34 lines
949 B
Markdown
34 lines
949 B
Markdown
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# Marathon open problem
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We are given a graph `G` and a starting node `S` and must find a path of marathon length (42.195 km)
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with an end node close to `S`.
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## Constraints
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Constraints for an acceptable path :
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- Path is valid
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- Path is accessible by foot
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- Path nodes are not visited twice
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- Path length is 42 195 +/- 40 meters
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- Starting node is less than 200 m away from end node.
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Constraints for an optimal path :
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- Path is acceptable
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- Path length is as close as possible to 42 195 meters
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AND/OR start and end node are as close as possible
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Note : the [Toulouse 2024 marathon][toulouse-2024] start and end points are roughly 200 meters apart.
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The algorithm should fail if no acceptable path can be found.
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[toulouse-2024]: https://toulouserunexperience.fr/marathon/
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## Algo ideas
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Use A* with an heuristic taking into account :
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- Path Length
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- and distance to end node.
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Score : `42 195 + | 42 195 - pathLength | + distance end to node`.
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