This recipe shows a way to generate a list of all strings (in this case, string=list of symbols) of a given alphabet having a specified length; by using list comprehensions.

UPDATE: The case for alphabet length = 1 is fixed.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
def allstrings(alphabet, length):
"""Find the list of all strings of 'alphabet' of length 'length'"""
if length == 0: return []
c = [[a] for a in alphabet[:]]
if length == 1: return c
c = [[x,y] for x in alphabet for y in alphabet]
if length == 2: return c
for l in range(2, length):
c = [[x]+y for x in alphabet for y in c]
return c
if __name__ == "__main__":
for p in allstrings([0,1,2],4):
print p
``` |

Strings (not the 'string' type) are frequently used in computer science; for example numbers are encoded as strings of base-2 numbers (having an alphabet of {0,1}). This implementation is just a quick hack; it uses cartesian product to find the stings, so it will consume a large space of memory (m**n lists of size n, where m is the size of the alphabet, and n is the desired length).

For more info. about strings: http://mathworld.wolfram.com/String.html

Simplified.The special cases for length zero, one, and two can be eliminated. All the logic you need is in the final block:Thanks for the modification; but I think the function should output [] for length=1. Here is another modification to do that:

Sorry.It should be, "but I think the function should output [] for length=0."there thats the easiest