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"question": {
"questionId": "3886",
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"categoryTitle": "Algorithms",
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"title": "Count Number of Trapezoids I",
"titleSlug": "count-number-of-trapezoids-i",
"content": "<p data-end=\"189\" data-start=\"146\">You are given a 2D integer array <code>points</code>, where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents the coordinates of the <code>i<sup>th</sup></code> point on the Cartesian plane.</p>\n\n<p data-end=\"579\" data-start=\"405\">A <strong>horizontal</strong> <strong>trapezoid</strong> is a convex quadrilateral with <strong data-end=\"496\" data-start=\"475\">at least one pair</strong> of horizontal sides (i.e. parallel to the x-axis). Two lines are parallel if and only if they have the same slope.</p>\n\n<p data-end=\"579\" data-start=\"405\">Return the <em data-end=\"330\" data-start=\"297\"> number of unique </em><strong><em>horizontal</em> <em>trapezoids</em></strong> that can be formed by choosing any four distinct points from <code>points</code>.</p>\n\n<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</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 = [[1,0],[2,0],[3,0],[2,2],[3,2]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/05/01/desmos-graph-6.png\" style=\"width: 250px; height: 250px;\" /> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/05/01/desmos-graph-7.png\" style=\"width: 250px; height: 250px;\" /> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/05/01/desmos-graph-8.png\" style=\"width: 250px; height: 250px;\" /></p>\n\n<p>There are three distinct ways to pick four points that form a horizontal trapezoid:</p>\n\n<ul>\n\t<li data-end=\"247\" data-start=\"193\">Using points <code data-end=\"213\" data-start=\"206\">[1,0]</code>, <code data-end=\"222\" data-start=\"215\">[2,0]</code>, <code data-end=\"231\" data-start=\"224\">[3,2]</code>, and <code data-end=\"244\" data-start=\"237\">[2,2]</code>.</li>\n\t<li data-end=\"305\" data-start=\"251\">Using points <code data-end=\"271\" data-start=\"264\">[2,0]</code>, <code data-end=\"280\" data-start=\"273\">[3,0]</code>, <code data-end=\"289\" data-start=\"282\">[3,2]</code>, and <code data-end=\"302\" data-start=\"295\">[2,2]</code>.</li>\n\t<li data-end=\"361\" data-start=\"309\">Using points <code data-end=\"329\" data-start=\"322\">[1,0]</code>, <code data-end=\"338\" data-start=\"331\">[3,0]</code>, <code data-end=\"347\" data-start=\"340\">[3,2]</code>, and <code data-end=\"360\" data-start=\"353\">[2,2]</code>.</li>\n</ul>\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 = [[0,0],[1,0],[0,1],[2,1]]</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><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/04/29/desmos-graph-5.png\" style=\"width: 250px; height: 250px;\" /></p>\n\n<p>There is only one horizontal trapezoid that can be formed.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>4 &lt;= points.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>&ndash;10<sup>8</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>8</sup></code></li>\n\t<li>All points are pairwise distinct.</li>\n</ul>\n",
"translatedTitle": "统计梯形的数目 I",
"translatedContent": "<p data-end=\"189\" data-start=\"146\">给你一个二维整数数组 <code>points</code>,其中 <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> 表示第 <code>i</code> 个点在笛卡尔平面上的坐标。</p>\n\n<p data-end=\"579\" data-start=\"405\"><strong>水平梯形</strong> 是一种凸四边形,具有&nbsp;<strong data-end=\"496\" data-start=\"475\">至少一对&nbsp;</strong>水平边(即平行于 x 轴的边)。两条直线平行当且仅当它们的斜率相同。</p>\n\n<p data-end=\"579\" data-start=\"405\">返回可以从 <code>points</code> 中任意选择四个不同点组成的&nbsp;<strong>水平梯形 </strong>数量。</p>\n\n<p>由于答案可能非常大,请返回结果对 <code>10<sup>9</sup> + 7</code> 取余数后的值。</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 = [[1,0],[2,0],[3,0],[2,2],[3,2]]</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/05/01/desmos-graph-6.png\" style=\"width: 250px; height: 250px;\" /> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/05/01/desmos-graph-7.png\" style=\"width: 250px; height: 250px;\" /> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/05/01/desmos-graph-8.png\" style=\"width: 250px; height: 250px;\" /></p>\n\n<p>有三种不同方式选择四个点组成一个水平梯形:</p>\n\n<ul>\n\t<li data-end=\"247\" data-start=\"193\">使用点 <code data-end=\"213\" data-start=\"206\">[1,0]</code>、<code data-end=\"222\" data-start=\"215\">[2,0]</code>、<code data-end=\"231\" data-start=\"224\">[3,2]</code> 和 <code data-end=\"244\" data-start=\"237\">[2,2]</code>。</li>\n\t<li data-end=\"305\" data-start=\"251\">使用点 <code data-end=\"271\" data-start=\"264\">[2,0]</code>、<code data-end=\"280\" data-start=\"273\">[3,0]</code>、<code data-end=\"289\" data-start=\"282\">[3,2]</code> 和 <code data-end=\"302\" data-start=\"295\">[2,2]</code>。</li>\n\t<li data-end=\"361\" data-start=\"309\">使用点 <code data-end=\"329\" data-start=\"322\">[1,0]</code>、<code data-end=\"338\" data-start=\"331\">[3,0]</code>、<code data-end=\"347\" data-start=\"340\">[3,2]</code> 和 <code data-end=\"360\" data-start=\"353\">[2,2]</code>。</li>\n</ul>\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 = [[0,0],[1,0],[0,1],[2,1]]</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><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/04/29/desmos-graph-5.png\" style=\"width: 250px; height: 250px;\" /></p>\n\n<p>只有一种方式可以组成一个水平梯形。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>4 &lt;= points.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>10<sup>8</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>8</sup></code></li>\n\t<li>所有点两两不同。</li>\n</ul>\n",
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