mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-10 18:48:13 +08:00
209 lines
24 KiB
JSON
209 lines
24 KiB
JSON
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"questionId": "2526",
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"title": "Longest Increasing Subsequence II",
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"content": "<p>You are given an integer array <code>nums</code> and an integer <code>k</code>.</p>\n\n<p>Find the longest subsequence of <code>nums</code> that meets the following requirements:</p>\n\n<ul>\n\t<li>The subsequence is <strong>strictly increasing</strong> and</li>\n\t<li>The difference between adjacent elements in the subsequence is <strong>at most</strong> <code>k</code>.</li>\n</ul>\n\n<p>Return<em> the length of the <strong>longest</strong> <strong>subsequence</strong> that meets the requirements.</em></p>\n\n<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [4,2,1,4,3,4,5,8,15], k = 3\n<strong>Output:</strong> 5\n<strong>Explanation:</strong>\nThe longest subsequence that meets the requirements is [1,3,4,5,8].\nThe subsequence has a length of 5, so we return 5.\nNote that the subsequence [1,3,4,5,8,15] does not meet the requirements because 15 - 8 = 7 is larger than 3.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [7,4,5,1,8,12,4,7], k = 5\n<strong>Output:</strong> 4\n<strong>Explanation:</strong>\nThe longest subsequence that meets the requirements is [4,5,8,12].\nThe subsequence has a length of 4, so we return 4.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,5], k = 1\n<strong>Output:</strong> 1\n<strong>Explanation:</strong>\nThe longest subsequence that meets the requirements is [1].\nThe subsequence has a length of 1, so we return 1.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i], k <= 10<sup>5</sup></code></li>\n</ul>\n",
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"translatedTitle": "最长递增子序列 II",
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"translatedContent": "<p>给你一个整数数组 <code>nums</code> 和一个整数 <code>k</code> 。</p>\n\n<p>找到 <code>nums</code> 中满足以下要求的最长子序列：</p>\n\n<ul>\n\t<li>子序列 <strong>严格递增</strong></li>\n\t<li>子序列中相邻元素的差值 <strong>不超过</strong> <code>k</code> 。</li>\n</ul>\n\n<p>请你返回满足上述要求的 <strong>最长子序列</strong> 的长度。</p>\n\n<p><strong>子序列</strong> 是从一个数组中删除部分元素后，剩余元素不改变顺序得到的数组。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>nums = [4,2,1,4,3,4,5,8,15], k = 3\n<b>输出：</b>5\n<strong>解释：</strong>\n满足要求的最长子序列是 [1,3,4,5,8] 。\n子序列长度为 5 ，所以我们返回 5 。\n注意子序列 [1,3,4,5,8,15] 不满足要求，因为 15 - 8 = 7 大于 3 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>nums = [7,4,5,1,8,12,4,7], k = 5\n<b>输出：</b>4\n<strong>解释：</strong>\n满足要求的最长子序列是 [4,5,8,12] 。\n子序列长度为 4 ，所以我们返回 4 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><b>输入：</b>nums = [1,5], k = 1\n<b>输出：</b>1\n<strong>解释：</strong>\n满足要求的最长子序列是 [1] 。\n子序列长度为 1 ，所以我们返回 1 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i], k <= 10<sup>5</sup></code></li>\n</ul>\n",
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"We can use dynamic programming. Let dp[i][val] be the answer using only the first i + 1 elements, and the last element in the subsequence is equal to val.",
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"The only value that might change between dp[i - 1] and dp[i] are dp[i - 1][val] and dp[i][val].",
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"Try using dp[i - 1] and the fact that the second last element in the subsequence has to fall within a range to calculate dp[i][val].",
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href=\\\"https:\\/\\/github.com\\/emirpasic\\/gods\\/tree\\/v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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