Answer by Especially Lime for Longest path through a rectangular board
In graph theory terms, what you are asking for is the longest path formed by an induced subgraph of the $h\times w$ grid graph.This problem (longest induced path) has been well studied for a slightly...
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The original problem: You have a $H\times W$ board. Your task is to color some tiles white and some black. There must be a unique beginning and end of the white trail and only one way to get from one...
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