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Figure 5.12.
Testing if one queen can capture another
cap.pl
% cap(r1,C1,E2,C2) tests if a queen placed on an 8x8 chess board
% at position (R1,C1) can capture another at position (R2,C2).
cap(R,_,R,_).
% Note the use of the _ here
cap(_,C,_,C).
% and here, too.
cap(R1,C1,R2,C2) :- R1-C1 =:= R2-C2.
cap(R1,C1,R2,C2) :- R1+C1 =:= R2+C2.
Figure 5.13.
A solution to the eight-queens problem
queens.pl
% Solve the 8-queens problem.
solution(C1,C2,C3,C4,C5,C6,C7,C8) :-
col(C1),
col(C2), \+ cap(2,C2,1,C1),
col(C3), \+ cap(3,C3,1,C1), \+ cap(3,C3,2,C2),
col(C4), \+ cap(4,C4,1,C1), \+ cap(4,C4,2,C2), \+ cap(4,C4,3,C3),
col(C5), \+ cap(5,C5,1,C1), \+ cap(5,C5,2,C2), \+ cap(5,C5,3,C3),
\+ cap(5,C5,4,C4),
col(C6), \+ cap(6,C6,1,C1), \+ cap(6,C6,2,C2), \+ cap(6,C6,3,C3),
\+ cap(6,C6,4,C4), \+ cap(6,C6,5,C5),
col(C7), \+ cap(7,C7,1,C1), \+ cap(7,C7,2,C2), \+ cap(7,C7,3,C3),
\+ cap(7,C7,4,C4), \+ cap(7,C7,5,C5), \+ cap(7,C7,6,C6),
col(C8), \+ cap(8,C8,1,C1), \+ cap(8,C8,2,C2), \+ cap(8,C8,3,C3),
\+ cap(8,C8,4,C4), \+ cap(8,C8,5,C5), \+ cap(8,C8,6,C6),
\+ cap(8,C8,7,C7).
% The columns
col(1). col(2). col(3). col(4). col(5). col(6). col(7). col(8).
% cap(R1,C1,R2,C2): a queen on (R1,C1) can capture one on (R2,C2).
cap(R,_,R,_).
% Note the use of the _ here
cap(_,C,_,C).
% and here, too.
cap(R1,C1,R2,C2) :- R1-C1 =:= R2-C2.
cap(R1,C1,R2,C2) :- R1+C1 =:= R2+C2.
Before writing the
solution
predicate for this problem, it is a good idea to write
the clauses for a predicate
cap
(
r
1
,
c
1
,
r
2
,
c
2
)
, which holds when a queen placed on
(
)
(
)
. The predicate will need four clauses
that mirror the four conditions. The resulting small program is shown in figure 5.12.
(Always test that an auxiliary predicate like
cap
is working properly before including
it in a larger program.)
r
1
,
c
1
can capture one that is placed on
r
2
,
c
2
