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47 lines
2.0 KiB
HTML
<p>A <strong>wiggle sequence</strong> is a sequence where the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with one element and a sequence with two non-equal elements are trivially wiggle sequences.</p>
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<ul>
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<li>For example, <code>[1, 7, 4, 9, 2, 5]</code> is a <strong>wiggle sequence</strong> because the differences <code>(6, -3, 5, -7, 3)</code> alternate between positive and negative.</li>
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<li>In contrast, <code>[1, 4, 7, 2, 5]</code> and <code>[1, 7, 4, 5, 5]</code> are not wiggle sequences. The first is not because its first two differences are positive, and the second is not because its last difference is zero.</li>
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</ul>
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<p>A <strong>subsequence</strong> is obtained by deleting some elements (possibly zero) from the original sequence, leaving the remaining elements in their original order.</p>
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<p>Given an integer array <code>nums</code>, return <em>the length of the longest <strong>wiggle subsequence</strong> of </em><code>nums</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,7,4,9,2,5]
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<strong>Output:</strong> 6
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<strong>Explanation:</strong> The entire sequence is a wiggle sequence with differences (6, -3, 5, -7, 3).
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,17,5,10,13,15,10,5,16,8]
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<strong>Output:</strong> 7
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<strong>Explanation:</strong> There are several subsequences that achieve this length.
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One is [1, 17, 10, 13, 10, 16, 8] with differences (16, -7, 3, -3, 6, -8).
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,2,3,4,5,6,7,8,9]
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<strong>Output:</strong> 2
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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>1 <= nums.length <= 1000</code></li>
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<li><code>0 <= nums[i] <= 1000</code></li>
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</ul>
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<p> </p>
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<p><strong>Follow up:</strong> Could you solve this in <code>O(n)</code> time?</p>
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