I've been playing with the cross product definition you gave me. It makes a
lot of sense, and I'm sure it will make it a lot easier for me to prove
associativity; however, I'm doing something wrong because when I run it, I
don't get the result I thought I would. Would you take a look and tell me
what I'm doing wrong?
def cross(set1,set2):
resulting_set = []
for s1 in set1:
for s2 in set2:
resulting_set.append( (s1, s2) )
return resulting_set
set = ['e','a','b', 'ab']
print set
s = cross(set,cross(set,set))
print s
When I run it, I get the following:
['e', 'a', 'b', 'ab']
[('e', ('e', 'e'))] #Shouldn't I get 64 pairs here instead of one?
I thought that a loop would do the trick, but I couldn't figure out how to
do it. Can you help? I want to get the entire 64 pairs on my printout.
Julieta
>From: Daniel Yoo <dyoo@hkn.eecs.berkeley.edu>
>To: Sheila King <sheila@thinkspot.net>
>CC: Julieta Rangel <julieta_rangel@hotmail.com>, tutor@python.org
>Subject: Re: [Tutor] stopping a loop [cross product instead of nested
>loops]
>Date: Sun, 6 May 2001 02:10:20 -0700 (PDT)
>
>On Sat, 5 May 2001, Sheila King wrote:
>
> > On Sat, 05 May 2001 20:24:52 -0500, "Julieta Rangel"
><julieta_rangel@hotmail.com>
> > wrote about RE: [Tutor] stopping a loop:
> >
> > :Are you implying a tripple nested loop? meaning
> > :for x in set:
> > : for y in set:
> > : for z in set:
> > : if ['x',('y','z')] == [('x','y'),'z']:
> > : return associativity holds
> > :
> > :Is this what you mean? If I give the computer those commands, will it
>look
> > :for the definition on my dictionary? You see, I'm not sure how I'm
>supposed
> > :to tell the computer to look in the dictionary for these values and
>compare
> > :them. Any more hints, ideas, suggestions, comments, questions?
> > :
> > :Julieta
> >
> > I'm not sure if Tim was implying a triply-nested loop, or not. It
>sounded kind of
> > like it to me, too. However, a double-nested loop will do fine.
> >
> > The key is, you need to use your dictionary to look up the values of the
>operations.
> > That is the key. That is why you built the dictionary in the first
>place.
>
>
>You might find the following definition useful: it's a way of producing
>the "cross" product of two lists:
>
>###
>def cross(set1, set2):
> resulting_set = []
> for s1 in set1:
> for s2 in set2:
> resulting_set.append( (s1, s2) )
> return resulting_set
>###
>
>
>One reason why the cross product is so useful is because, given any two
>lists, it can give back to us all possible pairs of those two lists, all
>in a nice list:
>
>###
> >>> cross([1, 2, 3, 4], [1, 2, 3, 4])
>[(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1),
>(3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)]
>###
>
>Or, more evocatively:
>
>###
> >>> numbers = ['1', '2']
> >>> cross(numbers, cross(numbers, numbers))
>[('1', ('1', '1')), ('1', ('1', '2')), ('1', ('2', '1')),
> ('1', ('2', '2')), ('2', ('1', '1')), ('2', ('1', '2')),
> ('2', ('2', '1')), ('2', ('2', '2'))]
>###
>
>By using the function above, you might not even need any nested loops in
>your own code.
>
>
>Hope this helps!
>
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