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, CAB, CBA
Here is a solution using backtracking.
- C/C++
- Python
# Python program to print all permutations with
# duplicates allowed# Function to swap values
def swap(a,l,r):t = a[l]a[l] = a[r]a[r] = treturn adef toList(string):List = []for x in string:List.append(x)return Listdef 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 xrange(l,r+1):a = swap(a,l,i)permute(a, l+1, r)a = swap(a,l,i) # backtrack# Driver program to test the above function
string = "ABC"
n = len(string)
a = toList(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!)
Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.