leetcode-problemset/leetcode-cn/originData/rectangle-area-ii.json

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            "title": "Rectangle Area II",
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            "content": "<p>You are given a 2D array of axis-aligned <code>rectangles</code>. Each <code>rectangle[i] = [x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub>]</code> denotes the <code>i<sup>th</sup></code> rectangle where <code>(x<sub>i1</sub>, y<sub>i1</sub>)</code> are the coordinates of the <strong>bottom-left corner</strong>, and <code>(x<sub>i2</sub>, y<sub>i2</sub>)</code> are the coordinates of the <strong>top-right corner</strong>.</p>\n\n<p>Calculate the <strong>total area</strong> covered by all <code>rectangles</code> in the plane. Any area covered by two or more rectangles should only be counted <strong>once</strong>.</p>\n\n<p>Return <em>the <strong>total area</strong></em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/06/rectangle_area_ii_pic.png\" style=\"width: 600px; height: 450px;\" />\n<pre>\n<strong>Input:</strong> rectangles = [[0,0,2,2],[1,0,2,3],[1,0,3,1]]\n<strong>Output:</strong> 6\n<strong>Explanation: </strong>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</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> rectangles = [[0,0,1000000000,1000000000]]\n<strong>Output:</strong> 49\n<strong>Explanation: </strong>The answer is 10<sup>18</sup> modulo (10<sup>9</sup> + 7), which is 49.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= rectangles.length &lt;= 200</code></li>\n\t<li><code>rectanges[i].length == 4</code></li>\n\t<li><code>0 &lt;= x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub> &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "矩形面积 II",
            "translatedContent": "<p>我们给出了一个（轴对齐的）二维矩形列表&nbsp;<code>rectangles</code>&nbsp;。 对于&nbsp;<code>rectangle[i] = [x1, y1, x2, y2]</code>，其中（x1，y1）是矩形&nbsp;<code>i</code>&nbsp;左下角的坐标，<meta charset=\"UTF-8\" />&nbsp;<code>(x<sub>i1</sub>, y<sub>i1</sub>)</code>&nbsp;是该矩形 <strong>左下角</strong> 的坐标，<meta charset=\"UTF-8\" />&nbsp;<code>(x<sub>i2</sub>, y<sub>i2</sub>)</code>&nbsp;是该矩形&nbsp;<strong>右上角</strong> 的坐标。</p>\n\n<p>计算平面中所有&nbsp;<code>rectangles</code>&nbsp;所覆盖的 <strong>总面积 </strong>。任何被两个或多个矩形覆盖的区域应只计算 <strong>一次</strong> 。</p>\n\n<p>返回<em> <strong>总面积</strong> </em>。因为答案可能太大，返回<meta charset=\"UTF-8\" />&nbsp;<code>10<sup>9</sup>&nbsp;+ 7</code> 的&nbsp;<strong>模</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/06/rectangle_area_ii_pic.png\" style=\"height: 300px; width: 400px;\" /></p>\n\n<pre>\n<strong>输入：</strong>rectangles = [[0,0,2,2],[1,0,2,3],[1,0,3,1]]\n<strong>输出：</strong>6\n<strong>解释：</strong>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</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>rectangles = [[0,0,1000000000,1000000000]]\n<strong>输出：</strong>49\n<strong>解释：</strong>答案是 10<sup>18</sup> 对 (10<sup>9</sup> + 7) 取模的结果， 即 49 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= rectangles.length &lt;= 200</code></li>\n\t<li><code>rectanges[i].length = 4</code><meta charset=\"UTF-8\" /></li>\n\t<li><code>0 &lt;= x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub>&nbsp;&lt;= 10<sup>9</sup></code></li>\n\t<li>矩形叠加覆盖后的总面积不会超越&nbsp;<code>2^63 - 1</code>&nbsp;，这意味着可以用一个&nbsp;64 位有符号整数来保存面积结果。</li>\n</ul>\n",
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