leetcode-problemset/leetcode-cn/originData/length-of-the-longest-increasing-path.json

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        "question": {
            "questionId": "3571",
            "questionFrontendId": "3288",
            "categoryTitle": "Algorithms",
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            "title": "Length of the Longest Increasing Path",
            "titleSlug": "length-of-the-longest-increasing-path",
            "content": "<p>You are given a 2D array of integers <code>coordinates</code> of length <code>n</code> and an integer <code>k</code>, where <code>0 &lt;= k &lt; n</code>.</p>\n\n<p><code>coordinates[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> indicates the point <code>(x<sub>i</sub>, y<sub>i</sub>)</code> in a 2D plane.</p>\n\n<p>An <strong>increasing path</strong> of length <code>m</code> is defined as a list of points <code>(x<sub>1</sub>, y<sub>1</sub>)</code>, <code>(x<sub>2</sub>, y<sub>2</sub>)</code>, <code>(x<sub>3</sub>, y<sub>3</sub>)</code>, ..., <code>(x<sub>m</sub>, y<sub>m</sub>)</code> such that:</p>\n\n<ul>\n\t<li><code>x<sub>i</sub> &lt; x<sub>i + 1</sub></code> and <code>y<sub>i</sub> &lt; y<sub>i + 1</sub></code> for all <code>i</code> where <code>1 &lt;= i &lt; m</code>.</li>\n\t<li><code>(x<sub>i</sub>, y<sub>i</sub>)</code> is in the given coordinates for all <code>i</code> where <code>1 &lt;= i &lt;= m</code>.</li>\n</ul>\n\n<p>Return the <strong>maximum</strong> length of an <strong>increasing path</strong> that contains <code>coordinates[k]</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\">coordinates = [[3,1],[2,2],[4,1],[0,0],[5,3]], k = 1</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><code>(0, 0)</code>, <code>(2, 2)</code>, <code>(5, 3)</code><!-- notionvc: 082cee9e-4ce5-4ede-a09d-57001a72141d --> is the longest increasing path that contains <code>(2, 2)</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\">coordinates = [[2,1],[7,0],[5,6]], k = 2</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><code>(2, 1)</code>, <code>(5, 6)</code> is the longest increasing path that contains <code>(5, 6)</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n == coordinates.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>coordinates[i].length == 2</code></li>\n\t<li><code>0 &lt;= coordinates[i][0], coordinates[i][1] &lt;= 10<sup>9</sup></code></li>\n\t<li>All elements in <code>coordinates</code> are <strong>distinct</strong>.<!-- notionvc: 6e412fc2-f9dd-4ba2-b796-5e802a2b305a --><!-- notionvc: c2cf5618-fe99-4909-9b4c-e6b068be22a6 --></li>\n\t<li><code>0 &lt;= k &lt;= n - 1</code></li>\n</ul>\n",
            "translatedTitle": "最长上升路径的长度",
            "translatedContent": "<p>给你一个长度为 <code>n</code>&nbsp;的二维整数数组&nbsp;<code>coordinates</code>&nbsp;和一个整数&nbsp;<code>k</code>&nbsp;，其中&nbsp;<code>0 &lt;= k &lt; n</code>&nbsp;。</p>\n\n<p><code>coordinates[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>&nbsp;表示二维平面里一个点&nbsp;<code>(x<sub>i</sub>, y<sub>i</sub>)</code>&nbsp;。</p>\n\n<p>如果一个点序列&nbsp;<code>(x<sub>1</sub>, y<sub>1</sub>)</code>, <code>(x<sub>2</sub>, y<sub>2</sub>)</code>, <code>(x<sub>3</sub>, y<sub>3</sub>)</code>, ..., <code>(x<sub>m</sub>, y<sub>m</sub>)</code>&nbsp;满足以下条件，那么我们称它是一个长度为 <code>m</code>&nbsp;的 <strong>上升序列</strong>&nbsp;：</p>\n\n<ul>\n\t<li>对于所有满足&nbsp;<code>1 &lt;= i &lt; m</code> 的&nbsp;<code>i</code>&nbsp;都有&nbsp;<code>x<sub>i</sub> &lt; x<sub>i + 1</sub></code>&nbsp;且&nbsp;<code>y<sub>i</sub> &lt; y<sub>i + 1</sub></code>&nbsp;。</li>\n\t<li>对于所有&nbsp;<code>1 &lt;= i &lt;= m</code>&nbsp;的&nbsp;<code>i</code>&nbsp;对应的点&nbsp;<code>(x<sub>i</sub>, y<sub>i</sub>)</code>&nbsp;都在给定的坐标数组里。</li>\n</ul>\n\n<p>请你返回包含坐标 <code>coordinates[k]</code>&nbsp;的 <strong>最长上升路径</strong>&nbsp;的长度。</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><span class=\"example-io\"><b>输入：</b>coordinates = [[3,1],[2,2],[4,1],[0,0],[5,3]], k = 1</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>3</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><code>(0, 0)</code>&nbsp;，<code>(2, 2)</code>&nbsp;，<code>(5, 3)</code><!-- notionvc: 082cee9e-4ce5-4ede-a09d-57001a72141d -->&nbsp;是包含坐标 <code>(2, 2)</code>&nbsp;的最长上升路径。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>coordinates = [[2,1],[7,0],[5,6]], k = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>2</span></p>\n\n<p><b>解释：</b></p>\n\n<p><code>(2, 1)</code>&nbsp;，<code>(5, 6)</code>&nbsp;是包含坐标 <code>(5, 6)</code>&nbsp;的最长上升路径。</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 == coordinates.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>coordinates[i].length == 2</code></li>\n\t<li><code>0 &lt;= coordinates[i][0], coordinates[i][1] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>coordinates</code>&nbsp;中的元素 <strong>互不相同</strong>&nbsp;。<!-- notionvc: 6e412fc2-f9dd-4ba2-b796-5e802a2b305a --><!-- notionvc: c2cf5618-fe99-4909-9b4c-e6b068be22a6 --></li>\n\t<li><code>0 &lt;= k &lt;= n - 1</code></li>\n</ul>\n",
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