ref: f4bd45e7b967980782663f4eb27e5006528283d3
parent: a35c6602849314ee42894e5cdecc09223f0cab07
author: Simon Tatham <anakin@pobox.com>
date: Tue Nov 4 16:39:59 EST 2008
Patch from Lambros to improve the generality of path-generation. In particular, Great Hexagonal tilings previously had virtually every (if not _actually_ every) hexagon on the inside of the path, and now don't. [originally from svn r8277]
--- a/loopy.c
+++ b/loopy.c
@@ -73,6 +73,7 @@
#include <stdio.h>
#include <stdlib.h>
+#include <stddef.h>
#include <string.h>
#include <assert.h>
#include <ctype.h>
@@ -1219,33 +1220,34 @@
* Loop generation and clue removal
*/
-/* We're going to store a list of current candidate faces for lighting.
+/* 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 length of the solution loop. We're trying to
+ * 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
- * light towards those with high scores */
-struct face {- int score;
+ * colour those with high scores */
+struct face_score {+ int white_score;
+ int black_score;
unsigned long random;
- grid_face *f;
+ /* 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 get_face_cmpfn(void *v1, void *v2)
+static int generic_sort_cmpfn(void *v1, void *v2, size_t offset)
{- struct face *f1 = v1;
- struct face *f2 = v2;
- /* These grid_face pointers always point into the same list of
- * 'grid_face's, so it's valid to subtract them. */
- return f1->f - f2->f;
-}
-
-static int face_sort_cmpfn(void *v1, void *v2)
-{- struct face *f1 = v1;
- struct face *f2 = v2;
+ struct face_score *f1 = v1;
+ struct face_score *f2 = v2;
int r;
- r = f2->score - f1->score;
+ r = *(int *)((char *)f2 + offset) - *(int *)((char *)f1 + offset);
if (r) {return r;
}
@@ -1258,64 +1260,74 @@
/*
* 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 grid's face-list.
+ * comparing based on the positions within the face_scores list.
* This introduces a tiny directional bias, but not a significant one.
*/
- return get_face_cmpfn(f1, f2);
+ return f1 - f2;
}
-enum { FACE_LIT, FACE_UNLIT };+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));
+}
+
+enum face_colour { FACE_WHITE, FACE_GREY, FACE_BLACK };+
/* face should be of type grid_face* here. */
-#define FACE_LIT_STATE(face) \
- ( (face) == NULL ? FACE_UNLIT : \
+#define FACE_COLOUR(face) \
+ ( (face) == NULL ? FACE_BLACK : \
board[(face) - g->faces] )
/* 'board' is an array of these enums, indicating which faces are
- * currently lit. Returns whether it's legal to light up the
- * given face. */
-static int can_light_face(grid *g, char* board, int face_index)
+ * 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;
int transitions;
- int current_state, s;
- int found_lit_neighbour = FALSE;
- assert(board[face_index] == FACE_UNLIT);
+ 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 lighting if it's adjacent to an
- * already lit face. */
+ /* 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_LIT_STATE(f) == FACE_LIT) {- found_lit_neighbour = TRUE;
+ if (FACE_COLOUR(f) == colour) {+ found_same_coloured_neighbour = TRUE;
break;
}
}
- if (!found_lit_neighbour)
+ if (!found_same_coloured_neighbour)
return FALSE;
- /* Need to avoid creating a loop of lit faces around some unlit faces.
- * Also need to avoid meeting another lit face at a corner, with
- * unlit faces in between. Here's a simple test that (I believe) takes
- * care of both these conditions:
+ /* 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 LIT/UNLIT 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 a completely unlit zone, or this face is a hole
- * in a completely lit zone. If the former, we would create a brand new
- * island by lighting this face. And the latter ought to be impossible -
- * it would mean there's already a lit loop, so something went wrong
- * earlier.
- * If 4 or greater, there are too many separate lit regions touching this
- * face, and lighting it up would create a loop or a corner-violation.
+ * 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.
@@ -1332,7 +1344,7 @@
}
current_face = starting_face;
transitions = 0;
- current_state = FACE_LIT_STATE(current_face);
+ current_state = (FACE_COLOUR(current_face) == colour);
do {/* Advance to next face.
@@ -1364,7 +1376,7 @@
}
/* (i,j) are now advanced to next face */
current_face = test_face->dots[i]->faces[j];
- s = FACE_LIT_STATE(current_face);
+ s = (FACE_COLOUR(current_face) == colour);
if (s != current_state) {++transitions;
current_state = s;
@@ -1376,14 +1388,11 @@
return (transitions == 2) ? TRUE : FALSE;
}
-/* The 'score' of a face reflects its current desirability for selection
- * as the next face to light. We want to encourage moving into uncharted
- * areas so we give scores according to how many of the face's neighbours
- * are currently unlit. */
-static int face_score(grid *g, char *board, grid_face *face)
+/* 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)
{- /* Simple formula: score = neighbours unlit - neighbours lit */
- int lit_count = 0, unlit_count = 0;
+ int colour_count = 0;
int i;
grid_face *f;
grid_edge *e;
@@ -1390,39 +1399,110 @@
for (i = 0; i < face->order; i++) {e = face->edges[i];
f = (e->face1 == face) ? e->face2 : e->face1;
- if (FACE_LIT_STATE(f) == FACE_LIT)
- ++lit_count;
- else
- ++unlit_count;
+ if (FACE_COLOUR(f) == colour)
+ ++colour_count;
}
- return unlit_count - lit_count;
+ return colour_count;
}
-/* Generate a new complete set of clues for the given game_state. */
+/* 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 set of clues for the given game_state.
+ * 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.
+ */
static void add_full_clues(game_state *state, random_state *rs)
{signed char *clues = state->clues;
char *board;
grid *g = state->game_grid;
- int i, j, c;
+ int i, j;
int num_faces = g->num_faces;
- int first_time = TRUE;
+ 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;
- struct face *face, *tmpface;
- struct face face_pos;
-
- /* These will contain exactly the same information, sorted into different
- * orders */
- tree234 *lightable_faces_sorted, *lightable_faces_gettable;
-
-#define IS_LIGHTING_CANDIDATE(i) \
- (board[i] == FACE_UNLIT && \
- can_light_face(g, board, i))
-
board = snewn(num_faces, char);
/* Make a board */
- memset(board, FACE_UNLIT, num_faces);
+ 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);
+ }
+
+ /* 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
@@ -1436,123 +1516,188 @@
* 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(face_sort_cmpfn);
- lightable_faces_gettable = newtree234(get_face_cmpfn);
-#define ADD_FACE(f) \
- do { \- struct face *x = add234(lightable_faces_sorted, f); \
- assert(x == f); \
- x = add234(lightable_faces_gettable, f); \
- assert(x == f); \
- } while (0)
+ lightable_faces_sorted = newtree234(white_sort_cmpfn);
+ darkable_faces_sorted = newtree234(black_sort_cmpfn);
-#define REMOVE_FACE(f) \
- do { \- struct face *x = del234(lightable_faces_sorted, f); \
- assert(x); \
- x = del234(lightable_faces_gettable, f); \
- assert(x); \
- } while (0)
+ /* 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);
+ }
+ }
- /* Light faces one at a time until the board is interesting enough */
+ /* Colour faces one at a time until no more faces are colourable. */
while (TRUE)
{- if (first_time) {- first_time = FALSE;
- /* lightable_faces_xxx are empty, so start the process by
- * lighting up the middle face. These tree234s should
- * remain empty, consistent with what would happen if
- * first_time were FALSE. */
- board[g->middle_face - g->faces] = FACE_LIT;
- face = snew(struct face);
- face->f = g->middle_face;
- /* No need to initialise any more of 'face' here, no other fields
- * are used in this case. */
- } else {- /* We have count234(lightable_faces_gettable) possibilities, and in
- * lightable_faces_sorted they are sorted with the most desirable
- * first. */
- c = count234(lightable_faces_sorted);
- if (c == 0)
- break;
- assert(c == count234(lightable_faces_gettable));
+ enum face_colour colour;
+ struct face_score *fs_white, *fs_black;
+ int c_lightable = count234(lightable_faces_sorted);
+ int c_darkable = count234(darkable_faces_sorted);
+ if (c_lightable == 0) {+ /* No more lightable faces. Because of how the algorithm
+ * works, there should be no more darkable faces either. */
+ assert(c_darkable == 0);
+ break;
+ }
- /* Check that the best face available is any good */
- face = (struct face *)index234(lightable_faces_sorted, 0);
- assert(face);
+ fs_white = (struct face_score *)index234(lightable_faces_sorted, 0);
+ fs_black = (struct face_score *)index234(darkable_faces_sorted, 0);
- /*
- * The situation for a general grid is slightly different from
- * a square grid. Decreasing the perimeter should be allowed
- * sometimes (think about creating a hexagon of lit triangles,
- * for example). For if it were _never_ done, then the user would
- * be able to illicitly deduce certain things. So we do it
- * sometimes but not always.
- */
- if (face->score <= 0 && random_upto(rs, 2) == 0) {- break;
- }
+ /* Choose a colour, and colour the best available face
+ * with that colour. */
+ colour = random_upto(rs, 2) ? FACE_WHITE : FACE_BLACK;
- assert(face->f); /* not the infinite face */
- assert(FACE_LIT_STATE(face->f) == FACE_UNLIT);
+ if (colour == FACE_WHITE)
+ fs = fs_white;
+ else
+ fs = fs_black;
+ assert(fs);
+ i = fs - face_scores;
+ assert(board[i] == FACE_GREY);
+ board[i] = colour;
- /* Update data structures */
- /* Light up the face and remove it from the lists */
- board[face->f - g->faces] = FACE_LIT;
- REMOVE_FACE(face);
- }
+ /* 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);
- /* The face we've just lit up potentially affects the lightability
- * 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 (i = 0; i < face->f->order; i++) {- grid_dot *d = face->f->dots[i];
+ /* 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 *f2 = d->faces[j];
- if (f2 == NULL)
+ grid_face *f = d->faces[j];
+ int fi; /* face index of f */
+
+ if (f == NULL)
continue;
- if (f2 == face->f)
+ if (f == cur_face)
continue;
- face_pos.f = f2;
- tmpface = find234(lightable_faces_gettable, &face_pos, NULL);
- if (tmpface) {- assert(tmpface->f == face_pos.f);
- assert(FACE_LIT_STATE(tmpface->f) == FACE_UNLIT);
- REMOVE_FACE(tmpface);
- } else {- tmpface = snew(struct face);
- tmpface->f = face_pos.f;
- tmpface->random = random_bits(rs, 31);
- }
- tmpface->score = face_score(g, board, tmpface->f);
-
- if (IS_LIGHTING_CANDIDATE(tmpface->f - g->faces)) {- ADD_FACE(tmpface);
- } else {- sfree(tmpface);
+
+ /* 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);
+ }
}
}
- sfree(face);
}
/* Clean up */
- while ((face = delpos234(lightable_faces_gettable, 0)) != NULL)
- sfree(face);
- freetree234(lightable_faces_gettable);
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);
+
/* Fill out all the clues by initialising to 0, then iterating over
* all edges and incrementing each clue as we find edges that border
- * between LIT/UNLIT faces */
+ * between BLACK/WHITE faces. While we're at it, we verify that the
+ * algorithm does work, and there aren't any GREY faces still there. */
memset(clues, 0, num_faces);
for (i = 0; i < g->num_edges; i++) {grid_edge *e = g->edges + i;
grid_face *f1 = e->face1;
grid_face *f2 = e->face2;
- if (FACE_LIT_STATE(f1) != FACE_LIT_STATE(f2)) {+ enum face_colour c1 = FACE_COLOUR(f1);
+ enum face_colour c2 = FACE_COLOUR(f2);
+ assert(c1 != FACE_GREY);
+ assert(c2 != FACE_GREY);
+ if (c1 != c2) {if (f1) clues[f1 - g->faces]++;
if (f2) clues[f2 - g->faces]++;
}