프로그래머 두뇌 단련 퍼즐 44제
TRANSCRIPT
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An Imprint o( ~WJlEY
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ISBN
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2008 2 20 2010 2 9 Dennis E. Shasha
1-81
(02)3673-0037~9()/ 3673-0114() (02)3673-0260 1 1-1 013 978-89-5674-420-9
12 000
Korean language edition published by Inlormation Publishing Group, Copyright @ 08
John Wiley & Sons, Inc . DTP,
Puzzles for Programmers and Pros by Dennis E. Shasha
ISBN 978-0470-12168-9
Copyright @ 2007 by Wiley Publishing, Inc
AII Rights Reserved. Tis translation published under linse with the original publisher John Wiley & Sons, Inc. No part 01 this publication may be
reprodud or transmitted in any lorm or by any means, electronic or mechanical, including photopylng rerding or by any inlormation storage retrieval system, thout permission Irom John Wiley & Sons, Inc
Trademarks: Wiley, the Wiley 1090, Wrox, the Wrox 1090, pr09rammer to Pr09rammer, and trade dress are trademarks or registered trademarks 01 John ley & Sons, Inc. in the United States and other untries and may not be used by permission
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T .T T' S . ( T d T' d' . d' < d. S T T' d' . S .) .
. ? T T
T .
162
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.
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.
163
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164
. . .
.
( ) 110%. 450 {
405 495 ). 350 { 315 385 ).
. (0, (300, 400).
( 110% )
?
(0, 450 (300, 400) 350
. ( 2-3) .
2-3: 450 350. (0, (300, 40 500.
-
| . .
(1) x 2 + i = 450 2 = 202500 (2) (x- 300)2 + (y - 400)2 = 3502 = 122500
.
3x + 4y = 1, 650
y (1) :
x2+(-3xI4 412.5)2 = x2 + 9x2/16 - 618. 75x+ 170156.2 = 202500
2 .
(-46.75, 447.5 (442 80.44)
.
( ) . : . O( ) . .
10% . .
1. ?
165
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166
T i
2. ( ) . 5000
? 2000 ?
3. 10% . (0, 0) (300, 400)
?
-
1.
?
2-4 .
2-4: +10% 10% .
60 . 601 . 60? 60 > / ((W) + (452))
70x90 . . . (-46.75, 447.56) (442.75, 80.44)
. (-46 447.56) . 70x90
. .
2. ( ) . 5.000
? 2.000 ?
167
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E
70x90 . (-46 447.56) (442.75, 80.44). . . 2-5
30 .
38.1 .
53. 1x70 . (38.1 .)
10% 38.1 4.2 42.3 { 3.8 ). (15+42.3+4.2)x70
{ 4310). 42.3 (70x60) .
/ t
/ /
/ /
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---------------------------------------------
~30-- 2-5: 30 .
. 42.3 .
168
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3. 10% . (0. 0) (300. 400) ?
169
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170
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l
(Sudoku )
. . . .
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.
. 9x9 l 9 3x3 .
.
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O .
171
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o o O O O o O O 7
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.
o o o
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172
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173
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0 .
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0 4 6 7 9 1, 2, 3, 5, 8. 0 .
174
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O O O
7 o 4 o 0 O 8 9 3
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8
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5
3, 4, 5, 6, 7, 8, 9 . 1 2. .
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7
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2, 3, 4, 5, 6, 7, 8, 9 1. 1 .
175
-
i 4
O o o o o o o O 7
7 o 4 O O o 8 9 3
O O 6 8 o 2 O O O
i o 7 5 2 8 6 O o
O 8 O o o 6 7 O 1
9 o 3 4 o O o 8 o
O O O 7 O 4 9 o o
6 7 o o 9 o O O o
4 5 9 o o o 1 7 8
.
o
o
O
1 o 7 5 2 8 6 o o
o 8 o
9 o 3
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1, 2, 3, 5, 6, 7, 8, 9 4. . ( 4 O 4
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176
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|
8 1 5 3 4 9 2 6 7
7 2 4 6 5 1 8 9 3
3 9 6 8 7 2 4 1 5 1 4 7 5 2 8 6 3 9
5 8 2 9 3 6 7 4 1
9 6 3 4 1 7 5 8 2
2 3 1 7 8 4 9 5 6
6 7 8 1 9 5 3 2 4
4 5 9 2 6 3 1 7 8
. - .
- . .
- bas icsud).
proc basicsud(state s ) stillchanging := true while stillchanging
stillchanging:= false for (s e| ) /1 e s o
if (e v ) e : =v
stillchanging:= true end if if ( e )
return " end if
end for end while
177
-
E
T / -
return s
end proc
. - .
1 9 .
- . . basicsud . (
) . .
.
(specsud) . .
.
proc specsud (state s) s : = basicsud(s) if (s ") then
return " end if if (s ) return s else
s Z R
for (R e ) e| V for (V v| )
s s":= S e v s' : = specsud (s ) i f (s" ) return s ' end if s
178
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f
end for end for
end if end proc specsud
. 3 . 103 100 . .
1. .
o 3 O O o 0 O 4 O
o 1 o o 9 7 0 5 o
O O 2 5 O 8 6 O o
o o 3 O 0 o 8 o o
9 o o o o 4 3 o o
o O 7 6 O O o o 4
o O 9 8 o 5 4 O O
o 7 O o o o 0 2 o
o 5 O o 7 1 O 8 O
179
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180
tBt-
12
1. .
. . ( ) . 50
.
8 3 5 1 2 6 7 4 9
4 1 6 3 9 7 2 5 8
7 9 2 5 4 8 6 3 1
6 4 3 9 1 2 8 7 5 9 8 1 7 5 4 3 6 2
5 2 7 6 8 3 1 9 4
2 6 9 8 3 5 4 1 7
1 7 8 4 6 9 5 2 3
3 5 4 2 7 1 9 8 6
. (Sudkill) . 2 .
( ) .
-
.
2 9 . 2, 3, 4, 5 ( ) .
1 9 . .
). .
GDF IHEC DFBIH FBIHECA HE FBIH I HE FBIHEC BIHE
K mm
FBlliEC FBlliECA FBlliEC .
. GDF, DFBIH, FBlliECA . GDFBCA G = 1, D = 2 ... , A = 9.
181
-
182
2
. .
1. ( ) EDHFHI ACBEDHG HFD EEBGH HGH FEBF IEDBFDG ACBFEB CBEEHGDG ACIFEHG CIFE BFDH
FDBFH I BFEBGDI IEDH EHG FEBGH CBEEBF CIFD EEB ED FEBG CIEEH
2. . .
ABBDH AFCFAE EBFG ADCI IHBID DCIHEI AFCFA DCFGAB FCIH HAE CFGAGF EIDB AEB EBD EGD CIHBBI AIF HBID EFCI HABG BIFG FCHABI ABID CFHEB
DCHGEBF ADCFAEG lAAGIB HBBDB FCFGAII FCHGBG EIDG ABBDB GEI AI DCIAE BIIB BIDH AABF EDCIHE CFABB GDB GIH HGAG FCI DCHGBBDH FGEGF BIFH
-
|
1. ( ) .
.
A 1, B 3 6, C 2, D 5 8, E 4 5, F 4 7, G 7 9, H 6 8 1 3 9.
2. . .
.
A 1 5 6, B 6 7 9, C 3, D 2 8, E 1 6, F 2 4 8, G 5 7 9, H 4 5 9, 1 4 7 8.
183
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12
f
184
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( ) .
.
.
. . .
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dbc ) ( ac abc), ( abc ac). rent ( ) let r l n } . l r n 2. 2.
. .
AGA TGGAG ? .
-
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T . G . G . A . G
O 1 2 3 4 5
A 1
G 2
A 3
2-7: . '1' 'TG . A AG AGA .
TGGAG AGA . (0) T (1) TG (2) ... , TGGAG
(5) (0) A .
.
. (0, 0) ( 0 O ) . (i, j) AGA 1 i TGGAG 1 j j -l j ( ) i j-1 ( ) -1 j-1 ( ) j
AGA i TGGAG j .
185
-
6 -,
t
differs ( i , j) AGA i 7} TGGAG j 1, 0 .
entry(i J ) = min(entry(i-1 J ) + 1 , entry(i j-1) + 1 , entry(i -1 j-1) + differs(i , j))
2-8 (1,1) A ) .
T A G G G
o\ 1 2 3 4 5 \ N N
A 1 1 - 2 - 3 3 - F .. 4
G
A
2-8: A "fGGAG . TGG G . ( A A 0) .
. o + differs(l ,l) = 0 + 1 = 1 1 + 1 = 2, 1 + 1 = 2
. A T A T . A T 2 .
A G . . A TG A T G .
2.
186
-
| (1, 4) ( A A) . 3 . AGA TGGAG A ffers(1 4) = 0 . T, G, G ( 3) A A
( . 4. G . .
. 2-9 (2, 2) (AGA G TGGAG G) 1 . A T G G .G T , G, G A A G G .
T G G A . G
O\ 1 2 3\ 4 5
3 -A 1 1 - f+ 2 - 3 4 | \ \ \
* 1\ G 2 2 1 2 - .... 3 3
A 3
2-9: . ( )
. 2- 10 .
187
-
188
,
q t
T G. G A. G
O 1 2 3 4 5
A 1 4
G 2 3
A 3 3
2-10: . GA GA G .
A T G G G A A G . 3 . . A T G
G G A A G .
. .
.
. TAGATGGTCf TGGAGACAGTCf . 2-11 .
-
|
{
T G G A G A C A G T C T
T
An
nU
AH
T
(U
nU
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2-11 : .
1. TAGATGGI TGGAGACAGT' . .
189
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190
m E
1. TAGATGGTCT TGGAGACAGTCT
. .
( ) 4. T T G G A A G G A A T C G A GTCf GTCf 2-12).
T G G A G A C A G T C T u
n
m
9
8
7
7
7
6
5
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m
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8
7
6
6
6
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4
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8
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5
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4
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6
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3
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2
3
4
5
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1
0
1
2
3
4
5
6
7
8
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o 12
3
4
5
6
7
8
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m
T A G A T G G T C T
2-12: TAGATGGTCT TGGAGACAGTCT . .
.
-
|
l 160 . 43 .
. -^} . 1
1607 .
( ) 1, 5, 10, 20 . 48 207 5 1
.
.
. 1 2 160 . 1 .
. . . .
.
: 1, 81 , 82, 83 ( 1 < 81 < 82 < 83) ( ) .
1. 160 . .
191
-
{
192
i c
2. . 1, s1 , s2, s3 1 .
for entry i = 2 to 160 if cost(i)
for entry j 1 to i- l if (cost(j) + cost(i- j)) < cost(i)
cost(i) := (cost(j) + cost(i- j)) end if
end for end if
end for
3. 160 .
. .
.
1. 1 160 ? ?
2. 50 517ij . 147H 53 47 .
? ?
-
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1. 1 160
? ?
. . 1 4OI96797} 657,359
. .
. 1, 6, 29, 37 4.7.
2. 507fl 51 . 14 53 477fl .
? ?
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160 360( 160 + (4 x 50)) . . 1, 5, 12, 32
( ) 4 .
193
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.
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? : J . X Y Y X
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.
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. ( ) . 2-13 .
CQ O O O O
O O O O O 2-13: C C . . ?
f : NP .
194
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C C { 2-1. . 2-15).
C
2-14: .
C
2-15: .
.
( ) .
.
. .
(- spanning tree) ( ) . (
A B B A ). ( ) . C .
I . C T . until ( )
if( E E E E ) E T
195
-
196
t
e nd if T E T .
end until
2-16 2-17 ( ).
O O
O O O
O O 2-16: . . .
2-17: 2- 16 1 . .
:
{ ). . ( )
.
. .
-
{ |
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. 2-18 .
O
O
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o 0 2-18: . . .
.
.
. . ( ) .
. 2-19 . . N.
3/2 .
. . ?
197
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198
m 4
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1. 2 . 2 .
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l
1. 2
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( 2-2.
C
O~ OOz 2-20: () 5. z C 60( ). z Y 6.Y Z
5 C 2-21 . C
. 85. 2-22 21 .
c ~ (J 60 /~~;
xO Oz ~
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199
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200
m E
/0\\]
XOK\ 0 /Oz 2-22: . 21
-
{
( )
. . (heuristic) .
. .
. . 2-23 .
. { 2-24). .
c=::: -\
2-23: . .
201
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2-24: . . .
. .
. . (
) .2) . .
. .
) (tabu rching) (integer programming), . Ziew Miccz @dB el How to Solve It: Modem Heurcs(Springer 2004) .
202
2) 1 l 1 l . g .
-
l (sat anneg) .
. lear prom19) . .
.
. 1983 . ( ) . NP- (IBM) . ( cstal) .
. ( ) . . . .
.
ABCD ACBD . .
.
.
2 . . ( 1 ) .
203
-
204
g
t
. .
.
rl . T . loop (T )
. r2 . if (r2 rl )
rl r2 else
e^((cost(rl) - cost(r2))/T) rl r2 end if T .
end loop
e 0 1 T 0 . .
.
. . .
. .
. NP- .
. NP- 10
-
| .
. 2-25 . .
l
2-25: . L .
. . .
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T1 3 19. 17.
T 4 23. 14.
T3 6 51. 10.
T4 3 30. 7.
T5 7 38. 13. T6 6 36. 11.
205
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206
17 7 45. 18. T8 3 16. 10.
T9 5 22. 13. T10 2 13. 16.
T1 1 8 12. 6.
T12 1 31. 15.
T13 5 17. 13.
T14 2 2. 13.
T15 7 30. 11.
T16 5 11. 18.
T17 4 4. 10.
T18 5 27 15.
T19 4 6. 15.
1. ?
( ) . . . .
. T18 15/5 = 3. { 51 ). .
T12: 15 T10: 8 T14: 6 . 5 T1: 5.666667 T1 9: 3 . 75 T16: 3 . 6 T2: 3.5 T8 : 3 . 333333
-
f
| 71 T18: 3 T9: 2.6 T13: 2.6 T7: 2.57l 429 T17: 2.5 T4: 2.333333 T5: 1.857143 T6: 1.833333 T3: 1.666667 T15: 1.57l 429 Tll: 0.75
. 51 . .
17 50 . T1~ T1~ T1~ T1 , T1~ T1~ T8, Tl8, T9, Tl3, 17, Tl7 187
T4 1( 2.3) . 189.3. 51 .
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T14 T19 T16 T10 T8 T1 1'2 T15 T12 T5 17 T3. 13, 15, 18, 16, 10, 17, 14, 11, 15, 13, 18, 10 170. 183 . .
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2-26 . .
Cl /
/
-C6
C2 ------ ------ - C4 C5 ------ ------ -C7
/
C3-
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C8 2-26: ( ) . C4 C5 . .
-
|
f
. . ( )
. . 2-26 . 2. 2-27 { 2).
U C6
C2 .------------ C4 ------------- C5 C7 / / / / / / / C3' . C8 2-27: C3 C4 , C5 C7 .
( C2 C4 , C5 C8) , .
2-26 2-27 1. . ?
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.
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. 1 . . 1 3
4 2 5 .
215
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4 x 3 x 3 x 3 x 3 = 324. 9/324 = 1/36. $50001 $10 . .
. 1/36 . .
.
1. 36 .
36 . . { 1 1 2 ).
1 -
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1 3 . 2 4 .
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217
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1. 36 .
1 .
1 2 3 4 5 1 2 3 4 5 6
7 8 9 10 11 12 13 14 15 16 17
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1, 2, 3, 4, 5, 6
2 1, 2, 3, 4, 5, 6
3 1, 2, 3, 4, 5, 6
3 1, 2, 3, 4, 5, 6
3 1, 2, 3, 4, 5, 6
3 1, 2, 3, 4, 5, 6
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2. 400 ?
3. 1/2, 1 1/4 1/3, 1/3, 1/3 . 400 ?
225
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.
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100 200
100 200
200 400
400 800
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.
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400 800
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