...algorithm 

According to Greek legend, Ariadne, the daughter of Minos, King of Crete, helped Theseus kill the Minotaur, a monster living in the Labyrinth, a huge maze built by Daedalus. The main difficulty faced by Theseus was to find his way through the Labyrinth. Ariadne brilliantly solved the problem by giving him a thread (or a clew) that he could unwind in order to find his path back.

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...point).

Another possible choice would be to give the value to the distance when a collision occurs. However, this is less informative than the chosen function because the first part of a colliding path could be a good start toward the goal and should not be discarded. Note that the cost function does not include any optimality criteria such as the length of the trajectory or the amount of energy used.

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