level.

What to learn next

From Axiom's Knowledge Graph.

A* Search

Explore the full Knowledge Graph →

Related concepts

Greedy Algorithms

Make the locally-best choice at every step, never reconsider it, and — for the specific class of problems where this provably reaches the global optimum — end up with the right answer in a single pass.