Find local minimum in n x n matrix in O(n) time

Question

So, this is not my home work question, but it is taken from an ungraded homework of the coursera course on algorithms and data structures (which is now complete).

Y

Answer 1

I think this is actually really easy.

Turn the problem into 3-D one to see why the algorithm works. Put the matrix on a table. Pretend there are pillars extending out of each cell and that the height of the pillar is directly proportional to its value. Put a ball on any pillar. Have the ball always fall onto the adjacent pillar that is the lowest altitude until it is at a local minimum.