3 ms·
The shape and size of the forest is known. If you know that the forest is long and thin, you're better off walking in a curved path so that you're guaranteed t
by cperciva 8y ago
The shape and size of the forest is known. If you know that the forest is long and thin, you're better off walking in a curved path so that you're guaranteed to hit the "side" of the forest rather than walking straight and potentially continuing until you hit the "end".
- paulpauper 8y agoIf you know the dimensions, you know that if you walked more then the width , then you have to make a left or right turn.
- cuboidGoat 8y agoWhat if the shape is the set of all finite curves arranged as a star and given equal length? If you accidentally start in the middle, there will always be a worst case scenario route determined for any arbitrary curve and no way to pick between curves to find the best one.
- rocqua 8y agoIsn't that set a circle?
- HelloNurse 8y agoYes, and the solution for a circle of radius r is easy(going straight, you don't need to walk more than 2r; if you turn anywhere, you risk walking more than that). Bellman put exact knowledge of the shape of the forest in the problem statement to make it nontrivial and therefore more difficult.