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- みがね かいじ
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1 MOO An optimal MOO strategy Tetsuro Tanaka, Faculty of Engineering, University of Tokyo MOO ( ) (exhaustive search). [1], MOO. MOO,.,, 0.5., MOO. 1 MOO MOO, Hit & Blow, Cow & Bull, ( MOO ), , MOO. MOO bull ( ) cow( ). 2 MOO bull, cow MOO. MOO 4 bull. 4 bull.. 1 MUD(Multi User Dungeon). 1
2 , C C B B B2C B 1: MOO. ( ) 6 MOO, MOO, BSD Unix MOO. 2 MOO, bull, cow MOO. [2] 1971.,,,,. MOO,, [3], [4] shell., MOO [2]. MOO 5040 ( 10 P 4 ). MOO,, 5040 MOO MOO. MOO π, MOO T, 4B, 3B, 2B2C, 2B1C, 2B, 1B3C, 1B2C, 1B1C, 1B, 4C, 3C, 2C, 1C, 0C 14, π t 1,..., t 14. f(t ), T. 2
3 J. Larmouth, n log(n), f(t )= t i log( t i )( 2log2 if T π) i [1,14],t i 0, 5.24., B. Landy f(t )=max( t i ) 14 f(t )= t i log(1 + t i ) i=1 14 f(t )= T i F ( t i ) where F (n) is the solution of x x = n i= bit [5]. f(t ),., B.Landy, 5.22( 26347). 3 f(t ), t 1,..., t ,,., 2., 5040 MOO, 1,.,,. [2],, This is far too expensive on computation.. [1]., 6 4 = 1296, MOO 10 P 4 = 5040, 3
4 4,,,., ,., (Sparc Station 20), 60, 30 ( 26274) MOO, , packed decimal. 10, 0-9 MOO 1. MOO a, b bull, a ^ b (^ ) , 64K. cow a & b 10 1, bull., 1K. MOO. typedef int Question2; int moo(question2 q1,question2 q2) { int bull,cow; } bull=bulltable[(q1^q2)&0xffff]; cow=cowtable[(q1&q2)>>16]; return(moo_product[bull][cow]); SS20, x5040, 1, 1 25M ( M ). 4
5 ([1234,3456,1256] [0,7,8,9] ). ( [5,6,7,8,9] ),,,.,.. 1. {a 1,a 2,..., a n }(a 1 <a 2 <... < a n ), a 1,a 2,... 2.,, ( 4! = 24),., , 0456, 4056, 0145, 0415, 4501, 1045, 1405, 0124, 0142, 0214, 0241, 1204, 1240, 1023, 1032, 0231, 1230) 19 3, 4, 1900, ,2,3 1,2,3,
6
7 4.4, 5040 heap sort. heap sort., n n 14, 1 1, 2 n 1,, 1+2(n 1) = 2n 1.,., (4-10)., n(4 n 10) MOO, m 1. 10,, 3 80, 9 3, , ,. C , 14, (0-13),., 14,. 7
8 1: n : 10 (n) 1 n 14 2n 1 15 n 127 3n n 864 4n n 5n 1006 C gcc, SS20., ( 5.213). 3.,, 4, 5040 MOO. 6 MOO,?. MOO,,, 3, 1 2.,. ( 0.5 ) γ n, Γ n = γ n
9 3: 1 2 ( ) 4B B2C B3C C B B1C B :08.3 1B2C :48.3 3C :00.5 0C B :52.5 1B1C :28.6 2C :12:29.7 1C :24:47.2 4:
10 . 5. 5: (Γ n ) , (, ). 58.,,. 6. 6: 1 2 ( ) 4B B2C B3C C B B1C B :01.8 1B2C :48.9 3C :29.5 0C B :18.1 1B1C :46:15.2 2C :23:42.8 1C :56:42.9, ( 26312),,, %., 50 % 10
11 , 50%. A, B, C, A>B,B>C,C>A,.,. 52,, 0.5., : C, 850, 650.,., WWW ( Knuth TeX,.,, Lisp,.,,. 8 MOO.,, 11
12 ,., 1.,,, MOO,,. 2.,,.., n, n,.,.,. [1] Kenji Koyama, Tony W.Lay: An optimal Mastermind Strategy, J. Recreational Mathematics, Vol. 25, No. 4, pp (1994). [2] ℵ 0 : Computer Recreations. SOFTWARE, Vol. 1, No. 2, pp (1971). [3] MOO,, pp (1979). [4] srekcah@sra.junet: Shell (2),, Vol.1, No.2, pp (1986). [5] :, bit, Vol.19, No.7 (1987). [6] Donald E.Knuth: The Computer as Master Mind, J. Recreational Mathematics Vol. 9, No. 1, pp. 1-6 ( ). 12
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