# Check if array can be sorted by swapping pairs having GCD equal to the smallest element in the array

Given an array arr[] of size N, the task is to check if an array can be sorted by swapping only the elements whose GCD (greatest common divisor) is equal to the smallest element of the array. Print “Yes” if it is possible to sort the array. Otherwise, print “No”.

Examples:

Input: arr[] = {4, 3, 6, 6, 2, 9}
Output: Yes
Explanation:
Smallest element in the array = 2
Swap arr and arr, since they have gcd equal to 2. Therefore, arr[] = {6, 3, 4, 6, 2, 9}
Swap arr and arr, since they have gcd equal to 2. Therefore, arr[] = {2, 3, 4, 6, 6, 9}
Input: arr[] = {2, 6, 2, 4, 5}
Output: No

Approach: The idea is to find the smallest element from the array and check if it is possible to sort the array. Below are the steps:

1. Find the smallest element of the array and store it in a variable, say mn.
2. Store the array in a temporary array, say B[].
3. Sort the original array arr[].
4. Now, iterate over the array, if there is an element which is not divisible by mn and whose position is changed after sorting, then print “NO”. Otherwise, rearrange the elements divisible by mn by swapping it with other elements.
5. If the position of all elements which are not divisible by mn remains unchanged, then print “YES”.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach` `#include ` `using` `namespace` `std;`   `// Function to check if it is` `// possible to sort array or not` `void` `isPossible(``int` `arr[], ``int` `N)` `{`   `    ``// Store the smallest element` `    ``int` `mn = INT_MAX;`   `    ``// Copy the original array` `    ``int` `B[N];`   `    ``// Iterate over the given array` `    ``for` `(``int` `i = 0; i < N; i++) {`   `        ``// Update smallest element` `        ``mn = min(mn, arr[i]);`   `        ``// Copy elements of arr[]` `        ``// to array B[]` `        ``B[i] = arr[i];` `    ``}`   `    ``// Sort original array` `    ``sort(arr, arr + N);`   `    ``// Iterate over the given array` `    ``for` `(``int` `i = 0; i < N; i++) {`   `        ``// If the i-th element is not` `        ``// in its sorted place` `        ``if` `(arr[i] != B[i]) {`   `            ``// Not possible to swap` `            ``if` `(B[i] % mn != 0) {` `                ``cout << ``"No"``;` `                ``return``;` `            ``}` `        ``}` `    ``}`   `    ``cout << ``"Yes"``;` `    ``return``;` `}`   `// Driver Code` `int` `main()` `{` `    ``// Given array` `    ``int` `N = 6;` `    ``int` `arr[] = { 4, 3, 6, 6, 2, 9 };`   `    ``// Function Call` `    ``isPossible(arr, N);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of ` `// the above approach` `import` `java.util.*;` `class` `GFG{`   `// Function to check if it is` `// possible to sort array or not` `static` `void` `isPossible(``int` `arr[], ` `                       ``int` `N)` `{` `  ``// Store the smallest element` `  ``int` `mn = Integer.MAX_VALUE;`   `  ``// Copy the original array` `  ``int` `[]B = ``new` `int``[N];`   `  ``// Iterate over the given array` `  ``for` `(``int` `i = ``0``; i < N; i++) ` `  ``{` `    ``// Update smallest element` `    ``mn = Math.min(mn, arr[i]);`   `    ``// Copy elements of arr[]` `    ``// to array B[]` `    ``B[i] = arr[i];` `  ``}`   `  ``// Sort original array` `  ``Arrays.sort(arr);`   `  ``// Iterate over the given array` `  ``for` `(``int` `i = ``0``; i < N; i++) ` `  ``{` `    ``// If the i-th element is not` `    ``// in its sorted place` `    ``if` `(arr[i] != B[i]) ` `    ``{` `      ``// Not possible to swap` `      ``if` `(B[i] % mn != ``0``) ` `      ``{` `        ``System.out.print(``"No"``);` `        ``return``;` `      ``}` `    ``}` `  ``}` `  ``System.out.print(``"Yes"``);` `  ``return``;` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `  ``// Given array` `  ``int` `N = ``6``;` `  ``int` `arr[] = {``4``, ``3``, ``6``, ``6``, ``2``, ``9``};`   `  ``// Function Call` `  ``isPossible(arr, N);` `}` `}`   `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 implementation of` `# the above approach` `import` `sys`   `# Function to check if it is` `# possible to sort array or not` `def` `isPossible(arr, N):` `  `  `    ``# Store the smallest element` `    ``mn ``=` `sys.maxsize;`   `    ``# Copy the original array` `    ``B ``=` `[``0``] ``*` `N;`   `    ``# Iterate over the given array` `    ``for` `i ``in` `range``(N):` `      `  `        ``# Update smallest element` `        ``mn ``=` `min``(mn, arr[i]);`   `        ``# Copy elements of arr` `        ``# to array B` `        ``B[i] ``=` `arr[i];`   `    ``# Sort original array` `    ``arr.sort();`   `    ``# Iterate over the given array` `    ``for` `i ``in` `range``(N):` `      `  `        ``# If the i-th element is not` `        ``# in its sorted place` `        ``if` `(arr[i] !``=` `B[i]):` `          `  `            ``# Not possible to swap` `            ``if` `(B[i] ``%` `mn !``=` `0``):` `                ``print``(``"No"``);` `                ``return``;`   `    ``print``(``"Yes"``);` `    ``return``;`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `  `  `    ``# Given array` `    ``N ``=` `6``;` `    ``arr ``=` `[``4``, ``3``, ``6``, ``6``, ``2``, ``9``];`   `    ``# Function Call` `    ``isPossible(arr, N);`   `# This code is contributed by 29AjayKumar`

## C#

 `// C# implementation of ` `// the above approach` `using` `System;` `class` `GFG{`   `// Function to check if it is` `// possible to sort array or not` `static` `void` `isPossible(``int` `[]arr, ` `                       ``int` `N)` `{` `  ``// Store the smallest element` `  ``int` `mn = ``int``.MaxValue;`   `  ``// Copy the original array` `  ``int` `[]B = ``new` `int``[N];`   `  ``// Iterate over the given array` `  ``for` `(``int` `i = 0; i < N; i++) ` `  ``{` `    ``// Update smallest element` `    ``mn = Math.Min(mn, arr[i]);`   `    ``// Copy elements of []arr` `    ``// to array []B` `    ``B[i] = arr[i];` `  ``}`   `  ``// Sort original array` `  ``Array.Sort(arr);`   `  ``// Iterate over the given array` `  ``for` `(``int` `i = 0; i < N; i++) ` `  ``{` `    ``// If the i-th element is not` `    ``// in its sorted place` `    ``if` `(arr[i] != B[i]) ` `    ``{` `      ``// Not possible to swap` `      ``if` `(B[i] % mn != 0) ` `      ``{` `        ``Console.Write(``"No"``);` `        ``return``;` `      ``}` `    ``}` `  ``}` `  ``Console.Write(``"Yes"``);` `  ``return``;` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `  ``// Given array` `  ``int` `N = 6;` `  ``int` `[]arr = {4, 3, 6, 6, 2, 9};`   `  ``// Function Call` `  ``isPossible(arr, N);` `}` `}`   `// This code is contributed by Rajput-Ji`

Output:

```Yes

```

Time Complexity: O(NlogN)
Auxiliary Space: O(N)

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Improved By : 29AjayKumar, Rajput-Ji