1551. Minimum Operations to Make Array Equal

LeetCode 1551. Minimum Operations to Make Array Equal

Description

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] -=1and 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

Tags

Math

Solution

The answer is the sum of the difference of n and each element in the first half of the array. res = n * n / 2 - sum(nums[:n/2])

$result = \frac{n}{2} \times n - (1+2\frac{n}{2}-1)\times \frac{n}{2} / 2 = n^2/4$

Complexity

• Time complexity: $O(1)$

• Space complexity: $O(1)$

Code

func minOperations(n int) int {
	return n * n >> 2
}