Minimum Operations to Make Array Equal

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

Solution

Java Program

class Solution {
    public int minOperations(int n) {
        int min = 1;
        int max = 2 * (n - 1) + 1;
        int equalNumber = (min + max)/2;
        
        int result = 0;
        for(int index = 0; index < (n/2); index++)
        {
            result += (equalNumber - (2 * index + 1));
        }
        return result;
    }
}

Code walkthrough

n = 6, arr = [1, 3, 5, 7, 9, 11]

1st Operation: arr = [2, 3, 5, 7, 9, 10];
2nd Operation: arr = [3, 3, 5, 7, 9, 9];
3rd Operation: arr = [3, 4, 5, 7, 8, 9];
4th Operation: arr = [4, 4, 5, 7, 8, 8];
5th Operation: arr = [4, 5, 5, 7, 7, 8];
6th Operation: arr = [5, 5, 5, 7, 7, 7];
7th Operation: arr = [5, 5, 6, 6, 7, 7];
8th Operation: arr = [1, 6, 6, 6, 6, 11];
9th Operation: arr = [6, 6, 6, 6, 6, 6];

Output: 9
From the above operations you can observe one thing that, 
min = 1
max = 11
equalNumber = (min + max)/2 = (1 + 11)/2 = 6;

result = (6-1) + (6-3) + (6-5) => 9

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