Dijkstra's Algorithm is a shortest-path algorithm published by Dutch computer scientist Edsger W. Dijkstra in 1956. It finds the shortest distance from one starting point to every other point in a weighted graph. Think of it as a wave that spreads outward, but unlike BFS, it accounts for passages that cost different amounts to traverse.
Game developers use Dijkstra to create "distance fields" ā a map showing how far every cell is from the exit. This data powers heat-map visualizations, difficulty scoring, and AI navigation. Our maze solver uses Dijkstra internally to compute optimal distances for complexity analysis.
Google Maps, Waze, and every GPS system use variants of Dijkstra. Road networks are weighted graphs ā highways are fast (low cost), side streets are slow (high cost). Dijkstra finds the cheapest route by actual travel time, not just shortest distance. It processes over 1 billion routing queries daily.
| Time Complexity | O(VĀ²) with array, O((V+E) log V) with binary heap |
| Space Complexity | O(V) ā distances and priority queue |
| Finds Shortest Path? | ā Yes (non-negative weights only) |
| Complete? | ā Yes |
| Handles Weights? | ā Yes (non-negative) |
| Data Structure | Priority queue (min-heap) |
| Best For | All-pairs shortest paths, distance maps, weighted graphs |
See how Dijkstra's explores every possible route to find the optimal one. Compare its thorough exploration against A*'s heuristic-guided approach.
Use Dijkstra when you need shortest distances to all cells (distance fields, heat maps), when there's no single target, or when a reliable heuristic is hard to define. A* is better for point-to-point pathfinding.
Almost. BFS uses a FIFO queue and treats all edges as equal cost. Dijkstra uses a priority queue and handles weighted edges. In an unweighted maze, Dijkstra behaves identically to BFS ā BFS is a special case.
No. Negative weights can invalidate already-visited nodes, breaking the algorithm's core assumption. For graphs with negative edges (rare in maze games), use the Bellman-Ford algorithm.