Generate all possible permutations of a Number divisible by N

Last Updated : 12 Jun, 2021

Given a numerical string S, the task is to print all the permutations of the string which are divisible by N.

Examples:

Input: N = 5, S = "125"
Output: 125 215
Explanation:
All possible permutations are S are {125, 152, 215, 251, 521, 512}.
Out of these 6 permutations, only 2 {125, 215} are divisible by N (= 5).

Input: N = 7, S = "4321"
Output: 4312 4123 3241

Approach: The idea is to generate all possible permutations and for each permutation, check if it is divisible by N or not. For each permutation found to be divisible by N, print them.

Below is the implementation of the above approach:

C++14

// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to Swap two
// characters
void swap_(char& a, char& b)
{
    char temp;
    temp = a;
    a = b;
    b = temp;
}

// Function to generate all permutations
// and print the ones that are
// divisible by the N
void permute(char* str, int l, int r, int n)
{
    int i;

    if (l == r) {

        // Convert string to integer
        int j = atoi(str);

        // Check for divisibility
        // and print it
        if (j % n == 0)
            cout << str << endl;

        return;
    }

    // Print all the permutations
    for (i = l; i < r; i++) {

        // Swap characters
        swap_(str[l], str[i]);

        // Permute remaining
        // characters
        permute(str, l + 1, r, n);

        // Revoke the swaps
        swap_(str[l], str[i]);
    }
}

// Driver Code
int main()
{
    char str[100] = "125";
    int n = 5;
    int len = strlen(str);

    if (len > 0)
        permute(str, 0, len, n);

    return 0;
}

Java

// Java program to implement
// the above approach
class GFG{

// Function to Swap two
// characters
static void swap_(char []a, int l, int i)
{
    char temp;
    temp = a[l];
    a[l] = a[i];
    a[i] = temp;
}

// Function to generate all permutations
// and print the ones that are
// divisible by the N
static void permute(char[] str, int l, 
                         int r, int n)
{
    int i;

    if (l == r)
    {
        
        // Convert String to integer
        int j = Integer.valueOf(String.valueOf(str));

        // Check for divisibility
        // and print it
        if (j % n == 0)
            System.out.print(String.valueOf(str) + "\n");

        return;
    }

    // Print all the permutations
    for(i = l; i < r; i++) 
    {
        
        // Swap characters
        swap_(str, l, i);

        // Permute remaining
        // characters
        permute(str, l + 1, r, n);

        // Revoke the swaps
        swap_(str, l, i);
    }
}

// Driver Code
public static void main(String[] args)
{
    String str = "125";
    int n = 5;
    int len = str.length();

    if (len > 0)
        permute(str.toCharArray(), 0, len, n);
}
}

// This code is contributed by amal kumar choubey

Python3

# Python3 Program to implement
# the above approach

# Function to generate all 
# permutations and print 
# the ones that are
# divisible by the N
def permute(st, l, r, n):

    if (l == r):

        # Convert string 
        # to integer
        p = ''.join(st)
        j = int(p)

        # Check for divisibility
        # and print it
        if (j % n == 0):
            print (p)

        return

    # Print all the 
    # permutations
    for i in range(l, r):

        # Swap characters
        st[l], st[i] = st[i], st[l]

        # Permute remaining
        # characters
        permute(st, l + 1, r, n)

        # Revoke the swaps
        st[l], st[i] = st[i] ,st[l]

# Driver Code
if __name__ == "__main__":

    st = "125"
    n = 5
    length = len(st)

    if (length > 0):
      p = list(st)
      permute(p, 0, length, n);

# This code is contributed by rutvik_56

// C# program to implement
// the above approach
using System;

class GFG{
 
// Function to Swap two
// characters
static void swap_(char []a, int l,
                            int i)
{
    char temp;
    temp = a[l];
    a[l] = a[i];
    a[i] = temp;
}
 
// Function to generate all permutations
// and print the ones that are
// divisible by the N
static void permute(char[] str, int l, 
                         int r, int n)
{
    int i;
 
    if (l == r)
    {
        
        // Convert String to integer
        int j = Int32.Parse(new string(str));
 
        // Check for divisibility
        // and print it
        if (j % n == 0)
            Console.Write(new string(str) + "\n");
 
        return;
    }
 
    // Print all the permutations
    for(i = l; i < r; i++) 
    {
        
        // Swap characters
        swap_(str, l, i);
 
        // Permute remaining
        // characters
        permute(str, l + 1, r, n);
 
        // Revoke the swaps
        swap_(str, l, i);
    }
}
 
// Driver Code
public static void Main(string[] args)
{
    string str = "125";
    int n = 5;
    int len = str.Length;
 
    if (len > 0)
        permute(str.ToCharArray(), 0, len, n);
}
}

// This code is contributed by rutvik_56

JavaScript

<script>

// Javascript program to implement
// the above approach

// Function to Swap two
// characters
function swap_(a, l, i)
{
    let temp;
    temp = a[l];
    a[l] = a[i];
    a[i] = temp;
}

// Function to generate all permutations
// and print the ones that are
// divisible by the N
function permute(str, l, r, n)
{
    let i;
 
    if (l == r)
    {
        
        // Convert String to integer
        let j = parseInt((str).join(""));
 
        // Check for divisibility
        // and print it
        if (j % n == 0)
            document.write((str).join("") + "<br>");
 
        return;
    }
 
    // Print all the permutations
    for(i = l; i < r; i++)
    {
        
        // Swap characters
        swap_(str, l, i);
 
        // Permute remaining
        // characters
        permute(str, l + 1, r, n);
 
        // Revoke the swaps
        swap_(str, l, i);
    }
}

// Driver Code
let str = "125";
let n = 5;
let len = str.length;

if (len > 0)
    permute(str.split(""), 0, len, n);

// This code is contributed by avanitrachhadiya2155

</script>

Output:

125
215

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

Breadth First Search or BFS for a Graph

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Generate all possible permutations of a Number divisible by N

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