2448. Minimum Cost to Make Array Equal

Problem Link

Description

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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
• Test cases are generated in a way that the output doesn't exceed 2⁵³-1

Solution

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Python3

class Solution:
    def minCost(self, nums: List[int], cost: List[int]) -> int:
 
        def count(k):
            return sum(abs(x - k) * c for x, c in zip(nums, cost))
        
        left, right = min(nums), max(nums)
        while left <= right:
            mid1 = left + (right - left) // 3
            mid2 = right - (right - left) // 3
 
            if count(mid1) <= count(mid2):
                right = mid2 - 1
            else:
                left = mid1 + 1
 
        # print(left, cost)
 
        return count(left)