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| <h2><a href="https://leetcode.com/problems/arithmetic-slices-ii-subsequence/">446. Arithmetic Slices II - Subsequence</a></h2><h3>Hard</h3><hr><div><p>Given an integer array <code>nums</code>, return <em>the number of all the <strong>arithmetic subsequences</strong> of</em> <code>nums</code>.</p> | ||
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| <p>A sequence of numbers is called arithmetic if it consists of <strong>at least three elements</strong> and if the difference between any two consecutive elements is the same.</p> | ||
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| <ul> | ||
| <li>For example, <code>[1, 3, 5, 7, 9]</code>, <code>[7, 7, 7, 7]</code>, and <code>[3, -1, -5, -9]</code> are arithmetic sequences.</li> | ||
| <li>For example, <code>[1, 1, 2, 5, 7]</code> is not an arithmetic sequence.</li> | ||
| </ul> | ||
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| <p>A <strong>subsequence</strong> of an array is a sequence that can be formed by removing some elements (possibly none) of the array.</p> | ||
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| <ul> | ||
| <li>For example, <code>[2,5,10]</code> is a subsequence of <code>[1,2,1,<strong><u>2</u></strong>,4,1,<u><strong>5</strong></u>,<u><strong>10</strong></u>]</code>.</li> | ||
| </ul> | ||
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| <p>The test cases are generated so that the answer fits in <strong>32-bit</strong> integer.</p> | ||
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| <p> </p> | ||
| <p><strong class="example">Example 1:</strong></p> | ||
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| <pre><strong>Input:</strong> nums = [2,4,6,8,10] | ||
| <strong>Output:</strong> 7 | ||
| <strong>Explanation:</strong> All arithmetic subsequence slices are: | ||
| [2,4,6] | ||
| [4,6,8] | ||
| [6,8,10] | ||
| [2,4,6,8] | ||
| [4,6,8,10] | ||
| [2,4,6,8,10] | ||
| [2,6,10] | ||
| </pre> | ||
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| <p><strong class="example">Example 2:</strong></p> | ||
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| <pre><strong>Input:</strong> nums = [7,7,7,7,7] | ||
| <strong>Output:</strong> 16 | ||
| <strong>Explanation:</strong> Any subsequence of this array is arithmetic. | ||
| </pre> | ||
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| <p> </p> | ||
| <p><strong>Constraints:</strong></p> | ||
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| <ul> | ||
| <li><code>1 <= nums.length <= 1000</code></li> | ||
| <li><code>-2<sup>31</sup> <= nums[i] <= 2<sup>31</sup> - 1</code></li> | ||
| </ul> | ||
| </div> |