BE_Graphes/Marathon.md

Marathon open problem

We are given a graph G and a starting node S and must find a path of marathon length (42.195 km) with an end node close to S.

Constraints

Constraints for an acceptable path :

• Path is valid
• Path is accessible by foot
• Path nodes are not visited twice
• Path length is 42 195 +/- 40 meters
• Starting node is less than 200 m away from end node.

Constraints for an optimal path :

• Path is acceptable
• Path length is as close as possible to 42 195 meters AND/OR start and end node are as close as possible

Note : the Toulouse 2024 marathon start and end points are roughly 200 meters apart.

The algorithm should fail if no acceptable path can be found.

Algo ideas

Use A* with an heuristic taking into account :

• Path Length
• and distance to end node.

Score : 42 195 + | 42 195 - pathLength | + distance end to node.