Check if possible to shuffle a matrix with adjacent movements

Given a N x M matrix which represents the number of rows and number of columns respectively. Each cell of a matrix is occupied by exactly one student. The task is to determine whether we can shuffle each student in such a way that each student should occupy a cell that is adjacent to that student’s original cell, i.e. immediately to the left, right, top or bottom of that cell and after shuffling each cell should occupy by exactly one student.

Examples:

Input: N = 3, M = 3 
Output: Shuffling not possible

Input: N = 4, M = 4 
Output: Shuffling is possible
One possible way to shuffle the student is as shown below: 

Approach: Check if the number of rows or the number of columns is even then shuffling is possible otherwise no shuffling is possible.

Below is the implementation of the above approach: 

C++

// C++ implementation of above approach
#include <iostream>
using namespace std;

// Function that will check whether
// Shuffling is possible or not
void Shuffling(int N, int M)
{
    if (N % 2 == 0 || M % 2 == 0)
        cout << "Shuffling is possible";
    else
        cout << "Shuffling not possible";
}

// Driver code
int main()
{
    int N = 4, M = 5;

    // Calling function.
    Shuffling(N, M);
    return 0;
}

Java

// Java implementation of above approach
import java.io.*;

class Main {

    // Function that will check whether
    // Shuffling is possible or not
    static void shuffling(int N, int M)
    {
        int a = N & 1; // check whether N is even numner or
                       // not using & operator.
        int b = M & 1; // check whether M is even numner or
                       // not using & operator.
        if (a != 1 || b != 1) // check whether N or M is
                              // even numner or not.
            System.out.println("Shuffling is possible");
        else
            System.out.println("Shuffling not possible");
    }

    // Driver code to start the code
    public static void main(String[] args)
    {

        int N = 4,M = 5; // Taken value from the given example.

        // calling function to check the shuffling
        shuffling(N, M);
    }
}

Python3

# Python3 implementation of above approach

# Function that will check whether
# Shuffling is possible or not
def Shuffling(N, M) :

    if (N % 2 == 0 or M % 2 == 0) :
        print("Shuffling is possible");
    else :
        print("Shuffling not possible");

# Driver Code
if __name__ == "__main__" :

    # Driver code
    N = 4;
    M = 5;

    # Calling function.
    Shuffling(N, M);

# This code is contributed by Ryuga

Javascript

<script>
// Javascript implementation of above approach

// Function that will check whether
// Shuffling is possible or not
function Shuffling(N, M)
{
    if (N % 2 == 0 || M % 2 == 0)
        document.write( "Shuffling is possible");
    else
       document.write("Shuffling not possible");
}

// Driver code
var N = 4, M = 5;

// Calling function.
Shuffling(N, M);

// This code is contributed by rrrtnx.
</script>

C#

// C# implementation of above approach
using System;

class GFG
{

// Function that will check whether
// Shuffling is possible or not
static void Shuffling(int N, int M)
{
    if (N % 2 == 0 || M % 2 == 0)
        Console.Write("Shuffling is possible");
    else
        Console.Write("Shuffling not possible");
}

    // Driver code
    public static void Main ()
    {
        int N = 4, M = 5;

        // Calling function.
        Shuffling(N, M);
    }
}

// This code is contributed by Ita_c.

PHP

<?php
// PHP implementation of above approach

// Function that will check whether
// Shuffling is possible or not
function Shuffling($N, $M)
{
    if ($N % 2 == 0 || $M % 2 == 0)
        echo "Shuffling is possible";
    else
        echo "Shuffling not possible";
}

// Driver code
$N = 4;
$M = 5;

// Calling function.
Shuffling($N, $M);

// This code is contributed by
// Shivi_Aggarwal
?>

Output

Shuffling is possible