Heap's Algorithm implementation with python

Heap's Algorithm is used to generate all the permutations of a given object. It was first proposed by B.R. Heap in the year 1963.

In this post, we will write a program using Heap's Algorithm which will generate permutations for a given object. Remember that the object should be iterable. Otherwise, you will get an error.

If you don't know what permutations is all about then you can visit some of the following websites:

Permutations - Wikipedia
Permutation - Wolfram math
Permutations and combinations - Math is fun and
Permutations Khan Academy

Here goes the program:
This function will take an iterable object as input and will generate all the permutations possible with the items in the object.
For example, if the input is:heap(["A", "B", "C"]) then the output will be a generator object. You can use a for loop to iterate over this object to see the output.
But remember that if you have any duplicates in the input(Ex: heap(["A", "B", "B"])) then you will also get duplicate permutations. (Ex output: [["A", "B", "B"], ["B", "A", "B"], ["B", "A", "B"], ["A", "B", "B"], ["B", "B", "A"], ["B", "B", "A"]])

You can eliminate duplicates by using python sets.

One of the best ways to understand this algorithm is by looking at the pseudo-code on Wikipedia Heaps Algorithm page.

We have used the nonrecursive method.

If you are not sure of what yield does, then you can have a look at this answer on Stack overflow by e-satis for the question What does the "yield" keyword do

If you use the above code and if you give a string as an input still you will get a list as output. To overcome this problem I have written a program, a slightly modified version of the above program so that we will get the output as a string.
The program is as follows:
The above program will take a string as input and will give a generator object as output, which on further iteration will give you a list of strings.

Line 14 is just swapping of the characters a[0] , a[i] in the string.

Line 16 is again swapping of the characters a[i], a[c[i]] in the string.

As we are doing string concatenation with more than two strings, the second program takes more time for execution than the first one.

If you have any doubt or didn't understand anything, then you can comment in the comment box below and I will be glad to help you.

If you have any suggestions or if you have found any typo then please comment in the comment box. I will be very happy to see your comment.

You can also contact me.

Thank you. Have a nice day. 😃

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