In this article we will discuss how to print all permutations of a given String using Python programming Language.

Before diving into the program, let us first see what is a Permutation.

#### Permutation

A permutation is the rearrangement of the characters of a string. Let us take an example of the string “ABC”. Here the permutations of the respective string are ABC ACB BAC BCA CBA CAB.

#### Useful Links:

Below is the recursion tree using backtrack to find Permutations.

#### Program

Now let us see the Python Program to print all the permutations of a string.

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def toStr(list): | |

return ''.join(list) | |

def permute(s, l, r): | |

""" | |

Function to find permutations of a given sting | |

:arg s : string, | |

:arg l : left element of the string, | |

:arg r : right element of the string. | |

""" | |

if l==r: | |

print(toStr(s)) | |

for i in range(l, r): | |

s[i], s[l] = s[l], s[i] | |

permute(s, l + 1, r) | |

s[i], s[l] = s[l], s[i] # backtrack | |

s = input('Enter a string:') | |

n = len(s) | |

a = list(s) | |

permute(a, 0, n) |

#### Time Complexity

Now let us analyse the time complexity of the above backtracing algorithm used. Here the time taken to print a permutation is n as it has to travel down to the depth of n to print a permutation. No of permutations of a string of size n is n! Hence the total time to print all the permutations is O(n x n!)