# All permutations of a string using iteration

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 )

Below are the permutations of string ABC.
ABC ACB BAC BCA CBA CAB

We have discussed different recursive approaches to print permutations here and here.

How to print all permutations iteratively?
A simple solution to use permutations of n-1 elements to generate permutations of n elements.

For example let us see how to generate permutations of size 3 using permutations of size 2.

Permutations of two elements are 1 2 and 2 1.
Permutations of three elements can be obtained by inserting 3 at different positions in all permutations of size 2.
Inserting 3 in different positions of 1 2 leads to 1 2 3, 1 3 2 and 3 1 2.
Inserting 3 in different positions of 2 1 leads to 2 1 3, 2 3 1 and 3 2 1.

To generate permutations of size four, we consider all above six permutations of size three and insert 4 at different positions in every permutation.

An efficient solution is to use Johnson and Trotter algorithm to generate all permutations iteratively.