We want to work out all the possible arrangements of a list of n items. Why? We don’t know. But we do know how to do it: seed with a list containing a single list containing a single item: [['a']]. Then step through each of the lists in our list, and make copies, inserting the next item ('b') at each index, so we get [['b', 'a'], ['a', 'b']]. Then we take this list as our seed and go round again, inserting the next item ('c'), so we get [['c', 'b', 'a'], ['b', 'c', 'a'], ['b', 'a', 'c'], ['c', 'a', 'b'], ['a', 'c', 'b'], ['a', 'b', 'c']]. And so on and so on, until we’ve permuted all of our items. These lists get pretty big pretty quickly (the length of the list is n! so 10 items generates 3628800 combinations, and doing this may bring your computer to its knees).
#!/usr/bin/env python
# class representing a list of permutations
class Unit(list):
# count the total number of Units spawned
count = 0
def __init__(self, seed = None):
# if this is the first Unit created, we need to prepare the seed
if Unit.count == 0: seed = [[seed]]
Unit.count += 1
# call our superclass. We are just a fancy list
super(Unit, self).__init__(seed)
# produce a new generation, splicing in the passed in value
def spawn(self, interloper):
# a temporary working list
l = []
# for each of our existing lists
for u in self:
# for each index (including length + 1)
for i in range(0, len(u) + 1):
# take a copy of the list
a = Unit(u)
# insert the new value at this index
a.insert(i, interloper)
# and add the modified copy to our working list
l.append(a)
# when we're done, return a new Unit seeded with the list we just built
return Unit(l)
# calculate and show some stats
def stats(self):
self.items = len(self[0])
self.combinations = len(self)
return "%d items, %d permutations" % (self.items, self.combinations)
# simple wrapper class representing the set of items we want to permute
class Inventory(list):
def __init__(self, chars):
# we are yet another variation on a list
super(Inventory, self).__init__(chars)
# do we have more items to give?
def has_next(self):
return len(self) > 0
# shift the first item off of the list
def next(self):
return self.pop(0)
# wrapper class that actually does the work. We extend the Unit class mainly
# because we want its stats() method
class Permutations(Unit):
def __init__(self, items):
# we need an inventory
self.i = Inventory(items)
# get the first item off of the inventory
self.u = Unit(self.i.next())
# now while the inventory has more items to give us
while self.i.has_next():
# make another generation of Units fed with the next item
self.u = self.u.spawn(self.i.next())
# at the end, we become whatever the final Unit.spawn() gave us
self.extend(self.u)
# if we're called on the command line
if __name__ == '__main__':
import sys
# we will permute the command line arguments
permutables = sys.argv[1:]
# if we got no arguments, default to this
if not permutables:
permutables = ["life", "the universe", "everything"]
# do the work
p = Permutations(permutables)
# sort the result (a Permutation is just a fancy list, after all)
p.sort()
# and print it
print p
print p.stats()
You can grab the code here: http://svn.cruft.co/code/combinatrics/Combinatrics.py
