leetcode-problemset/leetcode-cn/originData/longest-arithmetic-subsequence-of-given-difference.json

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            "categoryTitle": "Algorithms",
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            "title": "Longest Arithmetic Subsequence of Given Difference",
            "titleSlug": "longest-arithmetic-subsequence-of-given-difference",
            "content": "<p>Given an integer array <code>arr</code> and an integer <code>difference</code>, return the length of the longest subsequence in <code>arr</code> which is an arithmetic sequence such that the difference between adjacent elements in the subsequence equals <code>difference</code>.</p>\n\n<p>A <strong>subsequence</strong> is a sequence that can be derived from <code>arr</code> by deleting some or no elements without changing the order of the remaining elements.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [1,2,3,4], difference = 1\n<strong>Output:</strong> 4\n<strong>Explanation: </strong>The longest arithmetic subsequence is [1,2,3,4].</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [1,3,5,7], difference = 1\n<strong>Output:</strong> 1\n<strong>Explanation: </strong>The longest arithmetic subsequence is any single element.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [1,5,7,8,5,3,4,2,1], difference = -2\n<strong>Output:</strong> 4\n<strong>Explanation: </strong>The longest arithmetic subsequence is [7,5,3,1].\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>4</sup> &lt;= arr[i], difference &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
            "translatedTitle": "最长定差子序列",
            "translatedContent": "<p>给你一个整数数组 <code>arr</code> 和一个整数 <code>difference</code>，请你找出并返回 <code>arr</code> 中最长等差子序列的长度，该子序列中相邻元素之间的差等于 <code>difference</code> 。</p>\n\n<p><strong>子序列</strong> 是指在不改变其余元素顺序的情况下，通过删除一些元素或不删除任何元素而从 <code>arr</code> 派生出来的序列。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>arr = [1,2,3,4], difference = 1\n<strong>输出：</strong>4\n<strong>解释：</strong>最长的等差子序列是 [1,2,3,4]。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>arr = [1,3,5,7], difference = 1\n<strong>输出：</strong>1\n<strong>解释：</strong>最长的等差子序列是任意单个元素。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>arr = [1,5,7,8,5,3,4,2,1], difference = -2\n<strong>输出：</strong>4\n<strong>解释：</strong>最长的等差子序列是 [7,5,3,1]。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= arr.length <= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>4</sup> <= arr[i], difference <= 10<sup>4</sup></code></li>\n</ul>\n",
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                "Use dynamic programming.",
                "Let dp[i] be the maximum length of a subsequence of the given difference whose last element is i.",
                "dp[i] = 1 + dp[i-k]"
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