hadlock | stacking window manager

Well DFS isn't a great idea here because you're going to constantly revisit the same sub-paths, and also because you're going to have to explore ALL possible paths to find what's the shortest. Generally speaking when you have a recursive problem with duplication of work going on, you should think about dynamic programming. In this specific case though, you can use DFS, which is in fact pretty similar to what you would do with a standard DP solution for this problem.

Now some notes about your implementation:

• avoid mutation in general, and especially in functional algorithms. It's a bit weird to have a recursive function with side-effects rather than a return value, although it arguably helps reducing the size of the stack.
• I find it quite hard to calculate the complexity. It's basically equal to the number of valid paths of any length, so that's pretty massive in particular when there are few obstacles because there are many paths of length roughly equal to n*m.
• I can't find a problem with your logic itself. Are you sure it didn't just time out in the tests that failed?