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Python Program to print all permutations of a given string

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  • Difficulty Level : Medium
  • Last Updated : 13 Jan, 2022

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

Python3




# 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 range(l, r + 1):
            a[l], a[i] = a[i], a[l]
            permute(a, l + 1, r)
 
            # backtrack
            a[l], a[i] = a[i], a[l]
 
# Driver code
string = "ABC"
n = len(string)
a = list(string)
permute(a, 0, n-1)
# This code is contributed by Bhavya Jain

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 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

Another approach:

Python3




# Python program to implement
# the above approach
def permute(s, answer):
    if (len(s) == 0):
        print(answer, end = "  ")
        return
     
    for i in range(len(s)):
        ch = s[i]
        left_substr = s[0:i]
        right_substr = s[i + 1:]
        rest = left_substr + right_substr
        permute(rest, answer + ch)
 
# Driver Code
answer = ""
s = input("Enter the string : ")
print("All possible strings are : ")
permute(s, answer)
# This code is contributed by Harshit Srivastava

Output:

Enter the string : abc
All possible strings are : abc  acb  bac  bca  cab  cba

Time Complexity: O(n*n!) The time complexity is the same as the above approach, i.e. there are n! permutations and it requires O(n) time to print a permutation.

Auxiliary Space: O(|s|)


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