24 game/Solve
< 24 game
You are encouraged to solve this task according to the task description, using any language you may know.
- task
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.
Show examples of solutions generated by the program.
- Related task
11l
[Char = ((Float, Float) -> Float)] op
op[Char(‘+’)] = (x, y) -> x + y
op[Char(‘-’)] = (x, y) -> x - y
op[Char(‘*’)] = (x, y) -> x * y
op[Char(‘/’)] = (x, y) -> I y != 0 {x / y} E 9999999
F almost_equal(a, b)
R abs(a - b) <= 1e-5
F solve(nums)
V syms = ‘+-*/’
V sorted_nums = sorted(nums).map(Float)
L(x, y, z) cart_product(syms, syms, syms)
V n = copy(sorted_nums)
L
V (a, b, c, d) = (n[0], n[1], n[2], n[3])
I almost_equal(:op[x](:op[y](a, b), :op[z](c, d)), 24.0)
R ‘(’a‘ ’y‘ ’b‘) ’x‘ (’c‘ ’z‘ ’d‘)’
I almost_equal(:op[x](a, :op[y](b, :op[z](c, d))), 24.0)
R a‘ ’x‘ (’b‘ ’y‘ (’c‘ ’z‘ ’d‘))’
I almost_equal(:op[x](:op[y](:op[z](c, d), b), a), 24.0)
R ‘((’c‘ ’z‘ ’d‘) ’y‘ ’b‘) ’x‘ ’a
I almost_equal(:op[x](:op[y](b, :op[z](c, d)), a), 24.0)
R ‘(’b‘ ’y‘ (’c‘ ’z‘ ’d‘)) ’x‘’a
I !n.next_permutation()
L.break
R ‘not found’
L(nums) [[9, 4, 4, 5],
[1, 7, 2, 7],
[5, 7, 5, 4],
[1, 4, 6, 6],
[2, 3, 7, 3],
[8, 7, 9, 7],
[1, 6, 2, 6],
[7, 9, 4, 1],
[6, 4, 2, 2],
[5, 7, 9, 7],
[3, 3, 8, 8]]
print(‘solve(’nums‘) -> ’solve(nums))- Output:
solve([9, 4, 4, 5]) -> not found solve([1, 7, 2, 7]) -> ((7 * 7) - 1) / 2 solve([5, 7, 5, 4]) -> 4 * (7 - (5 / 5)) solve([1, 4, 6, 6]) -> 6 + (6 * (4 - 1)) solve([2, 3, 7, 3]) -> ((2 + 7) * 3) - 3 solve([8, 7, 9, 7]) -> not found solve([1, 6, 2, 6]) -> 6 + (6 * (1 + 2)) solve([7, 9, 4, 1]) -> (1 - 9) * (4 - 7) solve([6, 4, 2, 2]) -> (2 - 2) + (4 * 6) solve([5, 7, 9, 7]) -> (5 + 7) * (9 - 7) solve([3, 3, 8, 8]) -> 8 / (3 - (8 / 3))
AArch64 Assembly
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program game24Solvex64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
.equ NBDIGITS, 4 // digits number
.equ TOTAL, 24
.equ BUFFERSIZE, 80
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessRules: .ascii "24 Game\n"
.ascii "The program will display four randomly-generated \n"
.asciz "single-digit numbers and search a solution for a total to 24\n\n"
szMessDigits: .asciz "The four digits are @ @ @ @ and the score is 24. \n"
szMessOK: .asciz "Solution : \n"
szMessNotOK: .asciz "No solution for this problem !! \n"
szMessNewGame: .asciz "New game (y/n) ? \n"
szMessErrOper: .asciz "Error opérator in display result !!!"
szCarriageReturn: .asciz "\n"
.align 4
qGraine: .quad 123456
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
.align 4
sZoneConv: .skip 24
sBuffer: .skip BUFFERSIZE
qTabDigit: .skip 8 * NBDIGITS // digits table
qTabOperand1: .skip 8 * NBDIGITS // operand 1 table
qTabOperand2: .skip 8 * NBDIGITS // operand 2 table
qTabOperation: .skip 8 * NBDIGITS // operator table
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: // entry of program
ldr x0,qAdrszMessRules // display rules
bl affichageMess
1:
mov x3,#0
ldr x12,qAdrqTabDigit
ldr x5,qAdrszMessDigits
2: // loop generate random digits
mov x0,#8
bl genereraleas
add x0,x0,#1
str x0,[x12,x3,lsl 3] // store in table
ldr x1,qAdrsZoneConv
bl conversion10 // call decimal conversion
mov x0,x5
ldr x1,qAdrsZoneConv // insert conversion in message
bl strInsertAtCharInc
mov x5,x0
add x3,x3,#1
cmp x3,#NBDIGITS // end ?
blt 2b // no -> loop
mov x0,x5
bl affichageMess
mov x0,#0 // start leval
mov x1,x12 // address digits table
bl searchSoluce
cmp x0,#-1 // solution ?
bne 3f // no
ldr x0,qAdrszMessOK
bl affichageMess
bl writeSoluce // yes -> write solution in buffer
ldr x0,qAdrsBuffer // and display buffer
bl affichageMess
b 10f
3: // display message no solution
ldr x0,qAdrszMessNotOK
bl affichageMess
10: // display new game ?
ldr x0,qAdrszCarriageReturn
bl affichageMess
ldr x0,qAdrszMessNewGame
bl affichageMess
bl saisie
cmp x0,#'y'
beq 1b
cmp x0,#'Y'
beq 1b
100: // standard end of the program
mov x0,0 // return code
mov x8,EXIT // request to exit program
svc 0 // perform the system call
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrszMessRules: .quad szMessRules
qAdrszMessDigits: .quad szMessDigits
qAdrszMessNotOK: .quad szMessNotOK
qAdrszMessOK: .quad szMessOK
qAdrszMessNewGame: .quad szMessNewGame
qAdrsZoneConv: .quad sZoneConv
qAdrqTabDigit: .quad qTabDigit
/******************************************************************/
/* recherche solution */
/******************************************************************/
/* x0 level */
/* x1 table value address */
/* x0 return -1 if ok */
searchSoluce:
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
stp x10,x11,[sp,-16]! // save registres
stp x12,fp,[sp,-16]! // save registres
sub sp,sp,#8* NBDIGITS // reserve size new digits table
mov fp,sp // frame pointer = address stack
mov x10,x1 // save table
add x9,x0,#1 // new level
mov x13,#NBDIGITS
sub x3,x13,x9 // last element digits table
ldr x4,[x1,x3,lsl 3] // load last element
cmp x4,#TOTAL // equal to total to search ?
bne 0f // no
cmp x9,#NBDIGITS // all digits are used ?
bne 0f // no
mov x0,#-1 // yes -> it is ok -> end
b 100f
0:
mov x5,#0 // indice loop 1
1: // begin loop 1
cmp x5,x3
bge 9f
ldr x4,[x10,x5,lsl 3] // load first operand
ldr x8,qAdrqTabOperand1
str x4,[x8,x9,lsl 3] // and store in operand1 table
add x6,x5,#1 // indice loop 2
2: // begin loop 2
cmp x6,x3
bgt 8f
ldr x12,[x10,x6,lsl 3] // load second operand
ldr x8,qAdrqTabOperand2
str x12,[x8,x9,lsl 3] // and store in operand2 table
mov x7,#0 // k
mov x8,#0 // n
3:
cmp x7,x5
beq 4f
cmp x7,x6
beq 4f
ldr x0,[x10,x7,lsl 3] // copy other digits in new table on stack
str x0,[fp,x8,lsl 3]
add x8,x8,#1
4:
add x7,x7,#1
cmp x7,x3
ble 3b
add x7,x4,x12 // addition test
str x7,[fp,x8,lsl 3] // store result of addition
mov x7,#'+'
ldr x0,qAdrqTabOperation
str x7,[x0,x9,lsl 3] // store operator
mov x0,x9 // pass new level
mov x1,fp // pass new table address on stack
bl searchSoluce
cmp x0,#0
blt 100f
// soustraction test
sub x13,x4,x12
sub x14,x12,x4
cmp x4,x12
csel x7,x13,x14,gt
str x7,[fp,x8,lsl 3]
mov x7,#'-'
ldr x0,qAdrqTabOperation
str x7,[x0,x9,lsl 3]
mov x0,x9
mov x1,fp
bl searchSoluce
cmp x0,#0
blt 100f
mul x7,x4,x12 // multiplication test
str x7,[fp,x8,lsl 3]
mov x7,#'*'
ldr x0,qAdrqTabOperation
str x7,[x0,x9,lsl 3]
mov x0,x9
mov x1,fp
bl searchSoluce
cmp x0,#0
blt 100f
5: // division test
udiv x13,x4,x12
msub x14,x13,x12,x4
cmp x14,#0
bne 6f
str x13,[fp,x8,lsl 3]
mov x7,#'/'
ldr x0,qAdrqTabOperation
str x7,[x0,x9,lsl 3]
mov x0,x9
mov x1,fp
bl searchSoluce
b 7f
6:
udiv x13,x12,x4
msub x14,x13,x4,x12
cmp x14,#0
bne 7f
str x13,[fp,x8,lsl 3]
mov x7,#'/'
ldr x0,qAdrqTabOperation
str x7,[x0,x9,lsl 3]
mov x0,x9
mov x1,fp
bl searchSoluce
7:
cmp x0,#0
blt 100f
add x6,x6,#1 // increment indice loop 2
b 2b
8:
add x5,x5,#1 // increment indice loop 1
b 1b
9:
100:
add sp,sp,8* NBDIGITS // stack alignement
ldp x12,fp,[sp],16 // restaur des 2 registres
ldp x10,x11,[sp],16 // restaur des 2 registres
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
qAdrqTabOperand1: .quad qTabOperand1
qAdrqTabOperand2: .quad qTabOperand2
qAdrqTabOperation: .quad qTabOperation
/******************************************************************/
/* write solution */
/******************************************************************/
writeSoluce:
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
stp x10,x11,[sp,-16]! // save registres
stp x12,fp,[sp,-16]! // save registres
ldr x6,qAdrqTabOperand1
ldr x7,qAdrqTabOperand2
ldr x8,qAdrqTabOperation
ldr x10,qAdrsBuffer
mov x4,#0 // buffer indice
mov x9,#1
1:
ldr x13,[x6,x9,lsl 3] // operand 1
ldr x11,[x7,x9,lsl 3] // operand 2
ldr x12,[x8,x9,lsl 3] // operator
cmp x12,#'-'
beq 2f
cmp x12,#'/'
beq 2f
b 3f
2: // if division or soustraction
cmp x13,x11 // reverse operand if operand 1 is < operand 2
bge 3f
mov x2,x13
mov x13,x11
mov x11,x2
3: // conversion operand 1 = x13
mov x1,#10
udiv x2,x13,x1
msub x3,x1,x2,x13
cmp x2,#0
beq 31f
add x2,x2,#0x30
strb w2,[x10,x4]
add x4,x4,#1
31:
add x3,x3,#0x30
strb w3,[x10,x4]
add x4,x4,#1
ldr x2,[x7,x9,lsl 3]
strb w12,[x10,x4] // operator
add x4,x4,#1
mov x1,#10 // conversion operand 2 = x11
udiv x2,x11,x1
msub x3,x2,x1,x11
cmp x2,#0
beq 32f
add x2,x2,#0x30
strb w2,[x10,x4]
add x4,x4,#1
32:
add x3,x3,#0x30
strb w3,[x10,x4]
add x4,x4,#1
mov x0,#'='
strb w0,[x10,x4] // compute sous total
add x4,x4,#1
cmp x12,'+' // addition
bne 33f
add x0,x13,x11
b 37f
33:
cmp x12,'-' // soustraction
bne 34f
sub x0,x13,x11
b 37f
34:
cmp x12,'*' // multiplication
bne 35f
mul x0,x13,x11
b 37f
35:
cmp x12,'/' // division
bne 36f
udiv x0,x13,x11
b 37f
36: // error
ldr x0,qAdrszMessErrOper
bl affichageMess
b 100f
37: // and conversion ascii
mov x1,#10
udiv x2,x0,x1
msub x3,x2,x1,x0
cmp x2,#0
beq 36f
add x2,x2,#0x30
strb w2,[x10,x4]
add x4,x4,#1
36:
add x3,x3,#0x30
strb w3,[x10,x4]
add x4,x4,#1
mov x0,#'\n'
strb w0,[x10,x4]
add x4,x4,#1
add x9,x9,1
cmp x9,#NBDIGITS
blt 1b
mov x1,#0
strb w1,[x10,x4] // store 0 final
100:
ldp x12,fp,[sp],16 // restaur des 2 registres
ldp x10,x11,[sp],16 // restaur des 2 registres
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
qAdrsBuffer: .quad sBuffer
qAdrszMessErrOper: .quad szMessErrOper
/******************************************************************/
/* string entry */
/******************************************************************/
/* x0 return the first character of human entry */
saisie:
stp x1,lr,[sp,-16]! // save registres
stp x2,x8,[sp,-16]! // save registres
mov x0,#STDIN // Linux input console
ldr x1,qAdrsBuffer // buffer address
mov x2,#BUFFERSIZE // buffer size
mov x8,#READ // request to read datas
svc 0 // call system
ldr x1,qAdrsBuffer // buffer address
ldrb w0,[x1] // load first character
100:
ldp x2,x8,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/***************************************************/
/* Generation random number */
/***************************************************/
/* x0 contains limit */
genereraleas:
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
ldr x4,qAdrqGraine
ldr x2,[x4]
ldr x3,qNbDep1
mul x2,x3,x2
ldr x3,qNbDep2
add x2,x2,x3
str x2,[x4] // maj de la graine pour l appel suivant
cmp x0,#0
beq 100f
add x1,x0,#1 // divisor
mov x0,x2 // dividende
udiv x3,x2,x1
msub x0,x3,x1,x0 // résult = remainder
100: // end function
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/*****************************************************/
qAdrqGraine: .quad qGraine
qNbDep1: .quad 0x0019660d
qNbDep2: .quad 0x3c6ef35f
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"- Output:
The four digits are 6 8 3 1 and the score is 24. Solution : 6*8=48 3-1=2 48/2=24 New game (y/n) ? y The four digits are 8 6 6 5 and the score is 24. Solution : 8-5=3 6*3=18 6+18=24 New game (y/n) ?
ABAP
Will generate all possible solutions of any given four numbers according to the rules of the 24 game.
Note: the permute function was locally from here
data: lv_flag type c,
lv_number type i,
lt_numbers type table of i.
constants: c_no_val type i value 9999.
append 1 to lt_numbers.
append 1 to lt_numbers.
append 2 to lt_numbers.
append 7 to lt_numbers.
write 'Evaluating 24 with the following input: '.
loop at lt_numbers into lv_number.
write lv_number.
endloop.
perform solve_24 using lt_numbers.
form eval_formula using iv_eval type string changing ev_out type i.
call function 'EVAL_FORMULA' "analysis of a syntactically correct formula
exporting
formula = iv_eval
importing
value = ev_out
exceptions
others = 1.
if sy-subrc <> 0.
ev_out = -1.
endif.
endform.
" Solve a 24 puzzle.
form solve_24 using it_numbers like lt_numbers.
data: lv_flag type c,
lv_op1 type c,
lv_op2 type c,
lv_op3 type c,
lv_var1 type c,
lv_var2 type c,
lv_var3 type c,
lv_var4 type c,
lv_eval type string,
lv_result type i,
lv_var type i.
define retrieve_var.
read table it_numbers index &1 into lv_var.
&2 = lv_var.
end-of-definition.
define retrieve_val.
perform eval_formula using lv_eval changing lv_result.
if lv_result = 24.
write / lv_eval.
endif.
end-of-definition.
" Loop through all the possible number permutations.
do.
" Init. the operations table.
retrieve_var: 1 lv_var1, 2 lv_var2, 3 lv_var3, 4 lv_var4.
do 4 times.
case sy-index.
when 1.
lv_op1 = '+'.
when 2.
lv_op1 = '*'.
when 3.
lv_op1 = '-'.
when 4.
lv_op1 = '/'.
endcase.
do 4 times.
case sy-index.
when 1.
lv_op2 = '+'.
when 2.
lv_op2 = '*'.
when 3.
lv_op2 = '-'.
when 4.
lv_op2 = '/'.
endcase.
do 4 times.
case sy-index.
when 1.
lv_op3 = '+'.
when 2.
lv_op3 = '*'.
when 3.
lv_op3 = '-'.
when 4.
lv_op3 = '/'.
endcase.
concatenate '(' '(' lv_var1 lv_op1 lv_var2 ')' lv_op2 lv_var3 ')' lv_op3 lv_var4 into lv_eval separated by space.
retrieve_val.
concatenate '(' lv_var1 lv_op1 lv_var2 ')' lv_op2 '(' lv_var3 lv_op3 lv_var4 ')' into lv_eval separated by space.
retrieve_val.
concatenate '(' lv_var1 lv_op1 '(' lv_var2 lv_op2 lv_var3 ')' ')' lv_op3 lv_var4 into lv_eval separated by space.
retrieve_val.
concatenate lv_var1 lv_op1 '(' '(' lv_var2 lv_op2 lv_var3 ')' lv_op3 lv_var4 ')' into lv_eval separated by space.
retrieve_val.
concatenate lv_var1 lv_op1 '(' lv_var2 lv_op2 '(' lv_var3 lv_op3 lv_var4 ')' ')' into lv_eval separated by space.
retrieve_val.
enddo.
enddo.
enddo.
" Once we've reached the last permutation -> Exit.
perform permute using it_numbers changing lv_flag.
if lv_flag = 'X'.
exit.
endif.
enddo.
endform.
" Permutation function - this is used to permute:
" A = {A1...AN} -> Set of supplied variables.
" B = {B1...BN - 1} -> Set of operators.
" Can be used for an unbounded size set. Relies
" on lexicographic ordering of the set.
form permute using iv_set like lt_numbers
changing ev_last type c.
data: lv_len type i,
lv_first type i,
lv_third type i,
lv_count type i,
lv_temp type i,
lv_temp_2 type i,
lv_second type i,
lv_changed type c,
lv_perm type i.
describe table iv_set lines lv_len.
lv_perm = lv_len - 1.
lv_changed = ' '.
" Loop backwards through the table, attempting to find elements which
" can be permuted. If we find one, break out of the table and set the
" flag indicating a switch.
do.
if lv_perm <= 0.
exit.
endif.
" Read the elements.
read table iv_set index lv_perm into lv_first.
add 1 to lv_perm.
read table iv_set index lv_perm into lv_second.
subtract 1 from lv_perm.
if lv_first < lv_second.
lv_changed = 'X'.
exit.
endif.
subtract 1 from lv_perm.
enddo.
" Last permutation.
if lv_changed <> 'X'.
ev_last = 'X'.
exit.
endif.
" Swap tail decresing to get a tail increasing.
lv_count = lv_perm + 1.
do.
lv_first = lv_len + lv_perm - lv_count + 1.
if lv_count >= lv_first.
exit.
endif.
read table iv_set index lv_count into lv_temp.
read table iv_set index lv_first into lv_temp_2.
modify iv_set index lv_count from lv_temp_2.
modify iv_set index lv_first from lv_temp.
add 1 to lv_count.
enddo.
lv_count = lv_len - 1.
do.
if lv_count <= lv_perm.
exit.
endif.
read table iv_set index lv_count into lv_first.
read table iv_set index lv_perm into lv_second.
read table iv_set index lv_len into lv_third.
if ( lv_first < lv_third ) and ( lv_first > lv_second ).
lv_len = lv_count.
endif.
subtract 1 from lv_count.
enddo.
read table iv_set index lv_perm into lv_temp.
read table iv_set index lv_len into lv_temp_2.
modify iv_set index lv_perm from lv_temp_2.
modify iv_set index lv_len from lv_temp.
endform.
Sample Runs:
Evaluating 24 with the following input: 1 1 2 7 ( 1 + 2 ) * ( 1 + 7 ) ( 1 + 2 ) * ( 7 + 1 ) ( 1 + 7 ) * ( 1 + 2 ) ( 1 + 7 ) * ( 2 + 1 ) ( 2 + 1 ) * ( 1 + 7 ) ( 2 + 1 ) * ( 7 + 1 ) ( 7 + 1 ) * ( 1 + 2 ) ( 7 + 1 ) * ( 2 + 1 ) Evaluating 24 with the following input: 1 ( ( 1 + 2 ) + 3 ) * 4 ( 1 + ( 2 + 3 ) ) * 4 ( ( 1 * 2 ) * 3 ) * 4 ( 1 * 2 ) * ( 3 * 4 ) ( 1 * ( 2 * 3 ) ) * 4 1 * ( ( 2 * 3 ) * 4 ) 1 * ( 2 * ( 3 * 4 ) ) ( ( 1 * 2 ) * 4 ) * 3 ( 1 * 2 ) * ( 4 * 3 ) ( 1 * ( 2 * 4 ) ) * 3 1 * ( ( 2 * 4 ) * 3 ) 1 * ( 2 * ( 4 * 3 ) ) ( ( 1 + 3 ) + 2 ) * 4 ( 1 + ( 3 + 2 ) ) * 4 ( 1 + 3 ) * ( 2 + 4 ) ( ( 1 * 3 ) * 2 ) * 4 ( 1 * 3 ) * ( 2 * 4 ) ( 1 * ( 3 * 2 ) ) * 4 1 * ( ( 3 * 2 ) * 4 ) 1 * ( 3 * ( 2 * 4 ) ) ( 1 + 3 ) * ( 4 + 2 ) ( ( 1 * 3 ) * 4 ) * 2 ( 1 * 3 ) * ( 4 * 2 ) ( 1 * ( 3 * 4 ) ) * 2 1 * ( ( 3 * 4 ) * 2 ) 1 * ( 3 * ( 4 * 2 ) ) ( ( 1 * 4 ) * 2 ) * 3 ( 1 * 4 ) * ( 2 * 3 ) ( 1 * ( 4 * 2 ) ) * 3 1 * ( ( 4 * 2 ) * 3 ) 1 * ( 4 * ( 2 * 3 ) ) ( ( 1 * 4 ) * 3 ) * 2 ( 1 * 4 ) * ( 3 * 2 ) ( 1 * ( 4 * 3 ) ) * 2 1 * ( ( 4 * 3 ) * 2 ) 1 * ( 4 * ( 3 * 2 ) ) ( ( 2 + 1 ) + 3 ) * 4 ( 2 + ( 1 + 3 ) ) * 4 ( ( 2 * 1 ) * 3 ) * 4 ( 2 * 1 ) * ( 3 * 4 ) ( 2 * ( 1 * 3 ) ) * 4 2 * ( ( 1 * 3 ) * 4 ) 2 * ( 1 * ( 3 * 4 ) ) ( ( 2 / 1 ) * 3 ) * 4 ( 2 / 1 ) * ( 3 * 4 ) ( 2 / ( 1 / 3 ) ) * 4 2 / ( 1 / ( 3 * 4 ) ) 2 / ( ( 1 / 3 ) / 4 ) ( ( 2 * 1 ) * 4 ) * 3 ( 2 * 1 ) * ( 4 * 3 ) ( 2 * ( 1 * 4 ) ) * 3 2 * ( ( 1 * 4 ) * 3 ) 2 * ( 1 * ( 4 * 3 ) ) ( ( 2 / 1 ) * 4 ) * 3 ( 2 / 1 ) * ( 4 * 3 ) ( 2 / ( 1 / 4 ) ) * 3 2 / ( 1 / ( 4 * 3 ) ) 2 / ( ( 1 / 4 ) / 3 ) ( ( 2 + 3 ) + 1 ) * 4 ( 2 + ( 3 + 1 ) ) * 4 ( ( 2 * 3 ) * 1 ) * 4 ( 2 * 3 ) * ( 1 * 4 ) ( 2 * ( 3 * 1 ) ) * 4 2 * ( ( 3 * 1 ) * 4 ) 2 * ( 3 * ( 1 * 4 ) ) ( ( 2 * 3 ) / 1 ) * 4 ( 2 * ( 3 / 1 ) ) * 4 2 * ( ( 3 / 1 ) * 4 ) ( 2 * 3 ) / ( 1 / 4 ) 2 * ( 3 / ( 1 / 4 ) ) ( ( 2 * 3 ) * 4 ) * 1 ( 2 * 3 ) * ( 4 * 1 ) ( 2 * ( 3 * 4 ) ) * 1 2 * ( ( 3 * 4 ) * 1 ) 2 * ( 3 * ( 4 * 1 ) ) ( ( 2 * 3 ) * 4 ) / 1 ( 2 * 3 ) * ( 4 / 1 ) ( 2 * ( 3 * 4 ) ) / 1 2 * ( ( 3 * 4 ) / 1 ) 2 * ( 3 * ( 4 / 1 ) ) ( 2 + 4 ) * ( 1 + 3 ) ( ( 2 * 4 ) * 1 ) * 3 ( 2 * 4 ) * ( 1 * 3 ) ( 2 * ( 4 * 1 ) ) * 3 2 * ( ( 4 * 1 ) * 3 ) 2 * ( 4 * ( 1 * 3 ) ) ( ( 2 * 4 ) / 1 ) * 3 ( 2 * ( 4 / 1 ) ) * 3 2 * ( ( 4 / 1 ) * 3 ) ( 2 * 4 ) / ( 1 / 3 ) 2 * ( 4 / ( 1 / 3 ) ) ( 2 + 4 ) * ( 3 + 1 ) ( ( 2 * 4 ) * 3 ) * 1 ( 2 * 4 ) * ( 3 * 1 ) ( 2 * ( 4 * 3 ) ) * 1 2 * ( ( 4 * 3 ) * 1 ) 2 * ( 4 * ( 3 * 1 ) ) ( ( 2 * 4 ) * 3 ) / 1 ( 2 * 4 ) * ( 3 / 1 ) ( 2 * ( 4 * 3 ) ) / 1 2 * ( ( 4 * 3 ) / 1 ) 2 * ( 4 * ( 3 / 1 ) ) ( ( 3 + 1 ) + 2 ) * 4 ( 3 + ( 1 + 2 ) ) * 4 ( 3 + 1 ) * ( 2 + 4 ) ( ( 3 * 1 ) * 2 ) * 4 ( 3 * 1 ) * ( 2 * 4 ) ( 3 * ( 1 * 2 ) ) * 4 3 * ( ( 1 * 2 ) * 4 ) 3 * ( 1 * ( 2 * 4 ) ) ( ( 3 / 1 ) * 2 ) * 4 ( 3 / 1 ) * ( 2 * 4 ) ( 3 / ( 1 / 2 ) ) * 4 3 / ( 1 / ( 2 * 4 ) ) 3 / ( ( 1 / 2 ) / 4 ) ( 3 + 1 ) * ( 4 + 2 ) ( ( 3 * 1 ) * 4 ) * 2 ( 3 * 1 ) * ( 4 * 2 ) ( 3 * ( 1 * 4 ) ) * 2 3 * ( ( 1 * 4 ) * 2 ) 3 * ( 1 * ( 4 * 2 ) ) ( ( 3 / 1 ) * 4 ) * 2 ( 3 / 1 ) * ( 4 * 2 ) ( 3 / ( 1 / 4 ) ) * 2 3 / ( 1 / ( 4 * 2 ) ) 3 / ( ( 1 / 4 ) / 2 ) ( ( 3 + 2 ) + 1 ) * 4 ( 3 + ( 2 + 1 ) ) * 4 ( ( 3 * 2 ) * 1 ) * 4 ( 3 * 2 ) * ( 1 * 4 ) ( 3 * ( 2 * 1 ) ) * 4 3 * ( ( 2 * 1 ) * 4 ) 3 * ( 2 * ( 1 * 4 ) ) ( ( 3 * 2 ) / 1 ) * 4 ( 3 * ( 2 / 1 ) ) * 4 3 * ( ( 2 / 1 ) * 4 ) ( 3 * 2 ) / ( 1 / 4 ) 3 * ( 2 / ( 1 / 4 ) ) ( ( 3 * 2 ) * 4 ) * 1 ( 3 * 2 ) * ( 4 * 1 ) ( 3 * ( 2 * 4 ) ) * 1 3 * ( ( 2 * 4 ) * 1 ) 3 * ( 2 * ( 4 * 1 ) ) ( ( 3 * 2 ) * 4 ) / 1 ( 3 * 2 ) * ( 4 / 1 ) ( 3 * ( 2 * 4 ) ) / 1 3 * ( ( 2 * 4 ) / 1 ) 3 * ( 2 * ( 4 / 1 ) ) ( ( 3 * 4 ) * 1 ) * 2 ( 3 * 4 ) * ( 1 * 2 ) ( 3 * ( 4 * 1 ) ) * 2 3 * ( ( 4 * 1 ) * 2 ) 3 * ( 4 * ( 1 * 2 ) ) ( ( 3 * 4 ) / 1 ) * 2 ( 3 * ( 4 / 1 ) ) * 2 3 * ( ( 4 / 1 ) * 2 ) ( 3 * 4 ) / ( 1 / 2 ) 3 * ( 4 / ( 1 / 2 ) ) ( ( 3 * 4 ) * 2 ) * 1 ( 3 * 4 ) * ( 2 * 1 ) ( 3 * ( 4 * 2 ) ) * 1 3 * ( ( 4 * 2 ) * 1 ) 3 * ( 4 * ( 2 * 1 ) ) ( ( 3 * 4 ) * 2 ) / 1 ( 3 * 4 ) * ( 2 / 1 ) ( 3 * ( 4 * 2 ) ) / 1 3 * ( ( 4 * 2 ) / 1 ) 3 * ( 4 * ( 2 / 1 ) ) 4 * ( ( 1 + 2 ) + 3 ) 4 * ( 1 + ( 2 + 3 ) ) ( ( 4 * 1 ) * 2 ) * 3 ( 4 * 1 ) * ( 2 * 3 ) ( 4 * ( 1 * 2 ) ) * 3 4 * ( ( 1 * 2 ) * 3 ) 4 * ( 1 * ( 2 * 3 ) ) ( ( 4 / 1 ) * 2 ) * 3 ( 4 / 1 ) * ( 2 * 3 ) ( 4 / ( 1 / 2 ) ) * 3 4 / ( 1 / ( 2 * 3 ) ) 4 / ( ( 1 / 2 ) / 3 ) 4 * ( ( 1 + 3 ) + 2 ) 4 * ( 1 + ( 3 + 2 ) ) ( ( 4 * 1 ) * 3 ) * 2 ( 4 * 1 ) * ( 3 * 2 ) ( 4 * ( 1 * 3 ) ) * 2 4 * ( ( 1 * 3 ) * 2 ) 4 * ( 1 * ( 3 * 2 ) ) ( ( 4 / 1 ) * 3 ) * 2 ( 4 / 1 ) * ( 3 * 2 ) ( 4 / ( 1 / 3 ) ) * 2 4 / ( 1 / ( 3 * 2 ) ) 4 / ( ( 1 / 3 ) / 2 ) ( 4 + 2 ) * ( 1 + 3 ) 4 * ( ( 2 + 1 ) + 3 ) 4 * ( 2 + ( 1 + 3 ) ) ( ( 4 * 2 ) * 1 ) * 3 ( 4 * 2 ) * ( 1 * 3 ) ( 4 * ( 2 * 1 ) ) * 3 4 * ( ( 2 * 1 ) * 3 ) 4 * ( 2 * ( 1 * 3 ) ) ( ( 4 * 2 ) / 1 ) * 3 ( 4 * ( 2 / 1 ) ) * 3 4 * ( ( 2 / 1 ) * 3 ) ( 4 * 2 ) / ( 1 / 3 ) 4 * ( 2 / ( 1 / 3 ) ) ( 4 + 2 ) * ( 3 + 1 ) 4 * ( ( 2 + 3 ) + 1 ) 4 * ( 2 + ( 3 + 1 ) ) ( ( 4 * 2 ) * 3 ) * 1 ( 4 * 2 ) * ( 3 * 1 ) ( 4 * ( 2 * 3 ) ) * 1 4 * ( ( 2 * 3 ) * 1 ) 4 * ( 2 * ( 3 * 1 ) ) ( ( 4 * 2 ) * 3 ) / 1 ( 4 * 2 ) * ( 3 / 1 ) ( 4 * ( 2 * 3 ) ) / 1 4 * ( ( 2 * 3 ) / 1 ) 4 * ( 2 * ( 3 / 1 ) ) 4 * ( ( 3 + 1 ) + 2 ) 4 * ( 3 + ( 1 + 2 ) ) ( ( 4 * 3 ) * 1 ) * 2 ( 4 * 3 ) * ( 1 * 2 ) ( 4 * ( 3 * 1 ) ) * 2 4 * ( ( 3 * 1 ) * 2 ) 4 * ( 3 * ( 1 * 2 ) ) ( ( 4 * 3 ) / 1 ) * 2 ( 4 * ( 3 / 1 ) ) * 2 4 * ( ( 3 / 1 ) * 2 ) ( 4 * 3 ) / ( 1 / 2 ) 4 * ( 3 / ( 1 / 2 ) ) 4 * ( ( 3 + 2 ) + 1 ) 4 * ( 3 + ( 2 + 1 ) ) ( ( 4 * 3 ) * 2 ) * 1 ( 4 * 3 ) * ( 2 * 1 ) ( 4 * ( 3 * 2 ) ) * 1 4 * ( ( 3 * 2 ) * 1 ) 4 * ( 3 * ( 2 * 1 ) ) ( ( 4 * 3 ) * 2 ) / 1 ( 4 * 3 ) * ( 2 / 1 ) ( 4 * ( 3 * 2 ) ) / 1 4 * ( ( 3 * 2 ) / 1 ) 4 * ( 3 * ( 2 / 1 ) ) Evaluating 24 with the following input: 5 6 7 8 5 * ( 6 - ( 8 / 7 ) ) ( 5 + 7 ) * ( 8 - 6 ) ( ( 5 + 7 ) - 8 ) * 6 ( 5 + ( 7 - 8 ) ) * 6 ( ( 5 - 8 ) + 7 ) * 6 ( 5 - ( 8 - 7 ) ) * 6 6 * ( ( 5 + 7 ) - 8 ) 6 * ( 5 + ( 7 - 8 ) ) 6 * ( ( 5 - 8 ) + 7 ) 6 * ( 5 - ( 8 - 7 ) ) 6 * ( ( 7 + 5 ) - 8 ) 6 * ( 7 + ( 5 - 8 ) ) ( 6 / ( 7 - 5 ) ) * 8 6 / ( ( 7 - 5 ) / 8 ) 6 * ( ( 7 - 8 ) + 5 ) 6 * ( 7 - ( 8 - 5 ) ) ( 6 * 8 ) / ( 7 - 5 ) 6 * ( 8 / ( 7 - 5 ) ) ( 6 - ( 8 / 7 ) ) * 5 ( 7 + 5 ) * ( 8 - 6 ) ( ( 7 + 5 ) - 8 ) * 6 ( 7 + ( 5 - 8 ) ) * 6 ( ( 7 - 8 ) + 5 ) * 6 ( 7 - ( 8 - 5 ) ) * 6 ( 8 - 6 ) * ( 5 + 7 ) ( 8 * 6 ) / ( 7 - 5 ) 8 * ( 6 / ( 7 - 5 ) ) ( 8 - 6 ) * ( 7 + 5 ) ( 8 / ( 7 - 5 ) ) * 6 8 / ( ( 7 - 5 ) / 6 )
Argile
die "Please give 4 digits as argument 1\n" if argc < 2
print a function that given four digits argv[1] subject to the rules of \
the _24_ game, computes an expression to solve the game if possible.
use std, array
let digits be an array of 4 byte
let operators be an array of 4 byte
(: reordered arrays :)
let (type of digits) rdigits
let (type of operators) roperators
.: a function that given four digits <text digits> subject to
the rules of the _24_ game, computes an expression to solve
the game if possible. :. -> text
if #digits != 4 {return "[error: need exactly 4 digits]"}
operators[0] = '+' ; operators[1] = '-'
operators[2] = '*' ; operators[3] = '/'
for each (val int d) from 0 to 3
if (digits[d] < '1') || (digits[d] > '9')
return "[error: non-digit character given]"
(super digits)[d] = digits[d]
let expr = for each operand order stuff
return "" if expr is nil
expr
.:for each operand order stuff:. -> text
for each (val int a) from 0 to 3
for each (val int b) from 0 to 3
next if (b == a)
for each (val int c) from 0 to 3
next if (c == b) or (c == a)
for each (val int d) from 0 to 3
next if (d == c) or (d == b) or (d == a)
rdigits[0] = digits[a] ; rdigits[1] = digits[b]
rdigits[2] = digits[c] ; rdigits[3] = digits[d]
let found = for each operator order stuff
return found unless found is nil
nil
.:for each operator order stuff:. -> text
for each (val int i) from 0 to 3
for each (val int j) from 0 to 3
for each (val int k) from 0 to 3
roperators[0] = operators[i]
roperators[1] = operators[j]
roperators[2] = operators[k]
let found = for each RPN pattern stuff
return found if found isn't nil
nil
our (raw array of text) RPN_patterns = Cdata
"xx.x.x."
"xx.xx.."
"xxx..x."
"xxx.x.."
"xxxx..."
our (raw array of text) formats = Cdata
"((%c%c%c)%c%c)%c%c"
"(%c%c%c)%c(%c%c%c)"
"(%c%c(%c%c%c))%c%c"
"%c%c((%c%c%c)%c%c)"
"%c%c(%c%c(%c%c%c))"
our (raw array of array of 3 int) rrop = Cdata
{0;1;2}; {0;2;1}; {1;0;2}; {2;0;1}; {2;1;0}
.:for each RPN pattern stuff:. -> text
let RPN_stack be an array of 4 real
for each (val int rpn) from 0 to 4
let (nat) sp=0, op=0, dg=0.
let text p
for (p = RPN_patterns[rpn]) (*p != 0) (p++)
if *p == 'x'
if sp >= 4 {die "RPN stack overflow\n"}
if dg > 3 {die "RPN digits overflow\n"}
RPN_stack[sp++] = (rdigits[dg++] - '0') as real
if *p == '.'
if sp < 2 {die "RPN stack underflow\n"}
if op > 2 {die "RPN operators overflow\n"}
sp -= 2
let x = RPN_stack[sp]
let y = RPN_stack[sp + 1]
switch roperators[op++]
case '+' {x += y}
case '-' {x -= y}
case '*' {x *= y}
case '/' {x /= y}
default {die "RPN operator unknown\n"}
RPN_stack[sp++] = x
if RPN_stack[0] == 24.0
our array of 12 byte buffer (: 4 paren + 3 ops + 4 digits + null :)
snprintf (buffer as text) (size of buffer) (formats[rpn]) \
(rdigits[0]) (roperators[(rrop[rpn][0])]) (rdigits[1]) \
(roperators[(rrop[rpn][1])]) (rdigits[2]) \
(roperators[(rrop[rpn][2])]) (rdigits[3]);
return buffer as text
nilExamples:
$ arc 24_game_solve.arg -o 24_game_solve.c $ gcc -Wall 24_game_solve.c -o 24_game_solve $ ./24_game_solve 1234 ((1+2)+3)*4 $ ./24_game_solve 9999 $ ./24_game_solve 5678 ((5+7)-8)*6 $ ./24_game_solve 1127 (1+2)*(1+7)
ARM Assembly
/* ARM assembly Raspberry PI */
/* program game24Solver.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes */
/************************************/
.include "../constantes.inc"
.equ STDIN, 0 @ Linux input console
.equ READ, 3 @ Linux syscall
.equ NBDIGITS, 4 @ digits number
.equ TOTAL, 24
.equ BUFFERSIZE, 80
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessRules: .ascii "24 Game\n"
.ascii "The program will display four randomly-generated \n"
.asciz "single-digit numbers and search a solution for a total to 24\n\n"
szMessDigits: .asciz "The four digits are @ @ @ @ and the score is 24. \n"
szMessOK: .asciz "Solution : \n"
szMessNotOK: .asciz "No solution for this problem !! \n"
szMessNewGame: .asciz "New game (y/n) ? \n"
szCarriageReturn: .asciz "\n"
.align 4
iGraine: .int 123456
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
.align 4
sZoneConv: .skip 24
sBuffer: .skip BUFFERSIZE
iTabDigit: .skip 4 * NBDIGITS @ digits table
iTabOperand1: .skip 4 * NBDIGITS @ operand 1 table
iTabOperand2: .skip 4 * NBDIGITS @ operand 2 table
iTabOperation: .skip 4 * NBDIGITS @ operator table
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
ldr r0,iAdrszMessRules @ display rules
bl affichageMess
1:
mov r3,#0
ldr r12,iAdriTabDigit
ldr r5,iAdrszMessDigits
2: @ loop generate random digits
mov r0,#8
bl genereraleas
add r0,r0,#1
str r0,[r12,r3,lsl #2] @ store in table
ldr r1,iAdrsZoneConv
bl conversion10 @ call decimal conversion
mov r2,#0
strb r2,[r1,r0] @ reduce size display area with zéro final
mov r0,r5
ldr r1,iAdrsZoneConv @ insert conversion in message
bl strInsertAtCharInc
mov r5,r0
add r3,r3,#1
cmp r3,#NBDIGITS @ end ?
blt 2b @ no -> loop
mov r0,r5
bl affichageMess
mov r0,#0 @ start leval
mov r1,r12 @ address digits table
bl searchSoluce
cmp r0,#-1 @ solution ?
bne 3f @ no
ldr r0,iAdrszMessOK
bl affichageMess
bl writeSoluce @ yes -> write solution in buffer
ldr r0,iAdrsBuffer @ and display buffer
bl affichageMess
b 10f
3: @ display message no solution
ldr r0,iAdrszMessNotOK
bl affichageMess
10: @ display new game ?
ldr r0,iAdrszCarriageReturn
bl affichageMess
ldr r0,iAdrszMessNewGame
bl affichageMess
bl saisie
cmp r0,#'y'
beq 1b
cmp r0,#'Y'
beq 1b
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrszCarriageReturn: .int szCarriageReturn
iAdrszMessRules: .int szMessRules
iAdrszMessDigits: .int szMessDigits
iAdrszMessNotOK: .int szMessNotOK
iAdrszMessOK: .int szMessOK
iAdrszMessNewGame: .int szMessNewGame
iAdrsZoneConv: .int sZoneConv
iAdriTabDigit: .int iTabDigit
/******************************************************************/
/* recherche solution */
/******************************************************************/
/* r0 level */
/* r1 table value address */
/* r0 return -1 if ok */
searchSoluce:
push {r1-r12,lr} @ save registers
sub sp,#4* NBDIGITS @ reserve size new digits table
mov fp,sp @ frame pointer = address stack
mov r10,r1 @ save table
add r9,r0,#1 @ new level
rsb r3,r9,#NBDIGITS @ last element digits table
ldr r4,[r1,r3,lsl #2] @ load last element
cmp r4,#TOTAL @ equal to total to search ?
bne 0f @ no
cmp r9,#NBDIGITS @ all digits are used ?
bne 0f @ no
mov r0,#-1 @ yes -> it is ok -> end
b 100f
0:
mov r5,#0 @ indice loop 1
1: @ begin loop 1
cmp r5,r3
bge 9f
ldr r4,[r10,r5,lsl #2] @ load first operand
ldr r8,iAdriTabOperand1
str r4,[r8,r9,lsl #2] @ and store in operand1 table
add r6,r5,#1 @ indice loop 2
2: @ begin loop 2
cmp r6,r3
bgt 8f
ldr r12,[r10,r6,lsl #2] @ load second operand
ldr r8,iAdriTabOperand2
str r12,[r8,r9,lsl #2] @ and store in operand2 table
mov r7,#0 @ k
mov r8,#0 @ n
3:
cmp r7,r5
beq 4f
cmp r7,r6
beq 4f
ldr r0,[r10,r7,lsl #2] @ copy other digits in new table on stack
str r0,[fp,r8,lsl #2]
add r8,r8,#1
4:
add r7,r7,#1
cmp r7,r3
ble 3b
add r7,r4,r12 @ addition test
str r7,[fp,r8,lsl #2] @ store result of addition
mov r7,#'+'
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2] @ store operator
mov r0,r9 @ pass new level
mov r1,fp @ pass new table address on stack
bl searchSoluce
cmp r0,#0
blt 100f
@ soustraction test
cmp r4,r12
subgt r7,r4,r12
suble r7,r12,r4
str r7,[fp,r8,lsl #2]
mov r7,#'-'
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2]
mov r0,r9
mov r1,fp
bl searchSoluce
cmp r0,#0
blt 100f
mul r7,r4,r12 @ multiplication test
str r7,[fp,r8,lsl #2]
mov r7,#'*'
//vidregtit mult
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2]
mov r0,r9
mov r1,fp
bl searchSoluce
cmp r0,#0
blt 100f
5: @ division test
push {r1-r3}
mov r0,r4
mov r1,r12
bl division
// mov r7,r9
cmp r3,#0
bne 6f
str r2,[fp,r8,lsl #2]
mov r7,#'/'
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2]
mov r0,r9
mov r1,fp
bl searchSoluce
b 7f
6:
mov r0,r12
mov r1,r4
bl division
cmp r3,#0
bne 7f
str r2,[fp,r8,lsl #2]
mov r7,#'/'
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2]
mov r0,r9
mov r1,fp
bl searchSoluce
7:
pop {r1-r3}
cmp r0,#0
blt 100f
add r6,r6,#1 @ increment indice loop 2
b 2b
8:
add r5,r5,#1 @ increment indice loop 1
b 1b
9:
100:
add sp,#4* NBDIGITS @ stack alignement
pop {r1-r12,lr}
bx lr @ return
iAdriTabOperand1: .int iTabOperand1
iAdriTabOperand2: .int iTabOperand2
iAdriTabOperation: .int iTabOperation
/******************************************************************/
/* write solution */
/******************************************************************/
writeSoluce:
push {r1-r12,lr} @ save registers
ldr r6,iAdriTabOperand1
ldr r7,iAdriTabOperand2
ldr r8,iAdriTabOperation
ldr r10,iAdrsBuffer
mov r4,#0 @ buffer indice
mov r9,#1
1:
ldr r5,[r6,r9,lsl #2] @ operand 1
ldr r11,[r7,r9,lsl #2] @ operand 2
ldr r12,[r8,r9,lsl #2] @ operator
cmp r12,#'-'
beq 2f
cmp r12,#'/'
beq 2f
b 3f
2: @ if division or soustraction
cmp r5,r11 @ reverse operand if operand 1 is < operand 2
movlt r2,r5
movlt r5,r11
movlt r11,r2
3: @ conversion operand 1 = r0
mov r0,r5
mov r1,#10
bl division
cmp r2,#0
addne r2,r2,#0x30
strneb r2,[r10,r4]
addne r4,r4,#1
add r3,r3,#0x30
strb r3,[r10,r4]
add r4,r4,#1
ldr r2,[r7,r9,lsl #2]
strb r12,[r10,r4] @ operator
add r4,r4,#1
mov r0,r11 @ conversion operand 2
mov r1,#10
bl division
cmp r2,#0
addne r2,r2,#0x30
strneb r2,[r10,r4]
addne r4,r4,#1
add r3,r3,#0x30
strb r3,[r10,r4]
add r4,r4,#1
mov r0,#'='
str r0,[r10,r4] @ conversion sous total
add r4,r4,#1
cmp r12,#'+'
addeq r0,r5,r11
cmp r12,#'-'
subeq r0,r5,r11
cmp r12,#'*'
muleq r0,r5,r11
cmp r12,#'/'
udiveq r0,r5,r11
mov r1,#10
bl division
cmp r2,#0
addne r2,r2,#0x30
strneb r2,[r10,r4]
addne r4,r4,#1
add r3,r3,#0x30
strb r3,[r10,r4]
add r4,r4,#1
mov r0,#'\n'
str r0,[r10,r4]
add r4,r4,#1
add r9,#1
cmp r9,#NBDIGITS
blt 1b
mov r1,#0
strb r1,[r10,r4] @ store 0 final
100:
pop {r1-r12,lr}
bx lr @ return
iAdrsBuffer: .int sBuffer
/******************************************************************/
/* string entry */
/******************************************************************/
/* r0 return the first character of human entry */
saisie:
push {r1-r7,lr} @ save registers
mov r0,#STDIN @ Linux input console
ldr r1,iAdrsBuffer @ buffer address
mov r2,#BUFFERSIZE @ buffer size
mov r7,#READ @ request to read datas
svc 0 @ call system
ldr r1,iAdrsBuffer @ buffer address
ldrb r0,[r1] @ load first character
100:
pop {r1-r7,lr}
bx lr @ return
/***************************************************/
/* Generation random number */
/***************************************************/
/* r0 contains limit */
genereraleas:
push {r1-r4,lr} @ save registers
ldr r4,iAdriGraine
ldr r2,[r4]
ldr r3,iNbDep1
mul r2,r3,r2
ldr r3,iNbDep2
add r2,r2,r3
str r2,[r4] @ maj de la graine pour l appel suivant
cmp r0,#0
beq 100f
add r1,r0,#1 @ divisor
mov r0,r2 @ dividende
bl division
mov r0,r3 @ résult = remainder
100: @ end function
pop {r1-r4,lr} @ restaur registers
bx lr @ return
/*****************************************************/
iAdriGraine: .int iGraine
iNbDep1: .int 0x343FD
iNbDep2: .int 0x269EC3
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"- Output:
New game (y/n) ? y The four digits are 8 3 9 1 and the score is 24. Solution : 8*9=72 3*1=3 72/3=24 New game (y/n) ? y The four digits are 7 7 9 4 and the score is 24. No solution for this problem !! New game (y/n) ? y The four digits are 3 5 8 9 and the score is 24. Solution : 3*9=27 8-5=3 27-3=24 New game (y/n) ?
AutoHotkey
Output is in RPN.
#NoEnv
InputBox, NNNN ; user input 4 digits
NNNN := RegExReplace(NNNN, "(\d)(?=\d)", "$1,") ; separate with commas for the sort command
sort NNNN, d`, ; sort in ascending order for the permutations to work
StringReplace NNNN, NNNN, `,, , All ; remove comma separators after sorting
ops := "+-*/"
patterns := [ "x x.x.x."
,"x x.x x.."
,"x x x..x."
,"x x x.x.."
,"x x x x..." ]
; build bruteforce operator list ("+++, ++-, ++* ... ///")
a := b := c := 0
While (++a<5){
While (++b<5){
While (++c<5){
l := SubStr(ops, a, 1) . SubStr(ops, b, 1) . SubStr(ops, c, 1)
; build bruteforce template ("x x+x+x+, x x+x x++ ... x x x x///")
For each, pattern in patterns
{
Loop 3
StringReplace, pattern, pattern, ., % SubStr(l, A_Index, 1)
pat .= pattern "`n"
}
}c := 0
}b := 0
}
StringTrimRight, pat, pat, 1 ; remove trailing newline
; permutate input. As the lexicographic algorithm is used, each permutation generated is unique
While NNNN
{
StringSplit, N, NNNN
; substitute numbers in for x's and evaluate
Loop Parse, pat, `n
{
eval := A_LoopField ; current line
Loop 4
StringReplace, eval, eval, x, % N%A_Index% ; substitute number for "x"
If Round(evalRPN(eval), 4) = 24
final .= eval "`n"
}
NNNN := perm_next(NNNN) ; next lexicographic permutation of user's digits
}
MsgBox % final ? clipboard := final : "No solution"
; simple stack-based evaluation. Integers only. Whitespace is used to push a value.
evalRPN(s){
stack := []
Loop Parse, s
If A_LoopField is number
t .= A_LoopField
else
{
If t
stack.Insert(t), t := ""
If InStr("+-/*", l := A_LoopField)
{
a := stack.Remove(), b := stack.Remove()
stack.Insert( l = "+" ? b + a
:l = "-" ? b - a
:l = "*" ? b * a
:l = "/" ? b / a
:0 )
}
}
return stack.Remove()
}
perm_Next(str){
p := 0, sLen := StrLen(str)
Loop % sLen
{
If A_Index=1
continue
t := SubStr(str, sLen+1-A_Index, 1)
n := SubStr(str, sLen+2-A_Index, 1)
If ( t < n )
{
p := sLen+1-A_Index, pC := SubStr(str, p, 1)
break
}
}
If !p
return false
Loop
{
t := SubStr(str, sLen+1-A_Index, 1)
If ( t > pC )
{
n := sLen+1-A_Index, nC := SubStr(str, n, 1)
break
}
}
return SubStr(str, 1, p-1) . nC . Reverse(SubStr(str, p+1, n-p-1) . pC . SubStr(str, n+1))
}
Reverse(s){
Loop Parse, s
o := A_LoopField o
return o
}
- Output:
for 1127
1 2+1 7+* 1 2+7 1+* 1 7+1 2+* 1 7+2 1+* 2 1+1 7+* 2 1+7 1+* 7 1+1 2+* 7 1+2 1+*
And for 8338:
8 3 8 3/-/
BBC BASIC
PROCsolve24("1234")
PROCsolve24("6789")
PROCsolve24("1127")
PROCsolve24("5566")
END
DEF PROCsolve24(s$)
LOCAL F%, I%, J%, K%, L%, P%, T%, X$, o$(), p$(), t$()
DIM o$(4), p$(24,4), t$(11)
o$() = "", "+", "-", "*", "/"
RESTORE
FOR T% = 1 TO 11
READ t$(T%)
NEXT
DATA "abcdefg", "(abc)defg", "ab(cde)fg", "abcd(efg)", "(abc)d(efg)", "(abcde)fg"
DATA "ab(cdefg)", "((abc)de)fg", "(ab(cde))fg", "ab((cde)fg)", "ab(cd(efg))"
FOR I% = 1 TO 4
FOR J% = 1 TO 4
FOR K% = 1 TO 4
FOR L% = 1 TO 4
IF I%<>J% IF J%<>K% IF K%<>L% IF I%<>K% IF J%<>L% IF I%<>L% THEN
P% += 1
p$(P%,1) = MID$(s$,I%,1)
p$(P%,2) = MID$(s$,J%,1)
p$(P%,3) = MID$(s$,K%,1)
p$(P%,4) = MID$(s$,L%,1)
ENDIF
NEXT
NEXT
NEXT
NEXT
FOR I% = 1 TO 4
FOR J% = 1 TO 4
FOR K% = 1 TO 4
FOR T% = 1 TO 11
FOR P% = 1 TO 24
X$ = t$(T%)
MID$(X$, INSTR(X$,"a"), 1) = p$(P%,1)
MID$(X$, INSTR(X$,"b"), 1) = o$(I%)
MID$(X$, INSTR(X$,"c"), 1) = p$(P%,2)
MID$(X$, INSTR(X$,"d"), 1) = o$(J%)
MID$(X$, INSTR(X$,"e"), 1) = p$(P%,3)
MID$(X$, INSTR(X$,"f"), 1) = o$(K%)
MID$(X$, INSTR(X$,"g"), 1) = p$(P%,4)
F% = TRUE : ON ERROR LOCAL F% = FALSE
IF F% IF EVAL(X$) = 24 THEN PRINT X$ : EXIT FOR I%
RESTORE ERROR
NEXT
NEXT
NEXT
NEXT
NEXT
IF I% > 4 PRINT "No solution found"
ENDPROC
- Output:
(1+2+3)*4 6*8/(9-7) (1+2)*(1+7) (5+5-6)*6
C
Tested with GCC 10.2.0, but should work with all versions supporting C99.
Provided code prints all solutions or nothing in case no solutions are found.
It can be modified or extended to work with more than 4 numbers, goals other than 24 and additional operations.
Note: This a brute-force approach with time complexity O(6n.n.(2n-3)!!) and recursion depth n.
#include <stdio.h>
typedef struct {int val, op, left, right;} Node;
Node nodes[10000];
int iNodes;
int b;
float eval(Node x){
if (x.op != -1){
float l = eval(nodes[x.left]), r = eval(nodes[x.right]);
switch(x.op){
case 0: return l+r;
case 1: return l-r;
case 2: return r-l;
case 3: return l*r;
case 4: return r?l/r:(b=1,0);
case 5: return l?r/l:(b=1,0);
}
}
else return x.val*1.;
}
void show(Node x){
if (x.op != -1){
printf("(");
switch(x.op){
case 0: show(nodes[x.left]); printf(" + "); show(nodes[x.right]); break;
case 1: show(nodes[x.left]); printf(" - "); show(nodes[x.right]); break;
case 2: show(nodes[x.right]); printf(" - "); show(nodes[x.left]); break;
case 3: show(nodes[x.left]); printf(" * "); show(nodes[x.right]); break;
case 4: show(nodes[x.left]); printf(" / "); show(nodes[x.right]); break;
case 5: show(nodes[x.right]); printf(" / "); show(nodes[x.left]); break;
}
printf(")");
}
else printf("%d", x.val);
}
int float_fix(float x){ return x < 0.00001 && x > -0.00001; }
void solutions(int a[], int n, float t, int s){
if (s == n){
b = 0;
float e = eval(nodes[0]);
if (!b && float_fix(e-t)){
show(nodes[0]);
printf("\n");
}
}
else{
nodes[iNodes++] = (typeof(Node)){a[s],-1,-1,-1};
for (int op = 0; op < 6; op++){
int k = iNodes-1;
for (int i = 0; i < k; i++){
nodes[iNodes++] = nodes[i];
nodes[i] = (typeof(Node)){-1,op,iNodes-1,iNodes-2};
solutions(a, n, t, s+1);
nodes[i] = nodes[--iNodes];
}
}
iNodes--;
}
};
int main(){
// define problem
int a[4] = {8, 3, 8, 3};
float t = 24;
// print all solutions
nodes[0] = (typeof(Node)){a[0],-1,-1,-1};
iNodes = 1;
solutions(a, sizeof(a)/sizeof(int), t, 1);
return 0;
}
C++
This code may be extended to work with more than 4 numbers, goals other than 24, or different digit ranges. Operations have been manually determined for these parameters, with the belief they are complete.
#include <iostream>
#include <ratio>
#include <array>
#include <algorithm>
#include <random>
typedef short int Digit; // Typedef for the digits data type.
constexpr Digit nDigits{4}; // Amount of digits that are taken into the game.
constexpr Digit maximumDigit{9}; // Maximum digit that may be taken into the game.
constexpr short int gameGoal{24}; // Desired result.
typedef std::array<Digit, nDigits> digitSet; // Typedef for the set of digits in the game.
digitSet d;
void printTrivialOperation(std::string operation) { // Prints a commutative operation taking all the digits.
bool printOperation(false);
for(const Digit& number : d) {
if(printOperation)
std::cout << operation;
else
printOperation = true;
std::cout << number;
}
std::cout << std::endl;
}
void printOperation(std::string prefix, std::string operation1, std::string operation2, std::string operation3, std::string suffix = "") {
std::cout << prefix << d[0] << operation1 << d[1] << operation2 << d[2] << operation3 << d[3] << suffix << std::endl;
}
int main() {
std::mt19937_64 randomGenerator;
std::uniform_int_distribution<Digit> digitDistro{1, maximumDigit};
// Let us set up a number of trials:
for(int trial{10}; trial; --trial) {
for(Digit& digit : d) {
digit = digitDistro(randomGenerator);
std::cout << digit << " ";
}
std::cout << std::endl;
std::sort(d.begin(), d.end());
// We start with the most trivial, commutative operations:
if(std::accumulate(d.cbegin(), d.cend(), 0) == gameGoal)
printTrivialOperation(" + ");
if(std::accumulate(d.cbegin(), d.cend(), 1, std::multiplies<Digit>{}) == gameGoal)
printTrivialOperation(" * ");
// Now let's start working on every permutation of the digits.
do {
// Operations with 2 symbols + and one symbol -:
if(d[0] + d[1] + d[2] - d[3] == gameGoal) printOperation("", " + ", " + ", " - "); // If gameGoal is ever changed to a smaller value, consider adding more operations in this category.
// Operations with 2 symbols + and one symbol *:
if(d[0] * d[1] + d[2] + d[3] == gameGoal) printOperation("", " * ", " + ", " + ");
if(d[0] * (d[1] + d[2]) + d[3] == gameGoal) printOperation("", " * ( ", " + ", " ) + ");
if(d[0] * (d[1] + d[2] + d[3]) == gameGoal) printOperation("", " * ( ", " + ", " + ", " )");
// Operations with one symbol + and 2 symbols *:
if((d[0] * d[1] * d[2]) + d[3] == gameGoal) printOperation("( ", " * ", " * ", " ) + ");
if(d[0] * d[1] * (d[2] + d[3]) == gameGoal) printOperation("( ", " * ", " * ( ", " + ", " )");
if((d[0] * d[1]) + (d[2] * d[3]) == gameGoal) printOperation("( ", " * ", " ) + ( ", " * ", " )");
// Operations with one symbol - and 2 symbols *:
if((d[0] * d[1] * d[2]) - d[3] == gameGoal) printOperation("( ", " * ", " * ", " ) - ");
if(d[0] * d[1] * (d[2] - d[3]) == gameGoal) printOperation("( ", " * ", " * ( ", " - ", " )");
if((d[0] * d[1]) - (d[2] * d[3]) == gameGoal) printOperation("( ", " * ", " ) - ( ", " * ", " )");
// Operations with one symbol +, one symbol *, and one symbol -:
if(d[0] * d[1] + d[2] - d[3] == gameGoal) printOperation("", " * ", " + ", " - ");
if(d[0] * (d[1] + d[2]) - d[3] == gameGoal) printOperation("", " * ( ", " + ", " ) - ");
if(d[0] * (d[1] - d[2]) + d[3] == gameGoal) printOperation("", " * ( ", " - ", " ) + ");
if(d[0] * (d[1] + d[2] - d[3]) == gameGoal) printOperation("", " * ( ", " + ", " - ", " )");
if(d[0] * d[1] - (d[2] + d[3]) == gameGoal) printOperation("", " * ", " - ( ", " + ", " )");
// Operations with one symbol *, one symbol /, one symbol +:
if(d[0] * d[1] == (gameGoal - d[3]) * d[2]) printOperation("( ", " * ", " / ", " ) + ");
if(((d[0] * d[1]) + d[2]) == gameGoal * d[3]) printOperation("(( ", " * ", " ) + ", " ) / ");
if((d[0] + d[1]) * d[2] == gameGoal * d[3]) printOperation("(( ", " + ", " ) * ", " ) / ");
if(d[0] * d[1] == gameGoal * (d[2] + d[3])) printOperation("( ", " * ", " ) / ( ", " + ", " )");
// Operations with one symbol *, one symbol /, one symbol -:
if(d[0] * d[1] == (gameGoal + d[3]) * d[2]) printOperation("( ", " * ", " / ", " ) - ");
if(((d[0] * d[1]) - d[2]) == gameGoal * d[3]) printOperation("(( ", " * ", " ) - ", " ) / ");
if((d[0] - d[1]) * d[2] == gameGoal * d[3]) printOperation("(( ", " - ", " ) * ", " ) / ");
if(d[0] * d[1] == gameGoal * (d[2] - d[3])) printOperation("( ", " * ", " ) / ( ", " - ", " )");
// Operations with 2 symbols *, one symbol /:
if(d[0] * d[1] * d[2] == gameGoal * d[3]) printOperation("", " * ", " * ", " / ");
if(d[0] * d[1] == gameGoal * d[2] * d[3]) printOperation("", " * ", " / ( ", " * ", " )");
// Operations with 2 symbols /, one symbol -:
if(d[0] * d[3] == gameGoal * (d[1] * d[3] - d[2])) printOperation("", " / ( ", " - ", " / ", " )");
// Operations with 2 symbols /, one symbol *:
if(d[0] * d[1] == gameGoal * d[2] * d[3]) printOperation("( ", " * ", " / ", " ) / ", "");
} while(std::next_permutation(d.begin(), d.end())); // All operations are repeated for all possible permutations of the numbers.
}
return 0;
}
- Output:
8 3 7 9 3 * ( 7 + 9 - 8 ) 3 * ( 9 + 7 - 8 ) 1 4 3 1 ( 3 * 4 * ( 1 + 1 ) ( 4 * 3 * ( 1 + 1 ) 5 4 3 6 6 * ( 3 + 5 - 4 ) 6 * ( 5 + 3 - 4 ) 2 5 5 8 5 4 7 3 3 * 4 + 5 + 7 3 * 4 + 7 + 5 ( 3 * 4 * ( 7 - 5 ) 3 * ( 5 + 7 - 4 ) 3 * ( 7 + 5 - 4 ) 4 * 3 + 5 + 7 4 * 3 + 7 + 5 ( 4 * 3 * ( 7 - 5 ) 4 * 5 + 7 - 3 5 * 4 + 7 - 3 5 * ( 7 - 3 ) + 4 3 3 9 2 2 * 9 + 3 + 3 3 * ( 2 + 3 ) + 9 3 * ( 2 + 9 - 3 ) 3 * ( 3 + 2 ) + 9 3 * ( 9 - 2 ) + 3 3 * ( 9 + 2 - 3 ) 9 * 2 + 3 + 3 3 2 7 9 3 * ( 7 - 2 ) + 9 (( 7 + 9 ) * 3 ) / 2 (( 9 + 7 ) * 3 ) / 2 7 1 5 3 7 6 9 4 (( 7 + 9 ) * 6 ) / 4 (( 9 + 7 ) * 6 ) / 4 3 5 3 1 ( 1 * 3 * ( 3 + 5 ) ( 1 * 3 * ( 5 + 3 ) ( 3 * 1 * ( 3 + 5 ) ( 3 * 1 * ( 5 + 3 ) (( 3 + 5 ) * 3 ) / 1 (( 5 + 3 ) * 3 ) / 1
C#
Generate binary trees -> generate permutations -> create expression -> evaluate expression
This works with other targets and more numbers but it will of course become slower.
Redundant expressions are filtered out (based on https://www.4nums.com/theory/) but I'm not sure I caught them all.
using System;
using System.Collections.Generic;
using static System.Linq.Enumerable;
public static class Solve24Game
{
public static void Main2() {
var testCases = new [] {
new [] { 1,1,2,7 },
new [] { 1,2,3,4 },
new [] { 1,2,4,5 },
new [] { 1,2,7,7 },
new [] { 1,4,5,6 },
new [] { 3,3,8,8 },
new [] { 4,4,5,9 },
new [] { 5,5,5,5 },
new [] { 5,6,7,8 },
new [] { 6,6,6,6 },
new [] { 6,7,8,9 },
};
foreach (var t in testCases) Test(24, t);
Test(100, 9,9,9,9,9,9);
static void Test(int target, params int[] numbers) {
foreach (var eq in GenerateEquations(target, numbers)) Console.WriteLine(eq);
Console.WriteLine();
}
}
static readonly char[] ops = { '*', '/', '+', '-' };
public static IEnumerable<string> GenerateEquations(int target, params int[] numbers) {
var operators = Repeat(ops, numbers.Length - 1).CartesianProduct().Select(e => e.ToArray()).ToList();
return (
from pattern in Patterns(numbers.Length)
let expression = CreateExpression(pattern)
from ops in operators
where expression.WithOperators(ops).HasPreferredTree()
from permutation in Permutations(numbers)
let expr = expression.WithValues(permutation)
where expr.Value == target && expr.HasPreferredValues()
select $"{expr.ToString()} = {target}")
.Distinct()
.DefaultIfEmpty($"Cannot make {target} with {string.Join(", ", numbers)}");
}
///<summary>Generates postfix expression trees where 1's represent operators and 0's represent numbers.</summary>
static IEnumerable<int> Patterns(int length) {
if (length == 1) yield return 0; //0
if (length == 2) yield return 1; //001
if (length < 3) yield break;
//Of each tree, the first 2 bits must always be 0 and the last bit must be 1. Generate the bits in between.
length -= 2;
int len = length * 2 + 3;
foreach (int permutation in BinaryPatterns(length, length * 2)) {
(int p, int l) = ((permutation << 1) + 1, len);
if (IsValidPattern(ref p, ref l)) yield return (permutation << 1) + 1;
}
}
///<summary>Generates all numbers with the given number of 1's and total length.</summary>
static IEnumerable<int> BinaryPatterns(int ones, int length) {
int initial = (1 << ones) - 1;
int blockMask = (1 << length) - 1;
for (int v = initial; v >= initial; ) {
yield return v;
int w = (v | (v - 1)) + 1;
w |= (((w & -w) / (v & -v)) >> 1) - 1;
v = w & blockMask;
}
}
static bool IsValidPattern(ref int pattern, ref int len) {
bool isNumber = (pattern & 1) == 0;
pattern >>= 1;
len--;
if (isNumber) return true;
IsValidPattern(ref pattern, ref len);
IsValidPattern(ref pattern, ref len);
return len == 0;
}
static Expr CreateExpression(int pattern) {
return Create();
Expr Create() {
bool isNumber = (pattern & 1) == 0;
pattern >>= 1;
if (isNumber) return new Const(0);
Expr right = Create();
Expr left = Create();
return new Binary('*', left, right);
}
}
static IEnumerable<IEnumerable<T>> CartesianProduct<T>(this IEnumerable<IEnumerable<T>> sequences) {
IEnumerable<IEnumerable<T>> emptyProduct = new[] { Empty<T>() };
return sequences.Aggregate(
emptyProduct,
(accumulator, sequence) =>
from acc in accumulator
from item in sequence
select acc.Concat(new [] { item }));
}
private static List<int> helper = new List<int>();
public static IEnumerable<T[]> Permutations<T>(params T[] input) {
if (input == null || input.Length == 0) yield break;
helper.Clear();
for (int i = 0; i < input.Length; i++) helper.Add(i);
while (true) {
yield return input;
int cursor = helper.Count - 2;
while (cursor >= 0 && helper[cursor] > helper[cursor + 1]) cursor--;
if (cursor < 0) break;
int i = helper.Count - 1;
while (i > cursor && helper[i] < helper[cursor]) i--;
(helper[cursor], helper[i]) = (helper[i], helper[cursor]);
(input[cursor], input[i]) = (input[i], input[cursor]);
int firstIndex = cursor + 1;
for (int lastIndex = helper.Count - 1; lastIndex > firstIndex; ++firstIndex, --lastIndex) {
(helper[firstIndex], helper[lastIndex]) = (helper[lastIndex], helper[firstIndex]);
(input[firstIndex], input[lastIndex]) = (input[lastIndex], input[firstIndex]);
}
}
}
static Expr WithOperators(this Expr expr, char[] operators) {
int i = 0;
SetOperators(expr, operators, ref i);
return expr;
static void SetOperators(Expr expr, char[] operators, ref int i) {
if (expr is Binary b) {
b.Symbol = operators[i++];
SetOperators(b.Right, operators, ref i);
SetOperators(b.Left, operators, ref i);
}
}
}
static Expr WithValues(this Expr expr, int[] values) {
int i = 0;
SetValues(expr, values, ref i);
return expr;
static void SetValues(Expr expr, int[] values, ref int i) {
if (expr is Binary b) {
SetValues(b.Left, values, ref i);
SetValues(b.Right, values, ref i);
} else {
expr.Value = values[i++];
}
}
}
static bool HasPreferredTree(this Expr expr) => expr switch {
Const _ => true,
// a / b * c => a * c / b
((_, '/' ,_), '*', _) => false,
// c + a * b => a * b + c
(var l, '+', (_, '*' ,_) r) when l.Depth < r.Depth => false,
// c + a / b => a / b + c
(var l, '+', (_, '/' ,_) r) when l.Depth < r.Depth => false,
// a * (b + c) => (b + c) * a
(var l, '*', (_, '+' ,_) r) when l.Depth < r.Depth => false,
// a * (b - c) => (b - c) * a
(var l, '*', (_, '-' ,_) r) when l.Depth < r.Depth => false,
// (a +- b) + (c */ d) => ((c */ d) + a) +- b
((_, var p, _), '+', (_, var q, _)) when "+-".Contains(p) && "*/".Contains(q) => false,
// a + (b + c) => (a + b) + c
(var l, '+', (_, '+' ,_) r) => false,
// a + (b - c) => (a + b) - c
(var l, '+', (_, '-' ,_) r) => false,
// a - (b + c) => (a - b) + c
(_, '-', (_, '+', _)) => false,
// a * (b * c) => (a * b) * c
(var l, '*', (_, '*' ,_) r) => false,
// a * (b / c) => (a * b) / c
(var l, '*', (_, '/' ,_) r) => false,
// a / (b / c) => (a * c) / b
(var l, '/', (_, '/' ,_) r) => false,
// a - (b - c) * d => (c - b) * d + a
(_, '-', ((_, '-' ,_), '*', _)) => false,
// a - (b - c) / d => (c - b) / d + a
(_, '-', ((_, '-' ,_), '/', _)) => false,
// a - (b - c) => a + c - b
(_, '-', (_, '-', _)) => false,
// (a - b) + c => (a + c) - b
((_, '-', var b), '+', var c) => false,
(var l, _, var r) => l.HasPreferredTree() && r.HasPreferredTree()
};
static bool HasPreferredValues(this Expr expr) => expr switch {
Const _ => true,
// -a + b => b - a
(var l, '+', var r) when l.Value < 0 && r.Value >= 0 => false,
// b * a => a * b
(var l, '*', var r) when l.Depth == r.Depth && l.Value > r.Value => false,
// b + a => a + b
(var l, '+', var r) when l.Depth == r.Depth && l.Value > r.Value => false,
// (b o c) * (a o d) => (a o d) * (b o c)
((var a, _, _) l, '*', (var c, _, _) r) when l.Value == r.Value && l.Depth == r.Depth && a.Value < c.Value => false,
// (b o c) + (a o d) => (a o d) + (b o c)
((var a, var p, _) l, '+', (var c, var q, _) r) when l.Value == r.Value && l.Depth == r.Depth && a.Value < c.Value => false,
// (a * c) * b => (a * b) * c
((_, '*', var c), '*', var b) when b.Value < c.Value => false,
// (a + c) + b => (a + b) + c
((_, '+', var c), '+', var b) when b.Value < c.Value => false,
// (a - b) - c => (a - c) - b
((_, '-', var b), '-', var c) when b.Value < c.Value => false,
// a / 1 => a * 1
(_, '/', var b) when b.Value == 1 => false,
// a * b / b => a + b - b
((_, '*', var b), '/', var c) when b.Value == c.Value => false,
// a * 1 * 1 => a + 1 - 1
((_, '*', var b), '*', var c) when b.Value == 1 && c.Value == 1 => false,
(var l, _, var r) => l.HasPreferredValues() && r.HasPreferredValues()
};
private struct Fraction : IEquatable<Fraction>, IComparable<Fraction>
{
public readonly int Numerator, Denominator;
public Fraction(int numerator, int denominator)
=> (Numerator, Denominator) = (numerator, denominator) switch
{
(_, 0) => (Math.Sign(numerator), 0),
(0, _) => (0, 1),
(_, var d) when d < 0 => (-numerator, -denominator),
_ => (numerator, denominator)
};
public static implicit operator Fraction(int i) => new Fraction(i, 1);
public static Fraction operator +(Fraction a, Fraction b) =>
new Fraction(a.Numerator * b.Denominator + a.Denominator * b.Numerator, a.Denominator * b.Denominator);
public static Fraction operator -(Fraction a, Fraction b) =>
new Fraction(a.Numerator * b.Denominator + a.Denominator * -b.Numerator, a.Denominator * b.Denominator);
public static Fraction operator *(Fraction a, Fraction b) =>
new Fraction(a.Numerator * b.Numerator, a.Denominator * b.Denominator);
public static Fraction operator /(Fraction a, Fraction b) =>
new Fraction(a.Numerator * b.Denominator, a.Denominator * b.Numerator);
public static bool operator ==(Fraction a, Fraction b) => a.CompareTo(b) == 0;
public static bool operator !=(Fraction a, Fraction b) => a.CompareTo(b) != 0;
public static bool operator <(Fraction a, Fraction b) => a.CompareTo(b) < 0;
public static bool operator >(Fraction a, Fraction b) => a.CompareTo(b) > 0;
public static bool operator <=(Fraction a, Fraction b) => a.CompareTo(b) <= 0;
public static bool operator >=(Fraction a, Fraction b) => a.CompareTo(b) >= 0;
public bool Equals(Fraction other) => Numerator == other.Numerator && Denominator == other.Denominator;
public override string ToString() => Denominator == 1 ? Numerator.ToString() : $"[{Numerator}/{Denominator}]";
public int CompareTo(Fraction other) => (Numerator, Denominator, other.Numerator, other.Denominator) switch {
var ( n1, d1, n2, d2) when n1 == n2 && d1 == d2 => 0,
( 0, 0, _, _) => (-1),
( _, _, 0, 0) => 1,
var ( n1, d1, n2, d2) when d1 == d2 => n1.CompareTo(n2),
(var n1, 0, _, _) => Math.Sign(n1),
( _, _, var n2, 0) => Math.Sign(n2),
var ( n1, d1, n2, d2) => (n1 * d2).CompareTo(n2 * d1)
};
}
private abstract class Expr
{
protected Expr(char symbol) => Symbol = symbol;
public char Symbol { get; set; }
public abstract Fraction Value { get; set; }
public abstract int Depth { get; }
public abstract void Deconstruct(out Expr left, out char symbol, out Expr right);
}
private sealed class Const : Expr
{
public Const(Fraction value) : base('c') => Value = value;
public override Fraction Value { get; set; }
public override int Depth => 0;
public override void Deconstruct(out Expr left, out char symbol, out Expr right) => (left, symbol, right) = (this, Symbol, this);
public override string ToString() => Value.ToString();
}
private sealed class Binary : Expr
{
public Binary(char symbol, Expr left, Expr right) : base(symbol) => (Left, Right) = (left, right);
public Expr Left { get; }
public Expr Right { get; }
public override int Depth => Math.Max(Left.Depth, Right.Depth) + 1;
public override void Deconstruct(out Expr left, out char symbol, out Expr right) => (left, symbol, right) = (Left, Symbol, Right);
public override Fraction Value {
get => Symbol switch {
'*' => Left.Value * Right.Value,
'/' => Left.Value / Right.Value,
'+' => Left.Value + Right.Value,
'-' => Left.Value - Right.Value,
_ => throw new InvalidOperationException() };
set {}
}
public override string ToString() => Symbol switch {
'*' => ToString("+-".Contains(Left.Symbol), "+-".Contains(Right.Symbol)),
'/' => ToString("+-".Contains(Left.Symbol), "*/+-".Contains(Right.Symbol)),
'+' => ToString(false, false),
'-' => ToString(false, "+-".Contains(Right.Symbol)),
_ => $"[{Value}]"
};
private string ToString(bool wrapLeft, bool wrapRight) =>
$"{(wrapLeft ? $"({Left})" : $"{Left}")} {Symbol} {(wrapRight ? $"({Right})" : $"{Right}")}";
}
}
- Output:
(1 + 2) * (1 + 7) = 24 (1 + 3) * (2 + 4) = 24 1 * 2 * 3 * 4 = 24 (1 + 2 + 3) * 4 = 24 (5 - 1) * (2 + 4) = 24 (2 + 5 - 1) * 4 = 24 (7 * 7 - 1) / 2 = 24 4 / (1 - 5 / 6) = 24 6 / (5 / 4 - 1) = 24 8 / (3 - 8 / 3) = 24 Cannot make 24 with 4, 4, 5, 9 5 * 5 - 5 / 5 = 24 (8 - 6) * (5 + 7) = 24 6 * 8 / (7 - 5) = 24 (5 + 7 - 8) * 6 = 24 6 + 6 + 6 + 6 = 24 6 * 6 - 6 - 6 = 24 6 * 8 / (9 - 7) = 24 (9 / 9 + 9) * (9 / 9 + 9) = 100
Ceylon
Don't forget to import ceylon.random in your module.ceylon file.
import ceylon.random {
DefaultRandom
}
shared sealed class Rational(numerator, denominator = 1) satisfies Numeric<Rational> {
shared Integer numerator;
shared Integer denominator;
Integer gcd(Integer a, Integer b) => if (b == 0) then a else gcd(b, a % b);
shared Rational inverted => Rational(denominator, numerator);
shared Rational simplified =>
let (largestFactor = gcd(numerator, denominator))
Rational(numerator / largestFactor, denominator / largestFactor);
divided(Rational other) => (this * other.inverted).simplified;
negated => Rational(-numerator, denominator).simplified;
plus(Rational other) =>
let (top = numerator*other.denominator + other.numerator*denominator,
bottom = denominator * other.denominator)
Rational(top, bottom).simplified;
times(Rational other) =>
Rational(numerator * other.numerator, denominator * other.denominator).simplified;
shared Integer integer => numerator / denominator;
shared Float float => numerator.float / denominator.float;
string => denominator == 1 then numerator.string else "``numerator``/``denominator``";
shared actual Boolean equals(Object that) {
if (is Rational that) {
value simplifiedThis = this.simplified;
value simplifiedThat = that.simplified;
return simplifiedThis.numerator==simplifiedThat.numerator &&
simplifiedThis.denominator==simplifiedThat.denominator;
} else {
return false;
}
}
}
shared Rational? rational(Integer numerator, Integer denominator = 1) =>
if (denominator == 0)
then null
else Rational(numerator, denominator).simplified;
shared Rational numeratorOverOne(Integer numerator) => Rational(numerator);
shared abstract class Operation(String lexeme) of addition | subtraction | multiplication | division {
shared formal Rational perform(Rational left, Rational right);
string => lexeme;
}
shared object addition extends Operation("+") {
perform(Rational left, Rational right) => left + right;
}
shared object subtraction extends Operation("-") {
perform(Rational left, Rational right) => left - right;
}
shared object multiplication extends Operation("*") {
perform(Rational left, Rational right) => left * right;
}
shared object division extends Operation("/") {
perform(Rational left, Rational right) => left / right;
}
shared Operation[] operations = `Operation`.caseValues;
shared interface Expression of NumberExpression | OperationExpression {
shared formal Rational evaluate();
}
shared class NumberExpression(Rational number) satisfies Expression {
evaluate() => number;
string => number.string;
}
shared class OperationExpression(Expression left, Operation op, Expression right) satisfies Expression {
evaluate() => op.perform(left.evaluate(), right.evaluate());
string => "(``left`` ``op`` ``right``)";
}
shared void run() {
value twentyfour = numeratorOverOne(24);
value random = DefaultRandom();
function buildExpressions({Rational*} numbers, Operation* ops) {
assert (is NumberExpression[4] numTuple = numbers.collect(NumberExpression).tuple());
assert (is Operation[3] opTuple = ops.sequence().tuple());
value [a, b, c, d] = numTuple;
value [op1, op2, op3] = opTuple;
value opExp = OperationExpression; // this is just to give it a shorter name
return [
opExp(opExp(opExp(a, op1, b), op2, c), op3, d),
opExp(opExp(a, op1, opExp(b, op2, c)), op3, d),
opExp(a, op1, opExp(opExp(b, op2, c), op3, d)),
opExp(a, op1, opExp(b, op2, opExp(c, op3, d)))
];
}
print("Please enter your 4 numbers to see how they form 24 or enter the letter r for random numbers.");
if (exists line = process.readLine()) {
Rational[] chosenNumbers;
if (line.trimmed.uppercased == "R") {
chosenNumbers = random.elements(1..9).take(4).collect((Integer element) => numeratorOverOne(element));
print("The random numbers are ``chosenNumbers``");
} else {
chosenNumbers = line.split().map(Integer.parse).narrow<Integer>().collect(numeratorOverOne);
}
value expressions = {
for (numbers in chosenNumbers.permutations)
for (op1 in operations)
for (op2 in operations)
for (op3 in operations)
for (exp in buildExpressions(numbers, op1, op2, op3))
if (exp.evaluate() == twentyfour)
exp
};
print("The solutions are:");
expressions.each(print);
}
}
Clojure
(ns rosettacode.24game.solve
(:require [clojure.math.combinatorics :as c]
[clojure.walk :as w]))
(def ^:private op-maps
(map #(zipmap [:o1 :o2 :o3] %) (c/selections '(* + - /) 3)))
(def ^:private patterns '(
(:o1 (:o2 :n1 :n2) (:o3 :n3 :n4))
(:o1 :n1 (:o2 :n2 (:o3 :n3 :n4)))
(:o1 (:o2 (:o3 :n1 :n2) :n3) :n4)))
(defn play24 [& digits]
{:pre (and (every? #(not= 0 %) digits)
(= (count digits) 4))}
(->> (for [:let [digit-maps
(->> digits sort c/permutations
(map #(zipmap [:n1 :n2 :n3 :n4] %)))]
om op-maps, dm digit-maps]
(w/prewalk-replace dm
(w/prewalk-replace om patterns)))
(filter #(= (eval %) 24))
(map println)
doall
count))
The function play24 works by substituting the given digits and the four operations into the binary tree patterns (o (o n n) (o n n)), (o (o (o n n) n) n), and (o n (o n (o n n))).
The substitution is the complex part of the program: two pairs of nested maps (the function) are used to substitute in operations and digits, which are replaced into the tree patterns.
COBOL
>>SOURCE FORMAT FREE
*> This code is dedicated to the public domain
*> This is GNUCobol 2.0
identification division.
program-id. twentyfoursolve.
environment division.
configuration section.
repository. function all intrinsic.
input-output section.
file-control.
select count-file
assign to count-file-name
file status count-file-status
organization line sequential.
data division.
file section.
fd count-file.
01 count-record pic x(7).
working-storage section.
01 count-file-name pic x(64) value 'solutioncounts'.
01 count-file-status pic xx.
01 command-area.
03 nd pic 9.
03 number-definition.
05 n occurs 4 pic 9.
03 number-definition-9 redefines number-definition
pic 9(4).
03 command-input pic x(16).
03 command pic x(5).
03 number-count pic 9999.
03 l1 pic 99.
03 l2 pic 99.
03 expressions pic zzz,zzz,zz9.
01 number-validation.
03 px pic 99.
03 permutations value
'1234'
& '1243'
& '1324'
& '1342'
& '1423'
& '1432'
& '2134'
& '2143'
& '2314'
& '2341'
& '2413'
& '2431'
& '3124'
& '3142'
& '3214'
& '3241'
& '3423'
& '3432'
& '4123'
& '4132'
& '4213'
& '4231'
& '4312'
& '4321'.
05 permutation occurs 24 pic x(4).
03 cpx pic 9.
03 current-permutation pic x(4).
03 od1 pic 9.
03 od2 pic 9.
03 od3 pic 9.
03 operator-definitions pic x(4) value '+-*/'.
03 cox pic 9.
03 current-operators pic x(3).
03 rpn-forms value
'nnonono'
& 'nnonnoo'
& 'nnnonoo'
& 'nnnoono'
& 'nnnnooo'.
05 rpn-form occurs 5 pic x(7).
03 rpx pic 9.
03 current-rpn-form pic x(7).
01 calculation-area.
03 oqx pic 99.
03 output-queue pic x(7).
03 work-number pic s9999.
03 top-numerator pic s9999 sign leading separate.
03 top-denominator pic s9999 sign leading separate.
03 rsx pic 9.
03 result-stack occurs 8.
05 numerator pic s9999.
05 denominator pic s9999.
03 divide-by-zero-error pic x.
01 totals.
03 s pic 999.
03 s-lim pic 999 value 600.
03 s-max pic 999 value 0.
03 solution occurs 600 pic x(7).
03 sc pic 999.
03 sc1 pic 999.
03 sc2 pic 9.
03 sc-max pic 999 value 0.
03 sc-lim pic 999 value 600.
03 solution-counts value zeros.
05 solution-count occurs 600 pic 999.
03 ns pic 9999.
03 ns-max pic 9999 value 0.
03 ns-lim pic 9999 value 6561.
03 number-solutions occurs 6561.
05 ns-number pic x(4).
05 ns-count pic 999.
03 record-counts pic 9999.
03 total-solutions pic 9999.
01 infix-area.
03 i pic 9.
03 i-s pic 9.
03 i-s1 pic 9.
03 i-work pic x(16).
03 i-stack occurs 7 pic x(13).
procedure division.
start-twentyfoursolve.
display 'start twentyfoursolve'
perform display-instructions
perform get-command
perform until command-input = spaces
display space
initialize command number-count
unstring command-input delimited by all space
into command number-count
move command-input to number-definition
move spaces to command-input
evaluate command
when 'h'
when 'help'
perform display-instructions
when 'list'
if ns-max = 0
perform load-solution-counts
end-if
perform list-counts
when 'show'
if ns-max = 0
perform load-solution-counts
end-if
perform show-numbers
when other
if number-definition-9 not numeric
display 'invalid number'
else
perform get-solutions
perform display-solutions
end-if
end-evaluate
if command-input = spaces
perform get-command
end-if
end-perform
display 'exit twentyfoursolve'
stop run
.
display-instructions.
display space
display 'enter a number <n> as four integers from 1-9 to see its solutions'
display 'enter list to see counts of solutions for all numbers'
display 'enter show <n> to see numbers having <n> solutions'
display '<enter> ends the program'
.
get-command.
display space
move spaces to command-input
display '(h for help)?' with no advancing
accept command-input
.
ask-for-more.
display space
move 0 to l1
add 1 to l2
if l2 = 10
display 'more (<enter>)?' with no advancing
accept command-input
move 0 to l2
end-if
.
list-counts.
add 1 to sc-max giving sc
display 'there are ' sc ' solution counts'
display space
display 'solutions/numbers'
move 0 to l1
move 0 to l2
perform varying sc from 1 by 1 until sc > sc-max
or command-input <> spaces
if solution-count(sc) > 0
subtract 1 from sc giving sc1 *> offset to capture zero counts
display sc1 '/' solution-count(sc) space with no advancing
add 1 to l1
if l1 = 8
perform ask-for-more
end-if
end-if
end-perform
if l1 > 0
display space
end-if
.
show-numbers. *> with number-count solutions
add 1 to number-count giving sc1 *> offset for zero count
evaluate true
when number-count >= sc-max
display 'no number has ' number-count ' solutions'
exit paragraph
when solution-count(sc1) = 1 and number-count = 1
display '1 number has 1 solution'
when solution-count(sc1) = 1
display '1 number has ' number-count ' solutions'
when number-count = 1
display solution-count(sc1) ' numbers have 1 solution'
when other
display solution-count(sc1) ' numbers have ' number-count ' solutions'
end-evaluate
display space
move 0 to l1
move 0 to l2
perform varying ns from 1 by 1 until ns > ns-max
or command-input <> spaces
if ns-count(ns) = number-count
display ns-number(ns) space with no advancing
add 1 to l1
if l1 = 14
perform ask-for-more
end-if
end-if
end-perform
if l1 > 0
display space
end-if
.
display-solutions.
evaluate s-max
when 0 display number-definition ' has no solutions'
when 1 display number-definition ' has 1 solution'
when other display number-definition ' has ' s-max ' solutions'
end-evaluate
display space
move 0 to l1
move 0 to l2
perform varying s from 1 by 1 until s > s-max
or command-input <> spaces
*> convert rpn solution(s) to infix
move 0 to i-s
perform varying i from 1 by 1 until i > 7
if solution(s)(i:1) >= '1' and <= '9'
add 1 to i-s
move solution(s)(i:1) to i-stack(i-s)
else
subtract 1 from i-s giving i-s1
move spaces to i-work
string '(' i-stack(i-s1) solution(s)(i:1) i-stack(i-s) ')'
delimited by space into i-work
move i-work to i-stack(i-s1)
subtract 1 from i-s
end-if
end-perform
display solution(s) space i-stack(1) space space with no advancing
add 1 to l1
if l1 = 3
perform ask-for-more
end-if
end-perform
if l1 > 0
display space
end-if
.
load-solution-counts.
move 0 to ns-max *> numbers and their solution count
move 0 to sc-max *> solution counts
move spaces to count-file-status
open input count-file
if count-file-status <> '00'
perform create-count-file
move 0 to ns-max *> numbers and their solution count
move 0 to sc-max *> solution counts
open input count-file
end-if
read count-file
move 0 to record-counts
move zeros to solution-counts
perform until count-file-status <> '00'
add 1 to record-counts
perform increment-ns-max
move count-record to number-solutions(ns-max)
add 1 to ns-count(ns-max) giving sc *> offset 1 for zero counts
if sc > sc-lim
display 'sc ' sc ' exceeds sc-lim ' sc-lim
stop run
end-if
if sc > sc-max
move sc to sc-max
end-if
add 1 to solution-count(sc)
read count-file
end-perform
close count-file
.
create-count-file.
open output count-file
display 'Counting solutions for all numbers'
display 'We will examine 9*9*9*9 numbers'
display 'For each number we will examine 4! permutations of the digits'
display 'For each permutation we will examine 4*4*4 combinations of operators'
display 'For each permutation and combination we will examine 5 rpn forms'
display 'We will count the number of unique solutions for the given number'
display 'Each number and its counts will be written to file ' trim(count-file-name)
compute expressions = 9*9*9*9*factorial(4)*4*4*4*5
display 'So we will evaluate ' trim(expressions) ' statements'
display 'This will take a few minutes'
display 'In the future if ' trim(count-file-name) ' exists, this step will be bypassed'
move 0 to record-counts
move 0 to total-solutions
perform varying n(1) from 1 by 1 until n(1) = 0
perform varying n(2) from 1 by 1 until n(2) = 0
display n(1) n(2) '..' *> show progress
perform varying n(3) from 1 by 1 until n(3) = 0
perform varying n(4) from 1 by 1 until n(4) = 0
perform get-solutions
perform increment-ns-max
move number-definition to ns-number(ns-max)
move s-max to ns-count(ns-max)
move number-solutions(ns-max) to count-record
write count-record
add s-max to total-solutions
add 1 to record-counts
add 1 to ns-count(ns-max) giving sc *> offset by 1 for zero counts
if sc > sc-lim
display 'error: ' sc ' solution count exceeds ' sc-lim
stop run
end-if
add 1 to solution-count(sc)
end-perform
end-perform
end-perform
end-perform
close count-file
display record-counts ' numbers and counts written to ' trim(count-file-name)
display total-solutions ' total solutions'
display space
.
increment-ns-max.
if ns-max >= ns-lim
display 'error: numbers exceeds ' ns-lim
stop run
end-if
add 1 to ns-max
.
get-solutions.
move 0 to s-max
perform varying px from 1 by 1 until px > 24
move permutation(px) to current-permutation
perform varying od1 from 1 by 1 until od1 > 4
move operator-definitions(od1:1) to current-operators(1:1)
perform varying od2 from 1 by 1 until od2 > 4
move operator-definitions(od2:1) to current-operators(2:1)
perform varying od3 from 1 by 1 until od3 > 4
move operator-definitions(od3:1) to current-operators(3:1)
perform varying rpx from 1 by 1 until rpx > 5
move rpn-form(rpx) to current-rpn-form
move 0 to cpx cox
move spaces to output-queue
perform varying oqx from 1 by 1 until oqx > 7
if current-rpn-form(oqx:1) = 'n'
add 1 to cpx
move current-permutation(cpx:1) to nd
move n(nd) to output-queue(oqx:1)
else
add 1 to cox
move current-operators(cox:1) to output-queue(oqx:1)
end-if
end-perform
perform evaluate-rpn
if divide-by-zero-error = space
and 24 * top-denominator = top-numerator
perform varying s from 1 by 1 until s > s-max
or solution(s) = output-queue
continue
end-perform
if s > s-max
if s >= s-lim
display 'error: solutions ' s ' for ' number-definition ' exceeds ' s-lim
stop run
end-if
move s to s-max
move output-queue to solution(s-max)
end-if
end-if
end-perform
end-perform
end-perform
end-perform
end-perform
.
evaluate-rpn.
move space to divide-by-zero-error
move 0 to rsx *> stack depth
perform varying oqx from 1 by 1 until oqx > 7
if output-queue(oqx:1) >= '1' and <= '9'
*> push the digit onto the stack
add 1 to rsx
move top-numerator to numerator(rsx)
move top-denominator to denominator(rsx)
move output-queue(oqx:1) to top-numerator
move 1 to top-denominator
else
*> apply the operation
evaluate output-queue(oqx:1)
when '+'
compute top-numerator = top-numerator * denominator(rsx)
+ top-denominator * numerator(rsx)
compute top-denominator = top-denominator * denominator(rsx)
when '-'
compute top-numerator = top-denominator * numerator(rsx)
- top-numerator * denominator(rsx)
compute top-denominator = top-denominator * denominator(rsx)
when '*'
compute top-numerator = top-numerator * numerator(rsx)
compute top-denominator = top-denominator * denominator(rsx)
when '/'
compute work-number = numerator(rsx) * top-denominator
compute top-denominator = denominator(rsx) * top-numerator
if top-denominator = 0
move 'y' to divide-by-zero-error
exit paragraph
end-if
move work-number to top-numerator
end-evaluate
*> pop the stack
subtract 1 from rsx
end-if
end-perform
.
end program twentyfoursolve.
- Output:
prompt$ cobc -xj twentyfoursolve.cob start twentyfoursolve enter a number <n> as four integers from 1-9 to see its solutions enter list to see counts of solutions for all numbers enter show <n> to see numbers having <n> solutions <enter> ends the program (h for help)?5678 5678 has 026 solutions 57+8-6* (((5+7)-8)*6) 57+86-* ((5+7)*(8-6)) 578-+6* ((5+(7-8))*6) 58-7+6* (((5-8)+7)*6) 587--6* ((5-(8-7))*6) 657+8-* (6*((5+7)-8)) 6578-+* (6*(5+(7-8))) 658-7+* (6*((5-8)+7)) 6587--* (6*(5-(8-7))) 675+8-* (6*((7+5)-8)) 6758-+* (6*(7+(5-8))) 675-/8* ((6/(7-5))*8) 675-8// (6/((7-5)/8)) 678-5+* (6*((7-8)+5)) 6785--* (6*(7-(8-5))) 6875-/* (6*(8/(7-5))) 68*75-/ ((6*8)/(7-5)) 75+8-6* (((7+5)-8)*6) 75+86-* ((7+5)*(8-6)) 758-+6* ((7+(5-8))*6) 86-57+* ((8-6)*(5+7)) 86-75+* ((8-6)*(7+5)) 8675-/* (8*(6/(7-5))) 86*75-/ ((8*6)/(7-5)) 875-/6* ((8/(7-5))*6) 875-6// (8/((7-5)/6)) (h for help)?
CoffeeScript
# This program tries to find some way to turn four digits into an arithmetic
# expression that adds up to 24.
#
# Example solution for 5, 7, 8, 8:
# (((8 + 7) * 8) / 5)
solve_24_game = (digits...) ->
# Create an array of objects for our helper functions
arr = for digit in digits
{
val: digit
expr: digit
}
combo4 arr...
combo4 = (a, b, c, d) ->
arr = [a, b, c, d]
# Reduce this to a three-node problem by combining two
# nodes from the array.
permutations = [
[0, 1, 2, 3]
[0, 2, 1, 3]
[0, 3, 1, 2]
[1, 2, 0, 3]
[1, 3, 0, 2]
[2, 3, 0, 1]
]
for permutation in permutations
[i, j, k, m] = permutation
for combo in combos arr[i], arr[j]
answer = combo3 combo, arr[k], arr[m]
return answer if answer
null
combo3 = (a, b, c) ->
arr = [a, b, c]
permutations = [
[0, 1, 2]
[0, 2, 1]
[1, 2, 0]
]
for permutation in permutations
[i, j, k] = permutation
for combo in combos arr[i], arr[j]
answer = combo2 combo, arr[k]
return answer if answer
null
combo2 = (a, b) ->
for combo in combos a, b
return combo.expr if combo.val == 24
null
combos = (a, b) ->
[
val: a.val + b.val
expr: "(#{a.expr} + #{b.expr})"
,
val: a.val * b.val
expr: "(#{a.expr} * #{b.expr})"
,
val: a.val - b.val
expr: "(#{a.expr} - #{b.expr})"
,
val: b.val - a.val
expr: "(#{b.expr} - #{a.expr})"
,
val: a.val / b.val
expr: "(#{a.expr} / #{b.expr})"
,
val: b.val / a.val
expr: "(#{b.expr} / #{a.expr})"
,
]
# test
do ->
rand_digit = -> 1 + Math.floor (9 * Math.random())
for i in [1..15]
a = rand_digit()
b = rand_digit()
c = rand_digit()
d = rand_digit()
solution = solve_24_game a, b, c, d
console.log "Solution for #{[a,b,c,d]}: #{solution ? 'no solution'}"
- Output:
> coffee 24_game.coffee Solution for 8,3,1,8: ((1 + 8) * (8 / 3)) Solution for 6,9,5,7: (6 - ((5 - 7) * 9)) Solution for 4,2,1,1: no solution Solution for 3,5,1,3: (((3 + 5) * 1) * 3) Solution for 6,4,1,7: ((7 - (4 - 1)) * 6) Solution for 8,1,3,1: (((8 + 1) - 1) * 3) Solution for 6,1,3,3: (((6 + 1) * 3) + 3) Solution for 7,1,5,6: (((7 - 1) * 5) - 6) Solution for 4,2,3,1: ((3 + 1) * (4 + 2)) Solution for 8,8,5,8: ((5 * 8) - (8 + 8)) Solution for 3,8,4,1: ((1 - (3 - 8)) * 4) Solution for 6,4,3,8: ((8 - (6 / 3)) * 4) Solution for 2,1,8,7: (((2 * 8) + 1) + 7) Solution for 5,2,7,5: ((2 * 7) + (5 + 5)) Solution for 2,4,8,9: ((9 - (2 + 4)) * 8)
Common Lisp
(defconstant +ops+ '(* / + -))
(defun digits ()
(sort (loop repeat 4 collect (1+ (random 9))) #'<))
(defun expr-value (expr)
(eval expr))
(defun divides-by-zero-p (expr)
(when (consp expr)
(destructuring-bind (op &rest args) expr
(or (divides-by-zero-p (car args))
(and (eq op '/)
(or (and (= 1 (length args))
(zerop (expr-value (car args))))
(some (lambda (arg)
(or (divides-by-zero-p arg)
(zerop (expr-value arg))))
(cdr args))))))))
(defun solvable-p (digits &optional expr)
(unless (divides-by-zero-p expr)
(if digits
(destructuring-bind (next &rest rest) digits
(if expr
(some (lambda (op)
(solvable-p rest (cons op (list next expr))))
+ops+)
(solvable-p rest (list (car +ops+) next))))
(when (and expr
(eql 24 (expr-value expr)))
(merge-exprs expr)))))
(defun merge-exprs (expr)
(if (atom expr)
expr
(destructuring-bind (op &rest args) expr
(if (and (member op '(* +))
(= 1 (length args)))
(car args)
(cons op
(case op
((* +)
(loop for arg in args
for merged = (merge-exprs arg)
when (and (consp merged)
(eq op (car merged)))
append (cdr merged)
else collect merged))
(t (mapcar #'merge-exprs args))))))))
(defun solve-24-game (digits)
"Generate a lisp form using the operators in +ops+ and the given
digits which evaluates to 24. The first form found is returned, or
NIL if there is no solution."
(solvable-p digits))
- Output:
CL-USER 138 > (loop repeat 24 for soln = (solve-24-game (digits)) when soln do (pprint soln)) (+ 7 5 (* 4 3)) (* 6 4 (- 3 2)) (+ 9 8 4 3) (* 8 (- 6 (* 3 1))) (* 6 4 (/ 2 2)) (* 9 (/ 8 (- 8 5))) NIL
D
This uses the Rational struct and permutations functions of two other Rosetta Code Tasks.
import std.stdio, std.algorithm, std.range, std.conv, std.string,
std.concurrency, permutations2, arithmetic_rational;
string solve(in int target, in int[] problem) {
static struct T { Rational r; string e; }
Generator!T computeAllOperations(in Rational[] L) {
return new typeof(return)({
if (!L.empty) {
immutable x = L[0];
if (L.length == 1) {
yield(T(x, x.text));
} else {
foreach (const o; computeAllOperations(L.dropOne)) {
immutable y = o.r;
auto sub = [T(x * y, "*"), T(x + y, "+"), T(x - y, "-")];
if (y) sub ~= [T(x / y, "/")];
foreach (const e; sub)
yield(T(e.r, format("(%s%s%s)", x, e.e, o.e)));
}
}
}
});
}
foreach (const p; problem.map!Rational.array.permutations!false)
foreach (const sol; computeAllOperations(p))
if (sol.r == target)
return sol.e;
return "No solution";
}
void main() {
foreach (const prob; [[6, 7, 9, 5], [3, 3, 8, 8], [1, 1, 1, 1]])
writeln(prob, ": ", solve(24, prob));
}
- Output:
[6, 7, 9, 5]: (6+(9*(7-5))) [3, 3, 8, 8]: (8/(3-(8/3))) [1, 1, 1, 1]: No solution
EchoLisp
The program takes n numbers - not limited to 4 - builds the all possible legal rpn expressions according to the game rules, and evaluates them. Time saving : 4 5 + is the same as 5 4 + . Do not generate twice. Do not generate expressions like 5 6 * + which are not legal.
;; use task [[RPN_to_infix_conversion#EchoLisp]] to print results
(define (rpn->string rpn)
(if (vector? rpn)
(infix->string (rpn->infix rpn))
"😥 Not found"))
(string-delimiter "")
(define OPS #(* + - // )) ;; use float division
(define-syntax-rule (commutative? op) (or (= op *) (= op +)))
;; ---------------------------------
;; calc rpn -> num value or #f if bad rpn
;; rpn is a vector of ops or numbers
;; ----------------------------------
(define (calc rpn)
(define S (stack 'S))
(for ((token rpn))
(if (procedure? token)
(let [(op2 (pop S)) (op1 (pop S))]
(if (and op1 op2)
(push S (apply token (list op1 op2)))
(push S #f))) ;; not-well formed
(push S token ))
#:break (not (stack-top S)))
(if (= 1 (stack-length S)) (pop S) #f))
;; check for legal rpn -> #f if not legal
(define (rpn? rpn)
(define S (stack 'S))
(for ((token rpn))
(if (procedure? token)
(push S (and (pop S) (pop S)))
(push S token ))
#:break (not (stack-top S)))
(stack-top S))
;; --------------------------------------
;; build-rpn : push next rpn op or number
;; dleft is number of not used digits
;; ---------------------------------------
(define count 0)
(define (build-rpn into: rpn depth maxdepth digits ops dleft target &hit )
(define cmpop #f)
(cond
;; tooo long
[(> (++ count) 200_000) (set-box! &hit 'not-found)]
;; stop on first hit
[(unbox &hit) &hit]
;; partial rpn must be legal
[(not (rpn? rpn)) #f]
;; eval rpn if complete
[(> depth maxdepth)
(when (= target (calc rpn)) (set-box! &hit rpn))]
;; else, add a digit to rpn
[else
[when (< depth maxdepth) ;; digits anywhere except last
(for [(d digits) (i 10)]
#:continue (zero? d)
(vector-set! digits i 0) ;; mark used
(vector-set! rpn depth d)
(build-rpn rpn (1+ depth) maxdepth digits ops (1- dleft) target &hit)
(vector-set! digits i d)) ;; mark unused
] ;; add digit
;; or, add an op
;; ops anywhere except positions 0,1
[when (and (> depth 1) (<= (+ depth dleft) maxdepth));; cutter : must use all digits
(set! cmpop
(and (number? [rpn (1- depth)])
(number? [rpn (- depth 2)])
(> [rpn (1- depth)] [rpn (- depth 2)])))
(for [(op ops)]
#:continue (and cmpop (commutative? op)) ;; cutter : 3 4 + === 4 3 +
(vector-set! rpn depth op)
(build-rpn rpn (1+ depth) maxdepth digits ops dleft target &hit)
(vector-set! rpn depth 0))] ;; add op
] ; add something to rpn vector
)) ; build-rpn
;;------------------------
;;gen24 : num random numbers
;;------------------------
(define (gen24 num maxrange)
(->> (append (range 1 maxrange)(range 1 maxrange)) shuffle (take num)))
;;-------------------------------------------
;; try-rpn : sets starter values for build-rpn
;;-------------------------------------------
(define (try-rpn digits target)
(set! digits (list-sort > digits)) ;; seems to accelerate things
(define rpn (make-vector (1- (* 2 (length digits)))))
(define &hit (box #f))
(set! count 0)
(build-rpn rpn starter-depth: 0
max-depth: (1- (vector-length rpn))
(list->vector digits)
OPS
remaining-digits: (length digits)
target &hit )
(writeln target '= (rpn->string (unbox &hit)) 'tries= count))
;; -------------------------------
;; (task numdigits target maxrange)
;; --------------------------------
(define (task (numdigits 4) (target 24) (maxrange 10))
(define digits (gen24 numdigits maxrange))
(writeln digits '→ target)
(try-rpn digits target))
- Output:
(task 4) ;; standard 24-game (7 9 2 4) → 24 24 = 9 + 7 + 4 * 2 tries= 35 (task 4) (1 9 3 4) → 24 24 = 9 + (4 + 1) * 3 tries= 468 (task 5 ) ;; 5 digits (4 8 6 9 8) → 24 24 = 9 * 8 * (8 / (6 * 4)) tries= 104 (task 5 100) ;; target = 100 (5 6 5 1 3) → 100 100 = (6 + (5 * 3 - 1)) * 5 tries= 10688 (task 5 (random 100)) (1 1 8 6 8) → 31 31 = 8 * (6 - 1) - (8 + 1) tries= 45673 (task 6 (random 100)) ;; 6 digits (7 2 7 8 3 1) → 40 40 = 8 / (7 / (7 * (3 + 2 * 1))) tries= 154 (task 6 (random 1000) 100) ;; 6 numbers < 100 , target < 1000 (19 15 83 74 61 48) → 739 739 = (83 + (74 - (61 + 48))) * 15 + 19 tries= 29336 (task 6 (random 1000) 100) ;; 6 numbers < 100 (73 29 65 78 22 43) → 1 1 = 😥 Not found tries= 200033 (task 7 (random 1000) 100) ;; 7 numbers < 100 (7 55 94 4 71 58 93) → 705 705 = 94 + 93 + 71 + 58 + 55 * 7 + 4 tries= 5982 (task 6 (random -100) 10) ;; negative target (5 9 7 3 6 3) → -54 -54 = 9 * (7 + (6 - 5 * 3)) * 3 tries= 2576
Elixir
defmodule Game24 do
@expressions [ ["((", "", ")", "", ")", ""],
["(", "(", "", "", "))", ""],
["(", "", ")", "(", "", ")"],
["", "((", "", "", ")", ")"],
["", "(", "", "(", "", "))"] ]
def solve(digits) do
dig_perm = permute(digits) |> Enum.uniq
operators = perm_rep(~w[+ - * /], 3)
for dig <- dig_perm, ope <- operators, expr <- @expressions,
check?(str = make_expr(dig, ope, expr)),
do: str
end
defp check?(str) do
try do
{val, _} = Code.eval_string(str)
val == 24
rescue
ArithmeticError -> false # division by zero
end
end
defp permute([]), do: [[]]
defp permute(list) do
for x <- list, y <- permute(list -- [x]), do: [x|y]
end
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
- Output:
C:\Elixir>elixir game24.exs 1 1 3 4 found 12 solutions, including ((1+1)*3)*4 ["((1+1)*3)*4", "((1+1)*4)*3", "(1+1)*(3*4)", "(1+1)*(4*3)", "(3*(1+1))*4", "(3*4)*(1+1)", "(4*(1+1))*3", "(4*3)*(1+1)", "3*((1+1)*4)", "3*(4*(1+1))", "4*((1+1)*3)", "4*(3*(1+1))"] C:\Elixir>elixir game24.exs 6 7 8 9 found 8 solutions, including (6*8)/(9-7) ["(6*8)/(9-7)", "(6/(9-7))*8", "(8*6)/(9-7)", "(8/(9-7))*6", "6*(8/(9-7))", "6/((9-7)/8)", "8*(6/(9-7))", "8/((9-7)/6)"] C:\Elixir>elixir game24.exs 1 2 2 3 no solutions
ERRE
ERRE hasn't an "EVAL" function so we must write an evaluation routine; this task is solved via "brute-force".
PROGRAM 24SOLVE
LABEL 98,99,2540,2550,2560
! possible brackets
CONST NBRACKETS=11,ST_CONST$="+-*/^("
DIM D[4],PERM[24,4]
DIM BRAKETS$[NBRACKETS]
DIM OP$[3]
DIM STACK$[50]
PROCEDURE COMPATTA_STACK
IF NS>1 THEN
R=1
WHILE R<NS DO
IF INSTR(ST_CONST$,STACK$[R])=0 AND INSTR(ST_CONST$,STACK$[R+1])=0 THEN
FOR R1=R TO NS-1 DO
STACK$[R1]=STACK$[R1+1]
END FOR
NS=NS-1
END IF
R=R+1
END WHILE
END IF
END PROCEDURE
PROCEDURE CALC_ARITM
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="^" THEN
IF L>=NS2 THEN GOTO 99 END IF
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="^" THEN
RI#=N1#^N2#
END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="*" OR STACK$[L]="/" THEN
IF L>=NS2 THEN GOTO 99 END IF
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="*" THEN
RI#=N1#*N2#
ELSE
IF N2#<>0 THEN RI#=N1#/N2# ELSE NERR=6 RI#=0 END IF
END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="+" OR STACK$[L]="-" THEN
EXIT IF L>=NS2
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="+" THEN RI#=N1#+N2# ELSE RI#=N1#-N2# END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
99:
IF NOP<2 THEN ! precedenza tra gli operatori
DB#=VAL(STACK$[NS1])
ELSE
IF NOP<3 THEN
DB#=VAL(STACK$[NS1+2])
ELSE
DB#=VAL(STACK$[NS1+4])
END IF
END IF
END PROCEDURE
PROCEDURE SVOLGI_PAR
NPA=NPA-1
FOR J=NS TO 1 STEP -1 DO
EXIT IF STACK$[J]="("
END FOR
IF J=0 THEN
NS1=1 NS2=NS CALC_ARITM NERR=7
ELSE
FOR R=J TO NS-1 DO
STACK$[R]=STACK$[R+1]
END FOR
NS1=J NS2=NS-1 CALC_ARITM
IF NS1=2 THEN
NS1=1 STACK$[1]=STACK$[2]
END IF
NS=NS1
COMPATTA_STACK
END IF
END PROCEDURE
PROCEDURE MYEVAL(EXPRESSION$,DB#,NERR->DB#,NERR)
NOP=0 NPA=0 NS=1 K$="" NERR=0
STACK$[1]="@" ! init stack
FOR W=1 TO LEN(EXPRESSION$) DO
LOOP
CODE=ASC(MID$(EXPRESSION$,W,1))
IF (CODE>=48 AND CODE<=57) OR CODE=46 THEN
K$=K$+CHR$(CODE)
W=W+1 IF W>LEN(EXPRESSION$) THEN GOTO 98 END IF
ELSE
EXIT IF K$=""
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
IF FLAG=0 THEN
STACK$[NS]=K$
ELSE
STACK$[NS]=STR$(VAL(K$)*FLAG)
END IF
K$="" FLAG=0
EXIT
END IF
END LOOP
IF CODE=43 THEN K$="+" END IF
IF CODE=45 THEN K$="-" END IF
IF CODE=42 THEN K$="*" END IF
IF CODE=47 THEN K$="/" END IF
IF CODE=94 THEN K$="^" END IF
CASE CODE OF
43,45,42,47,94-> ! +-*/^
IF MID$(EXPRESSION$,W+1,1)="-" THEN FLAG=-1 W=W+1 END IF
IF INSTR(ST_CONST$,STACK$[NS])<>0 THEN
NERR=5
ELSE
NS=NS+1 STACK$[NS]=K$ NOP=NOP+1
IF NOP>=2 THEN
FOR J=NS TO 1 STEP -1 DO
IF STACK$[J]<>"(" THEN GOTO 2540 END IF
IF J<NS-2 THEN GOTO 2550 ELSE GOTO 2560 END IF
2540: END FOR
2550: NS1=J+1 NS2=NS CALC_ARITM
NS=NS2 STACK$[NS]=K$
REGISTRO_X#=VAL(STACK$[NS-1])
END IF
END IF
2560: END ->
40-> ! (
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
STACK$[NS]="(" NPA=NPA+1
IF MID$(EXPRESSION$,W+1,1)="-" THEN FLAG=-1 W=W+1 END IF
END ->
41-> ! )
SVOLGI_PAR
IF NERR=7 THEN
NERR=0 NOP=0 NPA=0 NS=1
ELSE
IF NERR=0 OR NERR=1 THEN
DB#=VAL(STACK$[NS])
REGISTRO_X#=DB#
ELSE
NOP=0 NPA=0 NS=1
END IF
END IF
END ->
OTHERWISE
NERR=8
END CASE
K$=""
END FOR
98:
IF K$<>"" THEN
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
IF FLAG=0 THEN STACK$[NS]=K$ ELSE STACK$[NS]=STR$(VAL(K$)*FLAG) END IF
END IF
IF INSTR(ST_CONST$,STACK$[NS])<>0 THEN
NERR=6
ELSE
WHILE NPA<>0 DO
SVOLGI_PAR
END WHILE
IF NERR<>7 THEN NS1=1 NS2=NS CALCARITM END IF
END IF
NS=1 NOP=0 NPA=0
END PROCEDURE
BEGIN
PRINT(CHR$(12);) ! CLS
! possible brackets
DATA("4#4#4#4")
DATA("(4#4)#4#4")
DATA("4#(4#4)#4")
DATA("4#4#(4#4)")
DATA("(4#4)#(4#4)")
DATA("(4#4#4)#4")
DATA("4#(4#4#4)")
DATA("((4#4)#4)#4")
DATA("(4#(4#4))#4")
DATA("4#((4#4)#4)")
DATA("4#(4#(4#4))")
FOR I=1 TO NBRACKETS DO
READ(BRAKETS$[I])
END FOR
INPUT("ENTER 4 DIGITS: ",A$)
ND=0
FOR I=1 TO LEN(A$) DO
C$=MID$(A$,I,1)
IF INSTR("123456789",C$)>0 THEN
ND=ND+1
D[ND]=VAL(C$)
END IF
END FOR
! precompute permutations. dumb way.
NPERM=1*2*3*4
N=0
FOR I=1 TO 4 DO
FOR J=1 TO 4 DO
FOR K=1 TO 4 DO
FOR L=1 TO 4 DO
! valid permutation (no dupes)
IF I<>J AND I<>K AND I<>L AND J<>K AND J<>L AND K<>L THEN
N=N+1
! actually,we can as well permute given digits
PERM[N,1]=D[I]
PERM[N,2]=D[J]
PERM[N,3]=D[K]
PERM[N,4]=D[L]
END IF
END FOR
END FOR
END FOR
END FOR
! operations: full search
COUNT=0
OPS$="+-*/"
FOR OP1=1 TO 4 DO
OP$[1]=MID$(OPS$,OP1,1)
FOR OP2=1 TO 4 DO
OP$[2]=MID$(OPS$,OP2,1)
FOR OP3=1 TO 4 DO
OP$[3]=MID$(OPS$,OP3,1)
! substitute all brackets
FOR T=1 TO NBRACKETS DO
TMPL$=BRAKETS$[T]
! now,substitute all digits: permutations.
FOR P=1 TO NPERM DO
RES$=""
NOP=0
ND=0
FOR I=1 TO LEN(TMPL$) DO
C$=MID$(TMPL$,I,1)
CASE C$ OF
"#"-> ! operations
NOP=NOP+1
RES$=RES$+OP$[NOP]
END ->
"4"-> ! digits
ND=NOP+1
RES$=RES$+MID$(STR$(PERM[P,ND]),2)
END ->
OTHERWISE ! brackets goes here
RES$=RES$+C$
END CASE
END FOR
! eval here
MY_EVAL(RES$,DB#,NERR->DB#,NERR)
IF DB#=24 AND NERR=0 THEN
PRINT("24=";RES$)
COUNT=COUNT+1
END IF
END FOR
END FOR
END FOR
END FOR
END FOR
IF COUNT=0 THEN
PRINT("If you see this, probably task cannot be solved with these digits")
ELSE
PRINT("Total=";COUNT)
END IF
END PROGRAM- Output:
ENTER 4 DIGITS: ? 6759 24=6+(7-5)*9 24=6+((7-5)*9) 24=6+9*(7-5) 24=6+(9*(7-5)) 24=6-(5-7)*9 24=6-((5-7)*9) 24=(7-5)*9+6 24=((7-5)*9)+6 24=6-9*(5-7) 24=6-(9*(5-7)) 24=9*(7-5)+6 24=(9*(7-5))+6 Total= 12
Euler Math Toolbox
Via brute force.
>function try24 (v) ...
$n=cols(v);
$if n==1 and v[1]~=24 then
$ "Solved the problem",
$ return 1;
$endif
$loop 1 to n
$ w=tail(v,2);
$ loop 1 to n-1
$ h=w; a=v[1]; b=w[1];
$ w[1]=a+b; if try24(w); ""+a+"+"+b+"="+(a+b), return 1; endif;
$ w[1]=a-b; if try24(w); ""+a+"-"+b+"="+(a-b), return 1; endif;
$ w[1]=a*b; if try24(w); ""+a+"*"+b+"="+(a*b), return 1; endif;
$ if not b~=0 then
$ w[1]=a/b; if try24(w); ""+a+"/"+b+"="+(a/b), return 1; endif;
$ endif;
$ w=rotright(w);
$ end;
$ v=rotright(v);
$end;
$return 0;
$endfunction>try24([1,2,3,4]);
Solved the problem
6*4=24
3+3=6
1+2=3
>try24([8,7,7,1]);
Solved the problem
22+2=24
14+8=22
7+7=14
>try24([8,4,7,1]);
Solved the problem
6*4=24
7-1=6
8-4=4
>try24([3,4,5,6]);
Solved the problem
4*6=24
-1+5=4
3-4=-1F#
The program wants to give all solutions for a given set of 4 digits. It eliminates all duplicate solutions which result from transposing equal digits. The basic solution is an adaption of the OCaml program.
open System
let rec gcd x y = if x = y || x = 0 then y else if x < y then gcd y x else gcd y (x-y)
let abs (x : int) = Math.Abs x
let sign (x: int) = Math.Sign x
let cint s = Int32.Parse(s)
type Rat(x : int, y : int) =
let g = if y = 0 then 0 else gcd (abs x) (abs y)
member this.n = if g = 0 then sign y * sign x else sign y * x / g // store a minus sign in the numerator
member this.d =
if y = 0 then 0 else sign y * y / g
static member (~-) (x : Rat) = Rat(-x.n, x.d)
static member (+) (x : Rat, y : Rat) = Rat(x.n * y.d + y.n * x.d, x.d * y.d)
static member (-) (x : Rat, y : Rat) = x + Rat(-y.n, y.d)
static member (*) (x : Rat, y : Rat) = Rat(x.n * y.n, x.d * y.d)
static member (/) (x : Rat, y : Rat) = x * Rat(y.d, y.n)
interface System.IComparable with
member this.CompareTo o =
match o with
| :? Rat as that -> compare (this.n * that.d) (that.n * this.d)
| _ -> invalidArg "o" "cannot compare values of differnet types."
override this.Equals(o) =
match o with
| :? Rat as that -> this.n = that.n && this.d = that.d
| _ -> false
override this.ToString() =
if this.d = 1 then this.n.ToString()
else sprintf @"<%d,%d>" this.n this.d
new(x : string, y : string) = if y = "" then Rat(cint x, 1) else Rat(cint x, cint y)
type expression =
| Const of Rat
| Sum of expression * expression
| Diff of expression * expression
| Prod of expression * expression
| Quot of expression * expression
let rec eval = function
| Const c -> c
| Sum (f, g) -> eval f + eval g
| Diff(f, g) -> eval f - eval g
| Prod(f, g) -> eval f * eval g
| Quot(f, g) -> eval f / eval g
let print_expr expr =
let concat (s : seq<string>) = System.String.Concat s
let paren p prec op_prec = if prec > op_prec then p else ""
let rec print prec = function
| Const c -> c.ToString()
| Sum(f, g) ->
concat [ (paren "(" prec 0); (print 0 f); " + "; (print 0 g); (paren ")" prec 0) ]
| Diff(f, g) ->
concat [ (paren "(" prec 0); (print 0 f); " - "; (print 1 g); (paren ")" prec 0) ]
| Prod(f, g) ->
concat [ (paren "(" prec 2); (print 2 f); " * "; (print 2 g); (paren ")" prec 2) ]
| Quot(f, g) ->
concat [ (paren "(" prec 2); (print 2 f); " / "; (print 3 g); (paren ")" prec 2) ]
print 0 expr
let rec normal expr =
let norm epxr =
match expr with
| Sum(x, y) -> if eval x <= eval y then expr else Sum(normal y, normal x)
| Prod(x, y) -> if eval x <= eval y then expr else Prod(normal y, normal x)
| _ -> expr
match expr with
| Const c -> expr
| Sum(x, y) -> norm (Sum(normal x, normal y))
| Prod(x, y) -> norm (Prod(normal x, normal y))
| Diff(x, y) -> Diff(normal x, normal y)
| Quot(x, y) -> Quot(normal x, normal y)
let rec insert v = function
| [] -> [[v]]
| x::xs as li -> (v::li) :: (List.map (fun y -> x::y) (insert v xs))
let permutations li =
List.foldBack (fun x z -> List.concat (List.map (insert x) z)) li [[]]
let rec comp expr rest = seq {
match rest with
| x::xs ->
yield! comp (Sum (expr, x)) xs;
yield! comp (Diff(x, expr)) xs;
yield! comp (Diff(expr, x)) xs;
yield! comp (Prod(expr, x)) xs;
yield! comp (Quot(x, expr)) xs;
yield! comp (Quot(expr, x)) xs;
| [] -> if eval expr = Rat(24,1) then yield print_expr (normal expr)
}
[<EntryPoint>]
let main argv =
let digits = List.init 4 (fun i -> Const (Rat(argv.[i],"")))
let solutions =
permutations digits
|> Seq.groupBy (sprintf "%A")
|> Seq.map snd |> Seq.map Seq.head
|> Seq.map (fun x -> comp (List.head x) (List.tail x))
|> Seq.choose (fun x -> if Seq.isEmpty x then None else Some x)
|> Seq.concat
if Seq.isEmpty solutions then
printfn "No solutions."
else
solutions
|> Seq.groupBy id
|> Seq.iter (fun x -> printfn "%s" (fst x))
0
- Output:
>solve24 3 3 3 4 4 * (3 * 3 - 3) 3 + 3 * (3 + 4) >solve24 3 3 3 5 No solutions. solve24 3 3 3 6 6 + 3 * (3 + 3) (3 / 3 + 3) * 6 3 * (3 + 6) - 3 3 + 3 + 3 * 6 >solve24 3 3 8 8 8 / (3 - 8 / 3) >solve24 3 8 8 9 3 * (9 - 8 / 8) (9 - 8) * 3 * 8 3 / (9 - 8) * 8 8 / ((9 - 8) / 3) 3 * (9 - 8) * 8 3 * 8 / (9 - 8) 3 / ((9 - 8) / 8)
Factor
Factor is well-suited for this task due to its homoiconicity and because it is a reverse-Polish notation evaluator. All we're doing is grouping each permutation of digits with three selections of the possible operators into quotations (blocks of code that can be stored like sequences). Then we call each quotation and print out the ones that equal 24. The recover word is an exception handler that is used to intercept divide-by-zero errors and continue gracefully by removing those quotations from consideration.
USING: continuations grouping io kernel math math.combinatorics
prettyprint quotations random sequences sequences.deep ;
IN: rosetta-code.24-game
: 4digits ( -- seq ) 4 9 random-integers [ 1 + ] map ;
: expressions ( digits -- exprs )
all-permutations [ [ + - * / ] 3 selections
[ append ] with map ] map flatten 7 group ;
: 24= ( exprs -- )
>quotation dup call( -- x ) 24 = [ . ] [ drop ] if ;
: 24-game ( -- )
4digits dup "The numbers: " write . "The solutions: "
print expressions [ [ 24= ] [ 2drop ] recover ] each ;
24-game
- Output:
The numbers: { 4 9 3 1 }
The solutions:
[ 4 9 3 1 * - * ]
[ 4 9 3 1 / - * ]
[ 4 9 1 3 * - * ]
[ 4 1 9 3 - * * ]
[ 4 1 9 3 - / / ]
[ 9 3 4 1 + * + ]
[ 9 3 1 4 + * + ]
[ 1 4 9 3 - * * ]
[ 1 4 9 3 * - - ]
[ 1 4 3 9 * - - ]
The numbers: { 1 7 4 9 }
The solutions:
The numbers: { 1 5 6 8 }
The solutions:
[ 6 1 5 8 - - * ]
[ 6 1 8 5 - + * ]
[ 6 8 1 5 - + * ]
[ 6 8 5 1 - - * ]
Fortran
program solve_24
use helpers
implicit none
real :: vector(4), reals(4), p, q, r, s
integer :: numbers(4), n, i, j, k, a, b, c, d
character, parameter :: ops(4) = (/ '+', '-', '*', '/' /)
logical :: last
real,parameter :: eps = epsilon(1.0)
do n=1,12
call random_number(vector)
reals = 9 * vector + 1
numbers = int(reals)
call Insertion_Sort(numbers)
permutations: do
a = numbers(1); b = numbers(2); c = numbers(3); d = numbers(4)
reals = real(numbers)
p = reals(1); q = reals(2); r = reals(3); s = reals(4)
! combinations of operators:
do i=1,4
do j=1,4
do k=1,4
if ( abs(op(op(op(p,i,q),j,r),k,s)-24.0) < eps ) then
write (*,*) numbers, ' : ', '((',a,ops(i),b,')',ops(j),c,')',ops(k),d
exit permutations
else if ( abs(op(op(p,i,op(q,j,r)),k,s)-24.0) < eps ) then
write (*,*) numbers, ' : ', '(',a,ops(i),'(',b,ops(j),c,'))',ops(k),d
exit permutations
else if ( abs(op(p,i,op(op(q,j,r),k,s))-24.0) < eps ) then
write (*,*) numbers, ' : ', a,ops(i),'((',b,ops(j),c,')',ops(k),d,')'
exit permutations
else if ( abs(op(p,i,op(q,j,op(r,k,s)))-24.0) < eps ) then
write (*,*) numbers, ' : ', a,ops(i),'(',b,ops(j),'(',c,ops(k),d,'))'
exit permutations
else if ( abs(op(op(p,i,q),j,op(r,k,s))-24.0) < eps ) then
write (*,*) numbers, ' : ', '(',a,ops(i),b,')',ops(j),'(',c,ops(k),d,')'
exit permutations
end if
end do
end do
end do
call nextpermutation(numbers,last)
if ( last ) then
write (*,*) numbers, ' : no solution.'
exit permutations
end if
end do permutations
end do
contains
pure real function op(x,c,y)
integer, intent(in) :: c
real, intent(in) :: x,y
select case ( ops(c) )
case ('+')
op = x+y
case ('-')
op = x-y
case ('*')
op = x*y
case ('/')
op = x/y
end select
end function op
end program solve_24
module helpers
contains
pure subroutine Insertion_Sort(a)
integer, intent(inout) :: a(:)
integer :: temp, i, j
do i=2,size(a)
j = i-1
temp = a(i)
do while ( j>=1 .and. a(j)>temp )
a(j+1) = a(j)
j = j - 1
end do
a(j+1) = temp
end do
end subroutine Insertion_Sort
subroutine nextpermutation(perm,last)
integer, intent(inout) :: perm(:)
logical, intent(out) :: last
integer :: k,l
k = largest1()
last = k == 0
if ( .not. last ) then
l = largest2(k)
call swap(l,k)
call reverse(k)
end if
contains
pure integer function largest1()
integer :: k, max
max = 0
do k=1,size(perm)-1
if ( perm(k) < perm(k+1) ) then
max = k
end if
end do
largest1 = max
end function largest1
pure integer function largest2(k)
integer, intent(in) :: k
integer :: l, max
max = k+1
do l=k+2,size(perm)
if ( perm(k) < perm(l) ) then
max = l
end if
end do
largest2 = max
end function largest2
subroutine swap(l,k)
integer, intent(in) :: k,l
integer :: temp
temp = perm(k)
perm(k) = perm(l)
perm(l) = temp
end subroutine swap
subroutine reverse(k)
integer, intent(in) :: k
integer :: i
do i=1,(size(perm)-k)/2
call swap(k+i,size(perm)+1-i)
end do
end subroutine reverse
end subroutine nextpermutation
end module helpers
- Output:
(using g95)
3 6 7 9 : 3 *(( 6 - 7 )+ 9 ) 3 9 5 8 : (( 3 * 9 )+ 5 )- 8 4 5 6 9 : (( 4 + 5 )+ 6 )+ 9 2 9 9 8 : ( 2 +( 9 / 9 ))* 8 1 4 7 5 : ( 1 +( 4 * 7 ))- 5 8 7 7 6 : no solution. 3 3 8 9 : ( 3 *( 3 + 8 ))- 9 1 5 6 7 : ( 1 +( 5 * 6 ))- 7 2 3 5 3 : 2 *(( 3 * 5 )- 3 ) 4 5 6 9 : (( 4 + 5 )+ 6 )+ 9 1 1 3 6 : ( 1 +( 1 * 3 ))* 6 2 4 6 8 : (( 2 / 4 )* 6 )* 8
Modern version using OpenMP
module game24_module
use omp_lib
use iso_fortran_env, only: int64
implicit none
! Define constants
integer, parameter :: max_limit = 8 ! Maximum allowed value for the number of inputs
integer, parameter :: expr_len = 200 ! Maximum length for expressions
! Precomputed total calls for n=6,7,8
integer(int64), parameter :: total_calls_n6 = 20000000_int64
integer(int64), parameter :: total_calls_n7 = 2648275200_int64
integer(int64), parameter :: total_calls_n8 = 444557593600_int64
!----------------------- Progress Indicator Variables ---------------------
integer(int64) :: total_calls = 0 ! Total number of recursive calls
integer(int64) :: completed_calls = 0 ! Number of completed recursive calls
integer :: last_percentage = -1 ! Last percentage reported
integer, parameter :: progress_bar_width = 50 ! Width of the progress bar
character(len=1) :: carriage_return = char(13) ! Carriage return character
logical :: show_progress = .false. ! Flag to show progress bar
!--------------------------------------------------------------------------
contains
!-----------------------------------------------------------------------
! ! Aborted function: calculate_total_calls
! ! Description:
! ! Estimates the total number of recursive calls for a given n,
! ! considering commutativity (addition and multiplication).
! ! Arguments:
! ! n: The number of input numbers.
! ! Returns:
! ! The estimated total number of recursive calls as an integer.
! !-----------------------------------------------------------------------
! integer function calculate_total_calls(n)
! implicit none
! integer, intent(in) :: n
! integer :: k
! calculate_total_calls = 1
! do k = 2, n
! ! For each pair, there are 6 possible operations:
! ! 1 addition, 1 multiplication (commutative)
! ! 2 subtraction, 2 division (non-commutative)
! calculate_total_calls = calculate_total_calls * ((k * (k - 1)) / 2) * 6
! end do
! end function calculate_total_calls
!-----------------------------------------------------------------------
! Subroutine: convert_to_number
! Description:
! Converts user input (numbers or card values) into numeric values.
! Handles card values such as 'A', 'J', 'Q', 'K' and converts them into
! corresponding numbers (A=1, J=11, Q=12, K=13).
! Arguments:
! input_str: Input string representing the number or card.
! number: Output real number after conversion.
! ios: I/O status indicator (0 for success, non-zero for error).
!-----------------------------------------------------------------------
subroutine convert_to_number(input_str, number, ios)
implicit none
character(len=*), intent(in) :: input_str
real, intent(out) :: number
integer, intent(out) :: ios
character(len=1) :: first_char
real :: temp_number
ios = 0 ! Reset the I/O status to 0 (valid input by default)
first_char = input_str(1:1)
select case (first_char)
case ('A', 'a')
number = 1.0
case ('J', 'j')
number = 11.0
case ('Q', 'q')
number = 12.0
case ('K', 'k')
number = 13.0
case default
read (input_str, *, iostat=ios) temp_number ! Attempt to read a real number
! If input is not a valid real number or is not an integer, set ios to 1
if (ios /= 0 .or. mod(temp_number, 1.0) /= 0.0) then
ios = 1 ! Invalid input
else
number = temp_number ! Valid integer input
end if
end select
end subroutine convert_to_number
!-----------------------------------------------------------------------
! Subroutine: remove_decimal_zeros
! Description:
! Removes trailing zeros after the decimal point from a string.
! Arguments:
! str: Input string that may contain trailing zeros.
! result: Output string with trailing zeros removed.
!-----------------------------------------------------------------------
subroutine remove_decimal_zeros(str, result)
implicit none
character(len=*), intent(in) :: str ! Input: String to remove zeros from
character(len=*), intent(out) :: result ! Output: String without trailing zeros
integer :: i, len_str ! Loop counter and string length
len_str = len_trim(str)
result = adjustl(str(1:len_str))
! Find the position of the decimal point
i = index(result, '.')
! If there's a decimal point, remove trailing zeros
if (i > 0) then
do while (len_str > i .and. result(len_str:len_str) == '0')
len_str = len_str - 1
end do
if (result(len_str:len_str) == '.') len_str = len_str - 1
result = result(1:len_str)
end if
end subroutine remove_decimal_zeros
!-----------------------------------------------------------------------
! Subroutine: create_new_arrays
! Description:
! Creates new arrays after performing an operation.
! Arguments:
! nums: Input array of numbers.
! exprs: Input array of expressions.
! idx1: Index of the first element to remove.
! idx2: Index of the second element to remove.
! result: Result of the operation.
! new_expr: New expression string.
! new_nums: Output array of numbers with elements removed and result added.
! new_exprs: Output array of expressions with elements removed and new_expr added.
!-----------------------------------------------------------------------
subroutine create_new_arrays(nums, exprs, idx1, idx2, result, new_expr, new_nums, new_exprs)
implicit none
real, intent(in) :: nums(:) ! Input: Array of numbers
character(len=expr_len), intent(in) :: exprs(:) ! Input: Array of expressions
integer, intent(in) :: idx1, idx2 ! Input: Indices of elements to remove
real, intent(in) :: result ! Input: Result of the operation
character(len=expr_len), intent(in) :: new_expr ! Input: New expression
real, allocatable, intent(out) :: new_nums(:) ! Output: New array of numbers
character(len=expr_len), allocatable, intent(out) :: new_exprs(:) ! Output: New array of expressions
integer :: i, j, n ! Loop counters and size of input arrays
n = size(nums)
allocate (new_nums(n - 1))
allocate (new_exprs(n - 1))
j = 0
do i = 1, n
if (i /= idx1 .and. i /= idx2) then
j = j + 1
new_nums(j) = nums(i)
new_exprs(j) = exprs(i)
end if
end do
! Add the result of the operation to the new arrays
new_nums(n - 1) = result
new_exprs(n - 1) = new_expr
end subroutine create_new_arrays
!-----------------------------------------------------------------------
! Subroutine: update_progress_bar
! Description:
! Updates and displays the horizontal percentage-based progress bar.
! Arguments:
! None
!-----------------------------------------------------------------------
subroutine update_progress_bar()
implicit none
real :: percentage
integer :: filled_length
character(len=progress_bar_width) :: bar
integer :: int_percentage
if (total_calls == 0 .or. .not. show_progress) return ! Avoid division by zero and check the flag
percentage = real(completed_calls) / real(total_calls) * 100.0
! Ensure percentage does not exceed 100%
if (percentage > 100.0) percentage = 100.0
! Calculate integer percentage
int_percentage = int(percentage)
! Update progress bar only when percentage increases by at least 1%
if (int_percentage > last_percentage) then
last_percentage = int_percentage
! Calculate the filled length of the progress bar
filled_length = min(int(percentage / 100.0 * progress_bar_width), progress_bar_width)
! Construct the progress bar string
bar = repeat('=', filled_length)
if (filled_length < progress_bar_width) then
bar = bar//'>'//repeat(' ', progress_bar_width - filled_length - 1)
end if
! Print the progress bar and integer percentage
write (*, '(A, F4.1, A)', advance='no') carriage_return//'['//bar//'] ', percentage, '%'
call flush (0) ! Ensure output is displayed immediately
end if
end subroutine update_progress_bar
!-----------------------------------------------------------------------
! Recursive Subroutine: solve_24
! Description:
! Recursively solves the 24 game by trying all possible operations.
! Utilizes OpenMP tasks for parallelization.
! Arguments:
! nums: Array of numbers to use in the game.
! exprs: Array of string expressions representing the numbers.
! found: Logical flag indicating if a solution has been found.
!-----------------------------------------------------------------------
recursive subroutine solve_24(nums, exprs, found)
use omp_lib
implicit none
real, intent(in) :: nums(:) ! Input: Array of numbers
character(len=expr_len), intent(in) :: exprs(:) ! Input: Array of expressions
logical, intent(inout) :: found ! Input/Output: Flag indicating if a solution is found
integer :: n ! Size of the input arrays
integer :: i, j, op ! Loop counters
real :: a, b, result ! Temporary variables for calculations
real, allocatable :: new_nums(:) ! Temp array to store numbers after an operation
character(len=expr_len), allocatable :: new_exprs(:) ! Temp array to store expressions after an operation
character(len=expr_len) :: expr_a, expr_b, new_expr ! Temp variables for expressions
n = size(nums)
! Increment the completed_calls counter and update progress bar
if (show_progress) then
!$omp atomic
completed_calls = completed_calls + 1
call update_progress_bar()
end if
! If a solution is found, return
if (found) return
! Base case: If only one number is left, check if it is 24
if (n == 1) then
if (abs(nums(1) - 24.0) < 1e-4) then
if (show_progress) then
write (*, '(A, F5.1, A)', advance='no') carriage_return//'['//repeat('=', progress_bar_width)//'] ', 100.0, '%'
write (*, '(A)') '' ! Insert a blank line
end if
!$omp critical
write (*, '(A, A, A, F10.7, A)') 'Solution found:', trim(exprs(1)), '= 24 (', nums(1), ')'
found = .true.
!$omp end critical
end if
return
end if
! Iterate over all pairs of numbers
do i = 1, n - 1
do j = i + 1, n
a = nums(i)
b = nums(j)
expr_a = exprs(i)
expr_b = exprs(j)
! Iterate over all operators
do op = 1, 4
! Avoid division by zero
if ((op == 4 .and. abs(b) < 1e-6)) cycle
! Perform the operation and create the new expression
select case (op)
case (1)
result = a + b
new_expr = '('//trim(expr_a)//'+'//trim(expr_b)//')'
case (2)
result = a - b
new_expr = '('//trim(expr_a)//'-'//trim(expr_b)//')'
case (3)
result = a * b
new_expr = '('//trim(expr_a)//'*'//trim(expr_b)//')'
case (4)
result = a / b
new_expr = '('//trim(expr_a)//'/'//trim(expr_b)//')'
end select
! Create new arrays with the selected numbers removed
call create_new_arrays(nums, exprs, i, j, result, new_expr, new_nums, new_exprs)
! For the first few recursion levels, create parallel tasks
if (n >= 6 .and. omp_get_level() < 2) then
!$omp task shared(found) firstprivate(new_nums, new_exprs)
call solve_24(new_nums, new_exprs, found)
!$omp end task
else
call solve_24(new_nums, new_exprs, found)
end if
! If a solution is found, deallocate memory and return
if (found) then
deallocate (new_nums)
deallocate (new_exprs)
return
end if
! Handle commutative operations only once
if (op == 1 .or. op == 3) cycle
! Swap operands for subtraction and division
if (op == 2 .or. op == 4) then
if (op == 4 .and. abs(a) < 1e-6) cycle ! Avoid division by zero
select case (op)
case (2)
result = b - a
new_expr = '('//trim(expr_b)//'-'//trim(expr_a)//')'
case (4)
result = b / a
new_expr = '('//trim(expr_b)//'/'//trim(expr_a)//')'
end select
! Create new arrays with the selected numbers removed
call create_new_arrays(nums, exprs, i, j, result, new_expr, new_nums, new_exprs)
! For the first few recursion levels, create parallel tasks
if (n >= 6 .and. omp_get_level() < 2) then
!$omp task shared(found) firstprivate(new_nums, new_exprs)
call solve_24(new_nums, new_exprs, found)
!$omp end task
else
! Recursively call the solve_24 function with the new arrays
call solve_24(new_nums, new_exprs, found)
end if
! If a solution is found, deallocate memory and return
if (found) then
deallocate (new_nums)
deallocate (new_exprs)
return
end if
end if
end do ! End of operator loop
end do ! End of j loop
end do ! End of i loop
end subroutine solve_24
end module game24_module
program game24
use game24_module
implicit none
! Declare variables
integer :: maxn ! Number of numbers to be entered by the user
real, allocatable :: numbers(:) ! Array to store the numbers entered by the user
character(len=expr_len), allocatable :: expressions(:) ! Array to store the expressions
integer :: i, ios ! Loop counter and I/O status
logical :: found_solution ! Flag to indicate if a solution was found
character(len=10) :: user_input ! Variable to store user input
character(len=1) :: play_again ! Variable to store the user's decision
do ! Game loop to allow restarting the game
! Prompt the user for the number of numbers to use in the game
do
write (*, '(A,I0,A)', advance='no') 'Enter the number of numbers (1 to ', max_limit, '): '
read (*, *, iostat=ios) maxn
! Check if the input is valid
if (ios /= 0) then
write (*, '(A,I0,A)') 'Invalid input. Please enter an integer between 1 and ', max_limit, '.'
cycle
end if
! Validate the input: Ensure the number of numbers is within the valid range
if (maxn < 1 .or. maxn > max_limit) then
write (*, '(A,I0,A)') 'Error: Number of numbers must be between 1 and ', max_limit, '. Try again.'
cycle
end if
exit ! Exit loop if the input is valid
end do
! Allocate memory for the arrays based on the number of numbers
allocate (numbers(maxn))
allocate (expressions(maxn))
! Prompt the user to enter the numbers or card values
write (*, '(A,I0,A)') 'Enter ', maxn, ' numbers or card values (A=1, J=11, Q=12, K=13).'
do i = 1, maxn
do
! Prompt the user to enter a number or card value
write (*, '(A,I0,A)', advance='no') 'Enter value for card ', i, ': '
read (*, '(A)', iostat=ios) user_input
! Check if input is an integer or valid card symbol (A, J, Q, K)
call convert_to_number(user_input, numbers(i), ios)
! If the input is valid, exit loop
if (ios == 0) exit
! Invalid input: prompt the user to try again
write (*, '(A)') 'Invalid input. Please enter an integer or valid card symbol (A, J, Q, K).'
end do
! Convert the number to a string expression and remove trailing zeros
write (expressions(i), '(F0.2)') numbers(i)
call remove_decimal_zeros(expressions(i), expressions(i))
end do
! Initialize the solution flag to false
found_solution = .false.
! Assign precomputed total_calls based on n
select case (maxn)
case (6)
total_calls = total_calls_n6
case (7)
total_calls = total_calls_n7
case (8)
total_calls = total_calls_n8
case default
total_calls = 0
end select
! Decide whether to show progress bar based on n
if (maxn >= 6) then
show_progress = .true.
completed_calls = 0
last_percentage = -1
! Initialize progress bar display
write (*, '(A)', advance='no') '['//repeat(' ', progress_bar_width)//'] 0%'
call flush (0) ! Ensure the output is displayed immediately
else
show_progress = .false.
end if
! Start parallel region
!$omp parallel
!$omp single nowait
call solve_24(numbers, expressions, found_solution)
!$omp end single
!$omp end parallel
! After search completes, ensure the progress bar reaches 100% if shown
if (show_progress .and. .not. found_solution) then
write (*, '(A, A)', advance='no') carriage_return//'['//repeat('=', progress_bar_width)//'] 100% '
call flush (0)
write (*, '(A)') '' ! Insert a blank line
end if
! If a solution was found and progress bar is shown, ensure a blank line
if (show_progress .and. found_solution) then
! Progress bar already refreshed to 100% and blank line inserted in solve_24
end if
! If no solution was found, print a message
if (.not. found_solution) then
write (*, '(A)') 'No valid solution found.'
end if
! Deallocate the memory used by the arrays
deallocate (numbers)
deallocate (expressions)
! Ask the user if they want to play again
if (show_progress) then
write (*, '(A)', advance='no') carriage_return//'Play again? (Enter y/n to continue or any other key to exit): '
else
write (*, '(A)', advance='no') 'Play again? (Enter y/n to continue or any other key to exit): '
end if
read (*, '(A)') play_again ! Read user input
! Check if the user wants to exit
if (play_again /= 'y' .and. play_again /= 'Y') exit
end do ! End of game loop
write (*, '(A)') 'Exiting the game...'
end program game24
- Output:
| n | inputs | outputs |
|---|---|---|
| 4 | (A, 2, 3, 4) | (4*(3+(1+2))) = 24 (24.0000000) |
| 4 | (3, 3, 8, 8) | (8/(3-(8/3))) = 24 (24.0000057) |
| 6 | (174, 985, 244, 192, 784, 454) | No valid solution found. |
| 7 | (174, 985, 244, 192, 784, 454, 520) | (((454*(520-244))-(192*754))/(174-985)) = 24 (24.0000000) |
| 8 | (17495, 3, -7, q, Q, a, A, 74) | ((12+12)+((1+1)/((74--7)*(17495+3)))) = 24 (24.0000019) |
FreeBASIC
Type GameState
digitos(3) As Double
operaciones(2) As String
End Type
Function randomDigits() As String
Dim As String resultado = ""
For i As Integer = 0 To 3
resultado &= Str(Int(Rnd * 9) + 1)
Next
Return resultado
End Function
Function evaluate(digitos() As Double, operaciones() As String) As Double
Dim As Double valor = digitos(0)
For i As Integer = 0 To 2
Select Case operaciones(i)
Case "+": valor += digitos(i +1)
Case "-": valor -= digitos(i +1)
Case "*": valor *= digitos(i +1)
Case "/": If digitos(i +1) <> 0 Then valor /= digitos(i +1)
End Select
Next
Return valor
End Function
Sub permute(digitos() As Double, soluciones() As GameState, Byref solutionCnt As Integer, k As Integer)
Dim As String*1 opChars(3) = {"+", "-", "*", "/"}
Dim As String ops(2)
Dim As Integer i, j, l, m
If k = 4 Then
For i = 0 To 3
ops(0) = opChars(i)
For j = 0 To 3
ops(1) = opChars(j)
For l = 0 To 3
ops(2) = opChars(l)
If Abs(evaluate(digitos(), ops()) - 24) < 0.001 Then
With soluciones(solutionCnt)
For m = 0 To 3: .digitos(m) = digitos(m): Next
For m = 0 To 2: .operaciones(m) = ops(m): Next
End With
solutionCnt += 1
Exit For 'Stop after first solution
End If
Next
If solutionCnt Then Exit For
Next
If solutionCnt Then Exit For
Next
Else
For i = k To 3
Swap digitos(i), digitos(k)
permute(digitos(), soluciones(), solutionCnt, k +1)
If solutionCnt Then Exit For
Swap digitos(k), digitos(i)
Next
End If
End Sub
' Main program
Randomize Timer
Dim As Integer i
Dim As String cmd
Dim As Double digitos(3)
Dim As String operaciones(2)
Do
Cls
Print "24 Game"
Print "Generating 4 digitos..."
Dim As String inputDigits = randomDigits()
Print "Make 24 using these digitos: ";
For i = 1 To Len(inputDigits)
Print Mid(inputDigits, i, 1); " ";
Next
Print
Line Input "Enter your expression (e.g. 4+5*3-2): ", cmd
Dim As Integer digitCnt = 0, opCnt = 0
' Parse user input
For i = 1 To Len(cmd)
Select Case Mid(cmd, i, 1)
Case "1" To "9"
digitos(digitCnt) = Val(Mid(cmd, i, 1))
digitCnt += 1
Case "+", "-", "*", "/"
operaciones(opCnt) = Mid(cmd, i, 1)
opCnt += 1
End Select
Next
Dim As Double resultado = evaluate(digitos(), operaciones())
Print "Your resultado: "; resultado
If Abs(resultado - 24) < 0.001 Then
Print !"\nCongratulations, you found a solution!"
Else
Print !"\nThe valor of your expression is "; resultado; " instead of 24!"
Dim As GameState soluciones(1000)
Dim As Integer solucCnt = 0
permute(digitos(), soluciones(), solucCnt, 0)
If solucCnt > 0 Then
Print !"\nA possible solution could have been: ";
With soluciones(0)
Print .digitos(0) & .operaciones(0) & .digitos(1) & .operaciones(1) & .digitos(2) & .operaciones(2) & .digitos(3)
End With
Else
Print !"\nThere was no known solution for these digitos."
End If
End If
Print !"\nDo you want to try again? (press N for exit, other key to continue)"
Loop Until (Ucase(Input(1)) = "N")
Sleep
- Output:
24 Game Generating 4 digitos... Make 24 using these digitos: 6 6 5 5 Enter your expression (e.g. 4+5*3-2): 5+5-6*6 Your resultado: 24 Congratulations, you found a solution! Do you want to try again? (press N for exit, other key to continue)
FutureBasic
This programme gives just the first-found (simplest) solution. To see the exhaustive list, we would remove the if k > 0 then exit fn statements.
begin globals
Short k
end globals
void local fn eval( t as CFStringRef )
CFMutableStringRef s = fn MutableStringNew
ExpressionRef x = fn ExpressionWithFormat( t )
CFRange r = fn CFRangeMake(0, fn StringLength( t ) )
CFNumberRef n = fn ExpressionValueWithObject( x, Null, Null )
Float f = dblval( n )
if f = 24 // found, so clean up
MutableStringSetString( s, t ) // duplicate string and pretend it was integers all along
MutableStringReplaceOccurrencesOfString( s, @".000000", @"", Null, r )
print s; @" = 24" : k ++
end if
end fn
clear local fn work( t as CFStringRef )
Short a, b, c, d, e, f, g
CGFloat n(3)
CFStringRef s, os = @"*/+-", o(3)
print t, : k = 0
// Put digits (as floats) and operators (as strings) in arrays
for a = 0 to 3 : s = mid( t, a, 1 ) : n(a) = fn StringFloatValue( s ) : o(a) = mid( os, a, 1 ) : next
// Permutions for the digits ...
for d = 0 to 3 : for e = 0 to 3 : for f = 0 to 3 : for g = 0 to 3
if d != e and d != f and d != g and e != f and e != g and f != g // ... without duplications
// Combinations for the operators (3 from 4, with replacement)
for a = 0 to 3 : for b = 0 to 3 : for c = 0 to 3
fn eval( fn StringWithFormat( @"%f %@ %f %@ %f %@ %f", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"%f %@ ( %f %@ %f ) %@ %f", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"%f %@ %f %@ ( %f %@ %f )", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"%f %@ ( %f %@ %f %@ %f )", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"( %f %@ %f ) %@ %f %@ %f", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"( %f %@ %f %@ %f ) %@ %f", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"%f %@ ( %f %@ ( %f %@ %f ) )", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"( %f %@ %f ) %@ ( %f %@ %f )", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"( %f %@ ( %f %@ %f )) %@ %f", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"( ( %f %@ %f ) %@ %f ) %@ %f", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
fn eval( fn StringWithFormat( @"%f %@ ( ( %f %@ %f ) %@ %f )", n(d), o(a), n(e), o(b), n(f), o(c), n(g) ) ) : if k > 0 then exit fn
next : next : next
end if
next : next : next : next
end fn
window 1, @"24 Game", ( 0, 0, 250, 250 )
fn work(@"3388")
fn work(@"1346")
fn work(@"8752")
handleevents- Output:
3388 8 / ( 3 - 8 / 3 ) = 24 1346 6 / ( 1 - 3 / 4 ) = 24 8752 8 * ( 5 * 2 - 7 ) = 24
GAP
# Solution in '''RPN'''
check := function(x, y, z)
local r, c, s, i, j, k, a, b, p;
i := 0;
j := 0;
k := 0;
s := [ ];
r := "";
for c in z do
if c = 'x' then
i := i + 1;
k := k + 1;
s[k] := x[i];
Append(r, String(x[i]));
else
j := j + 1;
b := s[k];
k := k - 1;
a := s[k];
p := y[j];
r[Size(r) + 1] := p;
if p = '+' then
a := a + b;
elif p = '-' then
a := a - b;
elif p = '*' then
a := a * b;
elif p = '/' then
if b = 0 then
continue;
else
a := a / b;
fi;
else
return fail;
fi;
s[k] := a;
fi;
od;
if s[1] = 24 then
return r;
else
return fail;
fi;
end;
Player24 := function(digits)
local u, v, w, x, y, z, r;
u := PermutationsList(digits);
v := Tuples("+-*/", 3);
w := ["xx*x*x*", "xx*xx**", "xxx**x*", "xxx*x**", "xxxx***"];
for x in u do
for y in v do
for z in w do
r := check(x, y, z);
if r <> fail then
return r;
fi;
od;
od;
od;
return fail;
end;
Player24([1,2,7,7]);
# "77*1-2/"
Player24([9,8,7,6]);
# "68*97-/"
Player24([1,1,7,7]);
# fail
# Solutions with only one distinct digit are found only for 3, 4, 5, 6:
Player24([3,3,3,3]);
# "33*3*3-"
Player24([4,4,4,4]);
# "44*4+4+"
Player24([5,5,5,5]);
# "55*55/-"
Player24([6,6,6,6]);
# "66*66+-"
# A tricky one:
Player24([3,3,8,8]);
"8383/-/"
Go
package main
import (
"fmt"
"math/rand"
"time"
)
const (
op_num = iota
op_add
op_sub
op_mul
op_div
)
type frac struct {
num, denom int
}
// Expression: can either be a single number, or a result of binary
// operation from left and right node
type Expr struct {
op int
left, right *Expr
value frac
}
var n_cards = 4
var goal = 24
var digit_range = 9
func (x *Expr) String() string {
if x.op == op_num {
return fmt.Sprintf("%d", x.value.num)
}
var bl1, br1, bl2, br2, opstr string
switch {
case x.left.op == op_num:
case x.left.op >= x.op:
case x.left.op == op_add && x.op == op_sub:
bl1, br1 = "", ""
default:
bl1, br1 = "(", ")"
}
if x.right.op == op_num || x.op < x.right.op {
bl2, br2 = "", ""
} else {
bl2, br2 = "(", ")"
}
switch {
case x.op == op_add:
opstr = " + "
case x.op == op_sub:
opstr = " - "
case x.op == op_mul:
opstr = " * "
case x.op == op_div:
opstr = " / "
}
return bl1 + x.left.String() + br1 + opstr +
bl2 + x.right.String() + br2
}
func expr_eval(x *Expr) (f frac) {
if x.op == op_num {
return x.value
}
l, r := expr_eval(x.left), expr_eval(x.right)
switch x.op {
case op_add:
f.num = l.num*r.denom + l.denom*r.num
f.denom = l.denom * r.denom
return
case op_sub:
f.num = l.num*r.denom - l.denom*r.num
f.denom = l.denom * r.denom
return
case op_mul:
f.num = l.num * r.num
f.denom = l.denom * r.denom
return
case op_div:
f.num = l.num * r.denom
f.denom = l.denom * r.num
return
}
return
}
func solve(ex_in []*Expr) bool {
// only one expression left, meaning all numbers are arranged into
// a binary tree, so evaluate and see if we get 24
if len(ex_in) == 1 {
f := expr_eval(ex_in[0])
if f.denom != 0 && f.num == f.denom*goal {
fmt.Println(ex_in[0].String())
return true
}
return false
}
var node Expr
ex := make([]*Expr, len(ex_in)-1)
// try to combine a pair of expressions into one, thus reduce
// the list length by 1, and recurse down
for i := range ex {
copy(ex[i:len(ex)], ex_in[i+1:len(ex_in)])
ex[i] = &node
for j := i + 1; j < len(ex_in); j++ {
node.left = ex_in[i]
node.right = ex_in[j]
// try all 4 operators
for o := op_add; o <= op_div; o++ {
node.op = o
if solve(ex) {
return true
}
}
// also - and / are not commutative, so swap arguments
node.left = ex_in[j]
node.right = ex_in[i]
node.op = op_sub
if solve(ex) {
return true
}
node.op = op_div
if solve(ex) {
return true
}
if j < len(ex) {
ex[j] = ex_in[j]
}
}
ex[i] = ex_in[i]
}
return false
}
func main() {
cards := make([]*Expr, n_cards)
rand.Seed(time.Now().Unix())
for k := 0; k < 10; k++ {
for i := 0; i < n_cards; i++ {
cards[i] = &Expr{op_num, nil, nil,
frac{rand.Intn(digit_range-1) + 1, 1}}
fmt.Printf(" %d", cards[i].value.num)
}
fmt.Print(": ")
if !solve(cards) {
fmt.Println("No solution")
}
}
}
- Output:
8 6 7 6: No solution 7 2 6 6: (7 - 2) * 6 - 6 4 8 7 3: 4 * (7 - 3) + 8 3 8 8 7: 3 * 8 * (8 - 7) 5 7 3 7: No solution 5 7 8 3: 5 * 7 - 8 - 3 3 6 5 2: ((3 + 5) * 6) / 2 8 4 5 4: (8 - 4) * 5 + 4 2 2 8 8: (2 + 2) * 8 - 8 6 8 8 2: 6 + 8 + 8 + 2
Gosu
uses java.lang.Integer
uses java.lang.Double
uses java.lang.System
uses java.util.ArrayList
uses java.util.LinkedList
uses java.util.List
uses java.util.Scanner
uses java.util.Stack
function permutations<T>( lst : List<T> ) : List<List<T>> {
if( lst.size() == 0 ) return {}
if( lst.size() == 1 ) return { lst }
var pivot = lst.get(lst.size()-1)
var sublist = new ArrayList<T>( lst )
sublist.remove( sublist.size() - 1 )
var subPerms = permutations( sublist )
var ret = new ArrayList<List<T>>()
for( x in subPerms ) {
for( e in x index i ) {
var next = new LinkedList<T>( x )
next.add( i, pivot )
ret.add( next )
}
x.add( pivot )
ret.add( x )
}
return ret
}
function readVals() : List<Integer> {
var line = new java.io.BufferedReader( new java.io.InputStreamReader( System.in ) ).readLine()
var scan = new Scanner( line )
var ret = new ArrayList<Integer>()
for( i in 0..3 ) {
var next = scan.nextInt()
if( 0 >= next || next >= 10 ) {
print( "Invalid entry: ${next}" )
return null
}
ret.add( next )
}
return ret
}
function getOp( i : int ) : char[] {
var ret = new char[3]
var ops = { '+', '-', '*', '/' }
ret[0] = ops[i / 16]
ret[1] = ops[(i / 4) % 4 ]
ret[2] = ops[i % 4 ]
return ret
}
function isSoln( nums : List<Integer>, ops : char[] ) : boolean {
var stk = new Stack<Double>()
for( n in nums ) {
stk.push( n )
}
for( c in ops ) {
var r = stk.pop().doubleValue()
var l = stk.pop().doubleValue()
if( c == '+' ) {
stk.push( l + r )
} else if( c == '-' ) {
stk.push( l - r )
} else if( c == '*' ) {
stk.push( l * r )
} else if( c == '/' ) {
// Avoid division by 0
if( r == 0.0 ) {
return false
}
stk.push( l / r )
}
}
return java.lang.Math.abs( stk.pop().doubleValue() - 24.0 ) < 0.001
}
function printSoln( nums : List<Integer>, ops : char[] ) {
// RPN: a b c d + - *
// Infix (a * (b - (c + d)))
print( "Found soln: (${nums.get(0)} ${ops[0]} (${nums.get(1)} ${ops[1]} (${nums.get(2)} ${ops[2]} ${nums.get(3)})))" )
}
System.out.print( "#> " )
var vals = readVals()
var opPerms = 0..63
var solnFound = false
for( i in permutations( vals ) ) {
for( j in opPerms ) {
var opList = getOp( j )
if( isSoln( i, opList ) ) {
printSoln( i, opList )
solnFound = true
}
}
}
if( ! solnFound ) {
print( "No solution!" )
}
Haskell
import Data.List
import Data.Ratio
import Control.Monad
import System.Environment (getArgs)
data Expr = Constant Rational |
Expr :+ Expr | Expr :- Expr |
Expr :* Expr | Expr :/ Expr
deriving (Eq)
ops = [(:+), (:-), (:*), (:/)]
instance Show Expr where
show (Constant x) = show $ numerator x
-- In this program, we need only print integers.
show (a :+ b) = strexp "+" a b
show (a :- b) = strexp "-" a b
show (a :* b) = strexp "*" a b
show (a :/ b) = strexp "/" a b
strexp :: String -> Expr -> Expr -> String
strexp op a b = "(" ++ show a ++ " " ++ op ++ " " ++ show b ++ ")"
templates :: [[Expr] -> Expr]
templates = do
op1 <- ops
op2 <- ops
op3 <- ops
[\[a, b, c, d] -> op1 a $ op2 b $ op3 c d,
\[a, b, c, d] -> op1 (op2 a b) $ op3 c d,
\[a, b, c, d] -> op1 a $ op2 (op3 b c) d,
\[a, b, c, d] -> op1 (op2 a $ op3 b c) d,
\[a, b, c, d] -> op1 (op2 (op3 a b) c) d]
eval :: Expr -> Maybe Rational
eval (Constant c) = Just c
eval (a :+ b) = liftM2 (+) (eval a) (eval b)
eval (a :- b) = liftM2 (-) (eval a) (eval b)
eval (a :* b) = liftM2 (*) (eval a) (eval b)
eval (a :/ b) = do
denom <- eval b
guard $ denom /= 0
liftM (/ denom) $ eval a
solve :: Rational -> [Rational] -> [Expr]
solve target r4 = filter (maybe False (== target) . eval) $
liftM2 ($) templates $
nub $ permutations $ map Constant r4
main = getArgs >>= mapM_ print . solve 24 . map (toEnum . read)
Example use:
$ runghc 24Player.hs 2 3 8 9 (8 * (9 - (3 * 2))) (8 * (9 - (2 * 3))) ((9 - (2 * 3)) * 8) ((9 - (3 * 2)) * 8) ((9 - 3) * (8 / 2)) ((8 / 2) * (9 - 3)) (8 * ((9 - 3) / 2)) (((9 - 3) / 2) * 8) ((9 - 3) / (2 / 8)) ((8 * (9 - 3)) / 2) (((9 - 3) * 8) / 2) (8 / (2 / (9 - 3)))
Alternative version
import Control.Applicative
import Data.List
import Text.PrettyPrint
data Expr = C Int | Op String Expr Expr
toDoc (C x ) = int x
toDoc (Op op x y) = parens $ toDoc x <+> text op <+> toDoc y
ops :: [(String, Int -> Int -> Int)]
ops = [("+",(+)), ("-",(-)), ("*",(*)), ("/",div)]
solve :: Int -> [Int] -> [Expr]
solve res = filter ((Just res ==) . eval) . genAst
where
genAst [x] = [C x]
genAst xs = do
(ys,zs) <- split xs
let f (Op op _ _) = op `notElem` ["+","*"] || ys <= zs
filter f $ Op <$> map fst ops <*> genAst ys <*> genAst zs
eval (C x ) = Just x
eval (Op "/" _ y) | Just 0 <- eval y = Nothing
eval (Op op x y) = lookup op ops <*> eval x <*> eval y
select :: Int -> [Int] -> [[Int]]
select 0 _ = [[]]
select n xs = [x:zs | k <- [0..length xs - n]
, let (x:ys) = drop k xs
, zs <- select (n - 1) ys
]
split :: [Int] -> [([Int],[Int])]
split xs = [(ys, xs \\ ys) | n <- [1..length xs - 1]
, ys <- nub . sort $ select n xs
]
main = mapM_ (putStrLn . render . toDoc) $ solve 24 [2,3,8,9]
- Output:
((8 / 2) * (9 - 3)) ((2 / 9) + (3 * 8)) ((3 * 8) - (2 / 9)) ((8 - (2 / 9)) * 3) (((2 / 9) + 8) * 3) (((8 + 9) / 2) * 3) ((2 + (8 * 9)) / 3) ((3 - (2 / 9)) * 8) ((9 - (2 * 3)) * 8) (((2 / 9) + 3) * 8) (((2 + 9) / 3) * 8) (((9 - 3) / 2) * 8) (((9 - 3) * 8) / 2)
Icon and Unicon
This shares code with and solves the 24 game. A series of pattern expressions are built up and then populated with the permutations of the selected digits. Equations are skipped if they have been seen before. The procedure 'eval' was modified to catch zero divides. The solution will find either all occurrences or just the first occurrence of a solution.
strings.icn provides deletec and permutes
J
perm=: (A.&i.~ !) 4
ops=: ' ',.'+-*%' {~ >,{i.each 4 4 4
cmask=: 1 + 0j1 * i.@{:@$@[ e. ]
left=: [ #!.'('~"1 cmask
right=: [ #!.')'~"1 cmask
paren=: 2 :'[: left&m right&n'
parens=: ], 0 paren 3, 0 paren 5, 2 paren 5, [: 0 paren 7 (0 paren 3)
all=: [: parens [:,/ ops ,@,."1/ perm { [:;":each
answer=: ({.@#~ 24 = ".)@all
This implementation tests all 7680 candidate sentences.
Example use:
answer 2 3 5 7 2+7+3*5 answer 8 4 7 1 8*7-4*1 answer 1 1 2 7 (1+2)*1+7
The answer will be either a suitable J sentence or blank if none can be found. "J sentence" means that, for example, the sentence 8*7-4*1 is equivalent to the sentence 8*(7-(4*1)). [Many infix languages use operator precedence to make polynomials easier to express without parenthesis, but J has other mechanisms for expressing polynomials and minimal operator precedence makes the language more regular.]
Here is an alternative version that supports multi-digit numbers. It prefers expressions without parens, but searches for ones with if needed.
ops=: > , { 3#<'+-*%'
perms=: [: ":"0 [: ~. i.@!@# A. ]
build=: 1 : '(#~ 24 = ".) @: u'
combp=: dyad define
'a b c d'=. y['f g h'=. x
('(',a,f,b,g,c,')',h,d),('(',a,f,b,')',g,c,h,d),(a,f,'(',b,g,c,')',h,d),:('((',a,f,b,')',g,c,')',h,d)
)
math24=: monad define
assert. 4 = # y NB. prefer expressions without parens & fallback if needed
es=. ([: ,/ ops ([: , (' ',[) ,. ])"1 2/ perms) build y
if. 0 = #es do. es =. ([: ,/ [: ,/ ops combp"1 2/ perms) build y end.
es -."1 ' '
)
- Output:
math24 2 3 5 12 12%3-5%2 math24 2 3 8 9 8*9-2*3 8*9-3*2 8%2%9-3 math24 3 6 6 11 (6+6*11)%3 (6+11*6)%3 ((6*11)+6)%3 ((11*6)+6)%3
Java
Playable version, will print solution on request.
Note that this version does not extend to different digit ranges.
import java.util.*;
public class Game24Player {
final String[] patterns = {"nnonnoo", "nnonono", "nnnoono", "nnnonoo",
"nnnnooo"};
final String ops = "+-*/^";
String solution;
List<Integer> digits;
public static void main(String[] args) {
new Game24Player().play();
}
void play() {
digits = getSolvableDigits();
Scanner in = new Scanner(System.in);
while (true) {
System.out.print("Make 24 using these digits: ");
System.out.println(digits);
System.out.println("(Enter 'q' to quit, 's' for a solution)");
System.out.print("> ");
String line = in.nextLine();
if (line.equalsIgnoreCase("q")) {
System.out.println("\nThanks for playing");
return;
}
if (line.equalsIgnoreCase("s")) {
System.out.println(solution);
digits = getSolvableDigits();
continue;
}
char[] entry = line.replaceAll("[^*+-/)(\\d]", "").toCharArray();
try {
validate(entry);
if (evaluate(infixToPostfix(entry))) {
System.out.println("\nCorrect! Want to try another? ");
digits = getSolvableDigits();
} else {
System.out.println("\nNot correct.");
}
} catch (Exception e) {
System.out.printf("%n%s Try again.%n", e.getMessage());
}
}
}
void validate(char[] input) throws Exception {
int total1 = 0, parens = 0, opsCount = 0;
for (char c : input) {
if (Character.isDigit(c))
total1 += 1 << (c - '0') * 4;
else if (c == '(')
parens++;
else if (c == ')')
parens--;
else if (ops.indexOf(c) != -1)
opsCount++;
if (parens < 0)
throw new Exception("Parentheses mismatch.");
}
if (parens != 0)
throw new Exception("Parentheses mismatch.");
if (opsCount != 3)
throw new Exception("Wrong number of operators.");
int total2 = 0;
for (int d : digits)
total2 += 1 << d * 4;
if (total1 != total2)
throw new Exception("Not the same digits.");
}
boolean evaluate(char[] line) throws Exception {
Stack<Float> s = new Stack<>();
try {
for (char c : line) {
if ('0' <= c && c <= '9')
s.push((float) c - '0');
else
s.push(applyOperator(s.pop(), s.pop(), c));
}
} catch (EmptyStackException e) {
throw new Exception("Invalid entry.");
}
return (Math.abs(24 - s.peek()) < 0.001F);
}
float applyOperator(float a, float b, char c) {
switch (c) {
case '+':
return a + b;
case '-':
return b - a;
case '*':
return a * b;
case '/':
return b / a;
default:
return Float.NaN;
}
}
List<Integer> randomDigits() {
Random r = new Random();
List<Integer> result = new ArrayList<>(4);
for (int i = 0; i < 4; i++)
result.add(r.nextInt(9) + 1);
return result;
}
List<Integer> getSolvableDigits() {
List<Integer> result;
do {
result = randomDigits();
} while (!isSolvable(result));
return result;
}
boolean isSolvable(List<Integer> digits) {
Set<List<Integer>> dPerms = new HashSet<>(4 * 3 * 2);
permute(digits, dPerms, 0);
int total = 4 * 4 * 4;
List<List<Integer>> oPerms = new ArrayList<>(total);
permuteOperators(oPerms, 4, total);
StringBuilder sb = new StringBuilder(4 + 3);
for (String pattern : patterns) {
char[] patternChars = pattern.toCharArray();
for (List<Integer> dig : dPerms) {
for (List<Integer> opr : oPerms) {
int i = 0, j = 0;
for (char c : patternChars) {
if (c == 'n')
sb.append(dig.get(i++));
else
sb.append(ops.charAt(opr.get(j++)));
}
String candidate = sb.toString();
try {
if (evaluate(candidate.toCharArray())) {
solution = postfixToInfix(candidate);
return true;
}
} catch (Exception ignored) {
}
sb.setLength(0);
}
}
}
return false;
}
String postfixToInfix(String postfix) {
class Expression {
String op, ex;
int prec = 3;
Expression(String e) {
ex = e;
}
Expression(String e1, String e2, String o) {
ex = String.format("%s %s %s", e1, o, e2);
op = o;
prec = ops.indexOf(o) / 2;
}
}
Stack<Expression> expr = new Stack<>();
for (char c : postfix.toCharArray()) {
int idx = ops.indexOf(c);
if (idx != -1) {
Expression r = expr.pop();
Expression l = expr.pop();
int opPrec = idx / 2;
if (l.prec < opPrec)
l.ex = '(' + l.ex + ')';
if (r.prec <= opPrec)
r.ex = '(' + r.ex + ')';
expr.push(new Expression(l.ex, r.ex, "" + c));
} else {
expr.push(new Expression("" + c));
}
}
return expr.peek().ex;
}
char[] infixToPostfix(char[] infix) throws Exception {
StringBuilder sb = new StringBuilder();
Stack<Integer> s = new Stack<>();
try {
for (char c : infix) {
int idx = ops.indexOf(c);
if (idx != -1) {
if (s.isEmpty())
s.push(idx);
else {
while (!s.isEmpty()) {
int prec2 = s.peek() / 2;
int prec1 = idx / 2;
if (prec2 >= prec1)
sb.append(ops.charAt(s.pop()));
else
break;
}
s.push(idx);
}
} else if (c == '(') {
s.push(-2);
} else if (c == ')') {
while (s.peek() != -2)
sb.append(ops.charAt(s.pop()));
s.pop();
} else {
sb.append(c);
}
}
while (!s.isEmpty())
sb.append(ops.charAt(s.pop()));
} catch (EmptyStackException e) {
throw new Exception("Invalid entry.");
}
return sb.toString().toCharArray();
}
void permute(List<Integer> lst, Set<List<Integer>> res, int k) {
for (int i = k; i < lst.size(); i++) {
Collections.swap(lst, i, k);
permute(lst, res, k + 1);
Collections.swap(lst, k, i);
}
if (k == lst.size())
res.add(new ArrayList<>(lst));
}
void permuteOperators(List<List<Integer>> res, int n, int total) {
for (int i = 0, npow = n * n; i < total; i++)
res.add(Arrays.asList((i / npow), (i % npow) / n, i % n));
}
}
- Output:
Make 24 using these digits: [5, 7, 1, 8] (Enter 'q' to quit, 's' for a solution) > (8-5) * (7+1) Correct! Want to try another? Make 24 using these digits: [3, 9, 2, 9] (Enter 'q' to quit, 's' for a solution) > (3*2) + 9 + 9 Correct! Want to try another? Make 24 using these digits: [4, 4, 8, 5] (Enter 'q' to quit, 's' for a solution) > s 4 * 5 - (4 - 8) Make 24 using these digits: [2, 5, 9, 1] (Enter 'q' to quit, 's' for a solution) > 2+5+9+1 Not correct. Make 24 using these digits: [2, 5, 9, 1] (Enter 'q' to quit, 's' for a solution) > 2 * 9 + 5 + 1 Correct! Want to try another? Make 24 using these digits: [8, 4, 3, 1] (Enter 'q' to quit, 's' for a solution) > s (8 + 4) * (3 - 1) Make 24 using these digits: [9, 4, 5, 6] (Enter 'q' to quit, 's' for a solution) > (9 +4) * 2 - 2 Not the same digits. Try again. Make 24 using these digits: [9, 4, 5, 6] (Enter 'q' to quit, 's' for a solution) > q Thanks for playing
JavaScript
This is a translation of the C code.
var ar=[],order=[0,1,2],op=[],val=[];
var NOVAL=9999,oper="+-*/",out;
function rnd(n){return Math.floor(Math.random()*n)}
function say(s){
try{document.write(s+"<br>")}
catch(e){WScript.Echo(s)}
}
function getvalue(x,dir){
var r=NOVAL;
if(dir>0)++x;
while(1){
if(val[x]!=NOVAL){
r=val[x];
val[x]=NOVAL;
break;
}
x+=dir;
}
return r*1;
}
function calc(){
var c=0,l,r,x;
val=ar.join('/').split('/');
while(c<3){
x=order[c];
l=getvalue(x,-1);
r=getvalue(x,1);
switch(op[x]){
case 0:val[x]=l+r;break;
case 1:val[x]=l-r;break;
case 2:val[x]=l*r;break;
case 3:
if(!r||l%r)return 0;
val[x]=l/r;
}
++c;
}
return getvalue(-1,1);
}
function shuffle(s,n){
var x=n,p=eval(s),r,t;
while(x--){
r=rnd(n);
t=p[x];
p[x]=p[r];
p[r]=t;
}
}
function parenth(n){
while(n>0)--n,out+='(';
while(n<0)++n,out+=')';
}
function getpriority(x){
for(var z=3;z--;)if(order[z]==x)return 3-z;
return 0;
}
function showsolution(){
var x=0,p=0,lp=0,v=0;
while(x<4){
if(x<3){
lp=p;
p=getpriority(x);
v=p-lp;
if(v>0)parenth(v);
}
out+=ar[x];
if(x<3){
if(v<0)parenth(v);
out+=oper.charAt(op[x]);
}
++x;
}
parenth(-p);
say(out);
}
function solve24(s){
var z=4,r;
while(z--)ar[z]=s.charCodeAt(z)-48;
out="";
for(z=100000;z--;){
r=rnd(256);
op[0]=r&3;
op[1]=(r>>2)&3;
op[2]=(r>>4)&3;
shuffle("ar",4);
shuffle("order",3);
if(calc()!=24)continue;
showsolution();
break;
}
}
solve24("1234");
solve24("6789");
solve24("1127");
Examples:
(((3*1)*4)*2) ((6*8)/((9-7))) (((1+7))*(2+1))
jq
The following solution is generic: the objective (e.g. 24) is specified as the argument to solve/1, and the user may specify any number of numbers.
Infrastructure:
# Generate a stream of the permutations of the input array.
def permutations:
if length == 0 then []
else range(0;length) as $i
| [.[$i]] + (del(.[$i])|permutations)
end ;
# Generate a stream of arrays of length n,
# with members drawn from the input array.
def take(n):
length as $l |
if n == 1 then range(0;$l) as $i | [ .[$i] ]
else take(n-1) + take(1)
end;
# Emit an array with elements that alternate between those in the input array and those in short,
# starting with the former, and using nothing if "short" is too too short.
def intersperse(short):
. as $in
| reduce range(0;length) as $i
([]; . + [ $in[$i], (short[$i] // empty) ]);
# Emit a stream of all the nested triplet groupings of the input array elements,
# e.g. [1,2,3,4,5] =>
# [1,2,[3,4,5]]
# [[1,2,3],4,5]
#
def triples:
. as $in
| if length == 3 then .
elif length == 1 then $in[0]
elif length < 3 then empty
else
(range(0; (length-1) / 2) * 2 + 1) as $i
| ($in[0:$i] | triples) as $head
| ($in[$i+1:] | triples) as $tail
| [$head, $in[$i], $tail]
end;Evaluation and pretty-printing of allowed expressions
# Evaluate the input, which must be a number or a triple: [x, op, y]
def eval:
if type == "array" then
.[1] as $op
| if .[0] == null or .[2] == null then null
else
(.[0] | eval) as $left | (.[2] | eval) as $right
| if $left == null or $right == null then null
elif $op == "+" then $left + $right
elif $op == "-" then $left - $right
elif $op == "*" then $left * $right
elif $op == "/" then
if $right == 0 then null
else $left / $right
end
else "invalid arithmetic operator: \($op)" | error
end
end
else .
end;
def pp:
"\(.)" | explode | map([.] | implode | if . == "," then " " elif . == "\"" then "" else . end) | join("");24 Game:
def OPERATORS: ["+", "-", "*", "/"];
# Input: an array of 4 digits
# o: an array of 3 operators
# Output: a stream
def EXPRESSIONS(o):
intersperse( o ) | triples;
def solve(objective):
length as $length
| [ (OPERATORS | take($length-1)) as $poperators
| permutations | EXPRESSIONS($poperators)
| select( eval == objective)
] as $answers
| if $answers|length > 3 then "That was too easy. I found \($answers|length) answers, e.g. \($answers[0] | pp)"
elif $answers|length > 1 then $answers[] | pp
else "You lose! There are no solutions."
end
;
solve(24), "Please try again."- Output:
$ jq -r -f Solve.jq
[1,2,3,4]
That was too easy. I found 242 answers, e.g. [4 * [1 + [2 + 3]]]
Please try again.
[1,2,3,40,1]
That was too easy. I found 636 answers, e.g. [[[1 / 2] * 40] + [3 + 1]]
Please try again.
[3,8,9]
That was too easy. I found 8 answers, e.g. [[8 / 3] * 9]
Please try again.
[4,5,6]
You lose! There are no solutions.
Please try again.
[1,2,3,4,5,6]
That was too easy. I found 197926 answers, e.g. [[2 * [1 + 4]] + [3 + [5 + 6]]]
Please try again.
Julia
For julia version 0.5 and higher, the Combinatorics package must be installed and imported (`using Combinatorics`). Combinatorial functions like `nthperm` have been moved from Base to that package and are not available by default anymore.
function solve24(nums)
length(nums) != 4 && error("Input must be a 4-element Array")
syms = [+,-,*,/]
for x in syms, y in syms, z in syms
for i = 1:24
a,b,c,d = nthperm(nums,i)
if round(x(y(a,b),z(c,d)),5) == 24
return "($a$y$b)$x($c$z$d)"
elseif round(x(a,y(b,z(c,d))),5) == 24
return "$a$x($b$y($c$z$d))"
elseif round(x(y(z(c,d),b),a),5) == 24
return "(($c$z$d)$y$b)$x$a"
elseif round(x(y(b,z(c,d)),a),5) == 24
return "($b$y($c$z$d))$x$a"
end
end
end
return "0"
end
- Output:
julia> for i in 1:10
nums = rand(1:9, 4)
println("solve24($nums) -> $(solve24(nums))")
end
solve24([9,4,4,5]) -> 0
solve24([1,7,2,7]) -> ((7*7)-1)/2
solve24([5,7,5,4]) -> 4*(7-(5/5))
solve24([1,4,6,6]) -> 6+(6*(4-1))
solve24([2,3,7,3]) -> ((2+7)*3)-3
solve24([8,7,9,7]) -> 0
solve24([1,6,2,6]) -> 6+(6*(1+2))
solve24([7,9,4,1]) -> (7-4)*(9-1)
solve24([6,4,2,2]) -> (2-2)+(6*4)
solve24([5,7,9,7]) -> (5+7)*(9-7)
Kotlin
// version 1.1.3
import java.util.Random
const val N_CARDS = 4
const val SOLVE_GOAL = 24
const val MAX_DIGIT = 9
class Frac(val num: Int, val den: Int)
enum class OpType { NUM, ADD, SUB, MUL, DIV }
class Expr(
var op: OpType = OpType.NUM,
var left: Expr? = null,
var right: Expr? = null,
var value: Int = 0
)
fun showExpr(e: Expr?, prec: OpType, isRight: Boolean) {
if (e == null) return
val op = when (e.op) {
OpType.NUM -> { print(e.value); return }
OpType.ADD -> " + "
OpType.SUB -> " - "
OpType.MUL -> " x "
OpType.DIV -> " / "
}
if ((e.op == prec && isRight) || e.op < prec) print("(")
showExpr(e.left, e.op, false)
print(op)
showExpr(e.right, e.op, true)
if ((e.op == prec && isRight) || e.op < prec) print(")")
}
fun evalExpr(e: Expr?): Frac {
if (e == null) return Frac(0, 1)
if (e.op == OpType.NUM) return Frac(e.value, 1)
val l = evalExpr(e.left)
val r = evalExpr(e.right)
return when (e.op) {
OpType.ADD -> Frac(l.num * r.den + l.den * r.num, l.den * r.den)
OpType.SUB -> Frac(l.num * r.den - l.den * r.num, l.den * r.den)
OpType.MUL -> Frac(l.num * r.num, l.den * r.den)
OpType.DIV -> Frac(l.num * r.den, l.den * r.num)
else -> throw IllegalArgumentException("Unknown op: ${e.op}")
}
}
fun solve(ea: Array<Expr?>, len: Int): Boolean {
if (len == 1) {
val final = evalExpr<