problem0850

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850. Rectangle Area II

题目

We are given a list of (axis-aligned)rectangles. Eachrectangle[i] = [x1, y1, x2, y2], where (x1, y1) are the coordinates of the bottom-left corner, and (x2, y2) are the coordinates of the top-right corner of the ith rectangle.

Find the total area covered by all rectangles in the plane. Since the answermay be too large, return it modulo 10^9 + 7.

Example 1:

Input: [[0,0,2,2],[1,0,2,3],[1,0,3,1]]
Output: 6
Explanation: As illustrated in the picture.

Example 2:

Input: [[0,0,1000000000,1000000000]]
Output: 49
Explanation: The answer is 10^18 modulo (10^9 + 7), which is (10^9)^2 = (-7)^2 = 49.

Note:

1. 1 <= rectangles.length <= 200
2. rectanges[i].length = 4
3. 0 <= rectangles[i][j] <= 10^9
4. The total area covered by all rectangles will never exceed2^63 - 1and thus will fit in a 64-bit signed integer.

解题思路

见程序注释