LeetCode 453. Minimum Moves to Equal Array Elements

453. Minimum Moves to Equal Array Elements

Description

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:

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]

Solution

题意即给一个n大小的数组，返回最小的更改次数（更改即+1，每次更改n-1个数），使得最终所有的数字相等。

我们先设sum是最后数组的和，m是最小的更改次数，min_num是原始数组中最小的数字，x是最终的数字。

那么我们有

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

并且有

x = minNum + m

(贪心的思想) 联立可以解出

sum - minNum * n = m

代码如下

int minMoves(int* nums, int numsSize) {
if (numsSize == 0) return 0;
int min_num = nums[0],sum = nums[0];
for (int i = 1;i < numsSize;i++) {
if (nums[i] < min_num) min_num = nums[i];
sum += nums[i];
}
return sum - numsSize * min_num;
}