Given a list rectangles [R1, R2, R3] defined by their lower left and upper right [(x1, y1), (x2, y2)] coordinates, and a value k.
Is there an optimal way to find area where k rectangles overlap?
For example:
R1: [(1, 1), (5, 5)]
R2: [(4, 4), (7, 6)]
R3: [(3, 3), (8, 7)]
rectangles = [R1, R2, R3]
k = 2
The area which is overlapped by two rectangles is 8.
If the coordinates are small enough (say, |x|, |y| <= 5000) you can use lazy update in RSQ 2D table. So, if you have N rectangles, X = width of board, Y = height of board, the complexity is O(1) for each lazy update, and the actual updating takes O(X*Y) so total complexity is O(N+X*Y) and then you count how many cells have value = K. If you need solution for bigger X and Y you should try with sweep line, but don't really know how.