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76 lines
2.5 KiB
HTML
76 lines
2.5 KiB
HTML
<p>Given two integers, <code>n</code> and <code>k</code>, an <strong>alternating permutation</strong> is a permutation of the first <code>n</code> positive integers such that no <strong>two</strong> adjacent elements are both odd or both even.</p>
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<p>Return the <strong>k-th</strong> <strong>alternating permutation</strong> sorted in <em>lexicographical order</em>. If there are fewer than <code>k</code> valid <strong>alternating permutations</strong>, return an empty list.</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">n = 4, k = 6</span></p>
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<p><strong>Output:</strong> <span class="example-io">[3,4,1,2]</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The lexicographically-sorted alternating permutations of <code>[1, 2, 3, 4]</code> are:</p>
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<ol>
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<li><code>[1, 2, 3, 4]</code></li>
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<li><code>[1, 4, 3, 2]</code></li>
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<li><code>[2, 1, 4, 3]</code></li>
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<li><code>[2, 3, 4, 1]</code></li>
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<li><code>[3, 2, 1, 4]</code></li>
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<li><code>[3, 4, 1, 2]</code> ← 6th permutation</li>
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<li><code>[4, 1, 2, 3]</code></li>
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<li><code>[4, 3, 2, 1]</code></li>
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</ol>
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<p>Since <code>k = 6</code>, we return <code>[3, 4, 1, 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">n = 3, k = 2</span></p>
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<p><strong>Output:</strong> <span class="example-io">[3,2,1]</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The lexicographically-sorted alternating permutations of <code>[1, 2, 3]</code> are:</p>
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<ol>
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<li><code>[1, 2, 3]</code></li>
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<li><code>[3, 2, 1]</code> ← 2nd permutation</li>
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</ol>
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<p>Since <code>k = 2</code>, we return <code>[3, 2, 1]</code>.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 2, k = 3</span></p>
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<p><strong>Output:</strong> <span class="example-io">[]</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The lexicographically-sorted alternating permutations of <code>[1, 2]</code> are:</p>
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<ol>
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<li><code>[1, 2]</code></li>
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<li><code>[2, 1]</code></li>
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</ol>
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<p>There are only 2 alternating permutations, but <code>k = 3</code>, which is out of range. Thus, we return an empty list <code>[]</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 <= 100</code></li>
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<li><code>1 <= k <= 10<sup>15</sup></code></li>
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</ul>
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