Discussion - Python List Comprehensions; power set?

ProgrammingThis forum is for all programming questions.
The question does not have to be directly related to Linux and any language is fair game.

Notices

Welcome to LinuxQuestions.org, a friendly and active Linux Community.

You are currently viewing LQ as a guest. By joining our community you will have the ability to post topics, receive our newsletter, use the advanced search, subscribe to threads and access many other special features. Registration is quick, simple and absolutely free. Join our community today!

Note that registered members see fewer ads, and ContentLink is completely disabled once you log in.

If you have any problems with the registration process or your account login, please contact us. If you need to reset your password, click here.

Having a problem logging in? Please visit this page to clear all LQ-related cookies.

Introduction to Linux - A Hands on Guide

This guide was created as an overview of the Linux Operating System, geared toward new users as an exploration tour and getting started guide, with exercises at the end of each chapter.
For more advanced trainees it can be a desktop reference, and a collection of the base knowledge needed to proceed with system and network administration. This book contains many real life examples derived from the author's experience as a Linux system and network administrator, trainer and consultant. They hope these examples will help you to get a better understanding of the Linux system and that you feel encouraged to try out things on your own.

Click Here to receive this Complete Guide absolutely free.

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.

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.

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) ]

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.

Distribution: slackware64 13.37 and -current, Dragonfly BSD

Posts: 1,810

Rep:

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.

LinuxQuestions.org is looking for people interested in writing
Editorials, Articles, Reviews, and more. If you'd like to contribute
content, let us know.