Hey! Does anybody have a solution in n log n for this? Given n rectangles, determinate a point which is included by a maximum number of rectangles (including the boundaries).

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Hey! Does anybody have a solution in n log n for this? Given n rectangles, determinate a point which is included by a maximum number of rectangles (including the boundaries).

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It can be solved with sweep line algo and segment tree in $$$O(N \lg N)$$$.

I think that when sweeplining, for a certain x, you should perform all addition events for that x, then check for a new max, then all subtraction events for that x. Otherwise you might miss the correct answer if you perform a subtraction, then a query, then an addition.

Yes, I just give a rough idea. Those parts should be taken care when implementing.

It’s a very nice sketch. I just wanted to add the detail since I had also been thinking of the same solution for a little bit. I hope it helps the asker.

Yes, it helped me. Is this algorithm similar to that one: "find the number of intersections of segments, all segments parallel either Ox either Oy"? I think they are 90% the same, am I wrong?

You can think of each segment of length L as an 1xL or an Lx1 rectangle, so the rectangle problem is a generalization of the line segment problem.