leetcode-problemset/leetcode-cn/originData/maximize-area-of-square-hole-in-grid.json

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            "questionId": "3214",
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            "categoryTitle": "Algorithms",
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            "title": "Maximize Area of Square Hole in Grid",
            "titleSlug": "maximize-area-of-square-hole-in-grid",
            "content": "<p>You are given the two integers, <code>n</code> and <code>m</code> and two integer arrays, <code>hBars</code> and <code>vBars</code>. The grid has <code>n + 2</code> horizontal and <code>m + 2</code> vertical bars, creating 1 x 1 unit cells. The bars are indexed starting from <code>1</code>.</p>\n\n<p>You can <strong>remove</strong> some of the bars in <code>hBars</code> from horizontal bars and some of the bars in <code>vBars</code> from vertical bars. Note that other bars are fixed and cannot be removed.</p>\n\n<p>Return an integer denoting the <strong>maximum area</strong> of a <em>square-shaped</em> hole in the grid, after removing some bars (possibly none).</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/05/screenshot-from-2023-11-05-22-40-25.png\" style=\"width: 411px; height: 220px;\" /></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>Input: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">n = 2, m = 1, hBars = [2,3], vBars = [2]</span></p>\n\n<p><strong>Output: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The left image shows the initial grid formed by the bars. The horizontal bars are <code>[1,2,3,4]</code>, and the vertical bars are&nbsp;<code>[1,2,3]</code>.</p>\n\n<p>One way to get the maximum square-shaped hole is by removing horizontal bar 2 and vertical bar 2.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/04/screenshot-from-2023-11-04-17-01-02.png\" style=\"width: 368px; height: 145px;\" /></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>Input: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">n = 1, m = 1, hBars = [2], vBars = [2]</span></p>\n\n<p><strong>Output: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>To get the maximum square-shaped hole, we remove horizontal bar 2 and vertical bar 2.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/03/12/unsaved-image-2.png\" style=\"width: 648px; height: 218px;\" /></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>Input: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">n = 2, m = 3, hBars = [2,3], vBars = [2,4]</span></p>\n\n<p><strong>Output: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><span style=\"color: var(--text-secondary); font-size: 0.875rem;\">One way to get the maximum square-shaped hole is by removing horizontal bar 3, and vertical bar 4.</span></p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= m &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= hBars.length &lt;= 100</code></li>\n\t<li><code>2 &lt;= hBars[i] &lt;= n + 1</code></li>\n\t<li><code>1 &lt;= vBars.length &lt;= 100</code></li>\n\t<li><code>2 &lt;= vBars[i] &lt;= m + 1</code></li>\n\t<li>All values in <code>hBars</code> are distinct.</li>\n\t<li>All values in <code>vBars</code> are distinct.</li>\n</ul>\n",
            "translatedTitle": "最大化网格图中正方形空洞的面积",
            "translatedContent": "<p>给你一个网格图，由&nbsp;<code>n + 2</code>&nbsp;条 <strong>横线段</strong>&nbsp;和&nbsp;<code>m + 2</code>&nbsp;条&nbsp;<strong>竖线段</strong>&nbsp;组成，一开始所有区域均为&nbsp;<code>1 x 1</code>&nbsp;的单元格。</p>\n\n<p>所有线段的编号从 <strong>1</strong>&nbsp;开始。</p>\n\n<p>给你两个整数&nbsp;<code>n</code> 和&nbsp;<code>m</code>&nbsp;。</p>\n\n<p>同时给你两个整数数组&nbsp;<code>hBars</code> 和&nbsp;<code>vBars</code>&nbsp;。</p>\n\n<ul>\n\t<li><code>hBars</code> 包含区间&nbsp;<code>[2, n + 1]</code>&nbsp;内&nbsp;<strong>互不相同</strong>&nbsp;的横线段编号。</li>\n\t<li><code>vBars</code>&nbsp;包含&nbsp;<code>[2, m + 1]</code>&nbsp;内&nbsp;<strong>互不相同的</strong>&nbsp;竖线段编号。</li>\n</ul>\n\n<p>如果满足以下条件之一，你可以 <strong>移除</strong>&nbsp;两个数组中的部分线段：</p>\n\n<ul>\n\t<li>如果移除的是横线段，它必须是&nbsp;<code>hBars</code>&nbsp;中的值。</li>\n\t<li>如果移除的是竖线段，它必须是&nbsp;<code>vBars</code>&nbsp;中的值。</li>\n</ul>\n\n<p>请你返回移除一些线段后（<strong>可能不移除任何线段）</strong>，剩余网格图中 <strong>最大正方形</strong>&nbsp;空洞的面积，正方形空洞的意思是正方形 <strong>内部</strong> 不含有任何线段。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/05/screenshot-from-2023-11-05-22-40-25.png\" style=\"width: 411px; height: 220px;\" /></p>\n\n<pre>\n<b>输入：</b>n = 2, m = 1, hBars = [2,3], vBars = [2]\n<b>输出：</b>4\n<b>解释：</b>左边的图是一开始的网格图。\n横线编号的范围是区间 [1,4] ，竖线编号的范围是区间 [1,3] 。\n可以移除的横线段为 [2,3] ，竖线段为 [2] 。\n一种得到最大正方形面积的方法是移除横线段 2 和竖线段 2 。\n操作后得到的网格图如右图所示。\n正方形空洞面积为 4。\n无法得到面积大于 4 的正方形空洞。\n所以答案为 4 。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/04/screenshot-from-2023-11-04-17-01-02.png\" style=\"width: 368px; height: 145px;\" /></p>\n\n<pre>\n<b>输入：</b>n = 1, m = 1, hBars = [2], vBars = [2]\n<b>输出：</b>4\n<b>解释：</b>左边的图是一开始的网格图。\n横线编号的范围是区间 [1,3] ，竖线编号的范围是区间 [1,3] 。\n可以移除的横线段为 [2] ，竖线段为 [2] 。\n一种得到最大正方形面积的方法是移除横线段 2 和竖线段 2 。\n操作后得到的网格图如右图所示。\n正方形空洞面积为 4。\n无法得到面积大于 4 的正方形空洞。\n所以答案为 4 。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/05/screenshot-from-2023-11-05-22-33-35.png\" style=\"width: 648px; height: 218px;\" /></p>\n\n<pre>\n<b>输入：</b>n = 2, m = 3, hBars = [2,3], vBars = [2,3,4]\n<b>输出：</b>9\n<b>解释：</b>左边的图是一开始的网格图。\n横线编号的范围是区间 [1,4] ，竖线编号的范围是区间 [1,5] 。\n可以移除的横线段为 [2,3] ，竖线段为 [2,3,4] 。\n一种得到最大正方形面积的方法是移除横线段 2、3 和竖线段 3、4 。\n操作后得到的网格图如右图所示。\n正方形空洞面积为 9。\n无法得到面积大于 9 的正方形空洞。\n所以答案为 9 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= m &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= hBars.length &lt;= 100</code></li>\n\t<li><code>2 &lt;= hBars[i] &lt;= n + 1</code></li>\n\t<li><code>1 &lt;= vBars.length &lt;= 100</code></li>\n\t<li><code>2 &lt;= vBars[i] &lt;= m + 1</code></li>\n\t<li><code>hBars</code>&nbsp;中的值互不相同。</li>\n\t<li><code>vBars</code> 中的值互不相同。</li>\n</ul>\n",
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                "Sort <code>hBars</code> and <code>vBars</code> and consider them separately.",
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