leetcode-problemset/leetcode-cn/problem (English)/最长等差数列(English) [longest-arithmetic-subsequence].html

<p>Given an array <code>nums</code> of integers, return the <strong>length</strong> of the longest arithmetic subsequence in <code>nums</code>.</p>

<p>Recall that a <em>subsequence</em> of an array <code>nums</code> is a list <code>nums[i<sub>1</sub>], nums[i<sub>2</sub>], ..., nums[i<sub>k</sub>]</code> with <code>0 &lt;= i<sub>1</sub> &lt; i<sub>2</sub> &lt; ... &lt; i<sub>k</sub> &lt;= nums.length - 1</code>, and that a sequence <code>seq</code> is <em>arithmetic</em> if <code>seq[i+1] - seq[i]</code> are all the same value (for <code>0 &lt;= i &lt; seq.length - 1</code>).</p>

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,6,9,12]
<strong>Output:</strong> 4
<strong>Explanation: </strong>
The whole array is an arithmetic sequence with steps of length = 3.
</pre>

<p><strong>Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [9,4,7,2,10]
<strong>Output:</strong> 3
<strong>Explanation: </strong>
The longest arithmetic subsequence is [4,7,10].
</pre>

<p><strong>Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [20,1,15,3,10,5,8]
<strong>Output:</strong> 4
<strong>Explanation: </strong>
The longest arithmetic subsequence is [20,15,10,5].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 500</code></li>
</ul>