24 game/Solve: Difference between revisions

=={{header|Prolog}}==

Works with SWI-Prolog.<BR>

The game is generic, you can choose to play with a goal different of 24, any number of numbers in other ranges than 1 .. 9 ! <BR>

rdiv/2 is use instead of //2 to enable the program to solve difficult cases as [3 3 8 8].

<lang Prolog>play24(Len, Range, Goal) :-

game(Len, Range, Goal, L, S),

maplist(my_write, L),

format(': ~w~n', [S]).

game(Len, Range, Value, L, S) :-

length(L, Len),

maplist(choose(Range), L),

compute(L, Value, [], S).

choose(Range, V) :-

V is random(Range) + 1.

write_tree([M], [M]).

write_tree([+, M, N], S) :-

write_tree(M, MS),

write_tree(N, NS),

append(MS, [+ | NS], S).

write_tree([-, M, N], S) :-

write_tree(M, MS),

write_tree(N, NS),

( is_add(N) -> append(MS, [-, '(' | NS], Temp), append(Temp, ')', S)

; append(MS, [- | NS], S)).

write_tree([Op, M, N], S) :-

member(Op, [*, /]),

write_tree(M, MS),

write_tree(N, NS),

( is_add(M) -> append(['(' | MS], [')'], TempM)

; TempM = MS),

( is_add(N) -> append(['(' | NS], [')'], TempN)

; TempN = NS),

append(TempM, [Op | TempN], S).

is_add([Op, _, _]) :-

member(Op, [+, -]).

compute([Value], Value, [[_R-S1]], S) :-

write_tree(S1, S2),

with_output_to(atom(S), maplist(write, S2)).

compute(L, Value, CS, S) :-

select(M, L, L1),

select(N, L1, L2),

next_value(M, N, R, CS, Expr),

compute([R|L2], Value, Expr, S).

next_value(M, N, R, CS,[[R - [+, M1, N1]] | CS2]) :-

R is M+N,

( member([M-ExprM], CS) -> select([M-ExprM], CS, CS1), M1 = ExprM

; M1 = [M], CS1 = CS

),

( member([N-ExprN], CS1) -> select([N-ExprN], CS1, CS2), N1 = ExprN

; N1 = [N], CS2 = CS1

).

next_value(M, N, R, CS,[[R - [-, M1, N1]] | CS2]) :-

R is M-N,

( member([M-ExprM], CS) -> select([M-ExprM], CS, CS1), M1 = ExprM

; M1 = [M], CS1 = CS

),

( member([N-ExprN], CS1) -> select([N-ExprN], CS1, CS2), N1 = ExprN

; N1 = [N], CS2 = CS1

).

next_value(M, N, R, CS,[[R - [*, M1, N1]] | CS2]) :-

R is M*N,

( member([M-ExprM], CS) -> select([M-ExprM], CS, CS1), M1 = ExprM

; M1 = [M], CS1 = CS

),

( member([N-ExprN], CS1) -> select([N-ExprN], CS1, CS2), N1 = ExprN

; N1 = [N], CS2 = CS1

).

next_value(M, N, R, CS,[[R - [/, M1, N1]] | CS2]) :-

N \= 0,

R is rdiv(M,N),

( member([M-ExprM], CS) -> select([M-ExprM], CS, CS1), M1 = ExprM

; M1 = [M], CS1 = CS

),

( member([N-ExprN], CS1) -> select([N-ExprN], CS1, CS2), N1 = ExprN

; N1 = [N], CS2 = CS1

).

my_write(V) :-

format('~w ', [V]).</lang>

Example of output :

<pre>?- play24(4,9, 24).

6 2 3 4 : (6-2+4)*3

true ;

6 2 3 4 : 3*(6-2+4)

true ;

6 2 3 4 : (6-2+4)*3

true ;

6 2 3 4 : 3*(6-2+4)

true ;

6 2 3 4 : (6*2-4)*3

true ;

6 2 3 4 : 3*(6*2-4)

true ;

6 2 3 4 : 3*4+6*2

true ;

6 2 3 4 : 3*4+6*2

true ;

6 2 3 4 : 4*3+6*2

true ;

6 2 3 4 : 4*3+6*2

true ;

6 2 3 4 : (6/2+3)*4

true ;

6 2 3 4 : 4*(6/2+3)

true ;

6 2 3 4 : (6/2+3)*4

true ;

6 2 3 4 : 4*(6/2+3)

true ;

6 2 3 4 : (6-3)*2*4

true ;

6 2 3 4 : 4*(6-3)*2

true ;

6 2 3 4 : (6-3)*4*2

...

?- play24(7,99, 1).

66 40 2 76 95 59 12 : (66+40)/2-76+95-59-12

true ;

66 40 2 76 95 59 12 : (66+40)/2-76+95-12-59

true ;

66 40 2 76 95 59 12 : (66+40)/2-76-59+95-12

true ;

66 40 2 76 95 59 12 : (66+40)/2-76-59-12+95

true ;

66 40 2 76 95 59 12 : 95+(66+40)/2-76-59-12

true ;

66 40 2 76 95 59 12 : 95+(66+40)/2-76-59-12

true ;

66 40 2 76 95 59 12 : 95-12+(66+40)/2-76-59

true ;

66 40 2 76 95 59 12 : (66+40)/2-76-59+95-12

....

</pre>