Shortest Path Algorithm Visualizer

Dijkstra's Algorithm — Greedy Shortest Path

Picks the unvisited vertex with the minimum known distance at each step. Works only with non-negative edge weights.

Graph (click a node to set as source)

Source

Current

Settled

Relaxed

Unvisited

Press ▶ Run or Step to begin...

Controls

Source:

Speed: 5

Ready

Time Complexity:
O(V²) with array | O((V+E) log V) with Min-Heap PQ

Distance Table

Node	Distance	Previous

Bellman-Ford Algorithm — Dynamic Programming

Relaxes ALL edges V−1 times. Handles negative weights and detects negative cycles. Slower than Dijkstra but more general.

Directed graph with negative edges

Source

Being Relaxed

Finalized

Negative Cycle

⚠️ Negative Weight Cycle Detected! Distances cannot be finalized — the cycle reduces cost infinitely.

Press ▶ Run or Step to begin...

Controls

Source:

Speed: 5

Iteration: 0 / 0

Ready

Time Complexity: O(V × E)
Space: O(V)

Distance Table

Node	Distance	Previous

Floyd-Warshall Algorithm — All-Pairs Shortest Path

Computes shortest paths between ALL pairs of vertices using dynamic programming. Considers each vertex as a potential intermediate node.

Directed weighted graph

Intermediate (k)

Source (i)

Target (j)

Finalized

Press ▶ Run or Step to begin...

Controls

Speed: 5

Intermediate node (k): —

Ready

Time Complexity: O(V³)
Space: O(V²)

Distance Matrix

A* Search Algorithm — Heuristic Shortest Path

Combines actual cost g(n) with a heuristic estimate h(n) to efficiently find the shortest path. Uses f(n) = g(n) + h(n) to prioritize exploration.

Grid (click = wall, shift+click = start, ctrl/cmd+click = end)

Start

End

Open Set

Closed Set

Path

Wall

Press ▶ Run or Step to begin...

Controls

Heuristic:

Diagonal:

Speed: 5

Ready

Time Complexity: O(E log V) — depends on heuristic
Space: O(V)

Statistics

Nodes Explored	0
Open Set Size	0
Path Length	—
Path Cost	—