Prolog-拉丁方解

我正试图用Prolog编写一个程序来寻找一个大小为N的拉丁方

我现在有这个：

delete(X, [X|T], T).
delete(X, [H|T], [H|S]) :-
   delete(X, T, S).

permutation([], []).
permutation([H|T], R) :-
   permutation(T, X),
   delete(H, R, X).

latinSqaure([_]).
latinSquare([A,B|T], N) :-
   permutation(A,B),
   isSafe(A,B),
   latinSquare([B|T]).

isSafe([], []).
isSafe([H1|T1], [H2|T2]) :- 
   H1 =\= H2, 
   isSafe(T1, T2).

---

使用SWI Prolog库：

:- module(latin_square, [latin_square/2]).
:- use_module(library(clpfd), [transpose/2]).

latin_square(N, S) :-
    numlist(1, N, Row),
    length(Rows, N),
    maplist(copy_term(Row), Rows),
    maplist(permutation, Rows, S),
    transpose(S, T),
    maplist(valid, T).

valid([X|T]) :-
    memberchk(X, T), !, fail.
valid([_|T]) :- valid(T).
valid([_]).

测试：

编辑您的代码，一旦更正并删除拼写错误，它将是一个验证器，而不是生成器，但是（正如ssBarBee在删除的注释中所指出的那样），它的缺陷在于缺少对非相邻行的测试。 这里是正确的代码

delete(X, [X|T], T).
delete(X, [H|T], [H|S]) :-
    delete(X, T, S).

permutation([], []).
permutation([H|T], R):-
    permutation(T, X),
    delete(H, R, X).

latinSquare([_]).
latinSquare([A,B|T]) :-
    permutation(A,B),
    isSafe(A,B),
    latinSquare([B|T]).

isSafe([], []).
isSafe([H1|T1], [H2|T2]) :-
    H1 =\= H2,
    isSafe(T1, T2).

还有一些测试

?- latinSquare([[1,2,3],[2,3,1],[3,2,1]]).
false.

?- latinSquare([[1,2,3],[2,3,1],[3,1,2]]).
true .

?- latinSquare([[1,2,3],[2,3,1],[1,2,3]]).
true .

---

注意最后一个测试是错误的，应该改为

false

。

像@capelical一样，我建议对此使用CLP（FD）约束，这在所有严重的Prolog系统中都可用

实际上，考虑更广泛地使用约束，从约束传播中受益。 例如：

:- use_module(library(clpfd)).

latin_square(N, Rows, Vs) :-
        length(Rows, N),
        maplist(same_length(Rows), Rows),
        maplist(all_distinct, Rows),
        transpose(Rows, Cols),
        maplist(all_distinct, Cols),
        append(Rows, Vs),
        Vs ins 1..N.

例如，计算

N=4

的所有解决方案：

?- findall(., (latin_square(4,_,Vs),labeling([ff],Vs)), Ls), length(Ls, L). L = 576, Ls = [...].

---

因此，我们直接看到它终止了，因此这加上任何后续的

标记/2

搜索都保证找到所有解。

我有更好的解，@capelical code对于N长度大于5的正方形需要很长的时间

:- use_module(library(clpfd)).

make_square(0,_,[]) :- !.
make_square(I,N,[Row|Rest]) :-
   length(Row,N),
   I1 is I - 1,
   make_square(I1,N,Rest).

 all_different_in_row([]) :- !.
 all_different_in_row([Row|Rest]) :-
    all_different(Row),
    all_different_in_row(Rest).


all_different_in_column(Square) :-
   transpose(Square,TSquare),
   all_different_in_row(TSquare).   

all_different_in_column1([[]|_]) :- !.
all_different_in_column1(Square) :-
   maplist(column,Square,Column,Rest),
   all_different(Column),
   all_different_in_column1(Rest).


   latin_square(N,Square) :-
   make_square(N,N,Square),
   append(Square,AllVars),
   AllVars ins 1..N,
   all_different_in_row(Square),
   all_different_in_column(Square),
   labeling([ff],AllVars).

?- latin_square(20, _, _), false. false.

:- use_module(library(clpfd)).

make_square(0,_,[]) :- !.
make_square(I,N,[Row|Rest]) :-
   length(Row,N),
   I1 is I - 1,
   make_square(I1,N,Rest).

 all_different_in_row([]) :- !.
 all_different_in_row([Row|Rest]) :-
    all_different(Row),
    all_different_in_row(Rest).


all_different_in_column(Square) :-
   transpose(Square,TSquare),
   all_different_in_row(TSquare).   

all_different_in_column1([[]|_]) :- !.
all_different_in_column1(Square) :-
   maplist(column,Square,Column,Rest),
   all_different(Column),
   all_different_in_column1(Rest).


   latin_square(N,Square) :-
   make_square(N,N,Square),
   append(Square,AllVars),
   AllVars ins 1..N,
   all_different_in_row(Square),
   all_different_in_column(Square),
   labeling([ff],AllVars).