Write a program to print all permutations of a given string

Difficulty Level : Medium
Last Updated : 03 Dec, 2020

A permutation, also called an “arrangement number” or “order,” is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. A string of length n has n! permutation.

Source: Mathword(http://mathworld.wolfram.com/Permutation.html)

Below are the permutations of string ABC.
ABC ACB BAC BCA CBA CAB

Here is a solution that is used as a basis in backtracking.

NewPermutation

C++

// C++ program to print all 
// permutations with duplicates allowed 
#include <bits/stdc++.h> 
using namespace std; 
 
 
// Function to print permutations of string 
// This function takes three parameters: 
// 1. String 
// 2. Starting index of the string 
// 3. Ending index of the string. 
void permute(string a, int l, int r) 
{ 
    // Base case 
    if (l == r) 
        cout<<a<<endl; 
    else
    { 
        // Permutations made 
        for (int i = l; i <= r; i++) 
        { 
 
            // Swapping done 
            swap(a[l], a[i]); 
 
            // Recursion called 
            permute(a, l+1, r); 
 
            //backtrack 
            swap(a[l], a[i]); 
        } 
    } 
} 
 
// Driver Code 
int main() 
{ 
    string str = "ABC"; 
    int n = str.size(); 
    permute(str, 0, n-1); 
    return 0; 
} 
 
// This is code is contributed by rathbhupendra 

C

// C program to print all permutations with duplicates allowed 
#include <stdio.h> 
#include <string.h> 
 
/* Function to swap values at two pointers */
void swap(char *x, char *y) 
{ 
    char temp; 
    temp = *x; 
    *x = *y; 
    *y = temp; 
} 
 
/* Function to print permutations of string 
This function takes three parameters: 
1. String 
2. Starting index of the string 
3. Ending index of the string. */
void permute(char *a, int l, int r) 
{ 
int i; 
if (l == r) 
    printf("%s\n", a); 
else
{ 
    for (i = l; i <= r; i++) 
    { 
        swap((a+l), (a+i)); 
        permute(a, l+1, r); 
        swap((a+l), (a+i)); //backtrack 
    } 
} 
} 
 
/* Driver program to test above functions */
int main() 
{ 
    char str[] = "ABC"; 
    int n = strlen(str); 
    permute(str, 0, n-1); 
    return 0; 
} 

Java

// Java program to print all permutations of a 
// given string. 
public class Permutation 
{ 
    public static void main(String[] args) 
    { 
        String str = "ABC"; 
        int n = str.length(); 
        Permutation permutation = new Permutation(); 
        permutation.permute(str, 0, n-1); 
    } 
 
    /** 
    * permutation function 
    * @param str string to calculate permutation for 
    * @param l starting index 
    * @param r end index 
    */
    private void permute(String str, int l, int r) 
    { 
        if (l == r) 
            System.out.println(str); 
        else
        { 
            for (int i = l; i <= r; i++) 
            { 
                str = swap(str,l,i); 
                permute(str, l+1, r); 
                str = swap(str,l,i); 
            } 
        } 
    } 
 
    /** 
    * Swap Characters at position 
    * @param a string value 
    * @param i position 1 
    * @param j position 2 
    * @return swapped string 
    */
    public String swap(String a, int i, int j) 
    { 
        char temp; 
        char[] charArray = a.toCharArray(); 
        temp = charArray[i] ; 
        charArray[i] = charArray[j]; 
        charArray[j] = temp; 
        return String.valueOf(charArray); 
    } 
 
} 
 
// This code is contributed by Mihir Joshi 

Python

# Python program to print all permutations with 
# duplicates allowed 
 
def toString(List): 
    return ''.join(List) 
 
# Function to print permutations of string 
# This function takes three parameters: 
# 1. String 
# 2. Starting index of the string 
# 3. Ending index of the string. 
def permute(a, l, r): 
    if l==r: 
        print toString(a) 
    else: 
        for i in xrange(l,r+1): 
            a[l], a[i] = a[i], a[l] 
            permute(a, l+1, r) 
            a[l], a[i] = a[i], a[l] # backtrack 
 
# Driver program to test the above function 
string = "ABC"
n = len(string) 
a = list(string) 
permute(a, 0, n-1) 
 
# This code is contributed by Bhavya Jain 

C#

// C# program to print all 
// permutations of a given string. 
using System; 
 
class GFG 
{ 
    /** 
    * permutation function 
    * @param str string to 
    calculate permutation for 
    * @param l starting index 
    * @param r end index 
    */
    private static void permute(String str, 
                                int l, int r) 
    { 
        if (l == r) 
            Console.WriteLine(str); 
        else
        { 
            for (int i = l; i <= r; i++) 
            { 
                str = swap(str, l, i); 
                permute(str, l + 1, r); 
                str = swap(str, l, i); 
            } 
        } 
    } 
 
    /** 
    * Swap Characters at position 
    * @param a string value 
    * @param i position 1 
    * @param j position 2 
    * @return swapped string 
    */
    public static String swap(String a, 
                            int i, int j) 
    { 
        char temp; 
        char[] charArray = a.ToCharArray(); 
        temp = charArray[i] ; 
        charArray[i] = charArray[j]; 
        charArray[j] = temp; 
        string s = new string(charArray); 
        return s; 
    } 
 
// Driver Code 
public static void Main() 
{ 
    String str = "ABC"; 
    int n = str.Length; 
    permute(str, 0, n-1); 
} 
} 
 
// This code is contributed by mits 

PHP

<?php 
// PHP program to print all 
// permutations of a given string. 
 
 
/** 
* permutation function 
* @param str string to 
* calculate permutation for 
* @param l starting index 
* @param r end index 
*/
function permute($str, $l, $r) 
{ 
    if ($l == $r) 
        echo $str. "\n"; 
    else
    { 
        for ($i = $l; $i <= $r; $i++) 
        { 
            $str = swap($str, $l, $i); 
            permute($str, $l + 1, $r); 
            $str = swap($str, $l, $i); 
        } 
    } 
} 
 
/** 
* Swap Characters at position 
* @param a string value 
* @param i position 1 
* @param j position 2 
* @return swapped string 
*/
function swap($a, $i, $j) 
{ 
    $temp; 
    $charArray = str_split($a); 
    $temp = $charArray[$i] ; 
    $charArray[$i] = $charArray[$j]; 
    $charArray[$j] = $temp; 
    return implode($charArray); 
} 
 
// Driver Code 
$str = "ABC"; 
$n = strlen($str); 
permute($str, 0, $n - 1); 
 
// This code is contributed by mits. 
?> 

Output:

ABC
ACB
BAC
BCA
CBA
CAB

Algorithm Paradigm: Backtracking

Time Complexity: O(n*n!) Note that there are n! permutations and it requires O(n) time to print a a permutation.

Note : The above solution prints duplicate permutations if there are repeating characters in input string. Please see below link for a solution that prints only distinct permutations even if there are duplicates in input.
Print all distinct permutations of a given string with duplicates.
Permutations of a given string using STL

Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.

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