# list of unique non-subset sets

Bengt Richter bokr at oz.net
Fri Mar 18 22:50:51 CET 2005

```On Thu, 17 Mar 2005 23:56:46 GMT, "Raymond Hettinger" <vze4rx4y at verizon.net> wrote:

>
>"Kent Johnson" <kent37 at tds.net> wrote in message
>> Raymond Hettinger wrote:
>> > [les_ander at yahoo.com]
>> >
>> >>I have many set objects some of which can contain same group of object
>> >>while others can be subset of the other. Given a list of sets,
>> >>I need to get a list of unique sets such that non of the set is an
>> >>subset of another or contain exactly the same members.
>> >>
>> >>Tried to do the following:
>> >>s1=set(['a','b','c'])
>> >>s2=set(['a','c'])
>> >>s3=set(['a','d','e','f'])
>> >>s4=set(['r','k','l'])
>> >>s5=set(['r','k','l'])
>> >>L=[s1,s2,s3,s4,s5]
>> >>----------------------- > cleaned-up list should contain s1, s3, s5
>> >
>> >
>> > This should do the trick:
>> >
>> >
>> > result = []
>> > for s1 in L:
>> >     for s2 in result:
>> >         if s1 <= s2:
>> >             break
>> >     else:
>> >         result.append(s1)
>> >
>> > print result
>>
>> If I understand the original post correctly, you also need to check for an
>existing set being a
>> subset of the set you are adding. A better test case is
>> s1=set(['a','b','c'])
>> s2=set(['a','c'])
>> s3=set(['a','d','e','f'])
>> s4=set(['r','k','l'])
>> s5=set(['r','k','l'])
>> s6=set(['g', 'h'])
>> s7=set(['h', 'i'])
>> s8=set(['g', 'h', 'i'])
>>
>> L=[s1,s2,s3,s4,s5,s6,s7,s8]
>> # ----------------------- > cleaned-up list should contain s1, s3, s5, s8
>
>Try this:
>
>result = []
>seen = set()
>for s1 in L:
>    for s2 in L:
>        if s1 < s2:
>            break
>    else:
>        if s1 not in seen:
>            result.append(s1)
>print result
>
Actually, ISTM there are more than one set of sets that can be drawn from the
original set that internally satisfy the criteria of no internal duplicates or subsets. E.g.,
here are some lists of sets selected from L above. I believe (unless I goofed) the requirement
"""
>> >>I need to get a list of unique sets such that non of the set is an
>> >>subset of another or contain exactly the same members.
"""
is satisfied internally within each list below.

[set(['h', 'g']), set(['i', 'h'])]
[set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f']), set(['h', 'g'])]
[set(['a', 'e', 'd', 'f']), set(['a', 'c']), set(['h', 'g']), set(['i', 'h'])]
[set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f'])]
[]
[set(['a', 'c', 'b']), set(['h', 'g']), set(['i', 'h'])]
[set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['a', 'c']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['h', 'g'])]
[set(['a', 'c', 'b'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f']), set(['i', 'h', 'g'])]
[set(['a', 'e', 'd', 'f']), set(['a', 'c']), set(['i', 'h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['i', 'h', 'g'])]
[set(['a', 'e', 'd', 'f']), set(['i', 'h'])]
[set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f']), set(['i', 'h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['a', 'c']), set(['i', 'h', 'g'])]
[set(['a', 'c'])]
[set(['k', 'r', 'l']), set(['a', 'c']), set(['h', 'g'])]
[set(['k', 'r', 'l']), set(['h', 'g']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f']), set(['i', 'h'])]
[set(['a', 'e', 'd', 'f']), set(['a', 'c']), set(['i', 'h'])]
[set(['a', 'c']), set(['h', 'g']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['a', 'c'])]
[set(['a', 'e', 'd', 'f']), set(['i', 'h', 'g'])]
[set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f']), set(['h', 'g']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['a', 'c']), set(['h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['h', 'g']), set(['i', 'h'])]
[set(['a', 'e', 'd', 'f']), set(['a', 'c'])]
[set(['k', 'r', 'l']), set(['h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'c']), set(['h', 'g']), set(['i', 'h'])]
[set(['h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['i', 'h'])]
[set(['a', 'c', 'b']), set(['i', 'h', 'g'])]
[set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f']), set(['h', 'g'])]
[set(['a', 'c', 'b']), set(['h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['a', 'e', 'd', 'f']), set(['h', 'g']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['i', 'h', 'g'])]
[set(['a', 'c', 'b']), set(['i', 'h'])]
[set(['a', 'c']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'c']), set(['i', 'h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f']), set(['a', 'c']), set(['h', 'g']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'e', 'd', 'f'])]
[set(['a', 'c']), set(['h', 'g'])]
[set(['k', 'r', 'l']), set(['i', 'h', 'g'])]
[set(['a', 'e', 'd', 'f']), set(['a', 'c']), set(['h', 'g'])]
[set(['a', 'e', 'd', 'f']), set(['h', 'g']), set(['i', 'h'])]
[set(['a', 'c']), set(['i', 'h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'c']), set(['i', 'h'])]
[set(['k', 'r', 'l']), set(['a', 'c'])]
[set(['a', 'e', 'd', 'f']), set(['h', 'g'])]
[set(['k', 'r', 'l']), set(['a', 'c', 'b']), set(['h', 'g']), set(['i', 'h'])]
[set(['a', 'e', 'd', 'f'])]
[set(['i', 'h', 'g'])]

Regards,
Bengt Richter

```