1551. Minimum Operations to Make Array Equal (M) Minimum Operations to Make Array Equal (M)

题目

You have an array arr of length n where arr[i] = (2 * i) + 1 for all valid values of i (i.e. 0 <= i < n).

In one operation, you can select two indices x and y where 0 <= x, y < n and subtract 1 from arr[x] and add 1 to arr[y] (i.e. perform arr[x] -=1 and arr[y] += 1). The goal is to make all the elements of the array equal. It is guaranteed that all the elements of the array can be made equal using some operations.

Given an integer n, the length of the array. Return the minimum number of operations needed to make all the elements of arr equal.

Example 1:

Input: n = 3
Output: 2
Explanation: arr = [1, 3, 5]
First operation choose x = 2 and y = 0, this leads arr to be [2, 3, 4]
In the second operation choose x = 2 and y = 0 again, thus arr = [3, 3, 3].

Example 2:

Input: n = 6
Output: 9

Constraints:

• 1 <= n <= 10^4

---

题意

给定一个长度为n的等差数列，每次可选取两个元素分别进行加1和减1，问最少需要几次操作使所有元素相等。

思路

找规律题。列出初始的几个数组[1]、[1, 3]、[1, 3, 5]、[1, 3, 5, 7]，很容易找到规律：若n是奇数，答案为 2 + 4 + 6 + ...，共(n-1)/2项；若n是偶数，答案为 1 + 3 + 5 + ...，共n/2项。

---

代码实现

Java

class Solution {
    public int minOperations(int n) {
        return n % 2 == 0 ? n * n / 4 : (n * n - 1) / 4;
    }
}