leetcode-problemset/leetcode-cn/originData/find-the-number-of-ways-to-place-people-i.json

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            "title": "Find the Number of Ways to Place People I",
            "titleSlug": "find-the-number-of-ways-to-place-people-i",
            "content": "<p>You are given a 2D array <code>points</code> of size <code>n x 2</code> representing integer coordinates of some points on a 2D-plane, where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>\n\n<p>We define the <strong>right</strong> direction as positive x-axis (<strong>increasing x-coordinate</strong>) and the <strong>left</strong> direction as negative x-axis (<strong>decreasing x-coordinate</strong>). Similarly, we define the <strong>up</strong> direction as positive y-axis (<strong>increasing y-coordinate</strong>) and the <strong>down</strong> direction as negative y-axis (<strong>decreasing y-coordinate</strong>)</p>\n\n<p>You have to place <code>n</code> people, including Alice and Bob, at these points such that there is <strong>exactly one</strong> person at every point. Alice wants to be alone with Bob, so Alice will build a rectangular fence with Alice&#39;s position as the <strong>upper left corner</strong> and Bob&#39;s position as the <strong>lower right corner</strong> of the fence (<strong>Note</strong> that the fence <strong>might not</strong> enclose any area, i.e. it can be a line). If any person other than Alice and Bob is either <strong>inside</strong> the fence or <strong>on</strong> the fence, Alice will be sad.</p>\n\n<p>Return <em>the number of <strong>pairs of points</strong> where you can place Alice and Bob, such that Alice <strong>does not</strong> become sad on building the fence</em>.</p>\n\n<p><strong>Note</strong> that Alice can only build a fence with Alice&#39;s position as the upper left corner, and Bob&#39;s position as the lower right corner. For example, Alice cannot build either of the fences in the picture below with four corners <code>(1, 1)</code>, <code>(1, 3)</code>, <code>(3, 1)</code>, and <code>(3, 3)</code>, because:</p>\n\n<ul>\n\t<li>With Alice at <code>(3, 3)</code> and Bob at <code>(1, 1)</code>, Alice&#39;s position is not the upper left corner and Bob&#39;s position is not the lower right corner of the fence.</li>\n\t<li>With Alice at <code>(1, 3)</code> and Bob at <code>(1, 1)</code>, Bob&#39;s position is not the lower right corner of the fence.</li>\n</ul>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/04/example0alicebob-1.png\" style=\"width: 750px; height: 308px;padding: 10px; background: #fff; border-radius: .5rem;\" />\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/04/example1alicebob.png\" style=\"width: 376px; height: 308px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;\" />\n<pre>\n<strong>Input:</strong> points = [[1,1],[2,2],[3,3]]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There is no way to place Alice and Bob such that Alice can build a fence with Alice&#39;s position as the upper left corner and Bob&#39;s position as the lower right corner. Hence we return 0. \n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/02/04/example2alicebob.png\" style=\"width: 1321px; height: 363px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;\" />\n<pre>\n<strong>Input:</strong> points = [[6,2],[4,4],[2,6]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> There are two ways to place Alice and Bob such that Alice will not be sad:\n- Place Alice at (4, 4) and Bob at (6, 2).\n- Place Alice at (2, 6) and Bob at (4, 4).\nYou cannot place Alice at (2, 6) and Bob at (6, 2) because the person at (4, 4) will be inside the fence.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/02/04/example4alicebob.png\" style=\"width: 1123px; height: 308px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;\" />\n<pre>\n<strong>Input:</strong> points = [[3,1],[1,3],[1,1]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> There are two ways to place Alice and Bob such that Alice will not be sad:\n- Place Alice at (1, 1) and Bob at (3, 1).\n- Place Alice at (1, 3) and Bob at (1, 1).\nYou cannot place Alice at (1, 3) and Bob at (3, 1) because the person at (1, 1) will be on the fence.\nNote that it does not matter if the fence encloses any area, the first and second fences in the image are valid.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 50</code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>0 &lt;= points[i][0], points[i][1] &lt;= 50</code></li>\n\t<li>All <code>points[i]</code> are distinct.</li>\n</ul>\n",
            "translatedTitle": "人员站位的方案数 I",
            "translatedContent": "<p>给你一个&nbsp;&nbsp;<code>n x 2</code>&nbsp;的二维数组 <code>points</code>&nbsp;，它表示二维平面上的一些点坐标，其中&nbsp;<code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>&nbsp;。</p>\n\n<p>我们定义 x 轴的正方向为 <strong>右</strong>&nbsp;（<strong>x 轴递增的方向</strong>），x 轴的负方向为 <strong>左</strong>&nbsp;（<strong>x 轴递减的方向</strong>）。类似的，我们定义 y 轴的正方向为 <strong>上</strong>&nbsp;（<strong>y 轴递增的方向</strong>），y 轴的负方向为 <strong>下</strong>&nbsp;（<strong>y 轴递减的方向</strong>）。</p>\n\n<p>你需要安排这 <code>n</code>&nbsp;个人的站位，这 <code>n</code>&nbsp;个人中包括&nbsp;liupengsay 和小羊肖恩&nbsp;。你需要确保每个点处&nbsp;<strong>恰好</strong>&nbsp;有&nbsp;<strong>一个</strong>&nbsp;人。同时，liupengsay 想跟小羊肖恩单独玩耍，所以&nbsp;liupengsay&nbsp;会以 liupengsay<b>&nbsp;</b>的坐标为 <strong>左上角</strong>&nbsp;，小羊肖恩的坐标为 <strong>右下角</strong>&nbsp;建立一个矩形的围栏（<strong>注意</strong>，围栏可能&nbsp;<strong>不</strong> 包含任何区域，也就是说围栏可能是一条线段）。如果围栏的 <strong>内部</strong>&nbsp;或者 <strong>边缘</strong>&nbsp;上有任何其他人，liupengsay 都会难过。</p>\n\n<p>请你在确保 liupengsay&nbsp;<strong>不会</strong> 难过的前提下，返回 liupengsay 和小羊肖恩可以选择的 <strong>点对</strong>&nbsp;数目。</p>\n\n<p><b>注意</b>，liupengsay 建立的围栏必须确保 liupengsay 的位置是矩形的左上角，小羊肖恩的位置是矩形的右下角。比方说，以&nbsp;<code>(1, 1)</code>&nbsp;，<code>(1, 3)</code>&nbsp;，<code>(3, 1)</code>&nbsp;和&nbsp;<code>(3, 3)</code>&nbsp;为矩形的四个角，给定下图的两个输入，liupengsay 都不能建立围栏，原因如下：</p>\n\n<ul>\n\t<li>图一中，liupengsay 在&nbsp;<code>(3, 3)</code>&nbsp;且小羊肖恩在&nbsp;<code>(1, 1)</code>&nbsp;，liupengsay 的位置不是左上角且小羊肖恩的位置不是右下角。</li>\n\t<li>图二中，liupengsay 在&nbsp;<code>(1, 3)</code>&nbsp;且小羊肖恩在&nbsp;<code>(1, 1)</code>&nbsp;，小羊肖恩的位置不是在围栏的右下角。</li>\n</ul>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/04/example0alicebob-1.png\" style=\"width: 750px; height: 308px;padding: 10px; background: #fff; border-radius: .5rem;\" />\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/2024/01/04/example1alicebob.png\" style=\"width: 376px; height: 308px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;\" /></p>\n\n<pre>\n<b>输入：</b>points = [[1,1],[2,2],[3,3]]\n<b>输出：</b>0\n<strong>解释：</strong>没有办法可以让 liupengsay 的围栏以 liupengsay 的位置为左上角且小羊肖恩的位置为右下角。所以我们返回 0 。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><strong class=\"example\"><a href=\"https://pic.leetcode.cn/1706880313-YelabI-example2.jpeg\"><img alt=\"\" src=\"https://pic.leetcode.cn/1706880313-YelabI-example2.jpeg\" style=\"width: 900px; height: 247px;\" /></a></strong></p>\n\n<pre>\n<b>输入：</b>points = [[6,2],[4,4],[2,6]]\n<b>输出：</b>2\n<b>解释：</b>总共有 2 种方案安排 liupengsay 和小羊肖恩的位置，使得 liupengsay 不会难过：\n- liupengsay 站在 (4, 4) ，小羊肖恩站在 (6, 2) 。\n- liupengsay 站在 (2, 6) ，小羊肖恩站在 (4, 4) 。\n不能安排 liupengsay 站在 (2, 6) 且小羊肖恩站在 (6, 2) ，因为站在 (4, 4) 的人处于围栏内。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<p><strong class=\"example\"><a href=\"https://pic.leetcode.cn/1706880311-mtPGYC-example3.jpeg\"><img alt=\"\" src=\"https://pic.leetcode.cn/1706880311-mtPGYC-example3.jpeg\" style=\"width: 900px; height: 247px;\" /></a></strong></p>\n\n<pre>\n<b>输入：</b>points = [[3,1],[1,3],[1,1]]\n<b>输出：</b>2\n<b>解释：</b>总共有 2 种方案安排 liupengsay 和小羊肖恩的位置，使得 liupengsay 不会难过：\n- liupengsay 站在 (1, 1) ，小羊肖恩站在 (3, 1) 。\n- liupengsay 站在 (1, 3) ，小羊肖恩站在 (1, 1) 。\n不能安排 liupengsay 站在 (1, 3) 且小羊肖恩站在 (3, 1) ，因为站在 (1, 1) 的人处于围栏内。\n注意围栏是可以不包含任何面积的，上图中第一和第二个围栏都是合法的。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 50</code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>0 &lt;= points[i][0], points[i][1] &lt;= 50</code></li>\n\t<li><code>points[i]</code>&nbsp;点对两两不同。</li>\n</ul>\n",
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