Program to Find all the Permutations of a String

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Q. Program to find all the permutations of a string.

To solve this problem, we need to understand the concept of backtracking.

According to the backtracking algorithm:

Fix a character in the first position and swap the rest of the character with the first character. Like in ABC, in the first iteration three strings are formed: ABC, BAC, and CBA by swapping A with A, B and C respectively.
Repeat step 1 for the rest of the characters like fixing second character B and so on.
Now swap again to go back to the previous position. E.g., from ABC, we formed ABC by fixing B again, and we backtrack to the previous position and swap B with C. So, now we got ABC and ACB.
Repeat these steps for BAC and CBA, to get all the permutations.

Program to find all the permutations of a string

Algorithm

Define a string.
Fix a character and swap the rest of the characters.
Call the generatePermutation() for rest of the characters.
Backtrack and swap the characters again.

Solution

Python

#Function for generating different permutations of the string
def generatePermutation(string,start,end):
    current = 0;
    #Prints the permutations
    if(start == end-1):
        print(string);
    else: 
        for current in range(start,end):

       #Swapping the string by fixing a character
            x = list(string);
            temp = x[start];
            x[start] = x[current];
            x[current] = temp;

      #Recursively calling function generatePermutation() for rest of the characters

            generatePermutation("".join(x),start+1,end);
            #Swapping the string by fixing a character
            temp = x[start];
            x[start] = x[current];
            x[current] = temp;

str = "ABC"
n = len(str);
print("All the permutations of the string are: ");
generatePermutation(str,0,n);

Output:

All the permutations of the string are: 
ABC
ACB
BAC
BCA
CBA
CAB

C

#include<stdio.h>
#include<string.h>
//Declaring generatePermutation()
void generatePermutation(char * , int , int );

int main()
{
  char str[] = "ABC";
  int n =strlen(str);
  printf("All the permutations of the string are: \n");
  generatePermutation(str,0,n);
}

//Function for generating different permutation of the string.
void generatePermutation(char *str,const int start, int end)
{
  char temp;
  int i,j;
  for(i = start; i < end-1; ++i){
  for(j = i+1; j < end; ++j)
  {
   //Swapping the string by fixing a character
    temp = str[i];
  str[i] = str[j];
    str[j] = temp;
    //Recursively calling function generatePermutation() for rest of the characters
  generatePermutation(str , i+1 ,end);
    //Backtracking and swapping the characters again
    temp = str[i];
    str[i] = str[j];
    str[j] = temp;
  }
  }
  //Print the permutations
  printf("%s\n",str);
}

Output:

All the permutations of the string are: 
ABC
ACB
BAC
BCA
CBA
CAB

JAVA

public class PermuteString {
    //Function for swapping the characters at position I with character at position j
    public static String swapString(String a, int i, int j) {
        char[] b =a.toCharArray();
        char ch;
        ch = b[i];
        b[i] = b[j];
        b[j] = ch;
        return String.valueOf(b);
    }
    
    public static void main(String[] args)
    {
        String str = "ABC";
        int len = str.length();
        System.out.println("All the permutations of the string are: ");
        generatePermutation(str, 0, len);
    }
    
    //Function for generating different permutations of the string
    public static void generatePermutation(String str, int start, int end)
    {
        //Prints the permutations
        if (start == end-1)
            System.out.println(str);
        else
        {
            for (int i = start; i < end; i++)
            {
                //Swapping the string by fixing a character
                str = swapString(str,start,i);
                //Recursively calling function generatePermutation() for rest of the characters 
                generatePermutation(str,start+1,end);
                //Backtracking and swapping the characters again.
                str = swapString(str,start,i);
            }
        }
    }
}

Output:

All the permutations of the string are: 
ABC
ACB
BAC
BCA
CBA
CAB

C#

using System;                    
public class Program
{
    //Function for swapping the characters at position I with character at position j
    public static String swapString(String a, int i, int j) {
        char[] b =a.ToCharArray();
        char ch;
        ch = b[i];
        b[i] = b[j];
        b[j] = ch;
        //Converting characters from array into single string
        return string.Join("",b);
    }
    
    public static void Main()
    {
        String str = "ABC";
        int len = str.Length;
        Console.WriteLine("All the permutations of the string are: ");
        generatePermutation(str, 0, len);
        
    }

    //Function for generating different permutations of the string
    public static void generatePermutation(String str, int start, int end)
    {
        //Prints the permutations
        if (start == end-1)
            Console.WriteLine(str);
        else
        {
            for (int i = start; i < end; i++)
            {
                //Swapping the string by fixing a character
                str = swapString(str,start,i);
                //Recursively calling function generatePermutation() for rest of the characters 
                generatePermutation(str,start+1,end);
                //Backtracking and swapping the characters again.
                str = swapString(str,start,i);
            }
        }
    }
}

Output:

All the permutations of the string are: 
ABC
ACB
BAC
BCA
CBA
CAB

PHP

<!DOCTYPE html> 
<html> 
<body> 
<?php 

  //Function for generating different permutations of the string
function generatePermutation($string,$start,$end){
  if($start == $end-1){
    echo "$string <br>";
  }
  else{
    for($i = $start; $i < $end; $i++){
      //Swapping the string by fixing a character
      $temp = $string[$start];
      $string[$start] = $string[$i];
      $string[$i] = $temp;
     //Recursively calling function generatePermutation() for rest of the characters
      generatePermutation($string,$start+1,$end);
      //Backtracking and swapping the characters again.
      $temp = $string[$start];
      $string[$start] = $string[$i];
      $string[$i] = $temp;
    }
  }
}
$str = "ABC";
$n = strlen($str);
echo "All the permutations of the string are: <br>";
generatePermutation($str,0,$n);
?> 
</body> 
</html> 

Output:

All the permutations of the string are: 
ABC
ACB
BAC
BCA
CBA
CAB

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