🗺️ Dijkstra — Shortest Paths

💡 Green = settled · blue = in the frontier · amber = relaxing. Click a node to set the source.

Distances from 0 (0/7 settled)

0:∞

1:∞

2:∞

3:∞

4:∞

5:∞

6:∞

Extract-min cost (V=7, E=11)

scan arrayO(V²)

binary-heap PQO((V+E) log V)

A heap is decisive on large sparse graphs; both give the same shortest paths.

Dijkstra

1dist[src] = 0, rest = ∞
2while unsettled nodes remain:
3  u = unsettled node with min dist   // priority queue
4  for (v, w) in edges(u): if dist[u]+w < dist[v]:
5    dist[v] = dist[u]+w; prev[v] = u   // relax

Speed: 50%

Dijkstra's Algorithm Visualizer: Shortest Paths on a Weighted Graph

This Dijkstra simulator runs single-source shortest paths on a weighted node-link graph, so the greedy heart of the algorithm is visible. Each step extracts the unsettled node with the smallest tentative distance (the priority-queue frontier), settles it in green, then relaxes its edges — an edge lights amber, and if dist[u] + weight beats the neighbour's current distance the neighbour flashes green and its label drops. Distance labels sit above every node, a live table tracks all distances and how many are settled, and the final shortest-path tree is highlighted. A cost card contrasts scanning all nodes (O(V²)) with a binary-heap priority queue (O((V+E) log V)). The signature interaction: Predict mode pauses before each extract-min and asks you to click the node you think is settled next — the one with the smallest distance.

What you can do in this simulation

Watch Dijkstra settle the closest unsettled node, relax its edges, and build the shortest-path tree in green
Distance labels update live above each node; a table shows all distances and the settled count
Predict mode: click the node you think is settled next (smallest distance) before each step, with a score
Click any node to make it the source and re-run; frontier nodes are blue, settled green, relaxing amber
A cost card compares array-scan O(V²) with a binary-heap priority queue O((V+E) log V)

Concepts covered

dijkstra's algorithm · shortest path · weighted graph · priority queue · edge relaxation · greedy algorithm · O((V+E) log V)

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1dist[src] = 0, rest = ∞

2while unsettled nodes remain:

3 u = unsettled node with min dist // priority queue

4 for (v, w) in edges(u): if dist[u]+w < dist[v]:

5 dist[v] = dist[u]+w; prev[v] = u // relax

Dijkstra's Algorithm Visualizer: Shortest Paths on a Weighted Graph

What you can do in this simulation

Watch Dijkstra settle the closest unsettled node, relax its edges, and build the shortest-path tree in green

Distance labels update live above each node; a table shows all distances and the settled count

Predict mode: click the node you think is settled next (smallest distance) before each step, with a score

Click any node to make it the source and re-run; frontier nodes are blue, settled green, relaxing amber

A cost card compares array-scan O(V²) with a binary-heap priority queue O((V+E) log V)