Watch A*, Dijkstra, and BFS find shortest paths on grids. Draw walls, add weights, and compare algorithm exploration patterns.
This tool runs three search algorithms (breadth-first search, Dijkstra, and A*) on a grid you configure by dragging a start cell, an end cell, walls, and optionally weighted cells, then animates each one cell by cell so you can see the order nodes are visited before the final path is drawn. The part people misread is the word 'shortest': BFS counts steps only, so on a weighted grid it can highlight a path that is short in cell count but not the cheapest one, while Dijkstra and A* optimize total cost and can legitimately draw a longer-looking route.
You place a single start and end cell on a rectangular grid, then click or drag to toggle cells into walls (impassable) or weighted cells (passable but costlier to enter). Each algorithm run treats walls as removed nodes and weights as added traversal cost, then steps through the search so you can watch the visited set and frontier grow before the final path is traced back from the end cell.
BFS expands nodes in ring order by number of steps and has no concept of cell cost, so it ignores weights when choosing a path. Dijkstra expands by lowest cumulative cost using a priority queue, correctly respecting weights. A* does the same but adds a distance-to-goal heuristic that biases expansion toward the end cell, typically visiting fewer cells than Dijkstra while still returning an optimal-cost path.
Only when every passable cell costs the same to enter and there is a single unique shortest route. As soon as you add weighted cells, BFS's fewest-cells path can differ from the lowest-cost path that Dijkstra and A* return, and with multiple equal-cost routes the algorithms can pick different ones depending on tie-breaking.
It explores fewer cells because its heuristic estimates distance to the goal and prioritizes promising directions, whereas Dijkstra expands uniformly outward by cost with no sense of where the goal is. A* still needs an admissible heuristic to guarantee an optimal path; it's a smarter search, not a fundamentally different guarantee.
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