Isn't this NP-complete? The "solution" here would be the steps to take in the path which can be found by brute-force

Wikipedia:

> 2. When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution.

> 3. The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.