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

• Last Updated : 13 Apr, 2021

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 notvoid 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 Codeint 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 approachimport java.util.*;class GFG{ // Function to check if it is// possible to sort array or notstatic 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 Codepublic 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 approachimport sys # Function to check if it is# possible to sort array or notdef isPossible(arr, N):       # Store the smallest element    mn = sys.maxsize;     # Copy the original array    B =  * 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 Codeif __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 approachusing System;class GFG{ // Function to check if it is// possible to sort array or notstatic 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 Codepublic 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

Javascript


Output:
Yes

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

My Personal Notes arrow_drop_up