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52 lines
3.2 KiB
HTML
52 lines
3.2 KiB
HTML
<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>
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<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>
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<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>
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<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">points = [[1,0],[2,0],[3,0],[2,2],[3,2]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">3</span></p>
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<p><strong>Explanation:</strong></p>
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<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>
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<p>There are three distinct ways to pick four points that form a horizontal trapezoid:</p>
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<ul>
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<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>
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<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>
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<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>
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</ul>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">points = [[0,0],[1,0],[0,1],[2,1]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">1</span></p>
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<p><strong>Explanation:</strong></p>
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<p><img alt="" src="https://assets.leetcode.com/uploads/2025/04/29/desmos-graph-5.png" style="width: 250px; height: 250px;" /></p>
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<p>There is only one horizontal trapezoid that can be formed.</p>
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</div>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>4 <= points.length <= 10<sup>5</sup></code></li>
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<li><code>–10<sup>8</sup> <= x<sub>i</sub>, y<sub>i</sub> <= 10<sup>8</sup></code></li>
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<li>All points are pairwise distinct.</li>
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</ul>
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