From 6d6773cd3e064657447722de237e2128faae220f Mon Sep 17 00:00:00 2001 From: Simon Tatham Date: Tue, 4 Nov 2008 21:39:59 +0000 Subject: [PATCH] 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. git-svn-id: svn://svn.tartarus.org/sgt/puzzles@8277 cda61777-01e9-0310-a592-d414129be87e --- loopy.c | 483 +++++++++++++++++++++++++++++++++++++++++----------------------- 1 file changed, 314 insertions(+), 169 deletions(-) diff --git a/loopy.c b/loopy.c index 0cb6921..39dec98 100644 --- a/loopy.c +++ b/loopy.c @@ -73,6 +73,7 @@ #include #include +#include #include #include #include @@ -1219,33 +1220,34 @@ static int face_setall(solver_state *sstate, int face, * 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) -{ - 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) +static int generic_sort_cmpfn(void *v1, void *v2, size_t offset) { - 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 @@ static int face_sort_cmpfn(void *v1, void *v2) /* * 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; +} + +static int white_sort_cmpfn(void *v1, void *v2) +{ + return generic_sort_cmpfn(v1, v2, offsetof(struct face_score,white_score)); } -enum { FACE_LIT, FACE_UNLIT }; +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 @@ static int can_light_face(grid *g, char* board, int face_index) } 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 @@ static int can_light_face(grid *g, char* board, int face_index) } /* (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; @@ -1376,53 +1388,121 @@ static int can_light_face(grid *g, char* board, int face_index) 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; 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 *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)) + 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; 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 @@ static void add_full_clues(game_state *state, random_state *rs) * 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)); - - /* Check that the best face available is any good */ - face = (struct face *)index234(lightable_faces_sorted, 0); - assert(face); - - /* - * 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; - } + 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; + } - assert(face->f); /* not the infinite face */ - assert(FACE_LIT_STATE(face->f) == FACE_UNLIT); + fs_white = (struct face_score *)index234(lightable_faces_sorted, 0); + fs_black = (struct face_score *)index234(darkable_faces_sorted, 0); - /* Update data structures */ - /* Light up the face and remove it from the lists */ - board[face->f - g->faces] = FACE_LIT; - REMOVE_FACE(face); - } + /* Choose a colour, and colour the best available face + * with that colour. */ + colour = random_upto(rs, 2) ? FACE_WHITE : FACE_BLACK; - /* 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]; + 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; + + /* 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 *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); + + /* 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); } - tmpface->score = face_score(g, board, tmpface->f); - - if (IS_LIGHTING_CANDIDATE(tmpface->f - g->faces)) { - ADD_FACE(tmpface); - } else { - sfree(tmpface); + /* 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]++; } -- 2.11.4.GIT