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"title": "Constrained Subsequence Sum",
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"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 < j</code>, the condition <code>j - i <= 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> </p>\n<p><strong>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>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>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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= k <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>4</sup> <= nums[i] <= 10<sup>4</sup></code></li>\n</ul>\n",
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"code": "class Solution {\npublic:\n int constrainedSubsetSum(vector<int>& nums, int k) {\n \n }\n};",
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"code": "class Solution(object):\n def constrainedSubsetSum(self, nums, k):\n \"\"\"\n :type nums: List[int]\n :type k: int\n :rtype: int\n \"\"\"\n ",
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"code": "/**\n * @param {number[]} nums\n * @param {number} k\n * @return {number}\n */\nvar constrainedSubsetSum = function(nums, k) {\n \n};",
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"code": "# @param {Integer[]} nums\n# @param {Integer} k\n# @return {Integer}\ndef constrained_subset_sum(nums, k)\n \nend",
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"code": "impl Solution {\n pub fn constrained_subset_sum(nums: Vec<i32>, k: i32) -> i32 {\n \n }\n}",
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"lang": "PHP",
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"code": "class Solution {\n\n /**\n * @param Integer[] $nums\n * @param Integer $k\n * @return Integer\n */\n function constrainedSubsetSum($nums, $k) {\n \n }\n}",
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"code": "function constrainedSubsetSum(nums: number[], k: number): number {\n\n};",
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"code": "-spec constrained_subset_sum(Nums :: [integer()], K :: integer()) -> integer().\nconstrained_subset_sum(Nums, K) ->\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])",
"Use a heap with the sliding window technique to optimize the dp."
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