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 :3Mean 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

**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 <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; ` `} ` |

*chevron_right*

*filter_none*

## 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.. ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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.. ` |

*chevron_right*

*filter_none*

**Output :**

3

**Time Complexity : **O(N)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.

## Recommended Posts:

- Find Harmonic mean using Arithmetic mean and Geometric mean
- Length of longest sub-array with maximum arithmetic mean.
- Number of ways to remove elements to maximize arithmetic mean
- Sort an array without changing position of negative numbers
- Divide array into increasing and decreasing subsequence without changing the order
- Arithmetic Mean
- Arrangement of words without changing the relative position of vowel and consonants
- Count of elements that can be deleted without disturbing the mean of the initial array
- Steps to make array empty by removing maximum and its right side
- Finding Mean, Median, Mode in Python without libraries
- Find K such that changing all elements of the Array greater than K to K will make array sum N
- Number of steps to sort the array by changing order of three elements in each step
- Count of Array elements greater than all elements on its left and at least K elements on its right
- Count of Array elements greater than all elements on its left and next K elements on its right
- Add two numbers without using arithmetic operators
- How to sum two integers without using arithmetic operators in C/C++?
- Decimal to binary conversion without using arithmetic operators
- Subtract 1 without arithmetic operators
- Find N numbers such that a number and its reverse are divisible by sum of its digits
- Smallest N digit number with none of its digits as its divisor

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.