Question

I am trying to create a program which outputs all permutations of a string of length n whilst avoiding a defined substring, of length k. For example:

Derive all possible strings, up to a length of 5 characters, that can be generated from an initial empty set, which can either go to A or B, but the string cannot contain the substring “AAB” which is not allowed.

i.e. base case of [""] is the empty set.
The dictionary would be – A:{A}, B:{A,B}

From the empty set we can go to A, and we can go to B. We can not go to a B after an A but we can go to an A after a B. And both A and B can access themselves

example output: a,b,aa,bb,ba,aaa,bbb,baa,bba … etc

How would I go about prompting a user to define a substring to avoid, and from that generate a dictionary which abides to these rules?

Any help or clarification would be greatly received.

Regards,
rkhad

Answer 1

The itertools module has a useful method called permutations():

(from http://docs.python.org/library/itertools.html#itertools.permutations)

itertools.permutations(iterable[, r])

Return successive r length permutations of elements in the iterable.

If r is not specified or is None, then r defaults to the length of the
iterable and all possible full-length permutations are generated.

Permutations are emitted in lexicographic sort order. So, if the input
iterable is sorted, the permutation tuples will be produced in sorted
order.

List comprehensions provide an easy way to filter generated permutations like this, but beware that if you are storing permutations of a large string that you will quickly get a very large list. You may want to therefore use a set to whittle down your list to non-duplicates. Also, you may find the function sorted to be useful if you intend to iterate through your “paths” in lexicographic order. Lastly, the in operator, when applied to strings, checks for a substring (x in y checks if x is a substring of y).

>>> from itertools import permutations
>>> perms = [''.join(p) for p in permutations('AAAABBBB', 4)]
>>> len(perms)
1680
>>> len(set(perms))
16
>>> filtered = [p for p in sorted(set(perms)) if 'AB' not in p]
>>> filtered
['AAAA', 'BAAA', 'BBAA', 'BBBA', 'BBBB']

I’m working on my dissertation right now too, in the area of Formal Languages. The concept of substring membership can be represented by a very simple regular grammar which corresponds to a deterministic finite automaton. To jog your memory:

http://en.wikipedia.org/wiki/Regular_grammar

http://en.wikipedia.org/wiki/Finite-state_machine

When you look into these you will find that you need to somehow keep track of the current “state” of your computation if you want it to have different “dictionaries” at different phases. I encourage you to read the wikipedia articles, and ask me some follow-up questions as I’d be happy to help you work through this.