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3505. Minimum Operations to Make Elements Within K Subarrays Equal

Description

You are given an integer array nums and two integers, x and k. You can perform the following operation any number of times (including zero):

• Increase or decrease any element of nums by 1.

Return the minimum number of operations needed to have at least k non-overlapping subarrays of size exactly x in nums, where all elements within each subarray are equal.

 

Example 1:

Input: nums = [5,-2,1,3,7,3,6,4,-1], x = 3, k = 2

Output: 8

Explanation:

• Use 3 operations to add 3 to nums[1] and use 2 operations to subtract 2 from nums[3]. The resulting array is [5, 1, 1, 1, 7, 3, 6, 4, -1].
• Use 1 operation to add 1 to nums[5] and use 2 operations to subtract 2 from nums[6]. The resulting array is [5, 1, 1, 1, 7, 4, 4, 4, -1].
• Now, all elements within each subarray [1, 1, 1] (from indices 1 to 3) and [4, 4, 4] (from indices 5 to 7) are equal. Since 8 total operations were used, 8 is the output.

Example 2:

Input: nums = [9,-2,-2,-2,1,5], x = 2, k = 2

Output: 3

Explanation:

• Use 3 operations to subtract 3 from nums[4]. The resulting array is [9, -2, -2, -2, -2, 5].
• Now, all elements within each subarray [-2, -2] (from indices 1 to 2) and [-2, -2] (from indices 3 to 4) are equal. Since 3 operations were used, 3 is the output.

 

Constraints:

• 2 <= nums.length <= 105
• -106 <= nums[i] <= 106
• 2 <= x <= nums.length
• 1 <= k <= 15
• 2 <= k * x <= nums.length

Solutions

Solution 1

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