Constrained Subsequence Sum

arraydynamic programmingqueue

Problem Statement

Given an integer array nums and an integer k , return the maximum sum of a non-empty subsequence of that array such that for every two consecutive integers in the subsequence, nums[i] and nums[j] , where i < j , the condition j - i <= k is satisfied.

A subsequence 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.

Examples

Example 1

Input: nums = [10,2,-10,5,20], k = 2
Output: 37
The subsequence is [10, 2, 5, 20].

Example 2

Input: nums = [-1,-2,-3], k = 1
Output: -1
The subsequence must be non-empty, so we choose the largest number.

Example 3

Input: nums = [10,-2,-10,-5,20], k = 2
Output: 23
The subsequence is [10, -2, -5, 20].

Constraints

1 <= k <= nums.length <= 10 ^5

-10 ^4 <= nums[i] <= 10 ^4

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming