Python | All Permutations of a string in lexicographical order without using recursion

Last Updated : 26 Aug, 2019

Write a python program to print all the permutations of a string in lexicographical order.

Examples:

Input  : python
Output : hnopty
hnopyt
hnotpy
hnotyp
hnoypt
......
ytpnho
ytpnoh
ytpohn
ytponh

Input  : xyz
Output : xyz
xzy
yxz
yzx
zxy
zyx

Method 1:
Using the default library itertools function permutations.
permutations function will create all the permutations of a given string and then we sort the result to get our desired output.

from itertools import permutations
  
def lexicographical_permutation(str):
    perm = sorted(''.join(chars) for chars in permutations(str))
    for x in perm:
        print(x)
          
str ='abc'
lexicographical_permutation(str)

Output :

abc
acb
bac
bca
cab
cba

Method 2:

First we create a loop that will run n! ties where n is the length of the string as there will be n! permutations.

Every iteration prints the string and finds its next larger lexicographical permutation to be printed in the next iteration.

The next higher permutation is found as :-

Let the string is called str, find the smallest index i such that all elements in str[i…end] are in descending order.

If str[i…end] is the entire sequence, i.e. i == 0, then str is the highest permutation. So we simply reverse the entire string to get the smallest permutation which we consider as the next permutation.

If i > 0, then we reverse str[i…end].

Then we look for the smallest element in str[i…end] that is greater than str[i – 1] and swap its position with str[i – 1].

This is then the next permutation.

# import library
from math import factorial
    
def lexicographical_permutations(str):
       
    # there are going to be n ! permutations where n = len(seq)
    for p in range(factorial(len(str))):         
        print(''.join(str))  
       
        i = len(str) - 1
          
        # find i such that str[i:] is the largest sequence with
        # elements in descending lexicographic order
        while i > 0 and str[i-1] > str[i]:       
            i -= 1
    
        # reverse str[i:]
        str[i:] = reversed(str[i:]) 
           
    
        if i > 0:
               
            q = i
            # find q such that str[q] is the smallest element
            # in str[p:] such that str[q] > str[i - 1]
            while str[i-1] > str[q]:  
                q += 1
              
            # swap str[i - 1] and str[q]
            temp = str[i-1] 
            str[i-1]= str[q]
            str[q]= temp
               
    
s = 'abcd'
s = list(s)
s.sort()
lexicographical_permutations(s)

Output :

abcd
abdc
acbd
acdb
adbc
adcb
bacd
badc
bcad
bcda
bdac
bdca
cabd
cadb
cbad
cbda
cdab
cdba
dabc
dacb
dbac
dbca
dcab
dcba

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Python | All Permutations of a string in lexicographical order without using recursion