13 :'(([: +/ [: *: -)"1& x)"1 y' 4 : '(([: +/ [: *: -)"1& x)"1 y'
13 : is not doing anything useful. A f B is equivalent to (([: +/ [: *: -)"1& A)"1 B So this is building up a function based on A which is being applied to each row of B. Note that it's first building up something based on each row of A and that this something is being used on each row of B. So we would expect the result to have a shape based on everything but the last dimension of B followed by everything but the last dimension of A followed by whatever the function itself produces. And, testing, we can see that this is the case: $A 3 2 $B 4 4 2 $(([: +/ [: *: -)"1& A)"1 B 4 4 3 So we get a number for each combination of row from A and row from B. So, next, let's consider an arbitrary row from A (4 1) and an arbitrary row from B (2 3): (([: +/ [: *: -)"1& (4 1))"1 (2 3) 8 Note that in this simplified case, we do not need the rank specifications: (([: +/ [: *: -)& 4 1)2 3 8 And, we can get rid of the & if we move the second argument to the unoccupied side of the verb that & was modifying: 2 3 ([: +/ [: *: -) 4 1 8 And, we can replace the train with an equivalent noun phrase, putting the left and right arguments on each odd verb (counting from the right) and eliminating any instances of [: +/ *: (2 3 - 4 1) 8 The parenthesis were not actually necessary here, but I included them because the other odd verbs were all eliminated so I did not have any place to show that parenthesis would be necessary. So, anyways, we see that it's the sum of the squares of the difference between the rows of A and the rows of B. Here's an equivalent expression: f=: +/@:*:@:-"1/~ Or, since you do not like @: f=: [: +/"1 [: *: -"1/~ -- Raul On Sun, Jun 3, 2012 at 10:03 PM, Linda Alvord <lindaalv...@verizon.net> wrote: > Your result looks interesting and I am able to get a tree from 5!:4 <'waveR'. > > Here's a real issue for me! What is function f doing to product the result > you get? > > A=:3 2$3 3 4 1 1 3 > B=:(i.4),."0 1 i.4 > f=: 13 :'(([: +/ [: *: -)"1& x)"1 y' > A f B > 18 17 10 > 13 16 5 > 10 17 2 > 9 20 1 > > 13 10 9 > 8 9 4 > 5 10 1 > 4 13 0 > > 10 5 10 > 5 4 5 > 2 5 2 > 1 8 1 > > 9 2 13 > 4 1 8 > 1 2 5 > 0 5 4 > > 5!:4 <'f' > ┌─ 4 > ── : ─┴─ ,:'(([: +/ [: *: -)"1& x)"1 y' > > When there is some way to untangle this so I can figure out what is > happening? I find the tree diagrams helpful but some code makes that > impossible. > > Can you give a simple translation for this function. > > Thanks in advance. > > Linda > > > -----Original Message----- > From: programming-boun...@jsoftware.com > [mailto:programming-boun...@jsoftware.com] On Behalf Of Raul Miller > Sent: Sunday, June 03, 2012 11:23 AM > To: Programming forum > Subject: Re: [Jprogramming] Challenge 11 Wave the Flag > > If by simplification you mean "fewer tokens while avoiding text definitions > and @ and @: then here is a variation on Jose's approach: > > waveR=: [:<"_1 [:|.&|:^:4 3 2 1 0 [:(|."_1~ [:>. +/ .=&' ' % _2:) [:> ;: > > I save 3 tokens by replacing (<5) with 4 3 2 1 0 > > I save 2 tokens by replacing > [: - [: <. [: -: ' '+/ .=~ > with > [: >. +/ .=&' ' % _2: > > I save 2 tokens by replacing > ([: |. |:) > with > |.&|: > > Note, however that if you are purely counting tokens, u@v and u@:v can be > simpler than ([: u v). > > Also, if you count text as a single token, text definitions are automatically > simpler than most everything. (But if you add to the token count the number > of tokens represented in the text, this goes > away.) > > -- > Raul > > On Sun, Jun 3, 2012 at 10:23 AM, Linda Alvord <lindaalv...@verizon.net> wrote: >> >> Viktor Cerovski and Jose Quintanta have provided solutions that are >> simplifying the waves. >> >> B=:'a big arrow focused somewhere' >> wave=: [: <"2 [: ([: |: |.)^:(<5) ([: > ;:)|."0 1~ [: - [: <. [: -: [: >> +/"1 ' ' = [: > ;: >> #;:'[: <"2 [: ([: |: |.)^:(<5) ([: > ;:) |."0 1~ [: - [: <. [: -: [: >> +/"1 '' '' = [: > ;:' >> 40 >> waveVC=:[: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: -: [: +/"1 ' >> ' = ]) [: > ;: >> #;:'[: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: -: [: +/"1 '' '' >> = ]) [: > ;' >> 39 >> waveJQ=.[: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: -: ' >> '+/ .=~ >> ]) [: > ;: >> #;:'[: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: -: '' ''+/ >> .=~ >> ]) [: > ;:' >> 38 >> Any more simplifications waiting in thewings? >> >> Linda >> >> -----Original Message----- >> From: programming-boun...@jsoftware.com >> [mailto:programming-boun...@jsoftware.com] On Behalf Of Jose Quintana >> Sent: Sunday, June 03, 2012 12:33 AM >> To: programming@jsoftware.com >> Subject: Re: [Jprogramming] Challenge 11 Wave the Flag >> >> >> Cheating... wave1=. [: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: >> -: ' ' +/ .=~ ]) [: > ;: >> >> cheat=. (lr<'wave1')&apply f. >> lr<'cheat' >> '[: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ ([: - [: <. [: -: '' '' +/ .=~ >> ])) >> [: > ;:'&(128!:2) >> #;:lr<'cheat' >> 7 >> ... and without cheating >> wave1=. [: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: -: ' ' >> +/ .=~ ]) [: > ;: >> #;: '[: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: -: '' >> '' +/ .=~ ]) [: > ;:' >> 38 > Date: Sat, 2 Jun 2012 02:38:40 -0700 >>> From: viktor.cerov...@gmail.com >>> To: programming@jsoftware.com >>> Subject: Re: [Jprogramming] Challenge 11 Wave the Flag >>> >>> >>> >>> >>> Linda Alvord wrote: >>> > >>> > >>> > >>> > It was David Ward Lambert's idea to write a one line expression >>> > with the fewest tokens. We worked together and got to 40 tokens. >>> > Any ideas to make this any better. >>> > >>> > >>> > >>> > B=:'a big arrow focused somewhere' >>> > >>> > NB. center justify (Hint from DWL x |."0 1 y) >>> > >>> > cj=: 13 :'(-<.-:+/"1 '' ''=>;:y)|."0 1>;:y' >>> > >>> > cj >>> > >>> > ([: - [: <. [: -: [: +/"1 ' ' = [: > ;:) |."0 1 [: > ;: >>> > >>> > cj B >>> > >>> > a >>> > big >>> > arrow >>> > focused >>> > somewhere >>> > >>> > NB. quarter turns >>> > >>> > qtla=: 13 :'y;(|:|.y);(|.|:|.|:y);(|.|:y);y' >>> > >>> > qtla >>> > >>> > ] ; ([: |: |.) ; ([: |. [: |: [: |. |:) ; ] ;~ [: |. |: >>> > >>> > qtla cj B >>> > >>> > ----------T-----T---------T-----T---------┐ >>> > │ a │s │erehwemos│ e│ a │ │ big │of │ >>> > desucof │ dr│ big │ │ arrow │moa │ worra │ wee│ arrow >>> > │ │ focused │ecrb │ gib │ gosh│ focused │ │somewhere│wuria│ >>> > a │airuw│somewhere│ │ │hsog │ │ brce│ │ >>> > │ │eew │ │ aom│ │ │ │rd │ >>> > │ fo│ │ │ │e │ │ s│ │ >>> > L---------+-----+---------+-----+---------- >>> > >>> > NB. 5 quarter turns David Ward Lambert >>> > >>> > qtdwl=: 13 :'<"2 ([:|:|.)^:(<5)y' >>> > >>> > qtdwl cj B >>> > >>> > ----------T---------T---------T---------T---------┐ >>> > │ a │s │erehwemos│ e │ a │ │ big │of >>> > │ desucof │ dr │ big │ │ arrow │moa │ worra │ >>> > wee │ arrow │ │ focused │ecrb │ gib │ gosh │ >>> > focused │ │somewhere│wuria │ a │airuw │somewhere│ │ >>> > │hsog │ │ brce │ │ │ │eew │ >>> > │ aom │ │ │ │rd │ │ fo │ >>> > │ │ │e │ │ s │ │ >>> > L---------+---------+---------+---------+---------- >>> > >>> > qtdwl >>> > >>> > [: <"2 ([: |: |.)^:(<5) >>> > >>> > >>> > >>> > wave=: [: <"2 [: ([: |: |.)^:(<5) ([: > ;:)|."0 1~ [: - [: <. [: -: >> [: >>> > +/"1 ' ' = [: > ;: >>> > >>> > >>> Here is a 39 token version: >>> >>> wave1=:[: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: -: [: >>> +/"1 >> ' >>> ' = ]) [: > ;: >>> >>> #;:'[: <"2 [: ([: |: |.)^:(<5) [: (|."0 1~ [: - [: <. [: -: [: +/"1 '' >> '' >>> = ]) [: > ;:' >>> 39 >>> >>> >>> >>> > >>> > wave B >>> > >>> > ----------T---------T---------T---------T---------┐ >>> > │ a │s │erehwemos│ e │ a │ │ big │of >>> > │ desucof │ dr │ big │ │ arrow │moa │ worra │ >>> > wee │ arrow │ │ focused │ecrb │ gib │ gosh │ >>> > focused │ │somewhere│wuria │ a │airuw │somewhere│ │ >>> > │hsog │ │ brce │ │ │ │eew │ >>> > │ aom │ │ │ │rd │ │ fo │ >>> > │ │ │e │ │ s │ │ >>> > L---------+---------+---------+---------+---------- >>> > >>> > wave >>> > >>> > [: <"2 [: ([: |: |.)^:(<5) ([: > ;:) |."0 1~ [: - [: <. [: -: [: +/"1 ' >> ' >>> > = >>> > [: > ;: >>> > >>> > #;:'[:<"2[:([:|:|.)^:(<5)([:>;:)|."0 1~[:-[:<.[:-:[:+/"1'' ''=[:>;:' >>> > >>> > 40 >>> > >>> > >>> > >>> > Hopefully David will send his version of 39 tokens but not simple J. >>> > Note also that you must paste the long line for wave together. >>> > >>> > >>> > >>> > Linda >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > From: Linda Alvord [mailto:lindaalv...@verizon.net] >>> > Sent: Tuesday, May 01, 2012 3:17 AM >>> > To: 'Linda Alvord' >>> > Subject: Challenge 11 Wave the Flag >>> > >>> > >>> > >>> > Challenge 10 Wave the Flag PLEASE DO NOT RESPOND UNTIL 5/28/2012 >>> > 12 >> am >>> > EST >>> > >>> > >>> > >>> > Here's a little preparation for Memorial Day. >>> > >>> > >>> > >>> > S=:10 16$(16$' '),176$(16$'* '),16$' * ' >>> > >>> > T=:10 36$(36$'#'),72$' ' >>> > >>> > U=:9 52$(104$' '),364$(52$'#'),104$' ' >>> > >>> > <' ',"1(((S,"1 ' '),.T),U),"1 ' ' >>> > >>> > --------------------------------------------------------┐ >>> > │ #################################### │ │ * * * >>> > * * * │ │ * * * * * >>> > │ │ * * * * * * #################################### │ │ * * >>> > * * * │ │ * * * * * * >>> > │ │ * * * * * #################################### │ │ * * >>> > * * * * │ │ * * * * * >>> > │ │ * * * * * * #################################### │ │ >>> > │ │ │ │ >>> > #################################################### │ │ >>> > │ │ │ │ >>> > #################################################### │ │ >>> > │ │ │ │ >>> > #################################################### │ >>> > L-------------------------------------------------------- >>> > >>> > >>> > >>> > Part 1: Use viewmat and create a little flag. Next design a >>> > function to rotate it clockwise 90 degrees successively until it is >>> > in the original position. >>> > >>> > >>> > >>> > load viewmat >>> > >>> > flag=: >>> > >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > >>> > wwwwwwwwwwwwww >>> > >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > >>> > wwwwwwwwwwwwww >>> > >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > >>> > wwwwwwwwwwwwww >>> > >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > >>> > wwwwwwwwwwwwww >>> > >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > wwwwwwww >>> > >>> > >>> > >>> > Part 2: >>> > >>> > >>> > >>> > A=:'we celebrate Memorial Day on May the twenty eighth' >>> > >>> > wave=: >>> > >>> > ------------T-----------T-----------T-----------T-----------┐ >>> > │----------┐│----------┐│----------┐│----------┐│----------┐│ >>> > ││ we │││ Mc │││ hthgie │││ e │││ we ││ >>> > ││celebrate│││et ee │││ ytnewt │││ tl │││celebrate││ >>> > ││Memorial │││iw ml │││ eht │││ aa yh│││Memorial ││ ││ >>> > Day │││getMoDoew│││ yaM │││ riy yett│││ Day ││ ││ on >>> > │││hnhanarbe│││ no │││ebranahnh│││ on ││ ││ May >>> > │││ttey yir │││ yaD │││weoDoMteg│││ May ││ ││ the │││hy >>> > aa │││ lairomeM│││ lm wi│││ the ││ ││ twenty │││ lt >>> > │││etarbelec│││ ee te│││ twenty ││ ││ eighth │││ e │││ >>> > ew │││ cM │││ eighth ││ >>> > │L----------│L----------│L----------│L----------│L----------│ >>> > L-----------+-----------+-----------+-----------+------------ >>> > >>> > >>> > >>> > Reshape A into a 9 9 square matrix. Justify all lines in the center. >>> > If a line has an even number of letters put the extra letter on the >>> > left. Now design a function to rotate the words in a similar >>> > fashion to the flag above. Note the letters in "we" as they move >>> > around clockwise. Your function should work for any square literal matrix. >>> > >>> > >>> > >>> > Happy Memorial Day! >>> > >>> > >>> > >>> > Linda >>> > >>> > ------------------------------------------------------------------- >>> > - >>> > -- For information about J forums see >>> > http://www.jsoftware.com/forums.htm >>> > >>> >>> -- >>> View this message in context: >>> http://old.nabble.com/Re%3A-Challenge-11-Wave-the-Flag-tp33948875s241 >>> 9 3p33948951.html Sent from the J Programming mailing list archive at >>> Nabble.com. >>> >>> --------------------------------------------------------------------- >>> - For information about J forums see >>> http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
