Algorithm - Find the the number of rectangles covering a given rectangle area?

It is straightforward to create, in O(n^4) space and O(n^5) time, a data structure that provides O(1) lookups. If M exceeds O(n^2) it might be worthwhile to do so. It also is straightforward to create, in O(n^2) space and O(n^3) time, a data structure that provides lookups in O(n) time.

If M is O(n^2), that may be a better tradeoff; ie, take O(n^3) precomputation time and O(n^3) time for O(n^2) lookups at O(n) each.

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