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49 lines
2.5 KiB
HTML
49 lines
2.5 KiB
HTML
<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 <= k < n</code>.</p>
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<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>
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<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>
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<ul>
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<li><code>x<sub>i</sub> < x<sub>i + 1</sub></code> and <code>y<sub>i</sub> < y<sub>i + 1</sub></code> for all <code>i</code> where <code>1 <= i < m</code>.</li>
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<li><code>(x<sub>i</sub>, y<sub>i</sub>)</code> is in the given coordinates for all <code>i</code> where <code>1 <= i <= m</code>.</li>
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</ul>
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<p>Return the <strong>maximum</strong> length of an <strong>increasing path</strong> that contains <code>coordinates[k]</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">coordinates = [[3,1],[2,2],[4,1],[0,0],[5,3]], k = 1</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><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>
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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">coordinates = [[2,1],[7,0],[5,6]], k = 2</span></p>
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<p><strong>Output:</strong> <span class="example-io">2</span></p>
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<p><strong>Explanation:</strong></p>
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<p><code>(2, 1)</code>, <code>(5, 6)</code> is the longest increasing path that contains <code>(5, 6)</code>.</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>1 <= n == coordinates.length <= 10<sup>5</sup></code></li>
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<li><code>coordinates[i].length == 2</code></li>
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<li><code>0 <= coordinates[i][0], coordinates[i][1] <= 10<sup>9</sup></code></li>
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<li>All elements in <code>coordinates</code> are <strong>distinct</strong>.<!-- notionvc: 6e412fc2-f9dd-4ba2-b796-5e802a2b305a --><!-- notionvc: c2cf5618-fe99-4909-9b4c-e6b068be22a6 --></li>
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<li><code>0 <= k <= n - 1</code></li>
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</ul>
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