Find the Largest Area of Square Inside Two Rectangles
There exist n rectangles in a 2D plane with edges parallel to the x and y axis. You are given two 2D integer arrays bottomLeft and topRight where bottomLeft[i] = [a_i, b_i] and topRight[i] = [c_i, d_i] represent the bottom-left and top-right coordinates of the i^th rectangle, respectively.
You need to find the maximum area of a square that can fit inside the intersecting region of at least two rectangles. Return 0 if such a square does not exist.
Example 1
Input
bottomLeft = [[1,1],[2,2],[3,1]], topRight = [[3,3],[4,4],[6,6]]Output
1A square with side length 1 can fit inside either the intersecting region of rectangles 0 and 1 or the intersecting region of rectangles 1 and 2, and no square with a greater side length can fit inside any intersecting region of two rectangles.
Example 2
Input
bottomLeft = [[1,1],[1,3],[1,5]], topRight = [[5,5],[5,7],[5,9]]Output
4A square with side length 2 can fit inside either the intersecting region of rectangles 0 and 1 or the intersecting region of rectangles 1 and 2, giving maximum area 2 * 2 = 4.
Constraints
- n == bottomLeft.length == topRight.length
- 2 <= n <= 10^3
- bottomLeft[i].length == topRight[i].length == 2
- 1 <= bottomLeft[i][0], bottomLeft[i][1] <= 10^7
- 1 <= topRight[i][0], topRight[i][1] <= 10^7
- bottomLeft[i][0] < topRight[i][0]
- bottomLeft[i][1] < topRight[i][1]