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Zonal Computing Olympiad 2015, 29 Nov 2014
We have a rectangular region that is 100000 units along the X-axis and 500 units along the Y -axis.
We assume that the origin (0, 0) is at the bottom-left corner of this region, so that the top-left corner is at (0, 500), the bottom-right at (100000, 0) and the top-right corner at (100000, 500). We are also given the coordinates of a set of N points inside this region. The points have only integer coordinates and do not appear along the X-axis or Y -axis.
We would like to draw a rectangle, with its base on the X-axis, of maximum area within the region such that it does not contain any of the N points in its interior. More specifically, the points may appear on the boundary but cannot be properly inside the rectangle.
For example, if there are 5 points: (1, 4), (2, 3), (3, 2), (5, 1) and (5, 2). Then the rectangle whose bottom-left and top-right corners are given by (0,0) and (2,3) is a possibility and its area is 6. Another possibility is the rectangle with bottom-left and top-right corners at (3,0) and (5,500) with area 1000. The rectangle with bottom-left at (2, 3) and top-right at (100000, 500) is not valid since its base does not lie on the X-axis. The largest rectangle that meets the requirements in this case is the one with its bottom-left corner at (5,0) and top-right at (100000,500) with area 49997500.
Your program should take a description of the N points and output the size of the maximum rectangle satisfying the above property that can be drawn within the 100000 × 500 region.
The first line contains a single integer N, giving the number of points marked in the region.
This is followed by N lines, each containing two integers separated by a space describing the coordinates of one point.
Output a single integer giving the area of the largest rectangle that may be drawn with its base on the X-axis and which does not contain any of the given N points in its interior.
In both subtasks, the X-coordinate of each of the N points is in the range 1 to 99999 inclusive, and the Y -coordinate of each of the N points is in the range 1 to 499 inclusive.
Subtask 1 (40 marks) : 1 ≤ N ≤ 5000.
Subtask 2 (60 marks) : 1 ≤ N ≤ 100000.
5 1 4 2 3 3 2 5 1 5 2
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6|
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