Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
76 lines
1.7 KiB
MiniZinc
76 lines
1.7 KiB
MiniZinc
% RUNS ON mzn20_fd
|
|
% RUNS ON mzn-fzn_fd
|
|
% RUNS ON mzn20_mip
|
|
% knights.mzn
|
|
% Ralph Becket
|
|
% vim: ft=zinc ts=4 sw=4 et
|
|
% Tue Aug 26 14:24:28 EST 2008
|
|
%
|
|
% Find a closed knight's tour of a chessboard (every square is visited exactly
|
|
% once, the tour forms a loop).
|
|
|
|
include "globals.mzn";
|
|
|
|
% n is the length of side of the chessboard.
|
|
%
|
|
int: n = 6;
|
|
|
|
% The ith square (r, c) on the path is given by p[i] = (r - 1) * n + c.
|
|
%
|
|
int: nn = n * n;
|
|
set of int: sq = 1..nn;
|
|
array [sq] of var sq: p;
|
|
|
|
set of int: row = 1..n;
|
|
set of int: col = 1..n;
|
|
|
|
% Break some symmetry by specifying the first and last moves.
|
|
%
|
|
constraint p[1] = 1;
|
|
constraint p[2] = n + 3;
|
|
constraint p[nn] = 2 * n + 2;
|
|
|
|
% All points along the path must be unique.
|
|
%
|
|
constraint alldifferent(p);
|
|
|
|
array [sq] of set of sq: neighbours =
|
|
[ { n * (R - 1) + C
|
|
|
|
|
i in 1..8,
|
|
R in {R0 + [-1, -2, -2, -1, 1, 2, 2, 1][i]},
|
|
C in {C0 + [-2, -1, 1, 2, 2, 1, -1, -2][i]}
|
|
where R in row /\ C in col
|
|
}
|
|
| R0 in row, C0 in col
|
|
];
|
|
|
|
constraint forall (i in sq where i > 1) (p[i] in neighbours[p[i - 1]]);
|
|
|
|
solve
|
|
:: int_search(
|
|
p,
|
|
input_order,
|
|
indomain_min,
|
|
complete
|
|
)
|
|
satisfy;
|
|
% It has been observed that Warnsdorf's heuristic of choosing the next
|
|
% square as the one with the fewest remaining neighbours leads almost
|
|
% directly to a solution. How might we express this in MiniZinc?
|
|
|
|
output ["p = " ++ show(p) ++ ";\n"];
|
|
|
|
% Invert the path to show the tour.
|
|
%
|
|
% array [sq] of var sq: q;
|
|
%
|
|
% constraint forall (i in sq) (q[p[i]] = i);
|
|
%
|
|
% output [ show(q[i]) ++ if i mod n = 0 then "\n" else " " endif
|
|
% | i in sq
|
|
% ] ++
|
|
% [ "\n"
|
|
% ];
|
|
|