This is an instance of the transitive closure problem. In the matrix form
it can be solved as +./ .*./~^:_ M , the power limit of repeated squaring
by the or-and inner product.
On Thu, Sep 12, 2013 at 3:44 PM, Richard Gaylord <rjgayl...@gmail.com>wrote:
> here's some code in the Wolfram Programming Language (the language
> underlying Mathematica) illustring the use of pattern matching.
>
>
>
> Society is a list of the attribute lists of people. As an illustration, we
> will create a society consisting of eight people, each with two attributes.
> In each person's attribute list,
> the first element (which is a number) represents the person's name ,
>
> the second element which is a list of numbers) is a list of the names of
> the members of the person's social network.
>
>
> society = {{1, {5, 7}},
> {2, {}},
> {3, {}},
> {4, {1, 2}},
> {5, {2, 7}},
> {6, {2}}},
> {7, {8}},
> {8, {5}}}
>
> We can modify society so that anyone who is in another person's social
> network includes that person in their own social network (i.e., reciprocal
> social connections).
>
> symSoc = society /.
> {a_Integer, b_} :> {a, Union[b, Cases[society, {x_, {___, a, ___}} :> x]]}
>
> symSoc = {{1, {4, 5, 7}},
> {2, {4, 5, 6}},
> {3, {}},
> {4, {1, 2}},
> {5, {1, 2, 7, 8}},
> {6, {2}},
> {7, {1, 5, 8}},
> {8, {5, 7}}}
>
> how would this be done in J?
>
> note: a pdf of the note set on the Wolfram Language in which the
> expressions for society and symSoc appear on p. 42 can be downloaded at
>
> http://library.wolfram.com/infocenter/MathSource/5216/
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