Removing a number from array without changing its arithmetic mean

Given an array a[] of positive integers of size N. The task is to remove one element from the given array such that the arithmetic mean of the array remains the same as it was before. If it is possible to remove any such number then print that number. Otherwise, print -1.
Examples:

Input : a[] = {1, 2, 3, 4, 5} 
Output : 3
Mean of the given array is 3. After removing the 3rd element 
array becomes {1, 2, 4, 5} whose mean is 3 too.
Input : a[] = {5, 4, 3, 6} 
Output : -1 

Approach :

An efficient approach is to find the mean of the array, and check whether the mean is present in the given array or not. We can only remove elements whose value is equal to mean. 

let mean of the original array be M, the sum of the elements be sum. Then sum = M * N. After removing M, the new mean will be ( (M * N ) – M) / (N – 1) = M, which remains same. So just use any search approach and print the element. 

Below is the implementation of the above approach : 

C++

// CPP program to remove a number from the
// array without changing its arithmetic mean
#include <bits/stdc++.h>
using namespace std;

// Function to remove a number from the
// array without changing its arithmetic mean
int FindElement(int a[], int n)
{
    // Find sum of all elements
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum = sum + a[i];

    // If mean is an integer
    if (sum % n == 0) {
        int m = sum / n;

        // Check if mean is present in the array or not
        for (int i = 0; i < n; i++)
            if (a[i] == m)
                return m;
    }

    return -1;
}

// Driver code
int main()
{
    int a[] = { 1, 2, 3, 4, 5 };

    int n = sizeof(a) / sizeof(int);

    cout << FindElement(a, n);

    return 0;
}

Java

// Java program to remove a number from the
// array without changing its arithmetic mean
import java.io.*;

class GFG
{

// Function to remove a number from the
// array without changing its arithmetic mean
static int FindElement(int a[], int n)
{
    // Find sum of all elements
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum = sum + a[i];

    // If mean is an integer
    if (sum % n == 0)
    {
        int m = sum / n;

        // Check if mean is present in the array or not
        for (int i = 0; i < n; i++)
            if (a[i] == m)
                return m;
    }

    return -1;
}

// Driver code
public static void main (String[] args)
{
    int a[] = { 1, 2, 3, 4, 5 };
    int n = a.length;

    System.out.print(FindElement(a, n));
}
}

// This code is contributed by anuj_67..

Python3

# Python3 program to remove a number from the
# array without changing its arithmetic mean

# Function to remove a number from the
# array without changing its arithmetic mean
def FindElement(a, n):

    # Find sum of all elements
    s = 0
    for i in range(n):
        s = s + a[i]

    # If mean is an integer
    if s % n == 0:
        m = s // n

        # Check if mean is present
        # in the array or not
        for j in range(n):
            if a[j] == m:
                return m
    return -1

# Driver code
if __name__ == "__main__":
    a = [1, 2, 3, 4, 5]
    n = len(a)
    print(FindElement(a, n))

# This code is contributed by
# sanjeev2552

C#

// C# program to remove a number from the
// array without changing its arithmetic mean
using System;

class GFG
{

// Function to remove a number from the
// array without changing its arithmetic mean
static int FindElement(int []a, int n)
{
    // Find sum of all elements
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum = sum + a[i];

    // If mean is an integer
    if (sum % n == 0)
    {
        int m = sum / n;

        // Check if mean is present in the array or not
        for (int i = 0; i < n; i++)
            if (a[i] == m)
                return m;
    }

    return -1;
}

// Driver code
public static void Main ()
{
    int []a = { 1, 2, 3, 4, 5 };
    int n = a.Length;

    Console.WriteLine(FindElement(a, n));
}
}

// This code is contributed by anuj_67..

Javascript

<script>

// Javascript program to remove a number from the
// array without changing its arithmetic mean

// Function to remove a number from the
// array without changing its arithmetic mean
function FindElement(a, n)
{
    // Find sum of all elements
    let sum = 0;
    for (let i = 0; i < n; i++)
        sum = sum + a[i];

    // If mean is an integer
    if (sum % n == 0) {
        let m = parseInt(sum / n);

        // Check if mean is present in
        // the array or not
        for (let i = 0; i < n; i++)
            if (a[i] == m)
                return m;
    }

    return -1;
}

// Driver code
    let a = [ 1, 2, 3, 4, 5 ];

    let n = a.length;

    document.write(FindElement(a, n));

</script>

Output:

3

Time Complexity : O(N)

Auxiliary Space: O(1)