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

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            "title": "Maximum Area Rectangle With Point Constraints I",
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            "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",
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                "If <code>(x1, y1)</code> and <code>(x2, y2)</code> are two opposite corners of a rectangle, then the other two would be <code>(x1, y2)</code> and <code>(x2, y1)</code>.",
                "Fix two points and find the other two using a set data structure.",
                "After determining the rectangle, iterate through the array of points to ensure no point lies on the rectangle’s border or within its interior."
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