# Make all array elements equal by repeated subtraction of absolute difference of pairs from their maximum

Given an array arr[] consisting of N integers, the task is to make all array elements equal by selecting any pair of integers from the array and replacing the larger integer from the pair with their absolute difference any number of times. Print the final value of all array elements.

Examples:

Input: arr[] ={2, 3, 4}
Output: 1
Explanation:
Step 1: Performing on the pair (2, 3) modifies arr[] = {2, 1, 4}
Step 2: Performing on the pair (2, 4) modifies arr[] = {2, 1, 2}
Step 3: Performing on the pair (2, 1) modifies {1, 1, 2}
Step 4: Performing on the pair (1, 2) modifies arr[] = {1, 1, 1}

Input: arr[] = {24, 60}
Output: 12

Approach: From the above problem statement, it can be observed that for any pair (a, b), the absolute difference is subtracted from the maximum element. Then this operation is similar to finding GCD of the pair. Therefore, from this observation, it is clear that all array elements need to be reduced to the GCD of the array. Follow the steps below to solve the problem:

gcd = gcd(arr[i], gcd), where 0 ≤ i < N

• After the above step, the value of gcd is the required array element after the given operation is applied to every distinct pair of elements.

Below is the implementation of the above approach:

 `// C++ Program to implement` `// the above approach` `#include ` `using` `namespace` `std;`   `// Function to return ` `// gcd of a and b` `int` `gcd(``int` `a, ``int` `b)` `{` `  ``// Base Case` `  ``if` `(a == 0)` `    ``return` `b;`   `  ``// Recursive Call` `  ``return` `gcd(b % a, a);` `}`   `// Function to find gcd of array` `int` `findGCD(``int` `arr[], ``int` `N)` `{` `  ``// Initialise the result` `  ``int` `result = 0;`   `  ``// Traverse the array arr[]` `  ``for` `(``int` `i = 0; i < N; i++) ` `  ``{` `    ``// Update result as gcd of` `    ``// the result and arr[i]` `    ``result = gcd(result, arr[i]);`   `    ``if` `(result == 1) ` `    ``{` `      ``return` `1;` `    ``}` `  ``}`   `  ``// Return the resultant GCD` `    ``return` `result;` `}`   `// Driver Code` `int` `main()` `{` `  ``// Given array arr[]` `  ``int` `arr[] = {2, 3, 4};`   `  ``int` `N = ``sizeof``(arr) / ` `          ``sizeof``(arr);`   `  ``// Function Call` `  ``cout << findGCD(arr, N);` `  ``return` `0;` `}`   `// This code is contributed by 29AjayKumar`

 `// Java program for the above approach`   `public` `class` `GCD {`   `    ``// Function to return gcd of a and b` `    ``static` `int` `gcd(``int` `a, ``int` `b)` `    ``{` `        ``// Base Case` `        ``if` `(a == ``0``)` `            ``return` `b;`   `        ``// Recursive Call` `        ``return` `gcd(b % a, a);` `    ``}`   `    ``// Function to find gcd of array` `    ``static` `int` `findGCD(``int` `arr[], ``int` `N)` `    ``{` `        ``// Initialise the result` `        ``int` `result = ``0``;`   `        ``// Traverse the array arr[]` `        ``for` `(``int` `element : arr) {`   `            ``// Update result as gcd of` `            ``// the result and arr[i]` `            ``result = gcd(result, element);`   `            ``if` `(result == ``1``) {` `                ``return` `1``;` `            ``}` `        ``}`   `        ``// Return the resultant GCD` `        ``return` `result;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``// Given array arr[]` `        ``int` `arr[] = { ``2``, ``3``, ``4` `};`   `        ``int` `N = arr.length;`   `        ``// Function Call` `        ``System.out.println(findGCD(arr, N));` `    ``}` `}`

 `# Python3 program for the above approach `   `# Function to return gcd of a and b` `def` `gcd(a, b):` `    `  `    ``# Base Case` `    ``if` `(a ``=``=` `0``):` `        ``return` `b`   `    ``# Recursive call` `    ``return` `gcd(b ``%` `a, a)`   `# Function to find gcd of array` `def` `findGCD(arr, N):` `    `  `    ``# Initialise the result` `    ``result ``=` `0`   `    ``# Traverse the array arr[]` `    ``for` `element ``in` `arr:`   `        ``# Update result as gcd of` `        ``# the result and arr[i]` `        ``result ``=` `gcd(result, element)`   `        ``if` `(result ``=``=` `1``):` `            ``return` `1`   `    ``# Return the resultant GCD` `    ``return` `result`   `# Driver Code`   `# Given array arr[]` `arr ``=` `[ ``2``, ``3``, ``4` `]`   `N ``=` `len``(arr)`   `# Function call` `print``(findGCD(arr, N))`   `# This code is contributed by sanjoy_62`

 `// C# program for the above approach ` `using` `System; `   `class` `GFG{`   `// Function to return gcd of a and b` `static` `int` `gcd(``int` `a, ``int` `b)` `{` `    `  `    ``// Base Case` `    ``if` `(a == 0)` `        ``return` `b;`   `    ``// Recursive call` `    ``return` `gcd(b % a, a);` `}`   `// Function to find gcd of array` `static` `int` `findGCD(``int``[] arr, ``int` `N)` `{` `    `  `    ``// Initialise the result` `    ``int` `result = 0;`   `    ``// Traverse the array arr[]` `    ``foreach``(``int` `element ``in` `arr)` `    ``{`   `        ``// Update result as gcd of` `        ``// the result and arr[i]` `        ``result = gcd(result, element);`   `        ``if` `(result == 1)` `        ``{` `            ``return` `1;` `        ``}` `    ``}`   `    ``// Return the resultant GCD` `    ``return` `result;` `}`   `// Driver Code` `public` `static` `void` `Main()` `{` `    `  `    ``// Given array arr[]` `    ``int``[] arr = { 2, 3, 4 };`   `    ``int` `N = arr.Length;`   `    ``// Function call` `    ``Console.WriteLine(findGCD(arr, N));` `}` `}`   `// This code is contributed by sanjoy_62`

Output
`1`

Time Complexity: O(N*logN), where N is the size of the given array.
Auxiliary Space: O(N)

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Improved By : sanjoy_62, 29AjayKumar

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