Watch A*, Dijkstra, BFS, and Greedy Best-First search the same grid — one cell per step. Paint walls, sprinkle in weighted terrain (mud costs more), pick a heuristic (Manhattan / Chebyshev / Euclidean / Octile), then race all four to see which explores fewer cells and which finds a truly optimal path.
Click Race all four above to run every algorithm on the current grid without animation and compare expansions vs path cost.
A* is optimal iff the heuristic is admissible (never over-estimates true remaining cost). Manhattan is admissible for 4-way; Octile for 8-way; Euclidean is always admissible. Greedy skips g-cost entirely — fast but can return a much longer path.
BFS — expands cells in FIFO order, so the first time it reaches the goal is guaranteed to be a fewest-hops path (ignores terrain weights).
Dijkstra — expands the unvisited cell with lowest g (cost from start). Optimal for any non-negative weights. Same as A* with h = 0.
Greedy Best-First — expands the cell with lowest h (heuristic to goal). Fast, but ignores accumulated cost, so its path can be arbitrarily bad.
A* — expands the cell with lowest f = g + h. If h is admissible, the returned path is optimal; if additionally consistent, no cell needs to be re-opened.