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 emoving the 3rd element
array becomes {1, 2, 4, 5} whose mean is 3 too.

Input : a[] = {5, 4, 3, 6}
Output : -1

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 a remove element 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 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..

Output :

3

Time Complexity : O(N)

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Improved By : vt_m, sanjeev2552, Akanksha_Rai

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