Python Program to print all permutations of a given string
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.
Python3
def toString( List ):
return ''.join( List )
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)
a[l], a[i] = a[i], a[l]
string = "ABC"
n = len (string)
a = list (string)
permute(a, 0 , n - 1 )
|
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
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)
answer = ""
s = input ( "Enter the string : " )
print ( "All possible strings are : " )
permute(s, answer)
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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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