leetcode-problemset/leetcode-cn/originData/find-the-maximum-length-of-a-good-subsequence-i.json

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            "categoryTitle": "Algorithms",
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            "title": "Find the Maximum Length of a Good Subsequence I",
            "titleSlug": "find-the-maximum-length-of-a-good-subsequence-i",
            "content": "<p>You are given an integer array <code>nums</code> and a <strong>non-negative</strong> integer <code>k</code>. A sequence of integers <code>seq</code> is called <strong>good</strong> if there are <strong>at most</strong> <code>k</code> indices <code>i</code> in the range <code>[0, seq.length - 2]</code> such that <code>seq[i] != seq[i + 1]</code>.</p>\n\n<p>Return the <strong>maximum</strong> possible length of a <strong>good</strong> <span data-keyword=\"subsequence-array\">subsequence</span> of <code>nums</code>.</p>\n\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 = [1,2,1,1,3], k = 2</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 maximum length subsequence is <code>[<u>1</u>,<u>2</u>,<u>1</u>,<u>1</u>,3]</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 = [1,2,3,4,5,1], k = 0</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The maximum length subsequence is <code>[<u>1</u>,2,3,4,5,<u>1</u>]</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 500</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= min(nums.length, 25)</code></li>\n</ul>\n",
            "translatedTitle": "求出最长好子序列 I",
            "translatedContent": "<p>给你一个整数数组&nbsp;<code>nums</code>&nbsp;和一个 <strong>非负</strong>&nbsp;整数&nbsp;<code>k</code>&nbsp;。如果一个整数序列&nbsp;<code>seq</code>&nbsp;满足在范围下标范围&nbsp;<code>[0, seq.length - 2]</code>&nbsp;中存在 <strong>不超过</strong>&nbsp;<code>k</code>&nbsp;个下标 <code>i</code>&nbsp;满足&nbsp;<code>seq[i] != seq[i + 1]</code>&nbsp;，那么我们称这个整数序列为&nbsp;<strong>好</strong>&nbsp;序列。</p>\n\n<p>请你返回 <code>nums</code>&nbsp;中&nbsp;<strong>好</strong> <span data-keyword=\"subsequence-array\">子序列</span>&nbsp;的最长长度</p>\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 = [1,2,1,1,3], k = 2</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>最长好子序列为&nbsp;<code>[<em><strong>1</strong></em>,<em><strong>2</strong></em>,<strong><em>1</em></strong>,<em><strong>1</strong></em>,3]</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 = [1,2,3,4,5,1], k = 0</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>最长好子序列为&nbsp;<code>[<strong><em>1</em></strong>,2,3,4,5,<strong><em>1</em></strong>]</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>1 &lt;= nums.length &lt;= 500</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= min(nums.length, 25)</code></li>\n</ul>\n",
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                "The absolute values in <code>nums</code> don’t really matter. So we can remap the set of values to the range <code>[0, n - 1]</code>.",
                "Let <code>dp[i][j]</code> be the length of the longest subsequence till index <code>j</code> with at most <code>i</code> positions such that <code>seq[i] != seq[i + 1]</code>.",
                "For each value <code>x</code> from left to right, update <code>dp[i][x] = max(dp[i][x] + 1, dp[i - 1][y] + 1)</code>, where <code>y != x</code>."
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