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Is there an easy algorithm to a) count the number of equivalent shortest paths on a manhattan grid b) enumerate them systematically? I wrote a dumb random algo and I could run it for a long time to count unique paths but I imagine there's a closed-form solution?
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I'm actually interested in a second-order problem: count the fraction of paths that go through a particular segment. If you walked to work on a manhattan grid everyday, making random choices, how long before you walked a specific block? A specific sequence of blocks?
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heh looks like I'm empircally rediscovering that
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manhattan grid possible world paths are really pretty if you add a bit of jitter to the path rendering interesting how if you make random choices (weighted by bounding box side lengths) most paths sorta go through the middle
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