int: h; set of int: H = 1..h; % board height
int: w; set of int: W = 1..w; % board width
array[H,W] of -1..5: b; % board
int: E = -1; % empty square
set of int: N = 0..4; % filled and numbered square
int: F = 5; % filled unnumbered square
% position (i1,j1) is visible to (i2,j2)
test visible(int: i1, int: j1, int: i2, int: j2) =
((i1 == i2) /\ forall(j in min(j1,j2)..max(j1,j2))(b[i1,j] == E))
\/ ((j1 == j2) /\ forall(i in min(i1,i2)..max(i1,i2))(b[i,j1] == E));
array[H,W] of var bool: l; % is there a light
% filled squares have no lights
constraint forall(i in H, j in W, where b[i,j] != E)(l[i,j] == false);
% lights next to filled numbered square agree
include "boolsum.mzn";
constraint forall(i in H, j in W where b[i,j] in N)(
bool_sum_eq([ l[i1,j1] | i1 in i-1..i+1, j1 in j-1..j+1 where
abs(i1 - i) + abs(j1 - j) == 1 /\
i1 in H /\ j1 in W ], b[i,j]));
% each blank square is illuminated
constraint forall(i in H, j in W where b[i,j] == E)(
exists(j1 in W where visible(i,j,i,j1))(l[i,j1]) \/
exists(i1 in H where visible(i,j,i1,j))(l[i1,j])
);
% no two lights see each other
constraint forall(i1,i2 in H, j1,j2 in W where
(i1 != i2 \/ j1 != j2) /\ b[i1,j1] == E
/\ b[i2,j2] == E /\ visible(i1,j1,i2,j2))(
not l[i1,j1] \/ not l[i2,j2]
);
solve satisfy;
output [ if b[i,j] != E then show(b[i,j])
else if fix(l[i,j]) then "L" else "." endif
endif ++ if j == w then "\n" else " " endif |
i in H, j in W];