3505 - Minimum Operations to Make Elements Within K Subarrays Equal.

Hard

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 non-empty 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:

• <code>2 <= nums.length <= 10⁵</code>

• <code>-10⁶<= numsi<= 10⁶</code>

• 2 <= x <= nums.length

• 1 <= k <= 15

• 2 <= k * x <= nums.length