[Tutor] help with list permutations

Chris Fuller cfuller084 at thinkingplanet.net
Fri Jan 4 08:15:33 CET 2008

This is a good case for recursion. My solution is in two steps. A straightforward application of recursion (I was casting about semi-randomly) yields a attractive tree structure:

       a                  b
 c     d     e      c     d    e
 f     f     f      f     f    f
g h   g h   g h    g h   g h  g h

It returns a list, of course, but when unpacked in two dimensions looks like a tree. Trees are often represented this way in programming.

One thing to note is that the tree structure naturally preserves the order of the lists, as required.

Here is the code:

def recursion_is_your_friend(l):
   if len(l) == 1:
      return l
      return [ (i, recursion_is_your_friend(l[1:])) for i in l[0] ]

l = recursion_is_your_friend([['a','b'],['c','d','e'],['f'],['g','h']])

The idea is that each element of the first list in the list has all the rest of the lists applied to it. Something like that. Talking about recursion isn't a skill I have much skill in. Cue groaning!

The next step is to trace all the paths from the root to the leaves. There is a wikipedia page that discusses this: http://en.wikipedia.org/wiki/Depth-first_search. Stacks would seem a natural way to do this to me. It can also be done with more recursion. I may implement something a little later, but this should get you started. Another way to look at step two is to start at the leaves and follow the (unique) path back to the root.


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