Make Array Elements Equal

Problem Statement - link #

You are given an integer N. Consider an array arr having N elements where arr[i] = 2*i+1. (The array is 0-indexed)

You are allowed to perform the given operation on the array any number of times:

1. Select two indices i and j and increase arr[i] by 1 and decrease arr[j] by 1.

Your task is to find the minimum number of such operations required to make all the elements of the array equal.

Your Task:

Complete the function minOperations() which takes the integer N as the input parameter, and returns the minimum operations required to make all the array elements equal.

Expected Time Complexity: O(1)
Expected Auxiliary Space: O(1)

Examples #

Example 1:

Input:
N = 3
Output:
2
Explanation:
Initially the array is {1, 3, 5}. If we perform
the operation once on the indices 0 and 2, the 
resulting array will be {2, 3, 4}. If we again 
perform the operation once on the indices 0
and 2, the resulting array will be {3, 3, 3}.
Hence, the minimum operations required is 2
in this case. 

Example 2:

Input: 
N = 2
Output:
1
Explanation: 
The array initially is {1, 3}. After performing 
an operation the array will be {2, 2}. Hence,
the answer is 1 in this case.

Constraints #

• 1 ≤ N ≤ 10^9

Solutions #

class Solution {
  public:
    long long int minOperations(int N) {
        if(N == 1) return 1;
        
        long long int cn = N;
        long long int hn = N/2;
        
        long long int res = hn*cn - hn*hn;
        return res;
    }
};