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sub list like subsets

asked 2010-09-16 23:08:08 -0500

sriram gravatar image

updated 2015-01-14 05:06:24 -0500

FrédéricC gravatar image

how to take lists of size from a list like subsets of size

example L = ([1,2,3,4],[3,5,6,7],[7,8,9,10]) From the above list find sublists of size 2

([1,2,3,4],[3,5,6,7]) ([1,2,3,4],[7,8,9,10]) ([3,5,6,7],[7,8,9,10])

subsets can also be size 3,4,5 as specified

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answered 2010-09-16 23:32:42 -0500

jsrn gravatar image

updated 2010-09-16 23:53:04 -0500

I'm not completely sure I understand your question, but what you're asking for sounds simply (at least almost simply) like cartesian product, which is implemented in Python in itertools.product. In the basic case, you could then just do:

sage: L = [ [1,2,3,4],[3,5,6,7],[7,8,9,10] ]  # note that this is a list, while you did a tuple
sage: from itertools import product
sage: list(product(L, L))
[([1, 2, 3, 4], [1, 2, 3, 4]), ([1, 2, 3, 4], [3, 5, 6, 7]), ...

(note the "list" around product, as product returns a generator)

The above can easily be generalised to having 3,4,...,n elements in each sublist (i.e. L^n) by modifying the last line to

list(product(repeat(L, n)))

However, this would also give those sublists where the same element might be present more than once in each list. If you don't want this, you can write a simple list-comprehension to handle the 2-case:

sage: [ [a,b] for a in L for b in L if a != b ]
[[[1, 2, 3, 4], [3, 5, 6, 7]], [[1, 2, 3, 4], [7, 8, 9, 10]], [[3, 5, 6, 7], [1, 2, 3, 4]], [[3, 5, 6, 7], [7, 8, 9, 10]], [[7, 8, 9, 10], [1, 2, 3, 4]], [[7, 8, 9, 10], [3, 5, 6, 7]]]

Manually, the above can also be extended to 3, 4, ... but not easily to any number n given as a parameter. Also, this has the drawback of creating the entire list in memory instead of being a light generator as the product returns. You would have to write a longer piece of code to get a generator with the above behaviour.

Note that this is all Python-stuff and not specific to Sage at all.

Cheers, Johan

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find all sublists of set of a specified size say 3,4,5... from a given given list of sets

sriram gravatar imagesriram ( 2010-09-16 23:46:00 -0500 )edit

You could also try, e.g., 'combinations([[1,2], [3,4,5], [6], [7,8,9]], 3)'. (See 'combinations?' for caveats.) There's also 'combinations_iterator'.

Mitesh Patel gravatar imageMitesh Patel ( 2010-09-17 00:17:16 -0500 )edit

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Asked: 2010-09-16 23:08:08 -0500

Seen: 578 times

Last updated: Sep 16 '10