Given a string S, the task is to write a program to print all permutations of a given string.
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! permutations.
Examples:
Input: S = “ABC”
Output: “ABC”, “ACB”, “BAC”, “BCA”, “CBA”, “CAB”Input: S = “XY”
Output: “XY”, “YX”
Print permutations of a given string using backtracking:
Recursion Tree for permutations of string “ABC”
Follow the given steps to solve the problem:
- Create a function permute() with parameters as input string, starting index of the string, ending index of the string
- Call this function with values input string, 0, size of string – 1
- In this function, if the value of L and R is the same then print the same string
- Else run a for loop from L to R and swap the current element in the for loop with the inputString[L]
- Then again call this same function by increasing the value of L by 1
- After that again swap the previously swapped values to initiate backtracking
- In this function, if the value of L and R is the same then print the same string
Below is the implementation of the above approach:
C++14
// 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(); // Function call 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 code */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 { // Function call 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 |
Python3
# Python3 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 range(l, r): a[l], a[i] = a[i], a[l] permute(a, l+1, r) a[l], a[i] = a[i], a[l] # backtrack # Driver code string = "ABC"n = len(string) a = list(string) # Function call permute(a, 0, n) # 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 |
Javascript
<script> // Javascript program to print all permutations of a // given string. function permute(str, l, r) { if (l == r) document.write(str+"<br>"); else { for (let i = l; i <= r; i++) { str = swap(str, l, i); permute(str, l + 1, r); str = swap(str, l, i); } } } function swap(a, i, j) { let temp; let charArray = a.split(""); temp = charArray[i] ; charArray[i] = charArray[j]; charArray[j] = temp; return (charArray).join(""); } let str = "ABC"; let n = str.length; permute(str, 0, n-1); // This code is contributed by avanitrachhadiya2155 </script> |
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
Time Complexity: O(N * N!) Note that there are N! permutations and it requires O(N) time to print a permutation.
Auxiliary Space: O(R – L)
Note: The above solution prints duplicate permutations if there are repeating characters in the input string. Please see the 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
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