leetcode-problemset/leetcode-cn/originData/constrained-subsequence-sum.json

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            "categoryTitle": "Algorithms",
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            "title": "Constrained Subsequence Sum",
            "titleSlug": "constrained-subsequence-sum",
            "content": "<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return the maximum sum of a <strong>non-empty</strong> subsequence of that array such that for every two <strong>consecutive</strong> integers in the subsequence, <code>nums[i]</code> and <code>nums[j]</code>, where <code>i &lt; j</code>, the condition <code>j - i &lt;= k</code> is satisfied.</p>\n\n<p>A <em>subsequence</em> of an array is obtained by deleting some number of elements (can be zero) from the array, leaving the remaining elements in their original order.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [10,2,-10,5,20], k = 2\n<strong>Output:</strong> 37\n<b>Explanation:</b> The subsequence is [10, 2, 5, 20].\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [-1,-2,-3], k = 1\n<strong>Output:</strong> -1\n<b>Explanation:</b> The subsequence must be non-empty, so we choose the largest number.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [10,-2,-10,-5,20], k = 2\n<strong>Output:</strong> 23\n<b>Explanation:</b> The subsequence is [10, -2, -5, 20].\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
            "translatedTitle": "带限制的子序列和",
            "translatedContent": "<p>给你一个整数数组&nbsp;<code>nums</code>&nbsp;和一个整数&nbsp;<code>k</code>&nbsp;，请你返回 <strong>非空</strong>&nbsp;子序列元素和的最大值，子序列需要满足：子序列中每两个 <strong>相邻</strong>&nbsp;的整数&nbsp;<code>nums[i]</code>&nbsp;和&nbsp;<code>nums[j]</code>&nbsp;，它们在原数组中的下标&nbsp;<code>i</code>&nbsp;和&nbsp;<code>j</code>&nbsp;满足&nbsp;<code>i &lt; j</code>&nbsp;且 <code>j - i &lt;= k</code> 。</p>\n\n<p>数组的子序列定义为：将数组中的若干个数字删除（可以删除 0 个数字），剩下的数字按照原本的顺序排布。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>nums = [10,2,-10,5,20], k = 2\n<strong>输出：</strong>37\n<strong>解释：</strong>子序列为 [10, 2, 5, 20] 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>nums = [-1,-2,-3], k = 1\n<strong>输出：</strong>-1\n<strong>解释：</strong>子序列必须是非空的，所以我们选择最大的数字。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><strong>输入：</strong>nums = [10,-2,-10,-5,20], k = 2\n<strong>输出：</strong>23\n<strong>解释：</strong>子序列为 [10, -2, -5, 20] 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= nums.length &lt;= 10^5</code></li>\n\t<li><code>-10^4&nbsp;&lt;= nums[i] &lt;= 10^4</code></li>\n</ul>\n",
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            "hints": [
                "Use dynamic programming.",
                "Let dp[i] be the solution for the prefix of the array that ends at index i, if the element at index i is in the subsequence.",
                "dp[i] = nums[i] + max(0, dp[i-k], dp[i-k+1], ..., dp[i-1])",
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