Split a number into 3 parts such that none of the parts is divisible by 3

You are given a number ‘N’. Your task is to split this number into 3 positive integers x, y, and z, such that their sum is equal to ‘N’ and none of the 3 integers is a multiple of 3. Given that N>=2.

Examples:

Input : N = 10 
Output : x = 1, y = 2, z = 7 
Note that x + y + z = N and x, y & z are not divisible by N.
Input : 18 
Output :x = 1, y = 1, z = 16  

Approach:
To split N into 3 numbers we split N as 

1. If N is divisible by 3, then the numbers x, y, z can be 1, 1, and N-2, respectively. All x, y, and z are not divisible by 3. And (1)+(1)+(N-2)=N .
2. If N is not divisible by 3 then N-3 will also not be divisible by 3. Therefore, we can have x=1, y=2, and z=N-3.Also, (1)+(2)+(N-3)=N . 

C++

// CPP program to split a number into three parts such
// than none of them is divisible by 3.
#include <iostream>
using namespace std;

void printThreeParts(int N)
{
    // Print x = 1, y = 1 and z = N - 2
    if (N % 3 == 0)
        cout << " x = 1, y = 1, z = " << N - 2 << endl;

    // Otherwise, print x = 1, y = 2 and z = N - 3
    else
        cout << " x = 1, y = 2, z = " << N - 3 << endl;
}

// Driver code
int main()
{
    int N = 10;
    printThreeParts(N);
    return 0;
}

Java

// Java program to split a number into three parts such
// than none of them is divisible by 3.
import java.util.*;

class solution
{

static void printThreeParts(int N)
{
    // Print x = 1, y = 1 and z = N - 2
    if (N % 3 == 0)

        System.out.println("x = 1, y = 1, z = "+ (N-2));

    // Otherwise, print x = 1, y = 2 and z = N - 3
    else
        System.out.println(" x = 1, y = 2, z = "+ (N-3));
}

// Driver code
public static void main(String args[])
{
    int N = 10;
    printThreeParts(N);

}
}

Python3

# Python3 program to split a number into three parts such
# than none of them is divisible by 3.

def printThreeParts(N) :

    # Print x = 1, y = 1 and z = N - 2
    if (N % 3 == 0) :
        print(" x = 1, y = 1, z = ",N - 2)

    # Otherwise, print x = 1, y = 2 and z = N - 3
    else :
        print(" x = 1, y = 2, z = ",N - 3)


# Driver code
if __name__ == "__main__" :

    N = 10
    printThreeParts(N)

# This code is contributed by Ryuga

C#

// C# program to split a number into three parts such
// than none of them is divisible by 3.
using System;

public class GFG{
    static void printThreeParts(int N)
{
    // Print x = 1, y = 1 and z = N - 2
    if (N % 3 == 0)
        Console.WriteLine(" x = 1, y = 1, z = "+(N - 2));

    // Otherwise, print x = 1, y = 2 and z = N - 3
    else
        Console.WriteLine(" x = 1, y = 2, z = "+(N - 3));
}

// Driver code
    static public void Main (){
    int N = 10;
    printThreeParts(N);


    }
// This code is contributed by ajit.
}

PHP

<?php
// PHP program to split a number into
// three parts such than none of them
// is divisible by 3.
function printThreeParts($N)
{
    // Print x = 1, y = 1 and z = N - 2
    if ($N % 3 == 0)
        echo " x = 1, y = 1, z = " .
                    ($N - 2) . "\n";

    // Otherwise, print x = 1,
    // y = 2 and z = N - 3
    else
        echo " x = 1, y = 2, z = " .
                    ($N - 3) . "\n";
}

// Driver code
$N = 10;
printThreeParts($N);

// This code is contributed by ita_c
?>

Javascript

<script>

// javascript program to split a number into three parts such
// than none of them is divisible by 3.

function printThreeParts(N)
{
    // Print x = 1, y = 1 and z = N - 2
    if (N % 3 == 0)

        document.write("x = 1, y = 1, z = "+ (N-2));

    // Otherwise, print x = 1, y = 2 and z = N - 3
    else
        document.write(" x = 1, y = 2, z = "+ (N-3));
}

// Driver code

var N = 10;
printThreeParts(N);


// This code contributed by Princi Singh

</script>

Output:

x = 1, y = 2, z = 7

Time Complexity: O(1), since there is no loop or recursion.

Auxiliary Space: O(1), since no extra space has been taken.