Dijkstra's Algorithm Simulator

Dijkstra's Algorithm Simulator

Dijkstra's algorithm finds shortest paths from a single source vertex in a graph whose edge weights are nonnegative. This simulator uses an undirected weighted graph, tentative distances, predecessors, and a min-priority queue.

How to use it

• Add or remove vertices (Remove Vertex deletes the vertex selected as Endpoint 1); pick two endpoints and a weight (0–99), then use Add / Update or Remove Edge. Drag vertices to tidy up the drawing.
• Pick a source and press Run: every settled vertex and every relaxation is shown step by step, and the priority queue and the distance / predecessor table update after each step.
• To highlight the shortest path found by the last run, pick a target and press Path to Target.
• Load Example loads the sample graph and Random a random one; Clear empties the graph and Cancel stops a running animation.

Dijkstra ideas

• Greedy settling: among the vertices not yet settled, the one with the smallest tentative distance is settled next. Because no weight is negative, that distance can no longer improve.
• Relaxation: for an edge (u, v) of weight w, if dist[u] + w < dist[v], set dist[v] = dist[u] + w and prev[v] = u.
• Path reconstruction: follow the predecessor links backward from the target to rebuild the shortest path.
• Unreachable vertices: a vertex outside the source's component keeps distance ∞, and there is no path to it.

When Dijkstra applies

With a binary heap the running time is O((n + m) log n), for n vertices and m edges.