leetcode-problemset/leetcode-cn/originData/find-the-maximum-length-of-valid-subsequence-ii.json

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            "categoryTitle": "Algorithms",
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            "title": "Find the Maximum Length of Valid Subsequence II",
            "titleSlug": "find-the-maximum-length-of-valid-subsequence-ii",
            "content": "You are given an integer array <code>nums</code> and a <strong>positive</strong> integer <code>k</code>.\n<p>A <span data-keyword=\"subsequence-array\">subsequence</span> <code>sub</code> of <code>nums</code> with length <code>x</code> is called <strong>valid</strong> if it satisfies:</p>\n\n<ul>\n\t<li><code>(sub[0] + sub[1]) % k == (sub[1] + sub[2]) % k == ... == (sub[x - 2] + sub[x - 1]) % k.</code></li>\n</ul>\nReturn the length of the <strong>longest</strong> <strong>valid</strong> subsequence of <code>nums</code>.\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,2,3,4,5], k = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The longest valid subsequence is <code>[1, 2, 3, 4, 5]</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,4,2,3,1,4], k = 3</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The longest valid subsequence is <code>[1, 4, 1, 4]</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= nums.length &lt;= 10<sup>3</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= 10<sup>3</sup></code></li>\n</ul>\n",
            "translatedTitle": "找出有效子序列的最大长度 II",
            "translatedContent": "给你一个整数数组&nbsp;<code>nums</code>&nbsp;和一个 <strong>正</strong>&nbsp;整数&nbsp;<code>k</code>&nbsp;。\n<p><code>nums</code>&nbsp;的一个&nbsp;<span data-keyword=\"subsequence-array\">子序列</span> <code>sub</code>&nbsp;的长度为 <code>x</code>&nbsp;，如果其满足以下条件，则称其为 <strong>有效子序列</strong>&nbsp;：</p>\n\n<ul>\n\t<li><code>(sub[0] + sub[1]) % k == (sub[1] + sub[2]) % k == ... == (sub[x - 2] + sub[x - 1]) % k</code></li>\n</ul>\n返回 <code>nums</code>&nbsp;的 <strong>最长</strong><strong>有效子序列</strong>&nbsp;的长度。\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [1,2,3,4,5], k = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>5</span></p>\n\n<p><b>解释：</b></p>\n\n<p>最长有效子序列是&nbsp;<code>[1, 2, 3, 4, 5]</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [1,4,2,3,1,4], k = 3</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>4</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>最长有效子序列是&nbsp;<code>[1, 4, 1, 4]</code>&nbsp;。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= nums.length &lt;= 10<sup>3</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= 10<sup>3</sup></code></li>\n</ul>\n",
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                "Fix the value of <code>(subs[0] + subs[1]) % k</code> from the <code>k</code> possible values. Let it be <code>val</code>.",
                "Let <code>dp[i]</code> store the maximum length of a subsequence with its last element <code>x</code> such that <code>x % k == i</code>.",
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