[Jprogramming] All subset keys

[Mike Day]

This is a tacit version and I'm adding the missing linefeed
to my earlier msg.

   allsskeys =: ~.@((i.~ ~.)"1@((#: i.@(*/))@(>:@i.)))

The following variant omits the 1st ~. in not reducing terms
to lowest possible key, eg the term 0 0 0 3 is not reduced to
0 0 0 1, with some time saving:

   allsskeys1 =: ~.@((i.~)"1@((#: i.@(*/))@(>:@i.)))
   ts'allsskeys 8'
0.086195 4.71981e6
   ts'allsskeys1 8'
0.0199724 4.71981e6

   NB. no change to the list of subsets
   key =: (allsskeys1 </."1 i.)
   key1 =: (allsskeys1 </."1 i.)
   (key -: key1) 8
1
   |: key 3
+-----+---+---+---+-+
|0 1 2|0 1|0 2|0  |0|
+-----+---+---+---+-+
|     |2  |1  |1 2|1|
+-----+---+---+---+-+
|     |   |   |   |2|
+-----+---+---+---+-+

Mike

Mike Day wrote:

> This generates the key array/s:
> allsskeys =: 13 : '~.(i.~~.)"1 r#: i.*/ r =. >:i.y.'
>
> I don't see the point of (say) allsskeys 3 for sets
> of size 4 but here goes:
>   NB. |: only to save display lines here ....
>   |:each allsskeys each 1 2 3 4 


> +-+---+---------+-----------------------------+
> |0|0 0|0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
> | |0 1|0 0 1 1 1|0 0 0 0 0 1 1 1 1 1 1 1 1 1 1|
> | |   |0 1 0 1 2|0 0 1 1 1 0 0 0 1 1 1 2 2 2 2|
> | |   |         |0 1 0 1 2 0 1 2 0 1 2 0 1 2 3|
> +-+---+---------+-----------------------------+
>   |:(allsskeys 4)</. "1 'abcd'
> +----+---+---+--+--+---+--+--+--+---+--+--+--+--+-+
> |abcd|abc|abd|ab|ab|acd|ac|ac|ad|a  |a |ad|a |a |a|
> +----+---+---+--+--+---+--+--+--+---+--+--+--+--+-+
> |    |d  |c  |cd|c |b  |bd|b |bc|bcd|bc|b |bd|b |b|
> +----+---+---+--+--+---+--+--+--+---+--+--+--+--+-+
> |    |   |   |  |d |   |  |d |  |   |d |c |c |cd|c|
> +----+---+---+--+--+---+--+--+--+---+--+--+--+--+-+
> |    |   |   |  |  |   |  |  |  |   |  |  |  |  |d|
> +----+---+---+--+--+---+--+--+--+---+--+--+--+--+-+
>
> I think there's a more efficient way, avoiding the
> redundancy removed by the ~. but this gets the ball
> rolling!
>
> Mike
>
>
> Oleg Kobchenko wrote:
>
>> Here is another puzzle (Not sure if the chosen
>> name is appropriate).
>>
>> For a given set magnitude N find list of all subset keys:
>>
>>   <@allss"0 i.5
>> ++-+---+-----+-------+
>> ||0|0 0|0 0 0|0 0 0 0|
>> || |0 1|0 0 1|0 0 0 1|
>> || |   |0 1 0|0 0 1 0|
>> || |   |0 1 1|0 0 1 1|
>> || |   |0 1 2|0 0 1 2|
>> || |   |     |0 1 0 0|
>> || |   |     |0 1 0 1|
>> || |   |     |0 1 0 2|
>> || |   |     |0 1 1 0|
>> || |   |     |0 1 1 1|
>> || |   |     |0 1 1 2|
>> || |   |     |0 1 2 0|
>> || |   |     |0 1 2 1|
>> || |   |     |0 1 2 2|
>> || |   |     |0 1 2 3|
>> ++-+---+-----+-------+
>>
>>   'abcd' ;:^:_1@(</.)"1~ allss 4
>> abcd   abc d  abd c  ab cd  ab c d acd b  ac bd  ac b d ad bc  a bcd  
>> a bc d ad b c a bd c a b cd a b c d
>>
>>
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