#70064 - 2002-09-21 09:13 PM
KixGolf Results/Code
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Howard Bullock
KiX Supporter
Registered: 2000-09-15
Posts: 5809
Loc: Harrisburg, PA USA
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Is it time to post the code?
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#70066 - 2002-09-21 09:17 PM
Re: KixGolf Results/Code
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Howard Bullock
KiX Supporter
Registered: 2000-09-15
Posts: 5809
Loc: Harrisburg, PA USA
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Game24 KiXtart Golf running under KiXtart v4.11
Numbers = 1, 2, 3, 4
Please doublecheck your solution to guarantee a correct result
(1.0+2.0+3.0)*4.0 = 24
Numbers = 2, 2, 6, 8
Please doublecheck your solution to guarantee a correct result
(2.0+6.0)+(8.0*2.0) = 24
Numbers = 4, 4, 6, 6
Correct answer answer, there is no solution to this combination
Numbers = 3, 3, 8, 8
Please doublecheck your solution to guarantee a correct result
8.0/(3.0-8.0/3.0) = 24
Numbers = 0, 0, 8, 4
No solution found
<> 24
Numbers = 3, 4, 7, 7
Please doublecheck your solution to guarantee a correct result
(3.0+4.0*7.0)-7.0 = 24
Numbers = 1, 2, 8, 9
Please doublecheck your solution to guarantee a correct result
(8.0*9.0)/(2.0+1.0) = 24
Time: 4546 ticks
KixGolf v3.0.3 score = 434, running under KiXtart v4.10 code:
function game24($a,$b,$c,$d)
Dim $h, $j, $l, $p, $q, $r, $s, $t, $v, $, $x, $y
$h = "+","-","/","*"
for $y=1 to 4
for $x=1 to 4
for each $p in $h
for each $q in $h
for each $r in $h
for each $j in split("0,8,10,18~0,12~4,16","~")
$ = ".0"
$s = ""+$a+$+$p+$b+$+$q+$c+$+$r+$d+$
for each $ in split($j,",")
$l = chr(40 + ($l="("))
$s = "" + left($s,$) + $l + substr($s,1+$)
next
$t = execute("$$v=$s")
if abs($v-24)< 1E-9
goto E
endif
next
next
next
next
$ = $b
$b = $c
$c = $d
$d = $
next
$ = $a
$a = $b
$b = $
next
$s = ""
:E
$game24 = $s
endfunction
[ 22. September 2002, 01:06: Message edited by: Howard Bullock ]
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#70067 - 2002-09-21 09:35 PM
Re: KixGolf Results/Code
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Sealeopard
KiX Master
Registered: 2001-04-25
Posts: 11165
Loc: Boston, MA, USA
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This script is from Richard Howarth who asked me to post it for him. So, the credits go to Richard. please note that he implemented a recursive function with a KiXtart Golf Score of 404.
quote:
Game24 KiXtart Golf running under KiXtart v4.12 Beta 1
Computer = Pentium III 1000 and 511 RAM
Numbers = 1, 2, 3, 4
4.0*(3.0*(2.0/1)) = 24
The formula validated correctly
Numbers = 2, 2, 6, 8
8.0+(2.0*(6.0+2)) = 24
The formula validated correctly
Numbers = 4, 4, 6, 6
Correct answer answer, there is no solution to this combination
Numbers = 3, 3, 8, 8
8.0/(3.0-(8.0/3)) = 24
The formula validated correctly
Numbers = 0, 8, 2, 7
No solution found
Numbers = 3, 4, 7, 7
7.0-(4.0-(7.0*3)) = 24
The formula validated correctly
Numbers = 1, 2, 8, 9
9.0*(8.0/(2.0+1)) = 24
The formula validated correctly
Time = 2594 ticks
And the function is:
code:
;!
Function game24($,$b,$c,$d)
$game24=f(""+$+$b+$c+$d,"")
EndFunction
Function f($,$b)
Dim $e,$x,$y,$z,$a
If($)
For $x=1 to Len($)
$e=f(Left($,$x-1)+SubStr($,$x+1),$b+SubStr($,$x,1))
If $e $f=$e EndIf
Next
Else
$e=Split("+ - * /")
For Each $x In $e
For Each $y In $e
For Each $z In $e
$=Left($b,1)+".0"+$x+"("+SubStr($b,2,1)+".0"+$y+"("+SubStr($b,3,1)+".0"+$z+Right($b,1)+"))"
$z=Execute("$$a="+$)
If "24"=$a $f=$ EndIf
Next
Next
Next
EndIf
EndFunction
_________________________
There are two types of vessels, submarines and targets.
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#70068 - 2002-09-21 09:54 PM
Re: KixGolf Results/Code
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Howard Bullock
KiX Supporter
Registered: 2000-09-15
Posts: 5809
Loc: Harrisburg, PA USA
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If Richard's double set of "()"'s holds up, then I re-submit my code:
Game24 KiXtart Golf running under KiXtart v4.11
Numbers = 1, 2, 3, 4
Please doublecheck your solution to guarantee a correct result
1.0*(2.0*(3.0*4.0)) = 24
Numbers = 2, 2, 6, 8
Please doublecheck your solution to guarantee a correct result
2.0+(6.0+(8.0*2.0)) = 24
Numbers = 4, 4, 6, 6
Correct answer answer, there is no solution to this combination
Numbers = 3, 3, 8, 8
Please doublecheck your solution to guarantee a correct result
8.0/(3.0-(8.0/3.0)) = 24
Numbers = 0, 4, 6, 8
Please doublecheck your solution to guarantee a correct result
0.0+(6.0*(8.0-4.0)) = 24
Numbers = 3, 4, 7, 7
Please doublecheck your solution to guarantee a correct result
3.0+(7.0*(7.0-4.0)) = 24
Numbers = 1, 2, 8, 9
Please doublecheck your solution to guarantee a correct result
8.0*(9.0/(2.0+1.0)) = 24
Time: 421 ticks
{edit}
Thanks Erik, Removed "exit" reduced score by four.
KixGolf v3.0.3 score = 314, running under KiXtart v4.10
code:
function game24($a,$b,$c,$d)
Dim $h, $p, $q, $r, $s, $t, $v, $, $x, $y
$h = "+","-","/","*"
for $y=1 to 4
for $x=1 to 4
for each $p in $h
for each $q in $h
for each $r in $h
$ = ".0"
$s = ""+$a+$+$p+"("+$b+$+$q+"("+$c+$+$r+$d+$+"))"
$t = execute("$$v=$s")
if abs($v-24)< 1E-9
goto E
endif
next
next
next
$ = $b
$b = $c
$c = $d
$d = $
next
$ = $a
$a = $b
$b = $
next
$s = ""
:E
$game24 = $s
endfunction
[ 21. September 2002, 23:28: Message edited by: Howard Bullock ]
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#70069 - 2002-09-21 11:22 PM
Re: KixGolf Results/Code
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kholm
Korg Regular
Registered: 2000-06-19
Posts: 714
Loc: Randers, Denmark
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Howard,
You can shawe of 4 by omitting the last Exit ![[Big Grin]](images/icons/grin.gif)
As usual, a golfmatch uncovers new possibilitys, i would never have dreamt of using a line like this:
if abs($v-24)< 1E-9
Cheers
-Erik
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#70070 - 2002-09-21 11:31 PM
Re: KixGolf Results/Code
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Howard Bullock
KiX Supporter
Registered: 2000-09-15
Posts: 5809
Loc: Harrisburg, PA USA
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I kinda liked my parentheses toggle from my first:
$l = chr(40 + ($l="("))
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#70071 - 2002-09-22 11:04 AM
Re: KixGolf Results/Code
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Anonymous
Anonymous
Unregistered
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For what it's worth
Golf Score 541
code:
FUNCTION Game24($n,$e,$r,$)
IF Ubound($n) < 0
$n = $n,$e,$r,$
$e='' $r=''
ENDIF
IF Len($e) < 4
FOR EACH $ in Split('0 1 2 3')
IF NOT Instr($e,$)
$ = Game24($n,$e+$,$r+' '+$n[$]+'. ',0)
IF $ $Game24 =$ RETURN ENDIF
ENDIF
NEXT
ELSE
DIM $a,$s,$e,$z,$y
$ = Split($r)
$s = Split('+ - * /')
FOR EACH $[3] IN $s
FOR EACH $[7] IN $s
FOR EACH $[11] IN $s
FOR EACH $a IN Split('/0 6/0 10/0 6 8 14/4 14','/')
$a = Split($a)
$e = $
FOR $z = 1 TO Ubound($a) STEP 2
$y=$a[$z-1] $e[$y] ='(' ; kixtart bug (?) '$e[$a[$z]] = ")"' is taken
$y=$a[$z] $e[$y] =')' ; as a comparison not as an assignment.
NEXT
$e = Join($e,'')
$z = Execute('$$y=ABS(24.-('+$e+'))<0.01')
IF $y $Game24 =$e RETURN ENDIF
NEXT
NEXT NEXT NEXT
ENDIF
$Game24=''
ENDFUNCTION
{edit} add in another set of parentheses (0 6) and remove 4 spaces
Golf score unchanged! {/edit}
[ 24. September 2002, 19:12: Message edited by: AJH ]
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#70072 - 2002-09-22 02:50 PM
Re: KixGolf Results/Code
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Howard Bullock
KiX Supporter
Registered: 2000-09-15
Posts: 5809
Loc: Harrisburg, PA USA
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AJH, it's worth a great deal. Your post shows the effort you put forth to solve the problem. You found an issue with nested arrays. Other people may not have been aware this issue existed. Your score is secondary. You are one a few that took the time and completed the task. Good work. ![[Cool]](images/icons/cool.gif)
{edit}
AJH, You can reduce your score score by four by compacting your execute string: '$$y=ABS(24.-('+$e+'))<0.01'. Remember spaces within quotes are counted for the next KixGolf outing.
[ 22. September 2002, 15:43: Message edited by: Howard Bullock ]
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#70073 - 2002-09-22 03:20 PM
Re: KixGolf Results/Code
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Jack Lothian
MM club member
Registered: 1999-10-22
Posts: 1169
Loc: Ottawa,Ontario, Canada
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I am a bit late since my home machine still isn't up to snuff. I actually lowered my score to 653. I might have tried to go lower but I couldn't seem to generate any method that worked consistently. I especially had trouble with Jooel's suggestion of testing the script with a large number of random selection. This code passes Jens test & seems to works properly for a large number of random selections but if I change the order of the permutations (i.e. use '+ - / *' instead of '+ - * /') it still fails.
code:
Function Game24($i,$j,$k,$l)
dim $a, $b, $c, $d, $e, $f, $g, $h, $m, $s, $t, $u, $v, $n[3], $[14], $o[3]
$n=$i,$j,$k,$l
$o = split('+ - * /')
$s='cdbl('
$u=')'
for $a=0 to 3
for $b=0 to 3
for $c=0 to 3
for $d=0 to 3
if $a<>$b&$a<>$c&$a<>$d&$b<>$c&$b<>$d&$c<>$d
$[1]=$s+$n[$a]+$u
$[5]=$s+$n[$b]+$u
$[9]=$s+$n[$c]+$u
$[13]=$s+$n[$d]+$u
for each $e in $o
for each $f in $o
for each $g in $o
$[3]= $e
$[7]= $f
$[11]= $g
for $h=0 to 6
for $m=0 to 7
$[2*$m]=''
next
if $h=1 or $h=3 or $h=6 $[0]='(' endif
if $h=2 or $h=4 $[4]='(' endif
if $h=3 or $h=6 $[6]=')' endif
if $h=5 or $h=6 $[8]='(' endif
if $h=1 or $h=4 $[10]=')' endif
if $h=2 or $h=5 or $h=6 $[14]=')' endif
$t=Join($)
$m=execute('$$v=$t')
if 24=$v
$Game24=Join($)
return
endif
next
next
next
next
endif
next
next
next
EndFunction
PS: Did you all verify that your code actually generates all the combinations & did you compare your results with Madruga's analysis? Richard's code is a thing of beauty but it doesn't generate all the possible combinations. Richard assumes the nested brackts "a (b(c d))" can be morphed into all possible solutions but it cannot be morphed into several of the unique solutions found by Madruga.
I think validating our results is a serious challange in this competition.
_________________________
Jack
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#70074 - 2002-09-22 03:56 PM
Re: KixGolf Results/Code
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Howard Bullock
KiX Supporter
Registered: 2000-09-15
Posts: 5809
Loc: Harrisburg, PA USA
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My first post, checked (ab)(cd), (abc)d, and a(bcd) which I think covers the required combinations as long as the numbers and operator all rotate through all combinations.
If Jens did not include the random input check then I think that if the other checks pass the script is good. But since the random numbers are part of the test, all possible combination of 1-9 would need to be checked. Since we currently have no good method of independently varifying a given set of random numbers at test time we can not be sure if the test scripts correctly found no solution or simply did not find the solution do to short comings of the code.
I applaud Jens for the time he spends setting this up and do not believe that absolute perfection is a requirement for this level of competition. The discussions so far have been quite interesting.
[ 22. September 2002, 16:00: Message edited by: Howard Bullock ]
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#70076 - 2002-09-22 04:13 PM
Re: KixGolf Results/Code
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Howard Bullock
KiX Supporter
Registered: 2000-09-15
Posts: 5809
Loc: Harrisburg, PA USA
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Now that you mention division by zero... I just executed my code using all 0's. No 'division by zero' failure occurred. I guess the floating point equivalent of zero is 'near zero' not zero.
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#70078 - 2002-09-22 04:18 PM
Re: KixGolf Results/Code
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Howard Bullock
KiX Supporter
Registered: 2000-09-15
Posts: 5809
Loc: Harrisburg, PA USA
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That is strange. Until now I have avoided division by zero. It is nice that the script does not ABEND, but this behavior is a disconcerting.
{edit}
Checking for and avoiding division by zero sure would have added some strokes.
[ 22. September 2002, 16:21: Message edited by: Howard Bullock ]
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#70082 - 2002-09-23 08:36 PM
Re: KixGolf Results/Code
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Fernando Madruga
Starting to like KiXtart
Registered: 2002-08-21
Posts: 149
Loc: Coimbra.Portugal.Europe.Earth....
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On second though, Howard, are you sure your code is ok? I mean, you work with only 16 permutations of the possible 24!! Try runing under my improved test script (streamlined the output, and fixed some bugs). Also, and since one of the solutions that your code fails to find is one that has nothing to do with the permutations, there's bound to be some major error in there other than the missing permutations... Try your code with the 5555 set and check it out...
code:
BREAK ON
Global $Target, $Valid
$Target = 24
$ErrorMargin = 0.0001
$Valid = "003800460128013601370138013901450146014701480155015602260234"
+ "023602380239024402460248025702580266026802690288033403350337"
+ "033803390344034603480349035803590366036703680378038803890445"
+ "044604470448045604660467046804690478048805660569058806890699"
+ "078908881118112611271128112911341135113611371138113911441145"
+ "114611471148114911551156115711581166116811691188122412251226"
+ "122712281229123312341235123612371238123912441245124612471248"
+ "124912551256125712581259126612671268126912771278127912881289"
+ "133313341335133613371338133913441345134613471348134913561357"
+ "135813591366136713681369137713781379138813891399144414451446"
+ "144714481449145514561457145814591466146714681469147714781479"
+ "148814891555155615591566156715681569157815791588158915991666"
+ "166816691679168816891699177917881789179918881889222322242225"
+ "222722282229223322342235223622372238223922442245224622472248"
+ "224922552256225722582259226622672268226922772278228822892333"
+ "233523362337233823392344234523462347234823492355235623572358"
+ "235923662367236823692377237823792388238923992444244524462447"
+ "244824492455245624572458245924662467246824692477247824792488"
+ "248924992557255825592566256725682569257725782579258825892666"
+ "266726682669267826792688268926992778278827892888288928993333"
+ "333433353336333733383339334433453346334733483349335533563357"
+ "335933663367336833693377337833793389339934443445344634473448"
+ "344934553456345734583459346634683469347734783479348934993556"
+ "355735583559356635673568356935783579358835893599366636673668"
+ "366936773678367936883689369937773778377937883789379938883889"
+ "389939994444444544464447444844494455445644574458446844694477"
+ "447844794488448945554556455745584559456645674568456945774578"
+ "457945884589459946664667466846694677467846794688468946994777"
+ "477847884789479948884889489955555556555955665567556855775578"
+ "558855895599566656675668566956775678567956885689569957795788"
+ "578958885889666666686669667966886689678967996888688968997889"
+ "3388"
$rc=SETOPTION('Explicit','ON')
$rc=SETOPTION('NoVarsInString','ON')
$rc=SRND(@MSECS)
? 'Game24 v 1.1 KiXtart Golf running under KiXtart v'@KIX
? ''
Dim $i
test24(1,2,3,4,1)
test24(2,2,6,8,1)
test24(4,4,6,6,2)
test24(3,3,8,8,1)
for $i = 1 to 20
test24(RND(9),RND(9),RND(9),RND(9),3)
next
test24(3,4,7,7,1)
test24(1,2,8,9,1)
test24(3,3,7,7,1)
? ""
; Inputs: $i1..$i4 => 4 numbers to pass to game24
; $behaviour = 1 -> Expected result
; $behaviour = 2 -> Expected to fail
; $behaviour = 3 -> Don't know (random)
function test24($i1,$i2,$i3,$i4,$behaviour)
DIM $rc, $out, $result, $error, $str, $i, $found, $temp, $nums[4], $numbers
$str = 'In: '+$i1+$i2+$i3+$i4+'; Out: '
$out=Game24($i1,$i2,$i3,$i4)
if instr($out,".") == 0
$i = 1
while $i <= Len($out)
if ( SubStr($out,$i,1) >= '0' ) and ( SubStr($out,$i,1) <= '9' )
$out = Left($out,$i) + '.0' + SubStr($out,$i+1)
$i = $i + 2;
endif;
$i = $i + 1;
loop
endif
$error=Execute("$$result=("+$out+")")
$result=Trim($result)
Dim $tmpStr
$tmpStr = $out
while (len($tmpStr)<22)
$tmpStr = $tmpStr + " "
loop
$str = $str + left($tmpStr, 22) + " = " + $result
if (len($result)<2)
$str = $str+" "
endif
if ( $behaviour = 3 )
; sort numbers used, so as to check array of possible solutions
$nums[0] = $i1
$nums[1] = $i2
$nums[2] = $i3
$nums[3] = $i4
do
$found = 0
for $i = 0 to 2
if $nums[$i] > $nums[$i+1]
$found = 1
$temp = $nums[$i+1]
$nums[$i+1] = $nums[$i]
$nums[$i] = $temp
endif
next
until $found == 0
$numbers = "" + $nums[0] + $nums[1] + $nums[2] + $nums[3]
; check for presence in array
$found = 0
$i = 1
while ( $found == 0 ) and ( $i < Len($Valid) )
if ( SubStr( $Valid, $i, 4 ) == $numbers )
$found = 1
endif
$i = $i + 4
loop
if $found and ( ($result>=$Target-$ErrorMargin) and
($result<=$Target+$ErrorMargin) )
$str = $str + " => Correct!!"
else
if not $found and $result=""
$str = $str + " => Correct!!"
else
$str = $str + " => WRONG!!"
endif
endif
else
if ( ($behaviour=1) and ($result>=$Target-$ErrorMargin) and
($result<=$Target+$ErrorMargin) )
or ( ($behaviour=2) and ($result='') )
$str = $str + " => Correct!!"
else
$str = $str + " => WRONG!!"
endif
endif
? $str
endfunction
Dim $shellcommand
$shellcommand='kix32 Kixgolf3.kix $f='+@scriptname
? $shellcommand
Shell $shellcommand
; Operators: 64 combinations
; +++ ++- ++* ++/ +-+ +-- +-* +-/ +*+ +*- +** +*/ +/+ +/- +/* +//
; -++ -+- -+* -+/ --+ --- --* --/ -*+ -*- -** -*/ -/+ -/- -/* -//
; *++ *+- *+* *+/ *-+ *-- *-* *-/ **+ **- *** **/ */+ */- */* *//
; /++ /+- /+* /+/ /-+ /-- /-* /-/ /*+ /*- /** /*/ //+ //- //* ///
; Digits: 24 permutations
; abcd abdc acbd acdb adbc adcb
; bacd badc bcad bcda bdac bdca
; cabd cadb cbad cbda cdab cdba
; dabc dacb dbac dbca dcab dcba
; Parentheses: 4 combinations
; 123456789 12345 (15 chars)
; a. b . c .d
; (a. b).(c .d)
; a.(b . c .d)
; (a. b . c).d
; 0 need (ab)cd
; 0 need a(bc)d
; 0 need ab(cd)
; ------------------
; 1 need (abc)d
; ------------------
; 3 need a(bcd)
; 13 need (ab)(cd)
; ------------------
; 131 need at least one '+'
; 174 need at least one '-'
; 306 need at least one '*'
; 36 need at least one '/'
;!
function game24($a,$b,$c,$d)
endfunction
;!
;!
{edit} Added an if to only add (.0)s if there's no '.' in the returned string. {/edit}
[ 23. September 2002, 20:40: Message edited by: Fernando Madruga ]
_________________________
Later,
[b]Mad[/b]ruga
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