[LeetCode]453. Minimum Moves to Equal Array Elements

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:

1
2
3
4
5
6
7
8
9
10
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

1
2
3
4
5
6
(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

1
2
3
4
5
6
7
8
9
10
11
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