{ "data": { "question": { "questionId": "880", "questionFrontendId": "850", "categoryTitle": "Algorithms", "boundTopicId": 1842, "title": "Rectangle Area II", "titleSlug": "rectangle-area-ii", "content": "

You are given a 2D array of axis-aligned rectangles. Each rectangle[i] = [xi1, yi1, xi2, yi2] denotes the ith rectangle where (xi1, yi1) are the coordinates of the bottom-left corner, and (xi2, yi2) are the coordinates of the top-right corner.

\n\n

Calculate the total area covered by all rectangles in the plane. Any area covered by two or more rectangles should only be counted once.

\n\n

Return the total area. Since the answer may be too large, return it modulo 109 + 7.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: rectangles = [[0,0,2,2],[1,0,2,3],[1,0,3,1]]\nOutput: 6\nExplanation: A total area of 6 is covered by all three rectangales, as illustrated in the picture.\nFrom (1,1) to (2,2), the green and red rectangles overlap.\nFrom (1,0) to (2,3), all three rectangles overlap.\n
\n\n

Example 2:

\n\n
\nInput: rectangles = [[0,0,1000000000,1000000000]]\nOutput: 49\nExplanation: The answer is 1018 modulo (109 + 7), which is 49.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "矩形面积 II", "translatedContent": "

我们给出了一个（轴对齐的）二维矩形列表 rectangles 。 对于 rectangle[i] = [x1, y1, x2, y2]，其中（x1，y1）是矩形 i 左下角的坐标， (xi1, yi1) 是该矩形 左下角 的坐标， (xi2, yi2) 是该矩形 右上角 的坐标。

\n\n

计算平面中所有 rectangles 所覆盖的 总面积 。任何被两个或多个矩形覆盖的区域应只计算 一次 。

\n\n

返回 总面积 。因为答案可能太大，返回 109 + 7 的 模 。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：rectangles = [[0,0,2,2],[1,0,2,3],[1,0,3,1]]\n输出：6\n解释：如图所示，三个矩形覆盖了总面积为6的区域。\n从(1,1)到(2,2)，绿色矩形和红色矩形重叠。\n从(1,0)到(2,3)，三个矩形都重叠。\n
\n\n

示例 2：

\n\n
\n输入：rectangles = [[0,0,1000000000,1000000000]]\n输出：49\n解释：答案是 1018 对 (109 + 7) 取模的结果， 即 49 。\n
\n\n

 

\n\n

提示：

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