--- /dev/null
+/*
+ * loopgen.c: loop generation functions for grid.[ch].
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stddef.h>
+#include <string.h>
+#include <assert.h>
+#include <ctype.h>
+#include <math.h>
+
+#include "puzzles.h"
+#include "tree234.h"
+#include "grid.h"
+#include "loopgen.h"
+
+
+/* We're going to store lists of current candidate faces for colouring black
+ * or white.
+ * Each face gets a 'score', which tells us how adding that face right
+ * now would affect the curliness of the solution loop. We're trying to
+ * maximise that quantity so will bias our random selection of faces to
+ * colour those with high scores */
+struct face_score {
+ int white_score;
+ int black_score;
+ unsigned long random;
+ /* No need to store a grid_face* here. The 'face_scores' array will
+ * be a list of 'face_score' objects, one for each face of the grid, so
+ * the position (index) within the 'face_scores' array will determine
+ * which face corresponds to a particular face_score.
+ * Having a single 'face_scores' array for all faces simplifies memory
+ * management, and probably improves performance, because we don't have to
+ * malloc/free each individual face_score, and we don't have to maintain
+ * a mapping from grid_face* pointers to face_score* pointers.
+ */
+};
+
+static int generic_sort_cmpfn(void *v1, void *v2, size_t offset)
+{
+ struct face_score *f1 = v1;
+ struct face_score *f2 = v2;
+ int r;
+
+ r = *(int *)((char *)f2 + offset) - *(int *)((char *)f1 + offset);
+ if (r) {
+ return r;
+ }
+
+ if (f1->random < f2->random)
+ return -1;
+ else if (f1->random > f2->random)
+ return 1;
+
+ /*
+ * It's _just_ possible that two faces might have been given
+ * the same random value. In that situation, fall back to
+ * comparing based on the positions within the face_scores list.
+ * This introduces a tiny directional bias, but not a significant one.
+ */
+ return f1 - f2;
+}
+
+static int white_sort_cmpfn(void *v1, void *v2)
+{
+ return generic_sort_cmpfn(v1, v2, offsetof(struct face_score,white_score));
+}
+
+static int black_sort_cmpfn(void *v1, void *v2)
+{
+ return generic_sort_cmpfn(v1, v2, offsetof(struct face_score,black_score));
+}
+
+/* 'board' is an array of enum face_colour, indicating which faces are
+ * currently black/white/grey. 'colour' is FACE_WHITE or FACE_BLACK.
+ * Returns whether it's legal to colour the given face with this colour. */
+static int can_colour_face(grid *g, char* board, int face_index,
+ enum face_colour colour)
+{
+ int i, j;
+ grid_face *test_face = g->faces + face_index;
+ grid_face *starting_face, *current_face;
+ grid_dot *starting_dot;
+ int transitions;
+ int current_state, s; /* booleans: equal or not-equal to 'colour' */
+ int found_same_coloured_neighbour = FALSE;
+ assert(board[face_index] != colour);
+
+ /* Can only consider a face for colouring if it's adjacent to a face
+ * with the same colour. */
+ for (i = 0; i < test_face->order; i++) {
+ grid_edge *e = test_face->edges[i];
+ grid_face *f = (e->face1 == test_face) ? e->face2 : e->face1;
+ if (FACE_COLOUR(f) == colour) {
+ found_same_coloured_neighbour = TRUE;
+ break;
+ }
+ }
+ if (!found_same_coloured_neighbour)
+ return FALSE;
+
+ /* Need to avoid creating a loop of faces of this colour around some
+ * differently-coloured faces.
+ * Also need to avoid meeting a same-coloured face at a corner, with
+ * other-coloured faces in between. Here's a simple test that (I believe)
+ * takes care of both these conditions:
+ *
+ * Take the circular path formed by this face's edges, and inflate it
+ * slightly outwards. Imagine walking around this path and consider
+ * the faces that you visit in sequence. This will include all faces
+ * touching the given face, either along an edge or just at a corner.
+ * Count the number of 'colour'/not-'colour' transitions you encounter, as
+ * you walk along the complete loop. This will obviously turn out to be
+ * an even number.
+ * If 0, we're either in the middle of an "island" of this colour (should
+ * be impossible as we're not supposed to create black or white loops),
+ * or we're about to start a new island - also not allowed.
+ * If 4 or greater, there are too many separate coloured regions touching
+ * this face, and colouring it would create a loop or a corner-violation.
+ * The only allowed case is when the count is exactly 2. */
+
+ /* i points to a dot around the test face.
+ * j points to a face around the i^th dot.
+ * The current face will always be:
+ * test_face->dots[i]->faces[j]
+ * We assume dots go clockwise around the test face,
+ * and faces go clockwise around dots. */
+
+ /*
+ * The end condition is slightly fiddly. In sufficiently strange
+ * degenerate grids, our test face may be adjacent to the same
+ * other face multiple times (typically if it's the exterior
+ * face). Consider this, in particular:
+ *
+ * +--+
+ * | |
+ * +--+--+
+ * | | |
+ * +--+--+
+ *
+ * The bottom left face there is adjacent to the exterior face
+ * twice, so we can't just terminate our iteration when we reach
+ * the same _face_ we started at. Furthermore, we can't
+ * condition on having the same (i,j) pair either, because
+ * several (i,j) pairs identify the bottom left contiguity with
+ * the exterior face! We canonicalise the (i,j) pair by taking
+ * one step around before we set the termination tracking.
+ */
+
+ i = j = 0;
+ current_face = test_face->dots[0]->faces[0];
+ if (current_face == test_face) {
+ j = 1;
+ current_face = test_face->dots[0]->faces[1];
+ }
+ transitions = 0;
+ current_state = (FACE_COLOUR(current_face) == colour);
+ starting_dot = NULL;
+ starting_face = NULL;
+ while (TRUE) {
+ /* Advance to next face.
+ * Need to loop here because it might take several goes to
+ * find it. */
+ while (TRUE) {
+ j++;
+ if (j == test_face->dots[i]->order)
+ j = 0;
+
+ if (test_face->dots[i]->faces[j] == test_face) {
+ /* Advance to next dot round test_face, then
+ * find current_face around new dot
+ * and advance to the next face clockwise */
+ i++;
+ if (i == test_face->order)
+ i = 0;
+ for (j = 0; j < test_face->dots[i]->order; j++) {
+ if (test_face->dots[i]->faces[j] == current_face)
+ break;
+ }
+ /* Must actually find current_face around new dot,
+ * or else something's wrong with the grid. */
+ assert(j != test_face->dots[i]->order);
+ /* Found, so advance to next face and try again */
+ } else {
+ break;
+ }
+ }
+ /* (i,j) are now advanced to next face */
+ current_face = test_face->dots[i]->faces[j];
+ s = (FACE_COLOUR(current_face) == colour);
+ if (!starting_dot) {
+ starting_dot = test_face->dots[i];
+ starting_face = current_face;
+ current_state = s;
+ } else {
+ if (s != current_state) {
+ ++transitions;
+ current_state = s;
+ if (transitions > 2)
+ break;
+ }
+ if (test_face->dots[i] == starting_dot &&
+ current_face == starting_face)
+ break;
+ }
+ }
+
+ return (transitions == 2) ? TRUE : FALSE;
+}
+
+/* Count the number of neighbours of 'face', having colour 'colour' */
+static int face_num_neighbours(grid *g, char *board, grid_face *face,
+ enum face_colour colour)
+{
+ int colour_count = 0;
+ int i;
+ grid_face *f;
+ grid_edge *e;
+ for (i = 0; i < face->order; i++) {
+ e = face->edges[i];
+ f = (e->face1 == face) ? e->face2 : e->face1;
+ if (FACE_COLOUR(f) == colour)
+ ++colour_count;
+ }
+ return colour_count;
+}
+
+/* The 'score' of a face reflects its current desirability for selection
+ * as the next face to colour white or black. We want to encourage moving
+ * into grey areas and increasing loopiness, so we give scores according to
+ * how many of the face's neighbours are currently coloured the same as the
+ * proposed colour. */
+static int face_score(grid *g, char *board, grid_face *face,
+ enum face_colour colour)
+{
+ /* Simple formula: score = 0 - num. same-coloured neighbours,
+ * so a higher score means fewer same-coloured neighbours. */
+ return -face_num_neighbours(g, board, face, colour);
+}
+
+/*
+ * Generate a new complete random closed loop for the given grid.
+ *
+ * The method is to generate a WHITE/BLACK colouring of all the faces,
+ * such that the WHITE faces will define the inside of the path, and the
+ * BLACK faces define the outside.
+ * To do this, we initially colour all faces GREY. The infinite space outside
+ * the grid is coloured BLACK, and we choose a random face to colour WHITE.
+ * Then we gradually grow the BLACK and the WHITE regions, eliminating GREY
+ * faces, until the grid is filled with BLACK/WHITE. As we grow the regions,
+ * we avoid creating loops of a single colour, to preserve the topological
+ * shape of the WHITE and BLACK regions.
+ * We also try to make the boundary as loopy and twisty as possible, to avoid
+ * generating paths that are uninteresting.
+ * The algorithm works by choosing a BLACK/WHITE colour, then choosing a GREY
+ * face that can be coloured with that colour (without violating the
+ * topological shape of that region). It's not obvious, but I think this
+ * algorithm is guaranteed to terminate without leaving any GREY faces behind.
+ * Indeed, if there are any GREY faces at all, both the WHITE and BLACK
+ * regions can be grown.
+ * This is checked using assert()ions, and I haven't seen any failures yet.
+ *
+ * Hand-wavy proof: imagine what can go wrong...
+ *
+ * Could the white faces get completely cut off by the black faces, and still
+ * leave some grey faces remaining?
+ * No, because then the black faces would form a loop around both the white
+ * faces and the grey faces, which is disallowed because we continually
+ * maintain the correct topological shape of the black region.
+ * Similarly, the black faces can never get cut off by the white faces. That
+ * means both the WHITE and BLACK regions always have some room to grow into
+ * the GREY regions.
+ * Could it be that we can't colour some GREY face, because there are too many
+ * WHITE/BLACK transitions as we walk round the face? (see the
+ * can_colour_face() function for details)
+ * No. Imagine otherwise, and we see WHITE/BLACK/WHITE/BLACK as we walk
+ * around the face. The two WHITE faces would be connected by a WHITE path,
+ * and the BLACK faces would be connected by a BLACK path. These paths would
+ * have to cross, which is impossible.
+ * Another thing that could go wrong: perhaps we can't find any GREY face to
+ * colour WHITE, because it would create a loop-violation or a corner-violation
+ * with the other WHITE faces?
+ * This is a little bit tricky to prove impossible. Imagine you have such a
+ * GREY face (that is, if you coloured it WHITE, you would create a WHITE loop
+ * or corner violation).
+ * That would cut all the non-white area into two blobs. One of those blobs
+ * must be free of BLACK faces (because the BLACK stuff is a connected blob).
+ * So we have a connected GREY area, completely surrounded by WHITE
+ * (including the GREY face we've tentatively coloured WHITE).
+ * A well-known result in graph theory says that you can always find a GREY
+ * face whose removal leaves the remaining GREY area connected. And it says
+ * there are at least two such faces, so we can always choose the one that
+ * isn't the "tentative" GREY face. Colouring that face WHITE leaves
+ * everything nice and connected, including that "tentative" GREY face which
+ * acts as a gateway to the rest of the non-WHITE grid.
+ */
+void generate_loop(grid *g, char *board, random_state *rs,
+ loopgen_bias_fn_t bias, void *biasctx)
+{
+ int i, j;
+ int num_faces = g->num_faces;
+ struct face_score *face_scores; /* Array of face_score objects */
+ struct face_score *fs; /* Points somewhere in the above list */
+ struct grid_face *cur_face;
+ tree234 *lightable_faces_sorted;
+ tree234 *darkable_faces_sorted;
+ int *face_list;
+ int do_random_pass;
+
+ /* Make a board */
+ memset(board, FACE_GREY, num_faces);
+
+ /* Create and initialise the list of face_scores */
+ face_scores = snewn(num_faces, struct face_score);
+ for (i = 0; i < num_faces; i++) {
+ face_scores[i].random = random_bits(rs, 31);
+ face_scores[i].black_score = face_scores[i].white_score = 0;
+ }
+
+ /* Colour a random, finite face white. The infinite face is implicitly
+ * coloured black. Together, they will seed the random growth process
+ * for the black and white areas. */
+ i = random_upto(rs, num_faces);
+ board[i] = FACE_WHITE;
+
+ /* We need a way of favouring faces that will increase our loopiness.
+ * We do this by maintaining a list of all candidate faces sorted by
+ * their score and choose randomly from that with appropriate skew.
+ * In order to avoid consistently biasing towards particular faces, we
+ * need the sort order _within_ each group of scores to be completely
+ * random. But it would be abusing the hospitality of the tree234 data
+ * structure if our comparison function were nondeterministic :-). So with
+ * each face we associate a random number that does not change during a
+ * particular run of the generator, and use that as a secondary sort key.
+ * Yes, this means we will be biased towards particular random faces in
+ * any one run but that doesn't actually matter. */
+
+ lightable_faces_sorted = newtree234(white_sort_cmpfn);
+ darkable_faces_sorted = newtree234(black_sort_cmpfn);
+
+ /* Initialise the lists of lightable and darkable faces. This is
+ * slightly different from the code inside the while-loop, because we need
+ * to check every face of the board (the grid structure does not keep a
+ * list of the infinite face's neighbours). */
+ for (i = 0; i < num_faces; i++) {
+ grid_face *f = g->faces + i;
+ struct face_score *fs = face_scores + i;
+ if (board[i] != FACE_GREY) continue;
+ /* We need the full colourability check here, it's not enough simply
+ * to check neighbourhood. On some grids, a neighbour of the infinite
+ * face is not necessarily darkable. */
+ if (can_colour_face(g, board, i, FACE_BLACK)) {
+ fs->black_score = face_score(g, board, f, FACE_BLACK);
+ add234(darkable_faces_sorted, fs);
+ }
+ if (can_colour_face(g, board, i, FACE_WHITE)) {
+ fs->white_score = face_score(g, board, f, FACE_WHITE);
+ add234(lightable_faces_sorted, fs);
+ }
+ }
+
+ /* Colour faces one at a time until no more faces are colourable. */
+ while (TRUE)
+ {
+ enum face_colour colour;
+ tree234 *faces_to_pick;
+ int c_lightable = count234(lightable_faces_sorted);
+ int c_darkable = count234(darkable_faces_sorted);
+ if (c_lightable == 0 && c_darkable == 0) {
+ /* No more faces we can use at all. */
+ break;
+ }
+ assert(c_lightable != 0 && c_darkable != 0);
+
+ /* Choose a colour, and colour the best available face
+ * with that colour. */
+ colour = random_upto(rs, 2) ? FACE_WHITE : FACE_BLACK;
+
+ if (colour == FACE_WHITE)
+ faces_to_pick = lightable_faces_sorted;
+ else
+ faces_to_pick = darkable_faces_sorted;
+ if (bias) {
+ /*
+ * Go through all the candidate faces and pick the one the
+ * bias function likes best, breaking ties using the
+ * ordering in our tree234 (which is why we replace only
+ * if score > bestscore, not >=).
+ */
+ int j, k;
+ struct face_score *best = NULL;
+ int score, bestscore = 0;
+
+ for (j = 0;
+ (fs = (struct face_score *)index234(faces_to_pick, j))!=NULL;
+ j++) {
+
+ assert(fs);
+ k = fs - face_scores;
+ assert(board[k] == FACE_GREY);
+ board[k] = colour;
+ score = bias(biasctx, board, k);
+ board[k] = FACE_GREY;
+ bias(biasctx, board, k); /* let bias know we put it back */
+
+ if (!best || score > bestscore) {
+ bestscore = score;
+ best = fs;
+ }
+ }
+ fs = best;
+ } else {
+ fs = (struct face_score *)index234(faces_to_pick, 0);
+ }
+ assert(fs);
+ i = fs - face_scores;
+ assert(board[i] == FACE_GREY);
+ board[i] = colour;
+ if (bias)
+ bias(biasctx, board, i); /* notify bias function of the change */
+
+ /* Remove this newly-coloured face from the lists. These lists should
+ * only contain grey faces. */
+ del234(lightable_faces_sorted, fs);
+ del234(darkable_faces_sorted, fs);
+
+ /* Remember which face we've just coloured */
+ cur_face = g->faces + i;
+
+ /* The face we've just coloured potentially affects the colourability
+ * and the scores of any neighbouring faces (touching at a corner or
+ * edge). So the search needs to be conducted around all faces
+ * touching the one we've just lit. Iterate over its corners, then
+ * over each corner's faces. For each such face, we remove it from
+ * the lists, recalculate any scores, then add it back to the lists
+ * (depending on whether it is lightable, darkable or both). */
+ for (i = 0; i < cur_face->order; i++) {
+ grid_dot *d = cur_face->dots[i];
+ for (j = 0; j < d->order; j++) {
+ grid_face *f = d->faces[j];
+ int fi; /* face index of f */
+
+ if (f == NULL)
+ continue;
+ if (f == cur_face)
+ continue;
+
+ /* If the face is already coloured, it won't be on our
+ * lightable/darkable lists anyway, so we can skip it without
+ * bothering with the removal step. */
+ if (FACE_COLOUR(f) != FACE_GREY) continue;
+
+ /* Find the face index and face_score* corresponding to f */
+ fi = f - g->faces;
+ fs = face_scores + fi;
+
+ /* Remove from lightable list if it's in there. We do this,
+ * even if it is still lightable, because the score might
+ * be different, and we need to remove-then-add to maintain
+ * correct sort order. */
+ del234(lightable_faces_sorted, fs);
+ if (can_colour_face(g, board, fi, FACE_WHITE)) {
+ fs->white_score = face_score(g, board, f, FACE_WHITE);
+ add234(lightable_faces_sorted, fs);
+ }
+ /* Do the same for darkable list. */
+ del234(darkable_faces_sorted, fs);
+ if (can_colour_face(g, board, fi, FACE_BLACK)) {
+ fs->black_score = face_score(g, board, f, FACE_BLACK);
+ add234(darkable_faces_sorted, fs);
+ }
+ }
+ }
+ }
+
+ /* Clean up */
+ freetree234(lightable_faces_sorted);
+ freetree234(darkable_faces_sorted);
+ sfree(face_scores);
+
+ /* The next step requires a shuffled list of all faces */
+ face_list = snewn(num_faces, int);
+ for (i = 0; i < num_faces; ++i) {
+ face_list[i] = i;
+ }
+ shuffle(face_list, num_faces, sizeof(int), rs);
+
+ /* The above loop-generation algorithm can often leave large clumps
+ * of faces of one colour. In extreme cases, the resulting path can be
+ * degenerate and not very satisfying to solve.
+ * This next step alleviates this problem:
+ * Go through the shuffled list, and flip the colour of any face we can
+ * legally flip, and which is adjacent to only one face of the opposite
+ * colour - this tends to grow 'tendrils' into any clumps.
+ * Repeat until we can find no more faces to flip. This will
+ * eventually terminate, because each flip increases the loop's
+ * perimeter, which cannot increase for ever.
+ * The resulting path will have maximal loopiness (in the sense that it
+ * cannot be improved "locally". Unfortunately, this allows a player to
+ * make some illicit deductions. To combat this (and make the path more
+ * interesting), we do one final pass making random flips. */
+
+ /* Set to TRUE for final pass */
+ do_random_pass = FALSE;
+
+ while (TRUE) {
+ /* Remember whether a flip occurred during this pass */
+ int flipped = FALSE;
+
+ for (i = 0; i < num_faces; ++i) {
+ int j = face_list[i];
+ enum face_colour opp =
+ (board[j] == FACE_WHITE) ? FACE_BLACK : FACE_WHITE;
+ if (can_colour_face(g, board, j, opp)) {
+ grid_face *face = g->faces +j;
+ if (do_random_pass) {
+ /* final random pass */
+ if (!random_upto(rs, 10))
+ board[j] = opp;
+ } else {
+ /* normal pass - flip when neighbour count is 1 */
+ if (face_num_neighbours(g, board, face, opp) == 1) {
+ board[j] = opp;
+ flipped = TRUE;
+ }
+ }
+ }
+ }
+
+ if (do_random_pass) break;
+ if (!flipped) do_random_pass = TRUE;
+ }
+
+ sfree(face_list);
+}
~mdw / sgt / puzzles / blobdiff