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41 lines
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41 lines
1.8 KiB
HTML
<p>Given an <code>n x n</code> <code>matrix</code> where each of the rows and columns is sorted in ascending order, return <em>the</em> <code>k<sup>th</sup></code> <em>smallest element in the matrix</em>.</p>
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<p>Note that it is the <code>k<sup>th</sup></code> smallest element <strong>in the sorted order</strong>, not the <code>k<sup>th</sup></code> <strong>distinct</strong> element.</p>
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<p>You must find a solution with a memory complexity better than <code>O(n<sup>2</sup>)</code>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> matrix = [[1,5,9],[10,11,13],[12,13,15]], k = 8
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<strong>Output:</strong> 13
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<strong>Explanation:</strong> The elements in the matrix are [1,5,9,10,11,12,13,<u><strong>13</strong></u>,15], and the 8<sup>th</sup> smallest number is 13
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> matrix = [[-5]], k = 1
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<strong>Output:</strong> -5
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</pre>
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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>n == matrix.length == matrix[i].length</code></li>
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<li><code>1 <= n <= 300</code></li>
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<li><code>-10<sup>9</sup> <= matrix[i][j] <= 10<sup>9</sup></code></li>
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<li>All the rows and columns of <code>matrix</code> are <strong>guaranteed</strong> to be sorted in <strong>non-decreasing order</strong>.</li>
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<li><code>1 <= k <= n<sup>2</sup></code></li>
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</ul>
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<p> </p>
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<p><strong>Follow up:</strong></p>
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<ul>
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<li>Could you solve the problem with a constant memory (i.e., <code>O(1)</code> memory complexity)?</li>
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<li>Could you solve the problem in <code>O(n)</code> time complexity? The solution may be too advanced for an interview but you may find reading <a href="http://www.cse.yorku.ca/~andy/pubs/X+Y.pdf" target="_blank">this paper</a> fun.</li>
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</ul>
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