Draw the map. Watch it rethink.

Paint walls, marsh and open ground with the mouse; drag the start and the goal anywhere. The search re-solves on every single edit, so you can wall off a route and watch the path snap to a new one in the same gesture. Nothing here is precomputed — put a wall across the corridor it is using and see what it costs.

Drag on the map to paint with the selected tool · pick Start or Goal and click to move them · every edit re-runs the chosen algorithm · try walling off the path while Instant is on.

Algorithm

Movement

Cells per frame 8

Brush wall

Brush size 2

Heuristic

Weight w 1.00

Generate

Overlay

The map A* · 8-way · octile · w = 1.00

settled, oldest → newest backward front frontier route returned true cheapest route — drawn only when the algorithm missed it

Cells settled

Frontier now / peak

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Map explored

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Route cost

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Cheapest possible

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Verdict

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Search trace frontier size, and the key of each cell as it is settled

frontier size key of the cell being settled — f for A*, g for Dijkstra, h for greedy Dijkstra and A* settle in non-decreasing key order — that monotonicity is the whole optimality proof. Switch to greedy or DFS and watch the amber line saw up and down: nothing is ever finished, so nothing can be guaranteed.