Re: Building clusters out of a nested list

• To: mathgroup at smc.vnet.net
• Subject: [mg114966] Re: Building clusters out of a nested list
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Fri, 24 Dec 2010 04:13:24 -0500 (EST)

```On 12/23/10 at 3:55 AM, dpesin at gmail.com (Dmitry) wrote:

>please, help me find a solution to the following problem:

>suppose I have a list of the form { {A,B,C},{C,D},{E,F},{F,H}}. I
>need to build a list whose entries are unions of all entries of the
>original list with nonzero intersection. For the example above, the
>end result is {{A,B,C,D},{E,F,H}}.

Here is one way:

In[6]:= Union[
Union /@ (Join @@@
DeleteCases[
Tuples[{{a, b, c}, {c, d}, {e, f}, {f, h}},
2], _?(Intersection @@ # == {} || SameQ @@ # &)])]

Out[6]= {{e,f,h},{a,b,c,d}}

Note, this is a brute force method in that it makes a list of
all possible pairings. There may be a more elegant way to do
this. Also, notice I changed your variables to lower case. It is
unwise to use single uppercase characters as variables as many
of these already have built in meaning.

```

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