Minimum Cost to Make Array Equal — LeetCode 2448 Python Solution

The problem

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.

Example

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:

Python solution

class Solution:
    def minCost(self, nums: List[int], cost: List[int]) -> int:
        arr = sorted(zip(nums, cost))
        n = len(arr)
        f = [0] * (n + 1)
        g = [0] * (n + 1)
        for i in range(1, n + 1):
            a, b = arr[i - 1]
            f[i] = f[i - 1] + a * b
            g[i] = g[i - 1] + b
        ans = inf
        for i in range(1, n + 1):
            a = arr[i - 1][0]
            l = a * g[i - 1] - f[i - 1]
            r = f[n] - f[i] - a * (g[n] - g[i])
            ans = min(ans, l + r)
        return ans

Complexity

Pattern: Prefix Sum

Precompute running totals once so any range query becomes a single subtraction. LeetCode 2448. Minimum Cost to Make Array Equal is filed here because LeetCode tags it Prefix Sum, which is the vocabulary this hub collects.

The prefix sum guide has the Python template for the pattern and the 157 LeetCode problems that use it.

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