#define ERR_VERTEX 1
#define ERR_SQUARE 2
-#define ERR_SQUARE_TMP 4
struct game_state {
struct game_params p;
state->clues->h = h;
state->clues->clues = snewn(W*H, signed char);
state->clues->refcount = 1;
- state->clues->tmpdsf = snewn(W*H, int);
+ state->clues->tmpdsf = snewn(W*H*2+W+H, int);
memset(state->clues->clues, -1, W*H);
while (*desc) {
int n = *desc++;
static int check_completion(game_state *state)
{
int w = state->p.w, h = state->p.h, W = w+1, H = h+1;
- int i, x, y, err = FALSE;
+ int x, y, err = FALSE;
int *dsf;
memset(state->errors, 0, W*H);
/*
* To detect loops in the grid, we iterate through each edge
- * building up a dsf of connected components, and raise the
- * alarm whenever we find an edge that connects two
- * already-connected vertices.
- *
+ * building up a dsf of connected components of the space
+ * around the edges; if there's more than one such component,
+ * we have a loop, and in particular we can then easily
+ * identify and highlight every edge forming part of a loop
+ * because it separates two nonequivalent regions.
+ *
* We use the `tmpdsf' scratch space in the shared clues
* structure, to avoid mallocing too often.
- *
- * When we find such an edge, we then search around the grid to
- * find the loop it is a part of, so that we can highlight it
- * as an error for the user. We do this by the hand-on-one-wall
- * technique: the search will follow branches off the inside of
- * the loop, discover they're dead ends, and unhighlight them
- * again when returning to the actual loop.
- *
- * This technique guarantees that every loop it tracks will
- * surround a disjoint area of the grid (since if an existing
- * loop appears on the boundary of a new one, so that there are
- * multiple possible paths that would come back to the starting
- * point, it will pick the one that allows it to turn right
- * most sharply and hence the one that does not re-surround the
- * area of the previous one). Thus, the total time taken in
- * searching round loops is linear in the grid area since every
- * edge is visited at most twice.
+ *
+ * For these purposes, the grid is considered to be divided
+ * into diamond-shaped regions surrounding an orthogonal edge.
+ * This means we have W*h vertical edges and w*H horizontal
+ * ones; so our vertical edges are indexed in the dsf as
+ * (y*W+x) (0<=y<h, 0<=x<W), and the horizontal ones as (W*h +
+ * y*w+x) (0<=y<H, 0<=x<w), where (x,y) is the topmost or
+ * leftmost point on the edge.
*/
dsf = state->clues->tmpdsf;
- dsf_init(dsf, W*H);
+ dsf_init(dsf, W*h + w*H);
+ /* Start by identifying all the outer edges with each other. */
+ for (y = 0; y < h; y++) {
+ dsf_merge(dsf, 0, y*W+0);
+ dsf_merge(dsf, 0, y*W+w);
+ }
+ for (x = 0; x < w; x++) {
+ dsf_merge(dsf, 0, W*h + 0*w+x);
+ dsf_merge(dsf, 0, W*h + h*w+x);
+ }
+ /* Now go through the actual grid. */
for (y = 0; y < h; y++)
for (x = 0; x < w; x++) {
- int i1, i2;
-
- if (state->soln[y*w+x] == 0)
- continue;
- if (state->soln[y*w+x] < 0) {
- i1 = y*W+x;
- i2 = (y+1)*W+(x+1);
- } else {
- i1 = y*W+(x+1);
- i2 = (y+1)*W+x;
- }
-
- /*
- * Our edge connects i1 with i2. If they're already
- * connected, flag an error. Otherwise, link them.
- */
- if (dsf_canonify(dsf, i1) == dsf_canonify(dsf, i2)) {
- int x1, y1, x2, y2, dx, dy, dt, pass;
-
- err = TRUE;
-
+ if (state->soln[y*w+x] >= 0) {
/*
- * Now search around the boundary of the loop to
- * highlight it.
- *
- * We have to do this in two passes. The first
- * time, we toggle ERR_SQUARE_TMP on each edge;
- * this pass terminates with ERR_SQUARE_TMP set on
- * exactly the loop edges. In the second pass, we
- * trace round that loop again and turn
- * ERR_SQUARE_TMP into ERR_SQUARE. We have to do
- * this because otherwise we might cancel part of a
- * loop highlighted in a previous iteration of the
- * outer loop.
+ * There isn't a \ in this square, so we can unify
+ * the top edge with the left, and the bottom with
+ * the right.
*/
-
- for (pass = 0; pass < 2; pass++) {
-
- x1 = i1 % W;
- y1 = i1 / W;
- x2 = i2 % W;
- y2 = i2 / W;
-
- do {
- /* Mark this edge. */
- if (pass == 0) {
- state->errors[min(y1,y2)*W+min(x1,x2)] ^=
- ERR_SQUARE_TMP;
- } else {
- state->errors[min(y1,y2)*W+min(x1,x2)] |=
- ERR_SQUARE;
- state->errors[min(y1,y2)*W+min(x1,x2)] &=
- ~ERR_SQUARE_TMP;
- }
-
- /*
- * Progress to the next edge by turning as
- * sharply right as possible. In fact we do
- * this by facing back along the edge and
- * turning _left_ until we see an edge we
- * can follow.
- */
- dx = x1 - x2;
- dy = y1 - y2;
-
- for (i = 0; i < 4; i++) {
- /*
- * Rotate (dx,dy) to the left.
- */
- dt = dx; dx = dy; dy = -dt;
-
- /*
- * See if (x2,y2) has an edge in direction
- * (dx,dy).
- */
- if (x2+dx < 0 || x2+dx >= W ||
- y2+dy < 0 || y2+dy >= H)
- continue; /* off the side of the grid */
- /* In the second pass, ignore unmarked edges. */
- if (pass == 1 &&
- !(state->errors[(y2-(dy<0))*W+x2-(dx<0)] &
- ERR_SQUARE_TMP))
- continue;
- if (state->soln[(y2-(dy<0))*w+x2-(dx<0)] ==
- (dx==dy ? -1 : +1))
- break;
- }
-
- /*
- * In pass 0, we expect to have found
- * _some_ edge we can follow, even if it
- * was found by rotating all the way round
- * and going back the way we came.
- *
- * In pass 1, because we're removing the
- * mark on each edge that allows us to
- * follow it, we expect to find _no_ edge
- * we can follow when we've come all the
- * way round the loop.
- */
- if (pass == 1 && i == 4)
- break;
- assert(i < 4);
-
- /*
- * Set x1,y1 to x2,y2, and x2,y2 to be the
- * other end of the new edge.
- */
- x1 = x2;
- y1 = y2;
- x2 += dx;
- y2 += dy;
- } while (y2*W+x2 != i2);
-
- }
-
- } else
- dsf_merge(dsf, i1, i2);
+ dsf_merge(dsf, y*W+x, W*h + y*w+x);
+ dsf_merge(dsf, y*W+(x+1), W*h + (y+1)*w+x);
+ }
+ if (state->soln[y*w+x] <= 0) {
+ /*
+ * There isn't a / in this square, so we can unify
+ * the top edge with the right, and the bottom
+ * with the left.
+ */
+ dsf_merge(dsf, y*W+x, W*h + (y+1)*w+x);
+ dsf_merge(dsf, y*W+(x+1), W*h + y*w+x);
+ }
+ }
+ /* Now go through again and mark the appropriate edges as erroneous. */
+ for (y = 0; y < h; y++)
+ for (x = 0; x < w; x++) {
+ int erroneous = 0;
+ if (state->soln[y*w+x] > 0) {
+ /*
+ * A / separates the top and left edges (which
+ * must already have been identified with each
+ * other) from the bottom and right (likewise).
+ * Hence it is erroneous if and only if the top
+ * and right edges are nonequivalent.
+ */
+ erroneous = (dsf_canonify(dsf, y*W+(x+1)) !=
+ dsf_canonify(dsf, W*h + y*w+x));
+ } else if (state->soln[y*w+x] < 0) {
+ /*
+ * A \ separates the top and right edges (which
+ * must already have been identified with each
+ * other) from the bottom and left (likewise).
+ * Hence it is erroneous if and only if the top
+ * and left edges are nonequivalent.
+ */
+ erroneous = (dsf_canonify(dsf, y*W+x) !=
+ dsf_canonify(dsf, W*h + y*w+x));
+ }
+ if (erroneous) {
+ state->errors[y*W+x] |= ERR_SQUARE;
+ err = TRUE;
+ }
}
/*
~mdw / sgt / puzzles / commitdiff