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3691. Maximum Total Subarray Value II

Description

You are given an integer array nums of length n and an integer k.

You must select exactly k distinct non-empty subarrays nums[l..r] of nums. Subarrays may overlap, but the exact same subarray (same l and r) cannot be chosen more than once.

The value of a subarray nums[l..r] is defined as: max(nums[l..r]) - min(nums[l..r]).

The total value is the sum of the values of all chosen subarrays.

Return the maximum possible total value you can achieve.

 

Example 1:

Input: nums = [1,3,2], k = 2

Output: 4

Explanation:

One optimal approach is:

  • Choose nums[0..1] = [1, 3]. The maximum is 3 and the minimum is 1, giving a value of 3 - 1 = 2.
  • Choose nums[0..2] = [1, 3, 2]. The maximum is still 3 and the minimum is still 1, so the value is also 3 - 1 = 2.

Adding these gives 2 + 2 = 4.

Example 2:

Input: nums = [4,2,5,1], k = 3

Output: 12

Explanation:

One optimal approach is:

  • Choose nums[0..3] = [4, 2, 5, 1]. The maximum is 5 and the minimum is 1, giving a value of 5 - 1 = 4.
  • Choose nums[1..3] = [2, 5, 1]. The maximum is 5 and the minimum is 1, so the value is also 4.
  • Choose nums[2..3] = [5, 1]. The maximum is 5 and the minimum is 1, so the value is again 4.

Adding these gives 4 + 4 + 4 = 12.

 

Constraints:

  • 1 <= n == nums.length <= 5 * 10​​​​​​​4
  • 0 <= nums[i] <= 109
  • 1 <= k <= min(105, n * (n + 1) / 2)

Solutions

Solution 1

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1


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1

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