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### bersub's blog

By bersub, history, 21 month(s) ago, ,

Hi!

There's a problem I'd appreciate some help with (maybe hints or a sketch of solution...)

You have an n \times n grid, with n \le 350. Every element of the grid is either '.' or '#'.

The problem asks to count the number of rectangles made of '#', where sides are bigger than or equal to 3.

So the minimal rectangle would be

###
#.#
###


IMPORTANT: There are 100 test cases, so the solution should be around O(N^2 lg N)

I tried to count the complement: As the total number of rectangles in a grid is easy to compute, I tried to focus on every dot and count the number of rectangles it interrupted, but I haven't figured out exactly how to avoid counting things multiple times...