Prolog 最少移动次数

在本页中 演示了如何解决流行的狼、山羊和卷心菜难题

change(e,w).
change(w,e).

move([X,   X,Goat,Cabbage],   wolf,[Y,   Y,Goat,Cabbage]) :- change(X,Y).
move([X,Wolf,   X,Cabbage],   goat,[Y,Wolf,   Y,Cabbage]) :- change(X,Y).
move([X,Wolf,Goat,      X],cabbage,[Y,Wolf,Goat,      Y]) :- change(X,Y).
move([X,Wolf,Goat,Cabbage],nothing,[Y,Wolf,Goat,Cabbage]) :- change(X,Y).

oneEq(X,X,_).
oneEq(X,_,X).

safe([Man,Wolf,Goat,Cabbage]) :-
    oneEq(Man,Goat,   Wolf),
    oneEq(Man,Goat,Cabbage).

solution([e,e,e,e],[]).
solution(Config,[FirstMove|OtherMoves]) :-     
    move(Config,FirstMove,NextConfig),     
    safe(NextConfig),                     
    solution(NextConfig,OtherMoves).

但为了找到该程序的实际解决方案，有必要指定所需的确切移动次数，如下所示：

?- length(X,7), solution([w,w,w,w],X).
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
false.

?- length(Xs,8), solution([w,w,w,w],Xs).   % try length = 8
false.                                     % no solutions!

?- length(Xs,9), solution([w,w,w,w],Xs).   % try length = 9
...

---

有没有一种标准方法可以在不必指定上述程序中的移动次数的情况下找到最小移动解决方案？

length/2具有生成功能，那么只需避免指定值：

?- length(X,_),solution([w,w,w,w],X).

---

正如我们所知，有有限数量的解具有相同的最小步数，我们将关注实现通用终止

minlen_solution(Xs,S) :-
   (   setof(t,solution([w,w,w,w],Xs),_)   % eliminate redundant answers
   *-> Xs = S
   ;   minlen_solution([_|Xs],S)           % no solution? try bigger length
   ).

minlen_solution/2

使用名为“软切割”的

（*->）/2

，以提交最小解决方案长度

关于便携性的说明：

• 在SWI Prolog中，构造具有以下形式
• SICStus Prolog通过谓词提供了这个特性。 可获得更多信息

示例查询：

?- minlen_solution([],Xs).
  Xs = [goat,nothing,cabbage,goat,   wolf,nothing,goat]
; Xs = [goat,nothing,   wolf,goat,cabbage,nothing,goat].

如果我们想找到所有长度大于或等于8的解，我们 可以这样做：

?- length(X,7), solution([w,w,w,w],X).
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, wolf, goat, cabbage, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
X = [goat, nothing, cabbage, goat, wolf, nothing, goat] ;
false.

?- length(Xs,8), solution([w,w,w,w],Xs).   % try length = 8
false.                                     % no solutions!

?- length(Xs,9), solution([w,w,w,w],Xs).   % try length = 9
...

然而，我们仍然必须承诺最低长度

使用

minlen_solutions/2

我们可以直接指定解决方案列表长度的下限，如下所示：

?- length(Xs,8),minlen_solution(Xs,S).
  S = [goat,   goat,   goat,nothing,cabbage,   goat,   wolf,nothing,goat]
; S = [goat,   goat,   goat,nothing,   wolf,   goat,cabbage,nothing,goat] 
; S = [goat,nothing,cabbage,cabbage,cabbage,   goat,   wolf,nothing,goat]
; S = [goat,nothing,cabbage,cabbage,   wolf,   goat,cabbage,nothing,goat]
; S = [goat,nothing,cabbage,   goat,   goat,   goat,   wolf,nothing,goat]
; S = [goat,nothing,cabbage,   goat,   wolf,cabbage,cabbage,nothing,goat]
; S = [goat,nothing,cabbage,   goat,   wolf,nothing,   goat,   goat,goat]
; S = [goat,nothing,cabbage,   goat,   wolf,nothing,nothing,nothing,goat]
; S = [goat,nothing,cabbage,   goat,   wolf,   wolf,   wolf,nothing,goat]
; S = [goat,nothing,nothing,nothing,cabbage,   goat,   wolf,nothing,goat]
; S = [goat,nothing,nothing,nothing,   wolf,   goat,cabbage,nothing,goat]
; S = [goat,nothing,   wolf,   goat,cabbage,cabbage,cabbage,nothing,goat]
; S = [goat,nothing,   wolf,   goat,cabbage,nothing,   goat,   goat,goat]
; S = [goat,nothing,   wolf,   goat,cabbage,nothing,nothing,nothing,goat]
; S = [goat,nothing,   wolf,   goat,cabbage,   wolf,   wolf,nothing,goat]
; S = [goat,nothing,   wolf,   goat,   goat,   goat,cabbage,nothing,goat]
; S = [goat,nothing,   wolf,   wolf,cabbage,   goat,   wolf,nothing,goat]
; S = [goat,nothing,   wolf,   wolf,   wolf,   goat,cabbage,nothing,goat].

为了可读性，上面只显示了

S

的答案替换

请注意，所有使用

minlen_solution/2

的查询都会普遍终止。

s（X）用于演示迭代深化。