2016 Update
This commit is contained in:
Tina Müller
parent
948b86eafa
commit
dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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@ -1,5 +1,9 @@
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;task:
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Write a program that takes four digits, either from user input or by random generation, and computes arithmetic expressions following the rules of the [[24 game]].
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Show examples of solutions generated by the program.
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C.F: [[Arithmetic Evaluator]]
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;Related task:
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* [[Arithmetic Evaluator]]
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<br><br>
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446
Task/24-game-Solve/COBOL/24-game-solve.cobol
Normal file
446
Task/24-game-Solve/COBOL/24-game-solve.cobol
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@ -0,0 +1,446 @@
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>>SOURCE FORMAT FREE
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*> This code is dedicated to the public domain
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*> This is GNUCobol 2.0
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identification division.
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program-id. twentyfoursolve.
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environment division.
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configuration section.
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repository. function all intrinsic.
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input-output section.
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file-control.
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select count-file
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assign to count-file-name
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file status count-file-status
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organization line sequential.
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data division.
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file section.
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fd count-file.
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01 count-record pic x(7).
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working-storage section.
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01 count-file-name pic x(64) value 'solutioncounts'.
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01 count-file-status pic xx.
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01 command-area.
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03 nd pic 9.
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03 number-definition.
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05 n occurs 4 pic 9.
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03 number-definition-9 redefines number-definition
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pic 9(4).
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03 command-input pic x(16).
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03 command pic x(5).
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03 number-count pic 9999.
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03 l1 pic 99.
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03 l2 pic 99.
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03 expressions pic zzz,zzz,zz9.
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01 number-validation.
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03 px pic 99.
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03 permutations value
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'1234'
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& '1243'
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& '1324'
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& '1342'
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& '1423'
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& '1432'
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& '2134'
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& '2143'
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& '2314'
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& '2341'
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& '2413'
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& '2431'
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& '3124'
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& '3142'
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& '3214'
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& '3241'
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& '3423'
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& '3432'
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& '4123'
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& '4132'
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& '4213'
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& '4231'
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& '4312'
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& '4321'.
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05 permutation occurs 24 pic x(4).
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03 cpx pic 9.
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03 current-permutation pic x(4).
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03 od1 pic 9.
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03 od2 pic 9.
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03 od3 pic 9.
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03 operator-definitions pic x(4) value '+-*/'.
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03 cox pic 9.
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03 current-operators pic x(3).
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03 rpn-forms value
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'nnonono'
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& 'nnonnoo'
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& 'nnnonoo'
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& 'nnnoono'
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& 'nnnnooo'.
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05 rpn-form occurs 5 pic x(7).
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03 rpx pic 9.
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03 current-rpn-form pic x(7).
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01 calculation-area.
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03 oqx pic 99.
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03 output-queue pic x(7).
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03 work-number pic s9999.
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03 top-numerator pic s9999 sign leading separate.
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03 top-denominator pic s9999 sign leading separate.
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03 rsx pic 9.
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03 result-stack occurs 8.
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05 numerator pic s9999.
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05 denominator pic s9999.
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03 divide-by-zero-error pic x.
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01 totals.
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03 s pic 999.
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03 s-lim pic 999 value 600.
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03 s-max pic 999 value 0.
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03 solution occurs 600 pic x(7).
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03 sc pic 999.
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03 sc1 pic 999.
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03 sc2 pic 9.
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03 sc-max pic 999 value 0.
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03 sc-lim pic 999 value 600.
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03 solution-counts value zeros.
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05 solution-count occurs 600 pic 999.
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03 ns pic 9999.
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03 ns-max pic 9999 value 0.
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03 ns-lim pic 9999 value 6561.
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03 number-solutions occurs 6561.
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05 ns-number pic x(4).
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05 ns-count pic 999.
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03 record-counts pic 9999.
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03 total-solutions pic 9999.
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01 infix-area.
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03 i pic 9.
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03 i-s pic 9.
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03 i-s1 pic 9.
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03 i-work pic x(16).
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03 i-stack occurs 7 pic x(13).
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procedure division.
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start-twentyfoursolve.
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display 'start twentyfoursolve'
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perform display-instructions
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perform get-command
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perform until command-input = spaces
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display space
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initialize command number-count
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unstring command-input delimited by all space
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into command number-count
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move command-input to number-definition
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move spaces to command-input
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evaluate command
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when 'h'
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when 'help'
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perform display-instructions
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when 'list'
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if ns-max = 0
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perform load-solution-counts
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end-if
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perform list-counts
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when 'show'
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if ns-max = 0
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perform load-solution-counts
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end-if
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perform show-numbers
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when other
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if number-definition-9 not numeric
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display 'invalid number'
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else
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perform get-solutions
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perform display-solutions
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end-if
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end-evaluate
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if command-input = spaces
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perform get-command
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end-if
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end-perform
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display 'exit twentyfoursolve'
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stop run
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.
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display-instructions.
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display space
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display 'enter a number <n> as four integers from 1-9 to see its solutions'
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display 'enter list to see counts of solutions for all numbers'
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display 'enter show <n> to see numbers having <n> solutions'
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display '<enter> ends the program'
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.
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get-command.
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display space
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move spaces to command-input
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display '(h for help)?' with no advancing
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accept command-input
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.
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ask-for-more.
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display space
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move 0 to l1
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add 1 to l2
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if l2 = 10
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display 'more (<enter>)?' with no advancing
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accept command-input
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move 0 to l2
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end-if
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.
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list-counts.
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add 1 to sc-max giving sc
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display 'there are ' sc ' solution counts'
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display space
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display 'solutions/numbers'
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move 0 to l1
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move 0 to l2
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perform varying sc from 1 by 1 until sc > sc-max
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or command-input <> spaces
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if solution-count(sc) > 0
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subtract 1 from sc giving sc1 *> offset to capture zero counts
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display sc1 '/' solution-count(sc) space with no advancing
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add 1 to l1
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if l1 = 8
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perform ask-for-more
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end-if
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end-if
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end-perform
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if l1 > 0
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display space
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end-if
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.
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show-numbers. *> with number-count solutions
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add 1 to number-count giving sc1 *> offset for zero count
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evaluate true
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when number-count >= sc-max
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display 'no number has ' number-count ' solutions'
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exit paragraph
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when solution-count(sc1) = 1 and number-count = 1
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display '1 number has 1 solution'
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when solution-count(sc1) = 1
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display '1 number has ' number-count ' solutions'
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when number-count = 1
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display solution-count(sc1) ' numbers have 1 solution'
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when other
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display solution-count(sc1) ' numbers have ' number-count ' solutions'
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end-evaluate
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display space
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move 0 to l1
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move 0 to l2
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perform varying ns from 1 by 1 until ns > ns-max
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or command-input <> spaces
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if ns-count(ns) = number-count
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display ns-number(ns) space with no advancing
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add 1 to l1
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if l1 = 14
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perform ask-for-more
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end-if
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end-if
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end-perform
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if l1 > 0
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display space
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end-if
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.
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display-solutions.
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evaluate s-max
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when 0 display number-definition ' has no solutions'
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when 1 display number-definition ' has 1 solution'
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when other display number-definition ' has ' s-max ' solutions'
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end-evaluate
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display space
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move 0 to l1
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move 0 to l2
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perform varying s from 1 by 1 until s > s-max
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or command-input <> spaces
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*> convert rpn solution(s) to infix
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move 0 to i-s
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perform varying i from 1 by 1 until i > 7
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if solution(s)(i:1) >= '1' and <= '9'
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add 1 to i-s
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move solution(s)(i:1) to i-stack(i-s)
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else
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subtract 1 from i-s giving i-s1
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move spaces to i-work
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string '(' i-stack(i-s1) solution(s)(i:1) i-stack(i-s) ')'
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delimited by space into i-work
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move i-work to i-stack(i-s1)
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subtract 1 from i-s
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end-if
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end-perform
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display solution(s) space i-stack(1) space space with no advancing
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add 1 to l1
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if l1 = 3
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perform ask-for-more
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end-if
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end-perform
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if l1 > 0
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display space
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end-if
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.
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load-solution-counts.
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move 0 to ns-max *> numbers and their solution count
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move 0 to sc-max *> solution counts
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move spaces to count-file-status
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open input count-file
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if count-file-status <> '00'
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perform create-count-file
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move 0 to ns-max *> numbers and their solution count
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move 0 to sc-max *> solution counts
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open input count-file
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end-if
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read count-file
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move 0 to record-counts
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move zeros to solution-counts
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perform until count-file-status <> '00'
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add 1 to record-counts
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perform increment-ns-max
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move count-record to number-solutions(ns-max)
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add 1 to ns-count(ns-max) giving sc *> offset 1 for zero counts
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if sc > sc-lim
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display 'sc ' sc ' exceeds sc-lim ' sc-lim
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stop run
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end-if
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if sc > sc-max
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move sc to sc-max
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end-if
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add 1 to solution-count(sc)
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read count-file
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end-perform
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close count-file
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.
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create-count-file.
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open output count-file
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display 'Counting solutions for all numbers'
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display 'We will examine 9*9*9*9 numbers'
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display 'For each number we will examine 4! permutations of the digits'
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display 'For each permutation we will examine 4*4*4 combinations of operators'
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display 'For each permutation and combination we will examine 5 rpn forms'
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display 'We will count the number of unique solutions for the given number'
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display 'Each number and its counts will be written to file ' trim(count-file-name)
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compute expressions = 9*9*9*9*factorial(4)*4*4*4*5
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display 'So we will evaluate ' trim(expressions) ' statements'
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display 'This will take a few minutes'
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display 'In the future if ' trim(count-file-name) ' exists, this step will be bypassed'
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move 0 to record-counts
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move 0 to total-solutions
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perform varying n(1) from 1 by 1 until n(1) = 0
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perform varying n(2) from 1 by 1 until n(2) = 0
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display n(1) n(2) '..' *> show progress
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perform varying n(3) from 1 by 1 until n(3) = 0
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perform varying n(4) from 1 by 1 until n(4) = 0
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perform get-solutions
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perform increment-ns-max
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move number-definition to ns-number(ns-max)
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move s-max to ns-count(ns-max)
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move number-solutions(ns-max) to count-record
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write count-record
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add s-max to total-solutions
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add 1 to record-counts
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add 1 to ns-count(ns-max) giving sc *> offset by 1 for zero counts
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if sc > sc-lim
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display 'error: ' sc ' solution count exceeds ' sc-lim
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stop run
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end-if
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add 1 to solution-count(sc)
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end-perform
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end-perform
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end-perform
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end-perform
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close count-file
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display record-counts ' numbers and counts written to ' trim(count-file-name)
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display total-solutions ' total solutions'
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display space
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.
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increment-ns-max.
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if ns-max >= ns-lim
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display 'error: numbers exceeds ' ns-lim
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stop run
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end-if
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add 1 to ns-max
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.
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get-solutions.
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move 0 to s-max
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perform varying px from 1 by 1 until px > 24
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move permutation(px) to current-permutation
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perform varying od1 from 1 by 1 until od1 > 4
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move operator-definitions(od1:1) to current-operators(1:1)
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perform varying od2 from 1 by 1 until od2 > 4
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move operator-definitions(od2:1) to current-operators(2:1)
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perform varying od3 from 1 by 1 until od3 > 4
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move operator-definitions(od3:1) to current-operators(3:1)
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perform varying rpx from 1 by 1 until rpx > 5
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move rpn-form(rpx) to current-rpn-form
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move 0 to cpx cox
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move spaces to output-queue
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perform varying oqx from 1 by 1 until oqx > 7
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if current-rpn-form(oqx:1) = 'n'
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add 1 to cpx
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move current-permutation(cpx:1) to nd
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move n(nd) to output-queue(oqx:1)
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else
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add 1 to cox
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move current-operators(cox:1) to output-queue(oqx:1)
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end-if
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end-perform
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perform evaluate-rpn
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if divide-by-zero-error = space
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and 24 * top-denominator = top-numerator
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perform varying s from 1 by 1 until s > s-max
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or solution(s) = output-queue
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continue
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end-perform
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if s > s-max
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if s >= s-lim
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display 'error: solutions ' s ' for ' number-definition ' exceeds ' s-lim
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stop run
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end-if
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move s to s-max
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move output-queue to solution(s-max)
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end-if
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end-if
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end-perform
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end-perform
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end-perform
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end-perform
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end-perform
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.
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evaluate-rpn.
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move space to divide-by-zero-error
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move 0 to rsx *> stack depth
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perform varying oqx from 1 by 1 until oqx > 7
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if output-queue(oqx:1) >= '1' and <= '9'
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*> push the digit onto the stack
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add 1 to rsx
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move top-numerator to numerator(rsx)
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move top-denominator to denominator(rsx)
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move output-queue(oqx:1) to top-numerator
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move 1 to top-denominator
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else
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*> apply the operation
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evaluate output-queue(oqx:1)
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when '+'
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compute top-numerator = top-numerator * denominator(rsx)
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+ top-denominator * numerator(rsx)
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compute top-denominator = top-denominator * denominator(rsx)
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when '-'
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compute top-numerator = top-denominator * numerator(rsx)
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- top-numerator * denominator(rsx)
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compute top-denominator = top-denominator * denominator(rsx)
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when '*'
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compute top-numerator = top-numerator * numerator(rsx)
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compute top-denominator = top-denominator * denominator(rsx)
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when '/'
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compute work-number = numerator(rsx) * top-denominator
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compute top-denominator = denominator(rsx) * top-numerator
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if top-denominator = 0
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move 'y' to divide-by-zero-error
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exit paragraph
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end-if
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move work-number to top-numerator
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end-evaluate
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*> pop the stack
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subtract 1 from rsx
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end-if
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end-perform
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.
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end program twentyfoursolve.
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46
Task/24-game-Solve/Elixir/24-game-solve.elixir
Normal file
46
Task/24-game-Solve/Elixir/24-game-solve.elixir
Normal file
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@ -0,0 +1,46 @@
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defmodule Game24 do
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@expressions [ ["((", "", ")", "", ")", ""],
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["(", "(", "", "", "))", ""],
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["(", "", ")", "(", "", ")"],
|
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["", "((", "", "", ")", ")"],
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["", "(", "", "(", "", "))"] ]
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|
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def solve(digits) do
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dig_perm = permute(digits) |> Enum.uniq
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operators = perm_rep(~w[+ - * /], 3)
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for dig <- dig_perm, ope <- operators, expr <- @expressions,
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check?(str = make_expr(dig, ope, expr)),
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do: str
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end
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|
||||
defp check?(str) do
|
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try do
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{val, _} = Code.eval_string(str)
|
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val == 24
|
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rescue
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||||
ArithmeticError -> false # division by zero
|
||||
end
|
||||
end
|
||||
|
||||
defp permute([]), do: [[]]
|
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defp permute(list) do
|
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for x <- list, y <- permute(list -- [x]), do: [x|y]
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||||
end
|
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|
||||
defp perm_rep([], _), do: [[]]
|
||||
defp perm_rep(_, 0), do: [[]]
|
||||
defp perm_rep(list, i) do
|
||||
for x <- list, y <- perm_rep(list, i-1), do: [x|y]
|
||||
end
|
||||
|
||||
defp make_expr([a,b,c,d], [x,y,z], [e0,e1,e2,e3,e4,e5]) do
|
||||
e0 <> a <> x <> e1 <> b <> e2 <> y <> e3 <> c <> e4 <> z <> d <> e5
|
||||
end
|
||||
end
|
||||
|
||||
case Game24.solve(System.argv) do
|
||||
[] -> IO.puts "no solutions"
|
||||
solutions ->
|
||||
IO.puts "found #{length(solutions)} solutions, including #{hd(solutions)}"
|
||||
IO.inspect Enum.sort(solutions)
|
||||
end
|
||||
|
|
@ -1,18 +1,19 @@
|
|||
use MONKEY-SEE-NO-EVAL;
|
||||
|
||||
my @digits;
|
||||
my $amount = 4;
|
||||
|
||||
# Get $amount digits from the user,
|
||||
# ask for more if they don't supply enough
|
||||
while @digits.elems < $amount {
|
||||
@digits ,= (prompt "Enter {$amount - @digits} digits from 1 to 9, "
|
||||
@digits.append: (prompt "Enter {$amount - @digits} digits from 1 to 9, "
|
||||
~ '(repeats allowed): ').comb(/<[1..9]>/);
|
||||
}
|
||||
# Throw away any extras
|
||||
@digits = @digits[^$amount];
|
||||
|
||||
# Generate combinations of operators
|
||||
my @op = <+ - * />;
|
||||
my @ops = map {my $a = $_; map {my $b = $_; map {[$a,$b,$_]}, @op}, @op}, @op;
|
||||
my @ops = [X,] <+ - * /> xx 3;
|
||||
|
||||
# Enough sprintf formats to cover most precedence orderings
|
||||
my @formats = (
|
||||
|
|
@ -26,34 +27,16 @@ my @formats = (
|
|||
);
|
||||
|
||||
# Brute force test the different permutations
|
||||
for unique permutations @digits -> @p {
|
||||
for unique @digits.permutations -> @p {
|
||||
for @ops -> @o {
|
||||
for @formats -> $format {
|
||||
my $string = sprintf $format, @p[0], @o[0],
|
||||
@p[1], @o[1], @p[2], @o[2], @p[3];
|
||||
my $result = try { EVAL($string) };
|
||||
my $string = sprintf $format, flat roundrobin(|@p; |@o);
|
||||
my $result = EVAL($string);
|
||||
say "$string = 24" and last if $result and $result == 24;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
# Perl 6 translation of Fischer-Krause ordered permutation algorithm
|
||||
sub permutations (@array) {
|
||||
my @index = ^@array;
|
||||
my $last = @index[*-1];
|
||||
my (@permutations, $rev, $fwd);
|
||||
loop {
|
||||
push @permutations, [@array[@index]];
|
||||
$rev = $last;
|
||||
--$rev while $rev and @index[$rev-1] > @index[$rev];
|
||||
return @permutations unless $rev;
|
||||
$fwd = $rev;
|
||||
push @index, @index.splice($rev).reverse;
|
||||
++$fwd while @index[$rev-1] > @index[$fwd];
|
||||
@index[$rev-1,$fwd] = @index[$fwd,$rev-1];
|
||||
}
|
||||
}
|
||||
|
||||
# Only return unique sub-arrays
|
||||
sub unique (@array) {
|
||||
my %h = map { $_.Str => $_ }, @array;
|
||||
|
|
|
|||
|
|
@ -1,29 +1,22 @@
|
|||
class TwentyFourGamePlayer
|
||||
class TwentyFourGame
|
||||
EXPRESSIONS = [
|
||||
'((%d %s %d) %s %d) %s %d',
|
||||
'(%d %s (%d %s %d)) %s %d',
|
||||
'(%d %s %d) %s (%d %s %d)',
|
||||
'%d %s ((%d %s %d) %s %d)',
|
||||
'%d %s (%d %s (%d %s %d))',
|
||||
].map{|expr| [expr, expr.gsub('%d', 'Rational(%d,1)')]}
|
||||
'((%dr %s %dr) %s %dr) %s %dr',
|
||||
'(%dr %s (%dr %s %dr)) %s %dr',
|
||||
'(%dr %s %dr) %s (%dr %s %dr)',
|
||||
'%dr %s ((%dr %s %dr) %s %dr)',
|
||||
'%dr %s (%dr %s (%dr %s %dr))',
|
||||
]
|
||||
|
||||
OPERATORS = [:+, :-, :*, :/].repeated_permutation(3)
|
||||
|
||||
OBJECTIVE = Rational(24,1)
|
||||
OPERATORS = [:+, :-, :*, :/].repeated_permutation(3).to_a
|
||||
|
||||
def self.solve(digits)
|
||||
solutions = []
|
||||
digits.permutation.to_a.uniq.each do |a,b,c,d|
|
||||
OPERATORS.each do |op1,op2,op3|
|
||||
EXPRESSIONS.each do |expr,expr_rat|
|
||||
# evaluate using rational arithmetic
|
||||
test = expr_rat % [a, op1, b, op2, c, op3, d]
|
||||
value = eval(test) rescue -1 # catch division by zero
|
||||
if value == OBJECTIVE
|
||||
solutions << expr % [a, op1, b, op2, c, op3, d]
|
||||
end
|
||||
end
|
||||
end
|
||||
perms = digits.permutation.to_a.uniq
|
||||
perms.product(OPERATORS, EXPRESSIONS) do |(a,b,c,d), (op1,op2,op3), expr|
|
||||
# evaluate using rational arithmetic
|
||||
text = expr % [a, op1, b, op2, c, op3, d]
|
||||
value = eval(text) rescue next # catch division by zero
|
||||
solutions << text.delete("r") if value == 24
|
||||
end
|
||||
solutions
|
||||
end
|
||||
|
|
@ -39,7 +32,7 @@ digits = ARGV.map do |arg|
|
|||
end
|
||||
digits.size == 4 or raise "error: need 4 digits, only have #{digits.size}"
|
||||
|
||||
solutions = TwentyFourGamePlayer.solve(digits)
|
||||
solutions = TwentyFourGame.solve(digits)
|
||||
if solutions.empty?
|
||||
puts "no solutions"
|
||||
else
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue