f=: 13 :' <"1 |:((>:i.#y)*/"0 |:((#y)#2)#:i.2^#y){'' '',y'
f 'ABC'
----T---T---T---T---T---T---T---┐
│ │ C│ B │ BC│A │A C│AB │ABC│
L---+---+---+---+---+---+---+----
This is a set of the subsets? I haven't looked at your example yet.
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of km
Sent: Thursday, November 14, 2013 3:18 PM
To: [email protected]
Subject: [Jprogramming] Sets
Here is my latest attempt at sets in J. Would anyone care to write a verb
ps (power set) such that ps y is the set of all subsets of set y? It's
called the power set in part because when a set has n elements its power set
has 2^n elements. --Kip Murray
NB. A set is a box with a sorted list of boxes inside.
NB. An element is the contents of a box in the list.
NB. A -: B tests whether set A is set B.
set =: [: < [: /:~ ~. NB. create set from list of boxes
NB. The list may have duplicates but the set has none.
EE =: <$0 NB. empty set, same as Ace a:
eo =: <@[ e. >@] NB. test whether x is an element of y
uu =: [: set ,&> NB. union
mm =: [: < -.&> NB. minus
sd =: mm uu mm~ NB. symmetric difference
cp =: uu mm sd NB. common part (intersection)
ss =: uu -: ] NB. test whether x is a subset of y
(set 1;2;3;3) -: set 3;1;2
1
]A =: set 2;'b';1;'a'
+---------+
|+-+-+-+-+|
||1|2|a|b||
|+-+-+-+-+|
+---------+
]B =: set 'b';'a';4;3;'a'
+---------+
|+-+-+-+-+|
||3|4|a|b||
|+-+-+-+-+|
+---------+
A uu B
+-------------+
|+-+-+-+-+-+-+|
||1|2|3|4|a|b||
|+-+-+-+-+-+-+|
+-------------+
A sd B
+---------+
|+-+-+-+-+|
||1|2|3|4||
|+-+-+-+-+|
+---------+
A cp B
+-----+
|+-+-+|
||a|b||
|+-+-+|
+-----+
NB. Below is the set of all subsets of set 0;1
set EE;(set <0);(set <1);<set 0;1
+------------------------+
|+--+-----+-------+-----+|
||++|+---+|+-----+|+---+||
||||||+-+|||+-+-+|||+-+|||
||++|||0|||||0|1|||||1||||
|| ||+-+|||+-+-+|||+-+|||
|| |+---+|+-----+|+---+||
|+--+-----+-------+-----+|
+------------------------+
Sent from my iPad
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