Question

我有一个nxn区域。并且我想列出在该区域中彼此不接触的可能kxk m个正方形（k

输入和输出应该是这样的：（k：小方块的大小，n：大方块的大小，m：小方块的数量）

>func(k,n,m,O).

>func(1,3,2,O).
O =[1-1,1-3]; 
O =[1-1,2-3]; 
O =[1-1,3-1]; 
O =[1-1,3-2]; 
O =[1-1,3-3]; 
O =[1-2,3-1]; 
O =[1-2,3-2]; 
O =[1-2,3-3];
O =[1-3,2-1];
O =[1-3,3-1]; 
O =[1-3,3-2]; 
O =[1-3,3-3];
O =[2-1,2-3];
O =[2-1,3-3];
O =[2-3,3-1];
O =[3-1,3-3];
No.

Answer 1

我发布了一个显示可能的Prolog编码的解决方案，风格为 generate and test 。有一些插槽可以放置适当的算术，只是为了完成你的作业。

%%  placing

place_squares(Big, Small, Squares) :-
    place_not_overlapping(Big, Small, [], Squares).

place_not_overlapping(Big, Small, SoFar, Squares) :-
    available_position(Big, Small, Position),
    \+ overlapping(Small, Position, SoFar),
    place_not_overlapping(Big, Small, [Position|SoFar], Squares).
place_not_overlapping(_Big, _Small, Squares, Sorted) :-
    sort(Squares, Sorted).

overlapping(Size, R*C, Squares) :-
    member(X*Y, Squares),
    ...  % write conditions here

available_position(Big, Small, Row*Col) :-
    Range is Big - Small + 1,
    between(1, Range, Row),
    between(1, Range, Col).

放置后，很容易显示

%%  drawing

draw_squares(Big, Small, Squares) :-
    forall(between(1, Big, Row),
           (forall(between(1, Big, Col),
               draw_point(Row*Col, Small, Squares)),
        nl
           )).
draw_point(Point, Small, Squares) :-
    (   nth1(I, Squares, Square),
        contained(Point, Square, Small)
    ) -> write(I) ; write('-').

contained(R*C, A*B, Size) :-
    ... % place arithmetic here

请求尺寸的结果和图纸

?- place_squares(5,2,Q),draw_squares(5,2,Q).
1122-
1122-
3344-
3344-
-----
Q = [1*1, 1*3, 3*1, 3*3] ;
1122-
1122-
33-44
33-44
-----
Q = [1*1, 1*3, 3*1, 3*4] ;
1122-
1122-
33---
3344-
--44-
Q = [1*1, 1*3, 3*1, 4*3] .
...

对place_squares / 3输出进行排序，以便于显示，并且可以用来摆脱对称性，并获得所有解决方案的计数：

9 ?- setof(Q, place_squares(5,2,Q), L), length(L, N).
L = [[], [1*1], [1*1, 1*3], [1*1, 1*3, 3*1], [1*1, 1*3, 3*1, ... * ...], [1*1, 1*3, ... * ...|...], [1*1, ... * ...|...], [... * ...|...], [...|...]|...],
N = 314.

您可以注意到这会接受具有“备用”空间的电路板。您可以过滤掉这些不完整的解决方案，以完成您的任务。

广场放置在Prolog

1 个答案: