leetcode-problemset/leetcode-cn/originData/find-the-largest-area-of-square-inside-two-rectangles.json

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            "questionId": "3325",
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            "title": "Find the Largest Area of Square Inside Two Rectangles",
            "titleSlug": "find-the-largest-area-of-square-inside-two-rectangles",
            "content": "<p>There exist <code>n</code> rectangles in a 2D plane. You are given two <strong>0-indexed</strong> 2D integer arrays <code>bottomLeft</code> and <code>topRight</code>, both of size <code>n x 2</code>, where <code>bottomLeft[i]</code> and <code>topRight[i]</code> represent the <strong>bottom-left</strong> and <strong>top-right</strong> coordinates of the <code>i<sup>th</sup></code> rectangle respectively.</p>\n\n<p>You can select a region formed from the <strong>intersection</strong> of&nbsp;two of the given rectangles. You need to find the <strong>largest </strong>area of a <strong>square</strong> that can fit <strong>inside</strong> this region if you select the region optimally.</p>\n\n<p>Return <em>the <strong>largest </strong>possible area of a square, or </em><code>0</code><em> if there <strong>do not</strong> exist any intersecting regions between the rectangles</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/05/example12.png\" style=\"width: 443px; height: 364px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;\" />\n<pre>\n<strong>Input:</strong> bottomLeft = [[1,1],[2,2],[3,1]], topRight = [[3,3],[4,4],[6,6]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> A square with side length 1 can fit inside either the intersecting region of rectangle 0 and rectangle 1, or the intersecting region of rectangle 1 and rectangle 2. Hence the largest area is side * side which is 1 * 1 == 1.\nIt can be shown that a square with a greater side length can not fit inside any intersecting region.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/04/rectanglesexample2.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 445px; height: 365px;\" />\n<pre>\n<strong>Input:</strong> bottomLeft = [[1,1],[2,2],[1,2]], topRight = [[3,3],[4,4],[3,4]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> A square with side length 1 can fit inside either the intersecting region of rectangle 0 and rectangle 1, the intersecting region of rectangle 1 and rectangle 2, or the intersection region of all 3 rectangles. Hence the largest area is side * side which is 1 * 1 == 1.\nIt can be shown that a square with a greater side length can not fit inside any intersecting region.\nNote that the region can be formed by the intersection of more than 2 rectangles.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/04/rectanglesexample3.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 444px; height: 364px;\" />\n<pre>\n<strong>Input:</strong> bottomLeft = [[1,1],[3,3],[3,1]], topRight = [[2,2],[4,4],[4,2]]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> No pair of rectangles intersect, hence, we return 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == bottomLeft.length == topRight.length</code></li>\n\t<li><code>2 &lt;= n &lt;= 10<sup>3</sup></code></li>\n\t<li><code>bottomLeft[i].length == topRight[i].length == 2</code></li>\n\t<li><code>1 &lt;= bottomLeft[i][0], bottomLeft[i][1] &lt;= 10<sup>7</sup></code></li>\n\t<li><code>1 &lt;= topRight[i][0], topRight[i][1] &lt;= 10<sup>7</sup></code></li>\n\t<li><code>bottomLeft[i][0] &lt; topRight[i][0]</code></li>\n\t<li><code>bottomLeft[i][1] &lt; topRight[i][1]</code></li>\n</ul>\n",
            "translatedTitle": "求交集区域内的最大正方形面积",
            "translatedContent": "<p>在二维平面上存在 <code>n</code> 个矩形。给你两个下标从 <strong>0</strong> 开始的二维整数数组 <code>bottomLeft</code> 和 <code>topRight</code>，两个数组的大小都是 <code>n x 2</code> ，其中 <code>bottomLeft[i]</code> 和 <code>topRight[i]</code> 分别代表第 <code>i</code> 个矩形的<strong> 左下角 </strong>和 <strong>右上角 </strong>坐标。</p>\n\n<p>我们定义 <strong>向右 </strong>的方向为 x 轴正半轴（<strong>x 坐标增加</strong>），<strong>向左 </strong>的方向为 x 轴负半轴（<strong>x 坐标减少</strong>）。同样地，定义 <strong>向上 </strong>的方向为 y 轴正半轴（<strong>y 坐标增加</strong>）<strong>，向下 </strong>的方向为 y 轴负半轴（<strong>y 坐标减少</strong>）。</p>\n\n<p>你可以选择一个区域，该区域由两个矩形的 <strong>交集</strong>&nbsp;形成。你需要找出能够放入该区域 <strong>内 </strong>的<strong> 最大 </strong>正方形面积，并选择最优解。</p>\n\n<p>返回能够放入交集区域的正方形的 <strong>最大 </strong>可能面积，如果矩形之间不存在任何交集区域，则返回 <code>0</code>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/05/example12.png\" style=\"width: 443px; height: 364px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;\" />\n<pre>\n<strong>输入：</strong>bottomLeft = [[1,1],[2,2],[3,1]], topRight = [[3,3],[4,4],[6,6]]\n<strong>输出：</strong>1\n<strong>解释：</strong>边长为 1 的正方形可以放入矩形 0 和矩形 1 的交集区域，或矩形 1 和矩形 2 的交集区域。因此最大面积是边长 * 边长，即 1 * 1 = 1。\n可以证明，边长更大的正方形无法放入任何交集区域。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/04/rectanglesexample2.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 445px; height: 365px;\" />\n<pre>\n<strong>输入：</strong>bottomLeft = [[1,1],[2,2],[1,2]], topRight = [[3,3],[4,4],[3,4]]\n<strong>输出：</strong>1\n<strong>解释：</strong>边长为 1 的正方形可以放入矩形 0 和矩形 1，矩形 1 和矩形 2，或所有三个矩形的交集区域。因此最大面积是边长 * 边长，即 1 * 1 = 1。\n可以证明，边长更大的正方形无法放入任何交集区域。\n请注意，区域可以由多于两个矩形的交集构成。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/04/rectanglesexample3.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 444px; height: 364px;\" />\n<pre>\n<strong>输入：</strong>bottomLeft = [[1,1],[3,3],[3,1]], topRight = [[2,2],[4,4],[4,2]]\n<strong>输出：</strong>0\n<strong>解释：</strong>不存在相交的矩形，因此，返回 0 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == bottomLeft.length == topRight.length</code></li>\n\t<li><code>2 &lt;= n &lt;= 10<sup>3</sup></code></li>\n\t<li><code>bottomLeft[i].length == topRight[i].length == 2</code></li>\n\t<li><code>1 &lt;= bottomLeft[i][0], bottomLeft[i][1] &lt;= 10<sup>7</sup></code></li>\n\t<li><code>1 &lt;= topRight[i][0], topRight[i][1] &lt;= 10<sup>7</sup></code></li>\n\t<li><code>bottomLeft[i][0] &lt; topRight[i][0]</code></li>\n\t<li><code>bottomLeft[i][1] &lt; topRight[i][1]</code></li>\n</ul>\n",
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