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there is O(m*n) solution for problem 1.

Yeah, dynamic programming. It's a well known problem. I'm pretty sure you can just convert the matrix to 1s and 0s, and dump it into Matlab.

Is it DP? I think DP is O(N^3)? That will be a funny way(Matlab) to solve this...

Eh, why not just use a flood-fill type algorithm?

Wouldn't the constrained that output area should be for a rectangle cause a problem?