P*,"9,.*_s_,_o^tl,plCo_
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LAUNCHINGPAD
-G" i.sfor Graphics
This programletsyou createanalphabetpicturebookfor childr€n.Eachtime
llley-t}?ein a lener,theygetbactanappropriare
picture appleforA.bear
rot tt , tor exunpte. by Maft ZnnQnan
38
T i r e do fT y p i n cg O T 0 ?T . yT - B u g... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s 4
The authorreviewsRadioShack'sT-BUGcass€tte,which allowsassembly
languageprograinmingon rheTt.S,SO.by Wiuian L. Cotshe.
DIGGING IN
Page38
PlannedPmgrarDming:
Th€ThoughtsBehindtheStructure- . . . . , . . . . . . ,2g
Careful planningbefor€you startwriting codemakesyour overallprograrnrningeffort muchsimpler.Justfollow rhestepsoutlinedin rhisanicle
ro producelogical. snucturedprcErans.bt Rob?i T. Nichohon
A GenerG
a la m P
e Lying
P r o g r a n .... . . . . . . . . . . . . . . , . . . . . . . , . . . . . . . . Z 0
Incorpomtingthis look-aheada.lgorithminio your gameslersyou play
agarnstthe compurer.The aurhorshowsyou how wirh Fograrnsfor Tic_
Tac-Toeand Kalah. ,y }l erbertL. Derchcm
Page43
DoublhgSpacc
onShgle.Sided
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Thissimple
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IN THE MONEY
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Manybusiness€s,
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Herear€someof rherhingsrharcangowrongwithyourbusiness
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ON THE LIGHTER SIDE
60
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A General
GamePlaving
Program
BY HERBERTL. DERSHEM
Progranmershaveusedthe look-ahead
strategy to develop competitive game
playhg programsfor gameslike check_
ers ard chess.A generalform of this
look-aheada.lgodthmcan be d€scrib€d
in terms of a recursiveprocedurcimplemented in BASIC for sDecific
games. If your BASIC proc€ssoraccopts recusive submutinecalls, then
you can use this a.lgorirhmro play any
suitable game by prograrruningthrEe
additional sutrourinesrhardescriberhe
game. (For mor€ informationon recursrve progmnrmrng, see ..Recursive
Prograruning in BASIC" , ADril pC. )
Considera gamewirh rwo ptayers
called compuEr" and "opponenC,
At any given point in the game, two
descripton describethe situation: the
gamesuos (cs), often thestitus of the
game boald; and the player to move
next (PM), either,,computer" or
''opponent".
EachcS, PM pair results
eilher in a complel€dgamewith a winner, or in a dmw, or in a set of legal
movesfor PM. Eachlegalmovemaps
theGS,PMpair.Lel's consider
thecase
where the players alt€mate moves,
making the new PM geneded by a
move always different from rhe previousPM.
Now we're r€adyto recursivelystate
lhe look-alrcadalgorithm which, giv€n
a CS,PM pair, €valuat€sall the legd
moves available to player PM and detelminesthe optimal one.
Algorithm Eyaluate b rtnd the besl
nove BM fot playet PM from ea,,u
statusGS v'ith evaluaabnof E.
Evaluate(GS,PM,E,BM)
2 Grnerare
tvIvrMV: MV". rhes€r
ol all legalmovesFom (CS,PM),and
GSr,CSz....,CS",
rhe corresponding
sel ot game status€safter the legal
movesar€appliedtocS.
L If PM = compurer,calt Evaluare
(CS, opponent,E, BM,) for i =
1,2,..., n; for q, the laree$ of
E,,8.....Ei, setE = q. g^,t = f,t\;
retum.
4. If PM : opponent,calt Evajuare
(CS,, computer,E,, BM) for i = t,
2,...,n;forq, thesmallest
ofE,.B....
Ei, setE = E(, BM : MVr; retum.
is always
_ Evaluationofa gamesratus
irom thecomputer's
poinrof view.The
larger the evaluation,the betterlhe slatus is for the computer.The.efore,the
pnnciple behind rhis algorirlm is that
the computeralwayschodes ftom the
legal moyes-that move rcsulring in a
gamesratuswilh laqest evaluarion.On
the other hand, the opponentalways
cbooses the move with the smattest
evaluation, sincerhat move is rh€ leasr
desirablefor the computer.
How does the computer determin€
whethera move is dfectly evaluarable?
If a garnestatusis lerminal, thereareno
further moves.Or som€timesthe computer stops wh€n a certain numberof
levelsof moveshavebeenexamined.
For example,a 3-tevel look-aheadwilt
examineall of the computer'slegal responses.As you cans€e,the numb€rof
moves tiat must be exarninedglows
rapidly as the level of th€ searcbinfinal level (level 3 in the exarnple
aoove), you must implement some
heuristic procedureto evaluatethe cS.
l. If(GS,PM) is dirccdy evalualable, PM pair.The abiliryof thisprocedure,
evaluateit andplacer€sullin E; rerurD_ the static evaluarionfuncrion.to ac
9.A.ine.
cumtely evaluate the game's status
Sreatly affects how well the computer
will compete-There's a trade-off t€,
tween the depth of look-aheadand the
validiry of rhe staiic evaluationturc
tior. If the staticevaluatioofunction is
perfect, the computercanus€it to eval,
uate all its altemativesdirectly andnol
look alEad at all. On the oth€rhand, if
the computer can look ahe3dclear to
the end of the garne,examiningall of
the altematiYes,it has no need for a
static evaluationfunction sincetheperfbct evaluationtunction is the garneresult: win, loseor dmw. In practicewe
find ourselves somewhere between
For the geneml BASIC version for
this algorithm,seeListing L Two additions to the algorithmhaveb€ennade
to speed up the search. Both halt the
PKrcesswhen it's obviousno more
searching
is needed.
Supposethe s€archis at a level generating the computer'sresporis€s.If, at
thepreceding
level,theopponenfsbest
move evaluatesto 4 andso far the com,
puter'sb€stmoveat thislevelevaluates
to 5, why continue the searchat this
level?The opponentwill neverchoose
the current move under considemtion
b€causeit will evaluateto no smaller
than5 which is alreadyI womethanthe
b€st move the opponenthasexamined
so far. This conditionis testedin line
2100of theprogramin Listingl. [n tr€e
searching this process, called alphabeta pruning, usually saves search
time,
Additional savings can resulr from
statement2130 where, as soon as a
player hasfound a surewinner for himself, he stopssearching.
Now lefs look at two implementations of the algorithm in Listing I . The
first, found in Listing 2, is the familiar
game of tic-tac-toe. The implementa
tion requireslhe addition of thrce submutines to the general garne status
evaluator at 2900. These a.re1000, a
move genemtor; 3000, a static move
evaluationfunction; andz{no, a gameover tester,But the choicesshownhere
are exampl€s:try designingyour own
improved venions of these subroutines.
The padicular impleme ation here
uses a maximum searchdepth of l0
levels. For tic-iac-toe, this l€vel implies all searcheswill be lerminatedby
the end of the game since the long€st
possible game is 9 moves. The static
evaluation function i€tums 100 if the
positionis awin for thecomputer,-Io0
if it's a win for the opponent,and 0 if
Subrouline2000 has beenmodified
slightly from that shownin Listing I to
acconrnodalethe pres€nceof only one
subscripted variable in Radio Shack
Level I BASIC, the syscm on which
this programwas implemented.
The ancientgame of Kalah, our second game, is played on a board wirh
six small pits on either side and larye
pits at eachend. The gamebeginswilh
3 marken in each of the snail pitr as
shownin Figurel.
Kalah
{Poooo[
Computer's
Pits
oooooo
0oooooo_.
0
PlayeisPits
T
Player's
I(aIah
FiPue 1 Initiat positionof
Kalahboard
!!, ^r'o I uL!€ lo{rid
rhd !!
The playen aiternatemovesaccording to thefollowingrulesl
I. A playerrnovesby choosinga pit
on his $ideof the boardanddistributing
the mark€n contained in that pit itrro
other pits counterclockwiseamundth€
board b€ginning with the counierclockwise neighborof the emptiedpit.
He places one ma.rkerin each pit and
Kalah in tum until all marken removed
are disrributed. Eraryle: If l\\e owonent beganplay fiom the initial board
shown aboveby emptyingthe fifth pit
from the left on his side,after his move
the boardwould look like Figure2.
inc
S,
oooooo@o
voooo@@v
6ry,=N.9).
.4o..
Box
2ot'l
J"yp. -N9).5s,oz
FiAure 2 Exampleofa move
c t F c L E8 6
P€rsonalCooputing 7l
2. If the last marke. distributed bv a
3. If rhe last markerdistdbutedon a computer's four
marken on the oDno_
player landsin tharptayer'aKalah, ;he
player'smovelandsin anemprypir on site
(Figure4).
side
must
pit
empry
another on his
Pmy€r
rhe ptayers side of rhe board,and if
The winner hasthe most markersin
side. This move is called a continua_ some.markers
are in his oppooenrs
pit
his.Kalah
at
tion. The €ontinuadonmighl have anorrecuyopposjlethis pit, rhenlhe tast a prayernasthe endof the$me. Wten
no moremekelsin hisDits
olher conrinuation,and so on. Erzn_
marker distributed and all the marken
and it s his tum to move, the same
ple. If the computer's responseto the
rn lhe oppositepir are placedin rhe
ends.At thatpointrheopponenr
aDove_move
wasto empiyfie thirdpor Kalahof the player
matinafte move. all the mdkes in hrJ pirs Diaces
rrom theleft. rl wouldreceiveaconrin_ This move is
inio hr
calteda caDite. Enn
Kalah.andrhewrnn€risd;rerrnrned
ualion. This move and ir5 continuation plerlf the
opponenr no\rr emDtiesrhe
Listing 3 showsthe applicationofrhe
areillustntedin Figure3_
lands in the empty pir andcap-tures
the game playing algorithm to rhis same.
The conlinuationcomplicalesm;tters
by requiringtwo locationsto storea
move a5 well a5 a specialcoding
scnemetor contlnuation
moves
GuesswhobuiHs
thisqreats19
o@@@oo@o
"oooo@@v
LogicProbe.
!lt
It/A,
r
rlJlt.
r
Yvro u 5Ei'sv-to-oul o Log C
ffii""l;:;i::,H;,".:";::,j1
lha'ksrooLrveryoescnprvesteO-bv-steo
.narua'-youhavea,u I pe forn
ancbooic
probe.
Wil\ [. rhetogc ,eveli|^a digtralcircJI
rransratestnto
rghttromtheH orLoLED:
putses
asnaffowas300nanoseconds
are
slretcled1tobrtrksofrhepr..rtse
_ED,
trggereq
lror e lr'teread,ngedge.you'I oeabtetoarobe
oeeperntologicw ththeLPK-1.
oneofthe
sma(ertoolsfromCSC.
Complete,
easy-to-follow
instructions
helpmakethisa
one-night
proj€ct.
Continuation
o@ooo@@o
'-oooo@@v
FiEureJ
Exarnple ofa move
and continuation
.\@@o@@@,1
Urr".."9
CONTNENIAI
SPECIAITIES
CORPORATbN
I'II
I:r.qf.E
Figure 4 Exampleofa capturc
I-aI
70F!hi ri( N€"r&fn cr06509pm)6
or|tF 0Frcs sinfimDYo(rt4t 3!
Calltolljreefordetails
1-800-243-6077
c l R c L E8 7
72 Perso@l Computilg
JINE€D
Now that you've se€n6ese exarnples, you can implemenrthis algorithm
tor other games. You. might wanr lo
rmprove the computer's p€rformance
on tbesegamesby pmviding bettersrar
ic evaluation tunctions or increasina
the maximum depth of search. you
must proceed with caurion, however.
Look,ahead algorithms c:m consume
lots of computet time. So be EeparEd
to wait fm thecomputer,smoves._ tr
Listing 1- Game-Playin€Algorithm
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Listing2 - Tic-Tac-Toe
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rs7,
Listin€ 3 - Kalah
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