leetcode-problemset/leetcode-cn/originData/maximum-area-rectangle-with-point-constraints-i.json

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            "questionId": "3681",
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            "title": "Maximum Area Rectangle With Point Constraints I",
            "titleSlug": "maximum-area-rectangle-with-point-constraints-i",
            "content": "<p>You are given an array <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents the coordinates of a point on an infinite plane.</p>\n\n<p>Your task is to find the <strong>maximum </strong>area of a rectangle that:</p>\n\n<ul>\n\t<li>Can be formed using <strong>four</strong> of these points as its corners.</li>\n\t<li>Does <strong>not</strong> contain any other point inside or on its border.</li>\n\t<li>Has its edges&nbsp;<strong>parallel</strong> to the axes.</li>\n</ul>\n\n<p>Return the <strong>maximum area</strong> that you can obtain or -1 if no such rectangle is possible.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">points = [[1,1],[1,3],[3,1],[3,3]]</span></p>\n\n<p><strong>Output: </strong>4</p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"Example 1 diagram\" src=\"https://assets.leetcode.com/uploads/2024/11/02/example1.png\" style=\"width: 229px; height: 228px;\" /></strong></p>\n\n<p>We can make a rectangle with these 4 points as corners and there is no other point that lies inside or on the border<!-- notionvc: f270d0a3-a596-4ed6-9997-2c7416b2b4ee -->. Hence, the maximum possible area would be 4.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">points = [[1,1],[1,3],[3,1],[3,3],[2,2]]</span></p>\n\n<p><strong>Output:</strong><b> </b>-1</p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"Example 2 diagram\" src=\"https://assets.leetcode.com/uploads/2024/11/02/example2.png\" style=\"width: 229px; height: 228px;\" /></strong></p>\n\n<p>There is only one rectangle possible is with points <code>[1,1], [1,3], [3,1]</code> and <code>[3,3]</code> but <code>[2,2]</code> will always lie inside it. Hence, returning -1.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">points = [[1,1],[1,3],[3,1],[3,3],[1,2],[3,2]]</span></p>\n\n<p><strong>Output: </strong>2</p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"Example 3 diagram\" src=\"https://assets.leetcode.com/uploads/2024/11/02/example3.png\" style=\"width: 229px; height: 228px;\" /></strong></p>\n\n<p>The maximum area rectangle is formed by the points <code>[1,3], [1,2], [3,2], [3,3]</code>, which has an area of 2. Additionally, the points <code>[1,1], [1,2], [3,1], [3,2]</code> also form a valid rectangle with the same area.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= points.length &lt;= 10</code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 100</code></li>\n\t<li>All the given points are <strong>unique</strong>.</li>\n</ul>\n",
            "translatedTitle": "用点构造面积最大的矩形 I",
            "translatedContent": "<p>给你一个数组 <code>points</code>，其中 <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> 表示无限平面上一点的坐标。</p>\n\n<p>你的任务是找出满足以下条件的矩形可能的&nbsp;<strong>最大&nbsp;</strong>面积：</p>\n\n<ul>\n\t<li>矩形的四个顶点必须是数组中的&nbsp;<strong>四个&nbsp;</strong>点。</li>\n\t<li>矩形的内部或边界上&nbsp;<strong>不能&nbsp;</strong>包含任何其他点。</li>\n\t<li>矩形的边与坐标轴&nbsp;<strong>平行&nbsp;</strong>。</li>\n</ul>\n\n<p>返回可以获得的&nbsp;<strong>最大面积&nbsp;</strong>，如果无法形成这样的矩形，则返回 -1。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">points = [[1,1],[1,3],[3,1],[3,3]]</span></p>\n\n<p><strong>输出：</strong>4</p>\n\n<p><strong>解释：</strong></p>\n\n<p><strong class=\"example\"><img alt=\"示例 1 图示\" src=\"https://assets.leetcode.com/uploads/2024/11/02/example1.png\" style=\"width: 229px; height: 228px;\" /></strong></p>\n\n<p>我们可以用这 4 个点作为顶点构成一个矩形，并且矩形内部或边界上没有其他点。因此，最大面积为 4 。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">points = [[1,1],[1,3],[3,1],[3,3],[2,2]]</span></p>\n\n<p><strong>输出：</strong>-1</p>\n\n<p><strong>解释：</strong></p>\n\n<p><strong class=\"example\"><img alt=\"示例 2 图示\" src=\"https://assets.leetcode.com/uploads/2024/11/02/example2.png\" style=\"width: 229px; height: 228px;\" /></strong></p>\n\n<p>唯一一组可能构成矩形的点为 <code>[1,1], [1,3], [3,1]</code> 和 <code>[3,3]</code>，但点 <code>[2,2]</code> 总是位于矩形内部。因此，返回 -1 。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">points = [[1,1],[1,3],[3,1],[3,3],[1,2],[3,2]]</span></p>\n\n<p><strong>输出：</strong>2</p>\n\n<p><strong>解释：</strong></p>\n\n<p><strong class=\"example\"><img alt=\"示例 3 图示\" src=\"https://assets.leetcode.com/uploads/2024/11/02/example3.png\" style=\"width: 229px; height: 228px;\" /></strong></p>\n\n<p>点 <code>[1,3], [1,2], [3,2], [3,3]</code>&nbsp;可以构成面积最大的矩形，面积为 2。此外，点 <code>[1,1], [1,2], [3,1], [3,2]</code> 也可以构成一个符合题目要求的矩形，面积相同。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= points.length &lt;= 10</code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 100</code></li>\n\t<li>给定的所有点都是 <strong>唯一</strong> 的。</li>\n</ul>\n",
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