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3424. Minimum Cost to Make Arrays Identical

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ArrayGreedySorting

You are given two integer arrays arr and brr of length n, and an integer k. You can perform the following operations on arr any number of times:

  • Split arr into any number of contiguous subarrays and rearrange these subarrays in any order. This operation has a fixed cost of k.

  • Choose any element in arr and add or subtract a positive integer x to it. The cost of this operation is x.

Return the minimum total cost to make arr equal to brr.

 

Example 1:

Input: arr = [-7,9,5], brr = [7,-2,-5], k = 2

Output: 13

Explanation:

  • Split arr into two contiguous subarrays: [-7] and [9, 5] and rearrange them as [9, 5, -7], with a cost of 2.
  • Subtract 2 from element arr[0]. The array becomes [7, 5, -7]. The cost of this operation is 2.
  • Subtract 7 from element arr[1]. The array becomes [7, -2, -7]. The cost of this operation is 7.
  • Add 2 to element arr[2]. The array becomes [7, -2, -5]. The cost of this operation is 2.

The total cost to make the arrays equal is 2 + 2 + 7 + 2 = 13.

Example 2:

Input: arr = [2,1], brr = [2,1], k = 0

Output: 0

Explanation:

Since the arrays are already equal, no operations are needed, and the total cost is 0.

 

Constraints:

  • 1 <= arr.length == brr.length <= 105
  • 0 <= k <= 2 * 1010
  • -105 <= arr[i] <= 105
  • -105 <= brr[i] <= 105

Hints

Hint 1
What does Operation 1 (rearranging subarrays) actually accomplish?
Hint 2
Calculate sum(abs(arr[i] - brr[i])) if you do not use Operation 1.
Hint 3
Calculate sum(abs(arr[i] - brr[i])) after sorting both arrays if you use Operation 1.
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