leetcode-problemset/leetcode-cn/originData/find-maximum-area-of-a-triangle.json

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            "title": "Find Maximum Area of a Triangle",
            "titleSlug": "find-maximum-area-of-a-triangle",
            "content": "<p>You are given a 2D array <code>coords</code> of size <code>n x 2</code>, representing the coordinates of <code>n</code> points in an infinite Cartesian plane.</p>\n\n<p>Find <strong>twice</strong> the <strong>maximum</strong> area of a triangle with its corners at <em>any</em> three elements from <code>coords</code>, such that at least one side of this triangle is <strong>parallel</strong> to the x-axis or y-axis. Formally, if the maximum area of such a triangle is <code>A</code>, return <code>2 * A</code>.</p>\n\n<p>If no such triangle exists, return -1.</p>\n\n<p><strong>Note</strong> that a triangle <em>cannot</em> have zero area.</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\">coords = [[1,1],[1,2],[3,2],[3,3]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img src=\"https://assets.leetcode.com/uploads/2025/04/19/image-20250420010047-1.png\" style=\"width: 300px; height: 289px;\" /></p>\n\n<p>The triangle shown in the image has a base 1 and height 2. Hence its area is <code>1/2 * base * height = 1</code>.</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\">coords = [[1,1],[2,2],[3,3]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">-1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The only possible triangle has corners <code>(1, 1)</code>, <code>(2, 2)</code>, and <code>(3, 3)</code>. None of its sides are parallel to the x-axis or the y-axis.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n == coords.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= coords[i][0], coords[i][1] &lt;= 10<sup>6</sup></code></li>\n\t<li>All <code>coords[i]</code> are <strong>unique</strong>.</li>\n</ul>\n",
            "translatedTitle": "找到最大三角形面积",
            "translatedContent": "<p>给你一个二维数组 <code>coords</code>，大小为 <code>n x 2</code>，表示一个无限笛卡尔平面上 <code>n</code> 个点的坐标。</p>\n\n<p>找出一个 <strong>最大</strong>&nbsp;三角形的 <strong>两倍&nbsp;</strong>面积，其中三角形的三个顶点来自 <code>coords</code> 中的任意三个点，并且该三角形至少有一条边与 x 轴或 y 轴平行。严格地说，如果该三角形的最大面积为 <code>A</code>，则返回 <code>2 * A</code>。</p>\n\n<p>如果不存在这样的三角形，返回 -1。</p>\n\n<p><strong>注意</strong>，三角形的面积 <strong>不能</strong> 为零。</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\">coords = [[1,1],[1,2],[3,2],[3,3]]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img src=\"https://assets.leetcode.com/uploads/2025/04/19/image-20250420010047-1.png\" style=\"width: 300px; height: 289px;\" /></p>\n\n<p>图中的三角形的底边为 1，高为 2。因此，它的面积为 <code>1/2 * 底边 * 高 = 1</code>。</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\">coords = [[1,1],[2,2],[3,3]]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">-1</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>唯一可能的三角形的顶点是 <code>(1, 1)</code>、<code>(2, 2)</code> 和 <code>(3, 3)</code>。它的任意边都不与 x 轴或 y 轴平行。</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;= n == coords.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= coords[i][0], coords[i][1] &lt;= 10<sup>6</sup></code></li>\n\t<li>所有 <code>coords[i]</code> 都是 <strong>唯一</strong> 的。</li>\n</ul>\n",
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                "<code>area * 2 = base * height</code>",
                "Let the base be parallel to the x‑axis or y‑axis",
                "Sort to find the maximum base for each fixed <code>x</code> (or <code>y</code>), then the maximum height comes from the extreme values of the other coordinate."
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