Actually ) can be in any position on the line. The restriction, in the versions of J that I have used, is that no other non-whitespace characters may appear on that line.
FYI, -- Raul On Wed, May 2, 2012 at 4:57 AM, Tom Arneson <t...@tomarneson.com> wrote: > Note is defined as > > Note > 3 : '0 0 $ 0 : 0' :[ > > And allows a multiline note terminated by ')' as the first char of a line. > > -----Original Message----- > From: programming-boun...@jsoftware.com > [mailto:programming-boun...@jsoftware.com] On Behalf Of Linda Alvord > Sent: Wednesday, May 02, 2012 00:38 > To: 'Programming forum' > Subject: Re: [Jprogramming] May knight's challenge > > Around line 43 the word Note should be NB. and then the following lines > need to be on one line. Then the ) is unnecessary. Is that what you > intend? > > Other than that that, all worked well and will take quite a while to digest. > > Linda > > -----Original Message----- > From: programming-boun...@jsoftware.com > [mailto:programming-boun...@jsoftware.com] On Behalf Of David Ward Lambert > Sent: Tuesday, May 01, 2012 10:38 PM > To: programming > Subject: [Jprogramming] May knight's challenge > > NB. The latter portion of this code demonstrates NB. various Markov chain > computations. > > Note 'code notes' > Use Raul Miller's easy, useful > NOUN Adverb Conjunction verb > name convention. > > Data structure: > o Board is a vector tallying *:N. Apparently, I > have virtualized BOARD. It exists in thought > only. > o The state is vector of 2 boxed knight paths > with next to move at head. > > program should work for N in [3,9] > The upper limit stems from the chess > algebraic display algorithm. > > 1 piece moves each ply > ) > > N=: 8 > > NB. convert array coordinates to vector index > index=: N&#. > > GRID=: 2 ({@:# <@:i.) N > CELLS=: ,/@:> GRID > > JUMPS=: (, |."1) 1 2 *"1 (1 1,_1 1,_1 _1,:1 _1) > LC=: 26 }. Alpha_j_ NB. lowercase > CD=: }. Num_j_ NB. counting digits > NAMES=: ((LC {~ {.) , (CD {~ {:))"1 CELLS > > NB. T are the circle of moves from each square > T=: <"2 CELLS+"1/JUMPS > > NB. VerifyRange Interval is (] > NB. 0 means in range, 1 for outside > VerifyRange=: &(1 ~: I.) > assert 1 1 0 0 0 0 1 1 1 1 -: 1 5 VerifyRange i.10 Note 'why adverb?' > I like adverbs. When I write in other languages I hard-code constants, > then I have to rewrite, extracting and naming constants to generalize > my code. Adverbs will help me overcome this. > ) > > assert 0 -: 2 9 VerifyRange N NB. process check > > none=: +:/ NB. works for a pair of numbers > MOVES2D=: (#~ none"1@:((_1+0,N)VerifyRange))&.> T > MOVES=: index&.> MOVES2D > > NB. sorry, I like commuted hook > 'WN BN'=: 2 ((A.~ ?)~ index) 1 1 ,: N - 2 2 > > choose=: {~ ?@:# > move=: choose@:>@:({&MOVES) > While=: conjunction def 'u^:v^:_' > position=: {:@:> > continue=: ~:&position/ > assert 1 -: continue 2 3;4 > assert 0 -: continue 2 3;4 2 3 > ply=: {: , (, move@:position)&.>@:{. > > NB. run the simulation > PATHS=: WN ply While continue@:;&, BN > > NB. report > WN 4 : 0 PATHS > > NB. algebraic notation for the moves > AN=. (('N' , [ , ' N' , ])/"2) NAMES {~ ,.&>/ y > > NB. display the numbered moves > smoutput 'Move 0 shows setup.' > smoutput 'White plays first. Black wins.' > smoutput (,.~ '. ' ,"1~ ":@:,.@:i.@:#) AN > ) > > > Note 'Markov chain' > Consider an (*:N) by (*:N) transition matrix. > Each row represents a square on the chess board, > so does each column. The row is the starting > square, the column is the index of end square. > The value at each row column cell is the > probability to move to the cell of the column starting from the cell > of the row. For example, the first row represents the corner cell a1. > From > a1 there are two legal moves, with equal > probability. Those two columns in top row will > have probability 1r2. > > The probability that a knight is located at a square is the matrix > product of the current location vector by the transition probability > matrix. Repeat the matrix multiplication for each hop. Begin! > ) > > NB. transition probability matrix > NB. sorry, I like commuted hook > P=: ((%@:x:@:#@:[`[`]}~ >)~"0 1 (0 $~ ,~@:#)) MOVES > > Note 'transition probability matrix' > 4x4 symmetric corner of 8x8 chess board. > The display is chopped at right hand side for email. > Perhaps difficult to understand. > a1 a2 a3 a4..b1 b2 b3 b4..c1 c2 c3 c4..d > +-------------------------------------------------- > a1| 0 0 0 0 0 0 1r2 0 0 1r2 0 0 > a2| 0 0 0 0 0 0 0 1r3 1r3 0 1r3 0 > a3| 0 0 0 0 1r4 0 0 0 0 1r4 0 1r4 > a4| 0 0 0 0 0 1r4 0 0 0 0 1r4 0 > . > b1| 0 0 1r3 0 0 0 0 0 0 0 1r3 0 > b2| 0 0 0 1r4 0 0 0 0 0 0 0 1r4 1r > b3|1r6 0 0 0 0 0 0 0 1r6 0 0 0 > b4| 0 1r6 0 0 0 0 0 0 0 1r6 0 0 > . > c1| 0 1r4 0 0 0 0 1r4 0 0 0 0 0 > c2|1r6 0 1r6 0 0 0 0 1r6 0 0 0 0 > c3| 0 1r8 0 1r8 1r8 0 0 0 0 0 0 0 1r > c4| 0 0 1r8 0 0 1r8 0 0 0 0 0 0 > . > d1| 0 0 0 0 0 1r4 0 0 0 0 1r4 0 > d2| 0 0 0 0 1r6 0 1r6 0 0 0 0 1r6 > d3| 0 0 0 0 0 1r8 0 1r8 1r8 0 0 0 > d4| 0 0 0 0 0 0 1r8 0 0 1r8 0 0 > ) > > start=: (i.@:# P)&= > mp=: +/ .* > > Note 'various probabilities' > NB. percent probability to land on a square > NB. after 80 and 81 jumps. > NB. Observe the white-black alternation. > <.0.5+100*(_1 x: P)mp~^:80 81(start@:index 1 1) > 1 0 2 0 2 0 2 0 0 2 0 4 0 4 0 2 2 0 5 0 5 0 4 0... > 0 2 0 2 0 2 0 1 2 0 4 0 4 0 2 0 0 4 0 5 0 5 0 2... > > NB. probability sum 1, knight still on board. > +/"1 (_1 x: P) mp~^:80 81 (start@:index 1 1) > 1 1 > > NB. compute probability to be on same square > NB. after 6 hops. Different question from > NB. "The first time they meet is at move 6." > > NB. locations after 6 hops > HOPS=: 6 > P_CELL=: WN mp&(_1 x: P)^:HOPS@:,:&start BN > > NB. show the probabilities (clipped at 50 colum > _ 50 {. 6j3 ": P_CELL > 0.013 0.000 0.030 0.000 0.026 0.000 0.016 0.000 0 > 0.007 0.000 0.016 0.000 0.018 0.000 0.016 0.000 0 > > NB. Probability to share square at move 6 > mp/ P_CELL > 0.0349013 > > NB. Probability to share after > NB. 0, 2, ... , 22 plies. > NB. (display clipped!) > mp/"2 WN mp&(_1 x: P)^:(<12)@:,:&start BN > 0 0 0.0117188 0.0226508 0.0313695 0.0322698 0.0349 > NB. First capture can occur at move 2. > ) > > > ---------------------------------------------------------------------- > 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
