2448. Minimum Cost to Make Array Equal

Description

You are given two 0-indexed arrays nums and cost consisting each of n positive integers.

You can do the following operation any number of times:

• Increase or decrease any element of the array nums by 1.

The cost of doing one operation on the ith element is cost[i].

Return the minimum total cost such that all the elements of the array nums become equal.

 

Example 1:

Input: nums = [1,3,5,2], cost = [2,3,1,14]
Output: 8
Explanation: We can make all the elements equal to 2 in the following way:
- Increase the 0th element one time. The cost is 2.
- Decrease the 1st element one time. The cost is 3.
- Decrease the 2nd element three times. The cost is 1 + 1 + 1 = 3.
The total cost is 2 + 3 + 3 = 8.
It can be shown that we cannot make the array equal with a smaller cost.

Example 2:

Input: nums = [2,2,2,2,2], cost = [4,2,8,1,3]
Output: 0
Explanation: All the elements are already equal, so no operations are needed.

 

Constraints:

• n == nums.length == cost.length
• 1 <= n <= 105
• 1 <= nums[i], cost[i] <= 106

Solution

minimum-cost-to-make-array-equal.py

class Solution:
    def minCost(self, nums: List[int], cost: List[int]) -> int:
        left, right = min(nums), max(nums)

        def good(k):
            res = 0

            for x, d in zip(nums, cost):
                res += (abs(k - x)) * d

            return res

        while left < right:
            mid = (left + right) // 2

            if good(mid) <= good(mid + 1):
                right = mid
            else:
                left = mid + 1

        return good(left)