Algorithm for Creating Supersets of Smaller Sets Based on Common Elements

[Mark Lawrence]

On 21/02/2015 19:46, TommyVee wrote:
> Start off with sets of elements as follows:
>
> 1. A,B,E,F
> 2. G,H,L,P,Q
> 3. C,D,E,F
> 4. E,X,Z
> 5. L,M,R
> 6. O,M,Y
>
> Note that sets 1, 3 and 4 all have the element 'E' in common, therefore
> they are "related" and form the following superset:
>
> A,B,C,D,E,F,X,Z
>
> Likewise, sets 2 and 5 have the element 'L' in common, then set 5 and 6
> have element 'M' in common, therefore they form the following superset:
>
> G,H,L,M,O,P,Q,R,Y
>
> I think you get the point.  As long as sets have at least 1 common
> element, they combine to form a superset.  Also "links" (common
> elements) between sets may go down multiple levels, as described in the
> second case above (2->5->6).  Cycles thankfully, are not possible.
>
> BTW, the number of individual sets (and resultant supersets) will be
> very large.
>
> I don't know where to start with this.  I thought about some type of
> recursive algorithm, but I'm not sure.  I could figure out the Python
> implementation easy enough, I'm just stumped on the algorithm itself.
>
> Anybody have an idea?
>
> Thanks, Tom

A naive approach but should give you something to think about.

from collections import defaultdict

sets = ({'A','B','E','F'},
{'G','H','L','P','Q'},
{'C','D','E','F'},
{'E','X','Z'},
{'L','M','R'},
{'O','M','Y'})

d = defaultdict(list)

for i, aSet in enumerate(sets):
     for a in aSet:
         d[a].append(i)

superSets = []
for k in d:
     if len(d[k]) > 1:
         superSet = set()
         for i in d[k]:
             superSet |= sets[i]
         superSets.append(superSet)

-- 
My fellow Pythonistas, ask not what our language can do for you, ask
what you can do for our language.

Mark Lawrence