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
