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robotsari

12-28-2010 09:27 PM

Discussion - Python List Comprehensions; power set?

Hi,

I teach an introductory programming class in Python and the staff and I are trying to stump each other with some "challenge" list comprehension problems to give to our students as a fun optional problem.

I'd love your take - can you think of any tricky ones?

Additionally, we've been debating if you can generate a power set from a single list comprehension. I've come kind of close but always miss a few. Can anyone prove either side of the debate? (it would suffice to be able to generate a near-complete powerset, eg one that omits the empty set [] or generally gives 2**n - 1 elements)

Thanks all, I look forward to reading your responses.

Sarina

ntubski

12-30-2010 01:15 AM

It kind of depends on how you define a "set":

Quote:

Suppose that some (possibly countably infinite) universe of discourse for sets is mapped into the non-negative integers. Then a set can be represented as a bit vector; an element is in the set if the bit whose index corresponds to that element is a one-bit.

Common Lisp the Language, 2nd Edition
12.7. Logical Operations on Numbers

Code:

range(2**s)

gives a power set. If you want the sets explicitly represented as lists a nested list comprehension is required (which probabably doesn't count as a "single list comprehension"):

Code:

[ [ x for x in range(int(floor(log(max(n,1)) / log(2) + 1))) if (1 << x) & n ]

  for n in range(2**5) ]

or more readably:

Code:

from math import log, floor



def bits(n):

    return int(floor(log(max(n,1)) / log(2) + 1))



def set_from_int(n):

    return [ x for x in range(bits(n)) if (1 << x) & n ]



def power_set(s):

    return [ set_from_int(n) for n in range(2**s) ]

robotsari

12-30-2010 11:54 PM

Agreed I phrased the problem incorrectly.

By "power set" we mean to define the problem as follows:

Given a list of numbers my_list = [1, 2, 3, 4], can you give a list comprehension that generates all possible subsets of my_list?

So the list comprehension you gave is the basic idea. We have not visited this problem again since I posted the question but will update if one of us thinks of an elegant solution, or comes up with another fun challenge problem.

bgeddy

01-02-2011 03:46 AM

Quote:

Given a list of numbers my_list = [1, 2, 3, 4], can you give a list comprehension that generates all possible subsets of my_list?

I'm not sure if I understand your concept of subsets of the list. The following provides a list of all possible combinations of length between 1 and the length of the list stored as tuples. I use the itertools module to make finding combinations easy and run a nested list comprehension.

Code:

import itertools

my_list=[1,2,3,4,5]

power_set=[result for number in range(1,len(my_list)+1) for result in itertools.combinations(my_list,number)]

print power_set

Hope that's useful. Personally I'd tend to use loops when list comprehensions become a bit tricky like this but each to his own.

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