[LeetCode]453. Minimum Moves to Equal Array Elements

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题目

Given a non-empty integer array of size n, find the minimum number of moves required to make all array elements equal, where a move is incrementing n - 1 elements by 1.

Example:

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Input:
[1,2,3]

Output:
3

Explanation:
Only three moves are needed (remember each move increments two elements):

[1,2,3]  =>  [2,3,3]  =>  [3,4,3]  =>  [4,4,4]

难度

Easy

方法

这是一个数学题，假设数组中最小的数为min，需要移动x次，最后数组中的数都为m，则其实是一个求x的方法

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(n - 1) * x + sum = n * m
min + x = m
nx - x + sum = n * (min + x)
nx - x + sum = n * min + nx
sum - x = n * min
x = sum - n * min

python代码

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class Solution(object):
    def minMoves(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        nums = sorted(nums)
        return sum(nums) - len(nums) * nums[0]

assert Solution().minMoves([1,2,3]) == 3
assert Solution().minMoves([1,1,3]) == 2