4 * An implementation of the Nikoli game 'Loop the loop'.
5 * (c) Mike Pinna, 2005, 2006
6 * Substantially rewritten to allowing for more general types of grid.
7 * (c) Lambros Lambrou 2008
9 * vim: set shiftwidth=4 :set textwidth=80:
13 * Possible future solver enhancements:
15 * - There's an interesting deductive technique which makes use
16 * of topology rather than just graph theory. Each _face_ in
17 * the grid is either inside or outside the loop; you can tell
18 * that two faces are on the same side of the loop if they're
19 * separated by a LINE_NO (or, more generally, by a path
20 * crossing no LINE_UNKNOWNs and an even number of LINE_YESes),
21 * and on the opposite side of the loop if they're separated by
22 * a LINE_YES (or an odd number of LINE_YESes and no
23 * LINE_UNKNOWNs). Oh, and any face separated from the outside
24 * of the grid by a LINE_YES or a LINE_NO is on the inside or
25 * outside respectively. So if you can track this for all
26 * faces, you figure out the state of the line between a pair
27 * once their relative insideness is known.
28 * + The way I envisage this working is simply to keep an edsf
29 * of all _faces_, which indicates whether they're on
30 * opposite sides of the loop from one another. We also
31 * include a special entry in the edsf for the infinite
33 * + So, the simple way to do this is to just go through the
34 * edges: every time we see an edge in a state other than
35 * LINE_UNKNOWN which separates two faces that aren't in the
36 * same edsf class, we can rectify that by merging the
37 * classes. Then, conversely, an edge in LINE_UNKNOWN state
38 * which separates two faces that _are_ in the same edsf
39 * class can immediately have its state determined.
40 * + But you can go one better, if you're prepared to loop
41 * over all _pairs_ of edges. Suppose we have edges A and B,
42 * which respectively separate faces A1,A2 and B1,B2.
43 * Suppose that A,B are in the same edge-edsf class and that
44 * A1,B1 (wlog) are in the same face-edsf class; then we can
45 * immediately place A2,B2 into the same face-edsf class (as
46 * each other, not as A1 and A2) one way round or the other.
47 * And conversely again, if A1,B1 are in the same face-edsf
48 * class and so are A2,B2, then we can put A,B into the same
50 * * Of course, this deduction requires a quadratic-time
51 * loop over all pairs of edges in the grid, so it should
52 * be reserved until there's nothing easier left to be
55 * - The generalised grid support has made me (SGT) notice a
56 * possible extension to the loop-avoidance code. When you have
57 * a path of connected edges such that no other edges at all
58 * are incident on any vertex in the middle of the path - or,
59 * alternatively, such that any such edges are already known to
60 * be LINE_NO - then you know those edges are either all
61 * LINE_YES or all LINE_NO. Hence you can mentally merge the
62 * entire path into a single long curly edge for the purposes
63 * of loop avoidance, and look directly at whether or not the
64 * extreme endpoints of the path are connected by some other
65 * route. I find this coming up fairly often when I play on the
66 * octagonal grid setting, so it might be worth implementing in
69 * - (Just a speed optimisation.) Consider some todo list queue where every
70 * time we modify something we mark it for consideration by other bits of
71 * the solver, to save iteration over things that have already been done.
87 /* Debugging options */
95 /* ----------------------------------------------------------------------
96 * Struct, enum and function declarations
111 grid *game_grid; /* ref-counted (internally) */
113 /* Put -1 in a face that doesn't get a clue */
116 /* Array of line states, to store whether each line is
117 * YES, NO or UNKNOWN */
120 unsigned char *line_errors;
121 int exactly_one_loop;
126 /* Used in game_text_format(), so that it knows what type of
127 * grid it's trying to render as ASCII text. */
132 SOLVER_SOLVED, /* This is the only solution the solver could find */
133 SOLVER_MISTAKE, /* This is definitely not a solution */
134 SOLVER_AMBIGUOUS, /* This _might_ be an ambiguous solution */
135 SOLVER_INCOMPLETE /* This may be a partial solution */
138 /* ------ Solver state ------ */
139 typedef struct solver_state {
141 enum solver_status solver_status;
142 /* NB looplen is the number of dots that are joined together at a point, ie a
143 * looplen of 1 means there are no lines to a particular dot */
146 /* Difficulty level of solver. Used by solver functions that want to
147 * vary their behaviour depending on the requested difficulty level. */
153 char *face_yes_count;
155 char *dot_solved, *face_solved;
158 /* Information for Normal level deductions:
159 * For each dline, store a bitmask for whether we know:
160 * (bit 0) at least one is YES
161 * (bit 1) at most one is YES */
164 /* Hard level information */
169 * Difficulty levels. I do some macro ickery here to ensure that my
170 * enum and the various forms of my name list always match up.
173 #define DIFFLIST(A) \
178 #define ENUM(upper,title,lower) DIFF_ ## upper,
179 #define TITLE(upper,title,lower) #title,
180 #define ENCODE(upper,title,lower) #lower
181 #define CONFIG(upper,title,lower) ":" #title
182 enum { DIFFLIST(ENUM) DIFF_MAX };
183 static char const *const diffnames[] = { DIFFLIST(TITLE) };
184 static char const diffchars[] = DIFFLIST(ENCODE);
185 #define DIFFCONFIG DIFFLIST(CONFIG)
188 * Solver routines, sorted roughly in order of computational cost.
189 * The solver will run the faster deductions first, and slower deductions are
190 * only invoked when the faster deductions are unable to make progress.
191 * Each function is associated with a difficulty level, so that the generated
192 * puzzles are solvable by applying only the functions with the chosen
193 * difficulty level or lower.
195 #define SOLVERLIST(A) \
196 A(trivial_deductions, DIFF_EASY) \
197 A(dline_deductions, DIFF_NORMAL) \
198 A(linedsf_deductions, DIFF_HARD) \
199 A(loop_deductions, DIFF_EASY)
200 #define SOLVER_FN_DECL(fn,diff) static int fn(solver_state *);
201 #define SOLVER_FN(fn,diff) &fn,
202 #define SOLVER_DIFF(fn,diff) diff,
203 SOLVERLIST(SOLVER_FN_DECL)
204 static int (*(solver_fns[]))(solver_state *) = { SOLVERLIST(SOLVER_FN) };
205 static int const solver_diffs[] = { SOLVERLIST(SOLVER_DIFF) };
206 static const int NUM_SOLVERS = sizeof(solver_diffs)/sizeof(*solver_diffs);
214 /* line_drawstate is the same as line_state, but with the extra ERROR
215 * possibility. The drawing code copies line_state to line_drawstate,
216 * except in the case that the line is an error. */
217 enum line_state { LINE_YES, LINE_UNKNOWN, LINE_NO };
218 enum line_drawstate { DS_LINE_YES, DS_LINE_UNKNOWN,
219 DS_LINE_NO, DS_LINE_ERROR };
221 #define OPP(line_state) \
225 struct game_drawstate {
232 char *clue_satisfied;
235 static const char *validate_desc(const game_params *params, const char *desc);
236 static int dot_order(const game_state* state, int i, char line_type);
237 static int face_order(const game_state* state, int i, char line_type);
238 static solver_state *solve_game_rec(const solver_state *sstate);
241 static void check_caches(const solver_state* sstate);
243 #define check_caches(s)
247 * Grid type config options available in Loopy.
249 * Annoyingly, we have to use an enum here which doesn't match up
250 * exactly to the grid-type enum in grid.h. Values in params->types
251 * are given by names such as LOOPY_GRID_SQUARE, which shouldn't be
252 * confused with GRID_SQUARE which is the value you pass to grid_new()
253 * and friends. So beware!
255 * (This is partly for historical reasons - Loopy's version of the
256 * enum is encoded in game parameter strings, so we keep it for
257 * backwards compatibility. But also, we need to store additional data
258 * here alongside each enum value, such as names for the presets menu,
259 * which isn't stored in grid.h; so we have to have our own list macro
260 * here anyway, and C doesn't make it easy to enforce that that lines
261 * up exactly with grid.h.)
263 * Do not add values to this list _except_ at the end, or old game ids
266 #define GRIDLIST(A) \
267 A("Squares",SQUARE,3,3) \
268 A("Triangular",TRIANGULAR,3,3) \
269 A("Honeycomb",HONEYCOMB,3,3) \
270 A("Snub-Square",SNUBSQUARE,3,3) \
271 A("Cairo",CAIRO,3,4) \
272 A("Great-Hexagonal",GREATHEXAGONAL,3,3) \
273 A("Octagonal",OCTAGONAL,3,3) \
274 A("Kites",KITE,3,3) \
275 A("Floret",FLORET,1,2) \
276 A("Dodecagonal",DODECAGONAL,2,2) \
277 A("Great-Dodecagonal",GREATDODECAGONAL,2,2) \
278 A("Penrose (kite/dart)",PENROSE_P2,3,3) \
279 A("Penrose (rhombs)",PENROSE_P3,3,3) \
280 A("Great-Great-Dodecagonal",GREATGREATDODECAGONAL,2,2) \
283 #define GRID_NAME(title,type,amin,omin) title,
284 #define GRID_CONFIG(title,type,amin,omin) ":" title
285 #define GRID_LOOPYTYPE(title,type,amin,omin) LOOPY_GRID_ ## type,
286 #define GRID_GRIDTYPE(title,type,amin,omin) GRID_ ## type,
287 #define GRID_SIZES(title,type,amin,omin) \
289 "Width and height for this grid type must both be at least " #amin, \
290 "At least one of width and height for this grid type must be at least " #omin,},
291 enum { GRIDLIST(GRID_LOOPYTYPE) LOOPY_GRID_DUMMY_TERMINATOR };
292 static char const *const gridnames[] = { GRIDLIST(GRID_NAME) };
293 #define GRID_CONFIGS GRIDLIST(GRID_CONFIG)
294 static grid_type grid_types[] = { GRIDLIST(GRID_GRIDTYPE) };
295 #define NUM_GRID_TYPES (sizeof(grid_types) / sizeof(grid_types[0]))
296 static const struct {
298 const char *aerr, *oerr;
299 } grid_size_limits[] = { GRIDLIST(GRID_SIZES) };
301 /* Generates a (dynamically allocated) new grid, according to the
302 * type and size requested in params. Does nothing if the grid is already
304 static grid *loopy_generate_grid(const game_params *params,
305 const char *grid_desc)
307 return grid_new(grid_types[params->type], params->w, params->h, grid_desc);
310 /* ----------------------------------------------------------------------
314 /* General constants */
315 #define PREFERRED_TILE_SIZE 32
316 #define BORDER(tilesize) ((tilesize) / 2)
317 #define FLASH_TIME 0.5F
319 #define BIT_SET(field, bit) ((field) & (1<<(bit)))
321 #define SET_BIT(field, bit) (BIT_SET(field, bit) ? FALSE : \
322 ((field) |= (1<<(bit)), TRUE))
324 #define CLEAR_BIT(field, bit) (BIT_SET(field, bit) ? \
325 ((field) &= ~(1<<(bit)), TRUE) : FALSE)
327 #define CLUE2CHAR(c) \
328 ((c < 0) ? ' ' : c < 10 ? c + '0' : c - 10 + 'A')
330 /* ----------------------------------------------------------------------
331 * General struct manipulation and other straightforward code
334 static game_state *dup_game(const game_state *state)
336 game_state *ret = snew(game_state);
338 ret->game_grid = state->game_grid;
339 ret->game_grid->refcount++;
341 ret->solved = state->solved;
342 ret->cheated = state->cheated;
344 ret->clues = snewn(state->game_grid->num_faces, signed char);
345 memcpy(ret->clues, state->clues, state->game_grid->num_faces);
347 ret->lines = snewn(state->game_grid->num_edges, char);
348 memcpy(ret->lines, state->lines, state->game_grid->num_edges);
350 ret->line_errors = snewn(state->game_grid->num_edges, unsigned char);
351 memcpy(ret->line_errors, state->line_errors, state->game_grid->num_edges);
352 ret->exactly_one_loop = state->exactly_one_loop;
354 ret->grid_type = state->grid_type;
358 static void free_game(game_state *state)
361 grid_free(state->game_grid);
364 sfree(state->line_errors);
369 static solver_state *new_solver_state(const game_state *state, int diff) {
371 int num_dots = state->game_grid->num_dots;
372 int num_faces = state->game_grid->num_faces;
373 int num_edges = state->game_grid->num_edges;
374 solver_state *ret = snew(solver_state);
376 ret->state = dup_game(state);
378 ret->solver_status = SOLVER_INCOMPLETE;
381 ret->dotdsf = snew_dsf(num_dots);
382 ret->looplen = snewn(num_dots, int);
384 for (i = 0; i < num_dots; i++) {
388 ret->dot_solved = snewn(num_dots, char);
389 ret->face_solved = snewn(num_faces, char);
390 memset(ret->dot_solved, FALSE, num_dots);
391 memset(ret->face_solved, FALSE, num_faces);
393 ret->dot_yes_count = snewn(num_dots, char);
394 memset(ret->dot_yes_count, 0, num_dots);
395 ret->dot_no_count = snewn(num_dots, char);
396 memset(ret->dot_no_count, 0, num_dots);
397 ret->face_yes_count = snewn(num_faces, char);
398 memset(ret->face_yes_count, 0, num_faces);
399 ret->face_no_count = snewn(num_faces, char);
400 memset(ret->face_no_count, 0, num_faces);
402 if (diff < DIFF_NORMAL) {
405 ret->dlines = snewn(2*num_edges, char);
406 memset(ret->dlines, 0, 2*num_edges);
409 if (diff < DIFF_HARD) {
412 ret->linedsf = snew_dsf(state->game_grid->num_edges);
418 static void free_solver_state(solver_state *sstate) {
420 free_game(sstate->state);
421 sfree(sstate->dotdsf);
422 sfree(sstate->looplen);
423 sfree(sstate->dot_solved);
424 sfree(sstate->face_solved);
425 sfree(sstate->dot_yes_count);
426 sfree(sstate->dot_no_count);
427 sfree(sstate->face_yes_count);
428 sfree(sstate->face_no_count);
430 /* OK, because sfree(NULL) is a no-op */
431 sfree(sstate->dlines);
432 sfree(sstate->linedsf);
438 static solver_state *dup_solver_state(const solver_state *sstate) {
439 game_state *state = sstate->state;
440 int num_dots = state->game_grid->num_dots;
441 int num_faces = state->game_grid->num_faces;
442 int num_edges = state->game_grid->num_edges;
443 solver_state *ret = snew(solver_state);
445 ret->state = state = dup_game(sstate->state);
447 ret->solver_status = sstate->solver_status;
448 ret->diff = sstate->diff;
450 ret->dotdsf = snewn(num_dots, int);
451 ret->looplen = snewn(num_dots, int);
452 memcpy(ret->dotdsf, sstate->dotdsf,
453 num_dots * sizeof(int));
454 memcpy(ret->looplen, sstate->looplen,
455 num_dots * sizeof(int));
457 ret->dot_solved = snewn(num_dots, char);
458 ret->face_solved = snewn(num_faces, char);
459 memcpy(ret->dot_solved, sstate->dot_solved, num_dots);
460 memcpy(ret->face_solved, sstate->face_solved, num_faces);
462 ret->dot_yes_count = snewn(num_dots, char);
463 memcpy(ret->dot_yes_count, sstate->dot_yes_count, num_dots);
464 ret->dot_no_count = snewn(num_dots, char);
465 memcpy(ret->dot_no_count, sstate->dot_no_count, num_dots);
467 ret->face_yes_count = snewn(num_faces, char);
468 memcpy(ret->face_yes_count, sstate->face_yes_count, num_faces);
469 ret->face_no_count = snewn(num_faces, char);
470 memcpy(ret->face_no_count, sstate->face_no_count, num_faces);
472 if (sstate->dlines) {
473 ret->dlines = snewn(2*num_edges, char);
474 memcpy(ret->dlines, sstate->dlines,
480 if (sstate->linedsf) {
481 ret->linedsf = snewn(num_edges, int);
482 memcpy(ret->linedsf, sstate->linedsf,
483 num_edges * sizeof(int));
491 static game_params *default_params(void)
493 game_params *ret = snew(game_params);
502 ret->diff = DIFF_EASY;
508 static game_params *dup_params(const game_params *params)
510 game_params *ret = snew(game_params);
512 *ret = *params; /* structure copy */
516 static const game_params loopy_presets_top[] = {
518 { 7, 7, DIFF_EASY, LOOPY_GRID_SQUARE },
519 { 7, 7, DIFF_NORMAL, LOOPY_GRID_SQUARE },
520 { 7, 7, DIFF_HARD, LOOPY_GRID_SQUARE },
521 { 7, 7, DIFF_HARD, LOOPY_GRID_TRIANGULAR },
522 { 5, 5, DIFF_HARD, LOOPY_GRID_SNUBSQUARE },
523 { 7, 7, DIFF_HARD, LOOPY_GRID_CAIRO },
524 { 5, 5, DIFF_HARD, LOOPY_GRID_KITE },
525 { 6, 6, DIFF_HARD, LOOPY_GRID_PENROSE_P2 },
526 { 6, 6, DIFF_HARD, LOOPY_GRID_PENROSE_P3 },
528 { 7, 7, DIFF_EASY, LOOPY_GRID_SQUARE },
529 { 10, 10, DIFF_EASY, LOOPY_GRID_SQUARE },
530 { 7, 7, DIFF_NORMAL, LOOPY_GRID_SQUARE },
531 { 10, 10, DIFF_NORMAL, LOOPY_GRID_SQUARE },
532 { 7, 7, DIFF_HARD, LOOPY_GRID_SQUARE },
533 { 10, 10, DIFF_HARD, LOOPY_GRID_SQUARE },
534 { 12, 10, DIFF_HARD, LOOPY_GRID_TRIANGULAR },
535 { 7, 7, DIFF_HARD, LOOPY_GRID_SNUBSQUARE },
536 { 9, 9, DIFF_HARD, LOOPY_GRID_CAIRO },
537 { 5, 5, DIFF_HARD, LOOPY_GRID_KITE },
538 { 10, 10, DIFF_HARD, LOOPY_GRID_PENROSE_P2 },
539 { 10, 10, DIFF_HARD, LOOPY_GRID_PENROSE_P3 },
543 static const game_params loopy_presets_more[] = {
545 { 7, 7, DIFF_HARD, LOOPY_GRID_HONEYCOMB },
546 { 5, 4, DIFF_HARD, LOOPY_GRID_GREATHEXAGONAL },
547 { 5, 5, DIFF_HARD, LOOPY_GRID_OCTAGONAL },
548 { 3, 3, DIFF_HARD, LOOPY_GRID_FLORET },
549 { 3, 3, DIFF_HARD, LOOPY_GRID_DODECAGONAL },
550 { 3, 3, DIFF_HARD, LOOPY_GRID_GREATDODECAGONAL },
551 { 3, 2, DIFF_HARD, LOOPY_GRID_GREATGREATDODECAGONAL },
553 { 10, 10, DIFF_HARD, LOOPY_GRID_HONEYCOMB },
554 { 5, 4, DIFF_HARD, LOOPY_GRID_GREATHEXAGONAL },
555 { 7, 7, DIFF_HARD, LOOPY_GRID_OCTAGONAL },
556 { 5, 5, DIFF_HARD, LOOPY_GRID_FLORET },
557 { 5, 4, DIFF_HARD, LOOPY_GRID_DODECAGONAL },
558 { 5, 4, DIFF_HARD, LOOPY_GRID_GREATDODECAGONAL },
559 { 5, 3, DIFF_HARD, LOOPY_GRID_GREATGREATDODECAGONAL },
563 static void preset_menu_add_preset_with_title(struct preset_menu *menu,
564 const game_params *params)
567 game_params *dup_params;
569 sprintf(buf, "%dx%d %s - %s", params->h, params->w,
570 gridnames[params->type], diffnames[params->diff]);
572 dup_params = snew(game_params);
573 *dup_params = *params;
575 preset_menu_add_preset(menu, dupstr(buf), dup_params);
578 static struct preset_menu *game_preset_menu(void)
580 struct preset_menu *top, *more;
583 top = preset_menu_new();
584 for (i = 0; i < lenof(loopy_presets_top); i++)
585 preset_menu_add_preset_with_title(top, &loopy_presets_top[i]);
587 more = preset_menu_add_submenu(top, dupstr("More..."));
588 for (i = 0; i < lenof(loopy_presets_more); i++)
589 preset_menu_add_preset_with_title(more, &loopy_presets_more[i]);
594 static void free_params(game_params *params)
599 static void decode_params(game_params *params, char const *string)
601 params->h = params->w = atoi(string);
602 params->diff = DIFF_EASY;
603 while (*string && isdigit((unsigned char)*string)) string++;
604 if (*string == 'x') {
606 params->h = atoi(string);
607 while (*string && isdigit((unsigned char)*string)) string++;
609 if (*string == 't') {
611 params->type = atoi(string);
612 while (*string && isdigit((unsigned char)*string)) string++;
614 if (*string == 'd') {
617 for (i = 0; i < DIFF_MAX; i++)
618 if (*string == diffchars[i])
620 if (*string) string++;
624 static char *encode_params(const game_params *params, int full)
627 sprintf(str, "%dx%dt%d", params->w, params->h, params->type);
629 sprintf(str + strlen(str), "d%c", diffchars[params->diff]);
633 static config_item *game_configure(const game_params *params)
638 ret = snewn(5, config_item);
640 ret[0].name = "Width";
641 ret[0].type = C_STRING;
642 sprintf(buf, "%d", params->w);
643 ret[0].u.string.sval = dupstr(buf);
645 ret[1].name = "Height";
646 ret[1].type = C_STRING;
647 sprintf(buf, "%d", params->h);
648 ret[1].u.string.sval = dupstr(buf);
650 ret[2].name = "Grid type";
651 ret[2].type = C_CHOICES;
652 ret[2].u.choices.choicenames = GRID_CONFIGS;
653 ret[2].u.choices.selected = params->type;
655 ret[3].name = "Difficulty";
656 ret[3].type = C_CHOICES;
657 ret[3].u.choices.choicenames = DIFFCONFIG;
658 ret[3].u.choices.selected = params->diff;
666 static game_params *custom_params(const config_item *cfg)
668 game_params *ret = snew(game_params);
670 ret->w = atoi(cfg[0].u.string.sval);
671 ret->h = atoi(cfg[1].u.string.sval);
672 ret->type = cfg[2].u.choices.selected;
673 ret->diff = cfg[3].u.choices.selected;
678 static const char *validate_params(const game_params *params, int full)
680 if (params->type < 0 || params->type >= NUM_GRID_TYPES)
681 return "Illegal grid type";
682 if (params->w < grid_size_limits[params->type].amin ||
683 params->h < grid_size_limits[params->type].amin)
684 return grid_size_limits[params->type].aerr;
685 if (params->w < grid_size_limits[params->type].omin &&
686 params->h < grid_size_limits[params->type].omin)
687 return grid_size_limits[params->type].oerr;
690 * This shouldn't be able to happen at all, since decode_params
691 * and custom_params will never generate anything that isn't
694 assert(params->diff < DIFF_MAX);
699 /* Returns a newly allocated string describing the current puzzle */
700 static char *state_to_text(const game_state *state)
702 grid *g = state->game_grid;
704 int num_faces = g->num_faces;
705 char *description = snewn(num_faces + 1, char);
706 char *dp = description;
710 for (i = 0; i < num_faces; i++) {
711 if (state->clues[i] < 0) {
712 if (empty_count > 25) {
713 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
719 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
722 dp += sprintf(dp, "%c", (int)CLUE2CHAR(state->clues[i]));
727 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
729 retval = dupstr(description);
735 #define GRID_DESC_SEP '_'
737 /* Splits up a (optional) grid_desc from the game desc. Returns the
738 * grid_desc (which needs freeing) and updates the desc pointer to
739 * start of real desc, or returns NULL if no desc. */
740 static char *extract_grid_desc(const char **desc)
742 char *sep = strchr(*desc, GRID_DESC_SEP), *gd;
745 if (!sep) return NULL;
747 gd_len = sep - (*desc);
748 gd = snewn(gd_len+1, char);
749 memcpy(gd, *desc, gd_len);
757 /* We require that the params pass the test in validate_params and that the
758 * description fills the entire game area */
759 static const char *validate_desc(const game_params *params, const char *desc)
766 /* It's pretty inefficient to do this just for validation. All we need to
767 * know is the precise number of faces. */
768 grid_desc = extract_grid_desc(&desc);
769 ret = grid_validate_desc(grid_types[params->type], params->w, params->h, grid_desc);
772 g = loopy_generate_grid(params, grid_desc);
773 if (grid_desc) sfree(grid_desc);
775 for (; *desc; ++desc) {
776 if ((*desc >= '0' && *desc <= '9') || (*desc >= 'A' && *desc <= 'Z')) {
781 count += *desc - 'a' + 1;
784 return "Unknown character in description";
787 if (count < g->num_faces)
788 return "Description too short for board size";
789 if (count > g->num_faces)
790 return "Description too long for board size";
797 /* Sums the lengths of the numbers in range [0,n) */
798 /* See equivalent function in solo.c for justification of this. */
799 static int len_0_to_n(int n)
801 int len = 1; /* Counting 0 as a bit of a special case */
804 for (i = 1; i < n; i *= 10) {
805 len += max(n - i, 0);
811 static char *encode_solve_move(const game_state *state)
816 int num_edges = state->game_grid->num_edges;
818 /* This is going to return a string representing the moves needed to set
819 * every line in a grid to be the same as the ones in 'state'. The exact
820 * length of this string is predictable. */
822 len = 1; /* Count the 'S' prefix */
823 /* Numbers in all lines */
824 len += len_0_to_n(num_edges);
825 /* For each line we also have a letter */
828 ret = snewn(len + 1, char);
831 p += sprintf(p, "S");
833 for (i = 0; i < num_edges; i++) {
834 switch (state->lines[i]) {
836 p += sprintf(p, "%dy", i);
839 p += sprintf(p, "%dn", i);
844 /* No point in doing sums like that if they're going to be wrong */
845 assert(strlen(ret) <= (size_t)len);
849 static game_ui *new_ui(const game_state *state)
854 static void free_ui(game_ui *ui)
858 static char *encode_ui(const game_ui *ui)
863 static void decode_ui(game_ui *ui, const char *encoding)
867 static void game_changed_state(game_ui *ui, const game_state *oldstate,
868 const game_state *newstate)
872 static void game_compute_size(const game_params *params, int tilesize,
875 int grid_width, grid_height, rendered_width, rendered_height;
878 grid_compute_size(grid_types[params->type], params->w, params->h,
879 &g_tilesize, &grid_width, &grid_height);
881 /* multiply first to minimise rounding error on integer division */
882 rendered_width = grid_width * tilesize / g_tilesize;
883 rendered_height = grid_height * tilesize / g_tilesize;
884 *x = rendered_width + 2 * BORDER(tilesize) + 1;
885 *y = rendered_height + 2 * BORDER(tilesize) + 1;
888 static void game_set_size(drawing *dr, game_drawstate *ds,
889 const game_params *params, int tilesize)
891 ds->tilesize = tilesize;
894 static float *game_colours(frontend *fe, int *ncolours)
896 float *ret = snewn(3 * NCOLOURS, float);
898 frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
900 ret[COL_FOREGROUND * 3 + 0] = 0.0F;
901 ret[COL_FOREGROUND * 3 + 1] = 0.0F;
902 ret[COL_FOREGROUND * 3 + 2] = 0.0F;
905 * We want COL_LINEUNKNOWN to be a yellow which is a bit darker
906 * than the background. (I previously set it to 0.8,0.8,0, but
907 * found that this went badly with the 0.8,0.8,0.8 favoured as a
908 * background by the Java frontend.)
910 ret[COL_LINEUNKNOWN * 3 + 0] = ret[COL_BACKGROUND * 3 + 0] * 0.9F;
911 ret[COL_LINEUNKNOWN * 3 + 1] = ret[COL_BACKGROUND * 3 + 1] * 0.9F;
912 ret[COL_LINEUNKNOWN * 3 + 2] = 0.0F;
914 ret[COL_HIGHLIGHT * 3 + 0] = 1.0F;
915 ret[COL_HIGHLIGHT * 3 + 1] = 1.0F;
916 ret[COL_HIGHLIGHT * 3 + 2] = 1.0F;
918 ret[COL_MISTAKE * 3 + 0] = 1.0F;
919 ret[COL_MISTAKE * 3 + 1] = 0.0F;
920 ret[COL_MISTAKE * 3 + 2] = 0.0F;
922 ret[COL_SATISFIED * 3 + 0] = 0.0F;
923 ret[COL_SATISFIED * 3 + 1] = 0.0F;
924 ret[COL_SATISFIED * 3 + 2] = 0.0F;
926 /* We want the faint lines to be a bit darker than the background.
927 * Except if the background is pretty dark already; then it ought to be a
928 * bit lighter. Oy vey.
930 ret[COL_FAINT * 3 + 0] = ret[COL_BACKGROUND * 3 + 0] * 0.9F;
931 ret[COL_FAINT * 3 + 1] = ret[COL_BACKGROUND * 3 + 1] * 0.9F;
932 ret[COL_FAINT * 3 + 2] = ret[COL_BACKGROUND * 3 + 2] * 0.9F;
934 *ncolours = NCOLOURS;
938 static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
940 struct game_drawstate *ds = snew(struct game_drawstate);
941 int num_faces = state->game_grid->num_faces;
942 int num_edges = state->game_grid->num_edges;
947 ds->lines = snewn(num_edges, char);
948 ds->clue_error = snewn(num_faces, char);
949 ds->clue_satisfied = snewn(num_faces, char);
950 ds->textx = snewn(num_faces, int);
951 ds->texty = snewn(num_faces, int);
954 memset(ds->lines, LINE_UNKNOWN, num_edges);
955 memset(ds->clue_error, 0, num_faces);
956 memset(ds->clue_satisfied, 0, num_faces);
957 for (i = 0; i < num_faces; i++)
958 ds->textx[i] = ds->texty[i] = -1;
963 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
967 sfree(ds->clue_error);
968 sfree(ds->clue_satisfied);
973 static int game_timing_state(const game_state *state, game_ui *ui)
978 static float game_anim_length(const game_state *oldstate,
979 const game_state *newstate, int dir, game_ui *ui)
984 static int game_can_format_as_text_now(const game_params *params)
986 if (params->type != 0)
991 static char *game_text_format(const game_state *state)
997 grid *g = state->game_grid;
1000 assert(state->grid_type == 0);
1002 /* Work out the basic size unit */
1003 f = g->faces; /* first face */
1004 assert(f->order == 4);
1005 /* The dots are ordered clockwise, so the two opposite
1006 * corners are guaranteed to span the square */
1007 cell_size = abs(f->dots[0]->x - f->dots[2]->x);
1009 w = (g->highest_x - g->lowest_x) / cell_size;
1010 h = (g->highest_y - g->lowest_y) / cell_size;
1012 /* Create a blank "canvas" to "draw" on */
1015 ret = snewn(W * H + 1, char);
1016 for (y = 0; y < H; y++) {
1017 for (x = 0; x < W-1; x++) {
1020 ret[y*W + W-1] = '\n';
1024 /* Fill in edge info */
1025 for (i = 0; i < g->num_edges; i++) {
1026 grid_edge *e = g->edges + i;
1027 /* Cell coordinates, from (0,0) to (w-1,h-1) */
1028 int x1 = (e->dot1->x - g->lowest_x) / cell_size;
1029 int x2 = (e->dot2->x - g->lowest_x) / cell_size;
1030 int y1 = (e->dot1->y - g->lowest_y) / cell_size;
1031 int y2 = (e->dot2->y - g->lowest_y) / cell_size;
1032 /* Midpoint, in canvas coordinates (canvas coordinates are just twice
1033 * cell coordinates) */
1036 switch (state->lines[i]) {
1038 ret[y*W + x] = (y1 == y2) ? '-' : '|';
1044 break; /* already a space */
1046 assert(!"Illegal line state");
1051 for (i = 0; i < g->num_faces; i++) {
1055 assert(f->order == 4);
1056 /* Cell coordinates, from (0,0) to (w-1,h-1) */
1057 x1 = (f->dots[0]->x - g->lowest_x) / cell_size;
1058 x2 = (f->dots[2]->x - g->lowest_x) / cell_size;
1059 y1 = (f->dots[0]->y - g->lowest_y) / cell_size;
1060 y2 = (f->dots[2]->y - g->lowest_y) / cell_size;
1061 /* Midpoint, in canvas coordinates */
1064 ret[y*W + x] = CLUE2CHAR(state->clues[i]);
1069 /* ----------------------------------------------------------------------
1074 static void check_caches(const solver_state* sstate)
1077 const game_state *state = sstate->state;
1078 const grid *g = state->game_grid;
1080 for (i = 0; i < g->num_dots; i++) {
1081 assert(dot_order(state, i, LINE_YES) == sstate->dot_yes_count[i]);
1082 assert(dot_order(state, i, LINE_NO) == sstate->dot_no_count[i]);
1085 for (i = 0; i < g->num_faces; i++) {
1086 assert(face_order(state, i, LINE_YES) == sstate->face_yes_count[i]);
1087 assert(face_order(state, i, LINE_NO) == sstate->face_no_count[i]);
1092 #define check_caches(s) \
1094 fprintf(stderr, "check_caches at line %d\n", __LINE__); \
1098 #endif /* DEBUG_CACHES */
1100 /* ----------------------------------------------------------------------
1101 * Solver utility functions
1104 /* Sets the line (with index i) to the new state 'line_new', and updates
1105 * the cached counts of any affected faces and dots.
1106 * Returns TRUE if this actually changed the line's state. */
1107 static int solver_set_line(solver_state *sstate, int i,
1108 enum line_state line_new
1110 , const char *reason
1114 game_state *state = sstate->state;
1118 assert(line_new != LINE_UNKNOWN);
1120 check_caches(sstate);
1122 if (state->lines[i] == line_new) {
1123 return FALSE; /* nothing changed */
1125 state->lines[i] = line_new;
1128 fprintf(stderr, "solver: set line [%d] to %s (%s)\n",
1129 i, line_new == LINE_YES ? "YES" : "NO",
1133 g = state->game_grid;
1136 /* Update the cache for both dots and both faces affected by this. */
1137 if (line_new == LINE_YES) {
1138 sstate->dot_yes_count[e->dot1 - g->dots]++;
1139 sstate->dot_yes_count[e->dot2 - g->dots]++;
1141 sstate->face_yes_count[e->face1 - g->faces]++;
1144 sstate->face_yes_count[e->face2 - g->faces]++;
1147 sstate->dot_no_count[e->dot1 - g->dots]++;
1148 sstate->dot_no_count[e->dot2 - g->dots]++;
1150 sstate->face_no_count[e->face1 - g->faces]++;
1153 sstate->face_no_count[e->face2 - g->faces]++;
1157 check_caches(sstate);
1162 #define solver_set_line(a, b, c) \
1163 solver_set_line(a, b, c, __FUNCTION__)
1167 * Merge two dots due to the existence of an edge between them.
1168 * Updates the dsf tracking equivalence classes, and keeps track of
1169 * the length of path each dot is currently a part of.
1170 * Returns TRUE if the dots were already linked, ie if they are part of a
1171 * closed loop, and false otherwise.
1173 static int merge_dots(solver_state *sstate, int edge_index)
1176 grid *g = sstate->state->game_grid;
1177 grid_edge *e = g->edges + edge_index;
1179 i = e->dot1 - g->dots;
1180 j = e->dot2 - g->dots;
1182 i = dsf_canonify(sstate->dotdsf, i);
1183 j = dsf_canonify(sstate->dotdsf, j);
1188 len = sstate->looplen[i] + sstate->looplen[j];
1189 dsf_merge(sstate->dotdsf, i, j);
1190 i = dsf_canonify(sstate->dotdsf, i);
1191 sstate->looplen[i] = len;
1196 /* Merge two lines because the solver has deduced that they must be either
1197 * identical or opposite. Returns TRUE if this is new information, otherwise
1199 static int merge_lines(solver_state *sstate, int i, int j, int inverse
1201 , const char *reason
1207 assert(i < sstate->state->game_grid->num_edges);
1208 assert(j < sstate->state->game_grid->num_edges);
1210 i = edsf_canonify(sstate->linedsf, i, &inv_tmp);
1212 j = edsf_canonify(sstate->linedsf, j, &inv_tmp);
1215 edsf_merge(sstate->linedsf, i, j, inverse);
1219 fprintf(stderr, "%s [%d] [%d] %s(%s)\n",
1221 inverse ? "inverse " : "", reason);
1228 #define merge_lines(a, b, c, d) \
1229 merge_lines(a, b, c, d, __FUNCTION__)
1232 /* Count the number of lines of a particular type currently going into the
1234 static int dot_order(const game_state* state, int dot, char line_type)
1237 grid *g = state->game_grid;
1238 grid_dot *d = g->dots + dot;
1241 for (i = 0; i < d->order; i++) {
1242 grid_edge *e = d->edges[i];
1243 if (state->lines[e - g->edges] == line_type)
1249 /* Count the number of lines of a particular type currently surrounding the
1251 static int face_order(const game_state* state, int face, char line_type)
1254 grid *g = state->game_grid;
1255 grid_face *f = g->faces + face;
1258 for (i = 0; i < f->order; i++) {
1259 grid_edge *e = f->edges[i];
1260 if (state->lines[e - g->edges] == line_type)
1266 /* Set all lines bordering a dot of type old_type to type new_type
1267 * Return value tells caller whether this function actually did anything */
1268 static int dot_setall(solver_state *sstate, int dot,
1269 char old_type, char new_type)
1271 int retval = FALSE, r;
1272 game_state *state = sstate->state;
1277 if (old_type == new_type)
1280 g = state->game_grid;
1283 for (i = 0; i < d->order; i++) {
1284 int line_index = d->edges[i] - g->edges;
1285 if (state->lines[line_index] == old_type) {
1286 r = solver_set_line(sstate, line_index, new_type);
1294 /* Set all lines bordering a face of type old_type to type new_type */
1295 static int face_setall(solver_state *sstate, int face,
1296 char old_type, char new_type)
1298 int retval = FALSE, r;
1299 game_state *state = sstate->state;
1304 if (old_type == new_type)
1307 g = state->game_grid;
1308 f = g->faces + face;
1310 for (i = 0; i < f->order; i++) {
1311 int line_index = f->edges[i] - g->edges;
1312 if (state->lines[line_index] == old_type) {
1313 r = solver_set_line(sstate, line_index, new_type);
1321 /* ----------------------------------------------------------------------
1322 * Loop generation and clue removal
1325 static void add_full_clues(game_state *state, random_state *rs)
1327 signed char *clues = state->clues;
1328 grid *g = state->game_grid;
1329 char *board = snewn(g->num_faces, char);
1332 generate_loop(g, board, rs, NULL, NULL);
1334 /* Fill out all the clues by initialising to 0, then iterating over
1335 * all edges and incrementing each clue as we find edges that border
1336 * between BLACK/WHITE faces. While we're at it, we verify that the
1337 * algorithm does work, and there aren't any GREY faces still there. */
1338 memset(clues, 0, g->num_faces);
1339 for (i = 0; i < g->num_edges; i++) {
1340 grid_edge *e = g->edges + i;
1341 grid_face *f1 = e->face1;
1342 grid_face *f2 = e->face2;
1343 enum face_colour c1 = FACE_COLOUR(f1);
1344 enum face_colour c2 = FACE_COLOUR(f2);
1345 assert(c1 != FACE_GREY);
1346 assert(c2 != FACE_GREY);
1348 if (f1) clues[f1 - g->faces]++;
1349 if (f2) clues[f2 - g->faces]++;
1356 static int game_has_unique_soln(const game_state *state, int diff)
1359 solver_state *sstate_new;
1360 solver_state *sstate = new_solver_state((game_state *)state, diff);
1362 sstate_new = solve_game_rec(sstate);
1364 assert(sstate_new->solver_status != SOLVER_MISTAKE);
1365 ret = (sstate_new->solver_status == SOLVER_SOLVED);
1367 free_solver_state(sstate_new);
1368 free_solver_state(sstate);
1374 /* Remove clues one at a time at random. */
1375 static game_state *remove_clues(game_state *state, random_state *rs,
1379 int num_faces = state->game_grid->num_faces;
1380 game_state *ret = dup_game(state), *saved_ret;
1383 /* We need to remove some clues. We'll do this by forming a list of all
1384 * available clues, shuffling it, then going along one at a
1385 * time clearing each clue in turn for which doing so doesn't render the
1386 * board unsolvable. */
1387 face_list = snewn(num_faces, int);
1388 for (n = 0; n < num_faces; ++n) {
1392 shuffle(face_list, num_faces, sizeof(int), rs);
1394 for (n = 0; n < num_faces; ++n) {
1395 saved_ret = dup_game(ret);
1396 ret->clues[face_list[n]] = -1;
1398 if (game_has_unique_soln(ret, diff)) {
1399 free_game(saved_ret);
1411 static char *new_game_desc(const game_params *params, random_state *rs,
1412 char **aux, int interactive)
1414 /* solution and description both use run-length encoding in obvious ways */
1415 char *retval, *game_desc, *grid_desc;
1417 game_state *state = snew(game_state);
1418 game_state *state_new;
1420 grid_desc = grid_new_desc(grid_types[params->type], params->w, params->h, rs);
1421 state->game_grid = g = loopy_generate_grid(params, grid_desc);
1423 state->clues = snewn(g->num_faces, signed char);
1424 state->lines = snewn(g->num_edges, char);
1425 state->line_errors = snewn(g->num_edges, unsigned char);
1426 state->exactly_one_loop = FALSE;
1428 state->grid_type = params->type;
1432 memset(state->lines, LINE_UNKNOWN, g->num_edges);
1433 memset(state->line_errors, 0, g->num_edges);
1435 state->solved = state->cheated = FALSE;
1437 /* Get a new random solvable board with all its clues filled in. Yes, this
1438 * can loop for ever if the params are suitably unfavourable, but
1439 * preventing games smaller than 4x4 seems to stop this happening */
1441 add_full_clues(state, rs);
1442 } while (!game_has_unique_soln(state, params->diff));
1444 state_new = remove_clues(state, rs, params->diff);
1449 if (params->diff > 0 && game_has_unique_soln(state, params->diff-1)) {
1451 fprintf(stderr, "Rejecting board, it is too easy\n");
1453 goto newboard_please;
1456 game_desc = state_to_text(state);
1461 retval = snewn(strlen(grid_desc) + 1 + strlen(game_desc) + 1, char);
1462 sprintf(retval, "%s%c%s", grid_desc, (int)GRID_DESC_SEP, game_desc);
1469 assert(!validate_desc(params, retval));
1474 static game_state *new_game(midend *me, const game_params *params,
1478 game_state *state = snew(game_state);
1479 int empties_to_make = 0;
1484 int num_faces, num_edges;
1486 grid_desc = extract_grid_desc(&desc);
1487 state->game_grid = g = loopy_generate_grid(params, grid_desc);
1488 if (grid_desc) sfree(grid_desc);
1492 num_faces = g->num_faces;
1493 num_edges = g->num_edges;
1495 state->clues = snewn(num_faces, signed char);
1496 state->lines = snewn(num_edges, char);
1497 state->line_errors = snewn(num_edges, unsigned char);
1498 state->exactly_one_loop = FALSE;
1500 state->solved = state->cheated = FALSE;
1502 state->grid_type = params->type;
1504 for (i = 0; i < num_faces; i++) {
1505 if (empties_to_make) {
1507 state->clues[i] = -1;
1513 n2 = *dp - 'A' + 10;
1514 if (n >= 0 && n < 10) {
1515 state->clues[i] = n;
1516 } else if (n2 >= 10 && n2 < 36) {
1517 state->clues[i] = n2;
1521 state->clues[i] = -1;
1522 empties_to_make = n - 1;
1527 memset(state->lines, LINE_UNKNOWN, num_edges);
1528 memset(state->line_errors, 0, num_edges);
1532 /* Calculates the line_errors data, and checks if the current state is a
1534 static int check_completion(game_state *state)
1536 grid *g = state->game_grid;
1538 int *dsf, *component_state;
1539 int nsilly, nloop, npath, largest_comp, largest_size, total_pathsize;
1540 enum { COMP_NONE, COMP_LOOP, COMP_PATH, COMP_SILLY, COMP_EMPTY };
1542 memset(state->line_errors, 0, g->num_edges);
1545 * Find loops in the grid, and determine whether the puzzle is
1548 * Loopy is a bit more complicated than most puzzles that care
1549 * about loop detection. In most of them, loops are simply
1550 * _forbidden_; so the obviously right way to do
1551 * error-highlighting during play is to light up a graph edge red
1552 * iff it is part of a loop, which is exactly what the centralised
1553 * findloop.c makes easy.
1555 * But Loopy is unusual in that you're _supposed_ to be making a
1556 * loop - and yet _some_ loops are not the right loop. So we need
1557 * to be more discriminating, by identifying loops one by one and
1558 * then thinking about which ones to highlight, and so findloop.c
1559 * isn't quite the right tool for the job in this case.
1561 * Worse still, consider situations in which the grid contains a
1562 * loop and also some non-loop edges: there are some cases like
1563 * this in which the user's intuitive expectation would be to
1564 * highlight the loop (if you're only about half way through the
1565 * puzzle and have accidentally made a little loop in some corner
1566 * of the grid), and others in which they'd be more likely to
1567 * expect you to highlight the non-loop edges (if you've just
1568 * closed off a whole loop that you thought was the entire
1569 * solution, but forgot some disconnected edges in a corner
1570 * somewhere). So while it's easy enough to check whether the
1571 * solution is _right_, highlighting the wrong parts is a tricky
1572 * problem for this puzzle!
1574 * I'd quite like, in some situations, to identify the largest
1575 * loop among the player's YES edges, and then light up everything
1576 * other than that. But finding the longest cycle in a graph is an
1577 * NP-complete problem (because, in particular, it must return a
1578 * Hamilton cycle if one exists).
1580 * However, I think we can make the problem tractable by
1581 * exercising the Puzzles principle that it isn't absolutely
1582 * necessary to highlight _all_ errors: the key point is that by
1583 * the time the user has filled in the whole grid, they should
1584 * either have seen a completion flash, or have _some_ error
1585 * highlight showing them why the solution isn't right. So in
1586 * principle it would be *just about* good enough to highlight
1587 * just one error in the whole grid, if there was really no better
1588 * way. But we'd like to highlight as many errors as possible.
1590 * In this case, I think the simple approach is to make use of the
1591 * fact that no vertex may have degree > 2, and that's really
1592 * simple to detect. So the plan goes like this:
1594 * - Form the dsf of connected components of the graph vertices.
1596 * - Highlight an error at any vertex with degree > 2. (It so
1597 * happens that we do this by lighting up all the edges
1598 * incident to that vertex, but that's an output detail.)
1600 * - Any component that contains such a vertex is now excluded
1601 * from further consideration, because it already has a
1604 * - The remaining components have no vertex with degree > 2, and
1605 * hence they all consist of either a simple loop, or a simple
1606 * path with two endpoints.
1608 * - For these purposes, group together all the paths and imagine
1609 * them to be a single component (because in most normal
1610 * situations the player will gradually build up the solution
1611 * _not_ all in one connected segment, but as lots of separate
1612 * little path pieces that gradually connect to each other).
1614 * - After doing that, if there is exactly one (sensible)
1615 * component - be it a collection of paths or a loop - then
1616 * highlight no further edge errors. (The former case is normal
1617 * during play, and the latter is a potentially solved puzzle.)
1619 * - Otherwise, find the largest of the sensible components,
1620 * leave that one unhighlighted, and light the rest up in red.
1623 dsf = snew_dsf(g->num_dots);
1625 /* Build the dsf. */
1626 for (i = 0; i < g->num_edges; i++) {
1627 if (state->lines[i] == LINE_YES) {
1628 grid_edge *e = g->edges + i;
1629 int d1 = e->dot1 - g->dots, d2 = e->dot2 - g->dots;
1630 dsf_merge(dsf, d1, d2);
1634 /* Initialise a state variable for each connected component. */
1635 component_state = snewn(g->num_dots, int);
1636 for (i = 0; i < g->num_dots; i++) {
1637 if (dsf_canonify(dsf, i) == i)
1638 component_state[i] = COMP_LOOP;
1640 component_state[i] = COMP_NONE;
1643 /* Check for dots with degree > 3. Here we also spot dots of
1644 * degree 1 in which the user has marked all the non-edges as
1645 * LINE_NO, because those are also clear vertex-level errors, so
1646 * we give them the same treatment of excluding their connected
1647 * component from the subsequent loop analysis. */
1648 for (i = 0; i < g->num_dots; i++) {
1649 int comp = dsf_canonify(dsf, i);
1650 int yes = dot_order(state, i, LINE_YES);
1651 int unknown = dot_order(state, i, LINE_UNKNOWN);
1652 if ((yes == 1 && unknown == 0) || (yes >= 3)) {
1653 /* violation, so mark all YES edges as errors */
1654 grid_dot *d = g->dots + i;
1656 for (j = 0; j < d->order; j++) {
1657 int e = d->edges[j] - g->edges;
1658 if (state->lines[e] == LINE_YES)
1659 state->line_errors[e] = TRUE;
1661 /* And mark this component as not worthy of further
1663 component_state[comp] = COMP_SILLY;
1665 } else if (yes == 0) {
1666 /* A completely isolated dot must also be excluded it from
1667 * the subsequent loop highlighting pass, but we tag it
1668 * with a different enum value to avoid it counting
1669 * towards the components that inhibit returning a win
1671 component_state[comp] = COMP_EMPTY;
1672 } else if (yes == 1) {
1673 /* A dot with degree 1 that didn't fall into the 'clearly
1674 * erroneous' case above indicates that this connected
1675 * component will be a path rather than a loop - unless
1676 * something worse elsewhere in the component has
1677 * classified it as silly. */
1678 if (component_state[comp] != COMP_SILLY)
1679 component_state[comp] = COMP_PATH;
1683 /* Count up the components. Also, find the largest sensible
1684 * component. (Tie-breaking condition is derived from the order of
1685 * vertices in the grid data structure, which is fairly arbitrary
1686 * but at least stays stable throughout the game.) */
1687 nsilly = nloop = npath = 0;
1689 largest_comp = largest_size = -1;
1690 for (i = 0; i < g->num_dots; i++) {
1691 if (component_state[i] == COMP_SILLY) {
1693 } else if (component_state[i] == COMP_PATH) {
1694 total_pathsize += dsf_size(dsf, i);
1696 } else if (component_state[i] == COMP_LOOP) {
1701 if ((this_size = dsf_size(dsf, i)) > largest_size) {
1703 largest_size = this_size;
1707 if (largest_size < total_pathsize) {
1708 largest_comp = -1; /* means the paths */
1709 largest_size = total_pathsize;
1712 if (nloop > 0 && nloop + npath > 1) {
1714 * If there are at least two sensible components including at
1715 * least one loop, highlight all edges in every sensible
1716 * component that is not the largest one.
1718 for (i = 0; i < g->num_edges; i++) {
1719 if (state->lines[i] == LINE_YES) {
1720 grid_edge *e = g->edges + i;
1721 int d1 = e->dot1 - g->dots; /* either endpoint is good enough */
1722 int comp = dsf_canonify(dsf, d1);
1723 if ((component_state[comp] == COMP_PATH &&
1724 -1 != largest_comp) ||
1725 (component_state[comp] == COMP_LOOP &&
1726 comp != largest_comp))
1727 state->line_errors[i] = TRUE;
1732 if (nloop == 1 && npath == 0 && nsilly == 0) {
1734 * If there is exactly one component and it is a loop, then
1735 * the puzzle is potentially complete, so check the clues.
1739 for (i = 0; i < g->num_faces; i++) {
1740 int c = state->clues[i];
1741 if (c >= 0 && face_order(state, i, LINE_YES) != c) {
1748 * Also, whether or not the puzzle is actually complete, set
1749 * the flag that says this game_state has exactly one loop and
1750 * nothing else, which will be used to vary the semantics of
1751 * clue highlighting at display time.
1753 state->exactly_one_loop = TRUE;
1756 state->exactly_one_loop = FALSE;
1759 sfree(component_state);
1765 /* ----------------------------------------------------------------------
1768 * Our solver modes operate as follows. Each mode also uses the modes above it.
1771 * Just implement the rules of the game.
1773 * Normal and Tricky Modes
1774 * For each (adjacent) pair of lines through each dot we store a bit for
1775 * whether at least one of them is on and whether at most one is on. (If we
1776 * know both or neither is on that's already stored more directly.)
1779 * Use edsf data structure to make equivalence classes of lines that are
1780 * known identical to or opposite to one another.
1785 * For general grids, we consider "dlines" to be pairs of lines joined
1786 * at a dot. The lines must be adjacent around the dot, so we can think of
1787 * a dline as being a dot+face combination. Or, a dot+edge combination where
1788 * the second edge is taken to be the next clockwise edge from the dot.
1789 * Original loopy code didn't have this extra restriction of the lines being
1790 * adjacent. From my tests with square grids, this extra restriction seems to
1791 * take little, if anything, away from the quality of the puzzles.
1792 * A dline can be uniquely identified by an edge/dot combination, given that
1793 * a dline-pair always goes clockwise around its common dot. The edge/dot
1794 * combination can be represented by an edge/bool combination - if bool is
1795 * TRUE, use edge->dot1 else use edge->dot2. So the total number of dlines is
1796 * exactly twice the number of edges in the grid - although the dlines
1797 * spanning the infinite face are not all that useful to the solver.
1798 * Note that, by convention, a dline goes clockwise around its common dot,
1799 * which means the dline goes anti-clockwise around its common face.
1802 /* Helper functions for obtaining an index into an array of dlines, given
1803 * various information. We assume the grid layout conventions about how
1804 * the various lists are interleaved - see grid_make_consistent() for
1807 /* i points to the first edge of the dline pair, reading clockwise around
1809 static int dline_index_from_dot(grid *g, grid_dot *d, int i)
1811 grid_edge *e = d->edges[i];
1816 if (i2 == d->order) i2 = 0;
1819 ret = 2 * (e - g->edges) + ((e->dot1 == d) ? 1 : 0);
1821 printf("dline_index_from_dot: d=%d,i=%d, edges [%d,%d] - %d\n",
1822 (int)(d - g->dots), i, (int)(e - g->edges),
1823 (int)(e2 - g->edges), ret);
1827 /* i points to the second edge of the dline pair, reading clockwise around
1828 * the face. That is, the edges of the dline, starting at edge{i}, read
1829 * anti-clockwise around the face. By layout conventions, the common dot
1830 * of the dline will be f->dots[i] */
1831 static int dline_index_from_face(grid *g, grid_face *f, int i)
1833 grid_edge *e = f->edges[i];
1834 grid_dot *d = f->dots[i];
1839 if (i2 < 0) i2 += f->order;
1842 ret = 2 * (e - g->edges) + ((e->dot1 == d) ? 1 : 0);
1844 printf("dline_index_from_face: f=%d,i=%d, edges [%d,%d] - %d\n",
1845 (int)(f - g->faces), i, (int)(e - g->edges),
1846 (int)(e2 - g->edges), ret);
1850 static int is_atleastone(const char *dline_array, int index)
1852 return BIT_SET(dline_array[index], 0);
1854 static int set_atleastone(char *dline_array, int index)
1856 return SET_BIT(dline_array[index], 0);
1858 static int is_atmostone(const char *dline_array, int index)
1860 return BIT_SET(dline_array[index], 1);
1862 static int set_atmostone(char *dline_array, int index)
1864 return SET_BIT(dline_array[index], 1);
1867 static void array_setall(char *array, char from, char to, int len)
1869 char *p = array, *p_old = p;
1870 int len_remaining = len;
1872 while ((p = memchr(p, from, len_remaining))) {
1874 len_remaining -= p - p_old;
1879 /* Helper, called when doing dline dot deductions, in the case where we
1880 * have 4 UNKNOWNs, and two of them (adjacent) have *exactly* one YES between
1881 * them (because of dline atmostone/atleastone).
1882 * On entry, edge points to the first of these two UNKNOWNs. This function
1883 * will find the opposite UNKNOWNS (if they are adjacent to one another)
1884 * and set their corresponding dline to atleastone. (Setting atmostone
1885 * already happens in earlier dline deductions) */
1886 static int dline_set_opp_atleastone(solver_state *sstate,
1887 grid_dot *d, int edge)
1889 game_state *state = sstate->state;
1890 grid *g = state->game_grid;
1893 for (opp = 0; opp < N; opp++) {
1894 int opp_dline_index;
1895 if (opp == edge || opp == edge+1 || opp == edge-1)
1897 if (opp == 0 && edge == N-1)
1899 if (opp == N-1 && edge == 0)
1902 if (opp2 == N) opp2 = 0;
1903 /* Check if opp, opp2 point to LINE_UNKNOWNs */
1904 if (state->lines[d->edges[opp] - g->edges] != LINE_UNKNOWN)
1906 if (state->lines[d->edges[opp2] - g->edges] != LINE_UNKNOWN)
1908 /* Found opposite UNKNOWNS and they're next to each other */
1909 opp_dline_index = dline_index_from_dot(g, d, opp);
1910 return set_atleastone(sstate->dlines, opp_dline_index);
1916 /* Set pairs of lines around this face which are known to be identical, to
1917 * the given line_state */
1918 static int face_setall_identical(solver_state *sstate, int face_index,
1919 enum line_state line_new)
1921 /* can[dir] contains the canonical line associated with the line in
1922 * direction dir from the square in question. Similarly inv[dir] is
1923 * whether or not the line in question is inverse to its canonical
1926 game_state *state = sstate->state;
1927 grid *g = state->game_grid;
1928 grid_face *f = g->faces + face_index;
1931 int can1, can2, inv1, inv2;
1933 for (i = 0; i < N; i++) {
1934 int line1_index = f->edges[i] - g->edges;
1935 if (state->lines[line1_index] != LINE_UNKNOWN)
1937 for (j = i + 1; j < N; j++) {
1938 int line2_index = f->edges[j] - g->edges;
1939 if (state->lines[line2_index] != LINE_UNKNOWN)
1942 /* Found two UNKNOWNS */
1943 can1 = edsf_canonify(sstate->linedsf, line1_index, &inv1);
1944 can2 = edsf_canonify(sstate->linedsf, line2_index, &inv2);
1945 if (can1 == can2 && inv1 == inv2) {
1946 solver_set_line(sstate, line1_index, line_new);
1947 solver_set_line(sstate, line2_index, line_new);
1954 /* Given a dot or face, and a count of LINE_UNKNOWNs, find them and
1955 * return the edge indices into e. */
1956 static void find_unknowns(game_state *state,
1957 grid_edge **edge_list, /* Edge list to search (from a face or a dot) */
1958 int expected_count, /* Number of UNKNOWNs (comes from solver's cache) */
1959 int *e /* Returned edge indices */)
1962 grid *g = state->game_grid;
1963 while (c < expected_count) {
1964 int line_index = *edge_list - g->edges;
1965 if (state->lines[line_index] == LINE_UNKNOWN) {
1973 /* If we have a list of edges, and we know whether the number of YESs should
1974 * be odd or even, and there are only a few UNKNOWNs, we can do some simple
1975 * linedsf deductions. This can be used for both face and dot deductions.
1976 * Returns the difficulty level of the next solver that should be used,
1977 * or DIFF_MAX if no progress was made. */
1978 static int parity_deductions(solver_state *sstate,
1979 grid_edge **edge_list, /* Edge list (from a face or a dot) */
1980 int total_parity, /* Expected number of YESs modulo 2 (either 0 or 1) */
1983 game_state *state = sstate->state;
1984 int diff = DIFF_MAX;
1985 int *linedsf = sstate->linedsf;
1987 if (unknown_count == 2) {
1988 /* Lines are known alike/opposite, depending on inv. */
1990 find_unknowns(state, edge_list, 2, e);
1991 if (merge_lines(sstate, e[0], e[1], total_parity))
1992 diff = min(diff, DIFF_HARD);
1993 } else if (unknown_count == 3) {
1995 int can[3]; /* canonical edges */
1996 int inv[3]; /* whether can[x] is inverse to e[x] */
1997 find_unknowns(state, edge_list, 3, e);
1998 can[0] = edsf_canonify(linedsf, e[0], inv);
1999 can[1] = edsf_canonify(linedsf, e[1], inv+1);
2000 can[2] = edsf_canonify(linedsf, e[2], inv+2);
2001 if (can[0] == can[1]) {
2002 if (solver_set_line(sstate, e[2], (total_parity^inv[0]^inv[1]) ?
2003 LINE_YES : LINE_NO))
2004 diff = min(diff, DIFF_EASY);
2006 if (can[0] == can[2]) {
2007 if (solver_set_line(sstate, e[1], (total_parity^inv[0]^inv[2]) ?
2008 LINE_YES : LINE_NO))
2009 diff = min(diff, DIFF_EASY);
2011 if (can[1] == can[2]) {
2012 if (solver_set_line(sstate, e[0], (total_parity^inv[1]^inv[2]) ?
2013 LINE_YES : LINE_NO))
2014 diff = min(diff, DIFF_EASY);
2016 } else if (unknown_count == 4) {
2018 int can[4]; /* canonical edges */
2019 int inv[4]; /* whether can[x] is inverse to e[x] */
2020 find_unknowns(state, edge_list, 4, e);
2021 can[0] = edsf_canonify(linedsf, e[0], inv);
2022 can[1] = edsf_canonify(linedsf, e[1], inv+1);
2023 can[2] = edsf_canonify(linedsf, e[2], inv+2);
2024 can[3] = edsf_canonify(linedsf, e[3], inv+3);
2025 if (can[0] == can[1]) {
2026 if (merge_lines(sstate, e[2], e[3], total_parity^inv[0]^inv[1]))
2027 diff = min(diff, DIFF_HARD);
2028 } else if (can[0] == can[2]) {
2029 if (merge_lines(sstate, e[1], e[3], total_parity^inv[0]^inv[2]))
2030 diff = min(diff, DIFF_HARD);
2031 } else if (can[0] == can[3]) {
2032 if (merge_lines(sstate, e[1], e[2], total_parity^inv[0]^inv[3]))
2033 diff = min(diff, DIFF_HARD);
2034 } else if (can[1] == can[2]) {
2035 if (merge_lines(sstate, e[0], e[3], total_parity^inv[1]^inv[2]))
2036 diff = min(diff, DIFF_HARD);
2037 } else if (can[1] == can[3]) {
2038 if (merge_lines(sstate, e[0], e[2], total_parity^inv[1]^inv[3]))
2039 diff = min(diff, DIFF_HARD);
2040 } else if (can[2] == can[3]) {
2041 if (merge_lines(sstate, e[0], e[1], total_parity^inv[2]^inv[3]))
2042 diff = min(diff, DIFF_HARD);
2050 * These are the main solver functions.
2052 * Their return values are diff values corresponding to the lowest mode solver
2053 * that would notice the work that they have done. For example if the normal
2054 * mode solver adds actual lines or crosses, it will return DIFF_EASY as the
2055 * easy mode solver might be able to make progress using that. It doesn't make
2056 * sense for one of them to return a diff value higher than that of the
2059 * Each function returns the lowest value it can, as early as possible, in
2060 * order to try and pass as much work as possible back to the lower level
2061 * solvers which progress more quickly.
2064 /* PROPOSED NEW DESIGN:
2065 * We have a work queue consisting of 'events' notifying us that something has
2066 * happened that a particular solver mode might be interested in. For example
2067 * the hard mode solver might do something that helps the normal mode solver at
2068 * dot [x,y] in which case it will enqueue an event recording this fact. Then
2069 * we pull events off the work queue, and hand each in turn to the solver that
2070 * is interested in them. If a solver reports that it failed we pass the same
2071 * event on to progressively more advanced solvers and the loop detector. Once
2072 * we've exhausted an event, or it has helped us progress, we drop it and
2073 * continue to the next one. The events are sorted first in order of solver
2074 * complexity (easy first) then order of insertion (oldest first).
2075 * Once we run out of events we loop over each permitted solver in turn
2076 * (easiest first) until either a deduction is made (and an event therefore
2077 * emerges) or no further deductions can be made (in which case we've failed).
2080 * * How do we 'loop over' a solver when both dots and squares are concerned.
2081 * Answer: first all squares then all dots.
2084 static int trivial_deductions(solver_state *sstate)
2086 int i, current_yes, current_no;
2087 game_state *state = sstate->state;
2088 grid *g = state->game_grid;
2089 int diff = DIFF_MAX;
2091 /* Per-face deductions */
2092 for (i = 0; i < g->num_faces; i++) {
2093 grid_face *f = g->faces + i;
2095 if (sstate->face_solved[i])
2098 current_yes = sstate->face_yes_count[i];
2099 current_no = sstate->face_no_count[i];
2101 if (current_yes + current_no == f->order) {
2102 sstate->face_solved[i] = TRUE;
2106 if (state->clues[i] < 0)
2110 * This code checks whether the numeric clue on a face is so
2111 * large as to permit all its remaining LINE_UNKNOWNs to be
2112 * filled in as LINE_YES, or alternatively so small as to
2113 * permit them all to be filled in as LINE_NO.
2116 if (state->clues[i] < current_yes) {
2117 sstate->solver_status = SOLVER_MISTAKE;
2120 if (state->clues[i] == current_yes) {
2121 if (face_setall(sstate, i, LINE_UNKNOWN, LINE_NO))
2122 diff = min(diff, DIFF_EASY);
2123 sstate->face_solved[i] = TRUE;
2127 if (f->order - state->clues[i] < current_no) {
2128 sstate->solver_status = SOLVER_MISTAKE;
2131 if (f->order - state->clues[i] == current_no) {
2132 if (face_setall(sstate, i, LINE_UNKNOWN, LINE_YES))
2133 diff = min(diff, DIFF_EASY);
2134 sstate->face_solved[i] = TRUE;
2138 if (f->order - state->clues[i] == current_no + 1 &&
2139 f->order - current_yes - current_no > 2) {
2141 * One small refinement to the above: we also look for any
2142 * adjacent pair of LINE_UNKNOWNs around the face with
2143 * some LINE_YES incident on it from elsewhere. If we find
2144 * one, then we know that pair of LINE_UNKNOWNs can't
2145 * _both_ be LINE_YES, and hence that pushes us one line
2146 * closer to being able to determine all the rest.
2148 int j, k, e1, e2, e, d;
2150 for (j = 0; j < f->order; j++) {
2151 e1 = f->edges[j] - g->edges;
2152 e2 = f->edges[j+1 < f->order ? j+1 : 0] - g->edges;
2154 if (g->edges[e1].dot1 == g->edges[e2].dot1 ||
2155 g->edges[e1].dot1 == g->edges[e2].dot2) {
2156 d = g->edges[e1].dot1 - g->dots;
2158 assert(g->edges[e1].dot2 == g->edges[e2].dot1 ||
2159 g->edges[e1].dot2 == g->edges[e2].dot2);
2160 d = g->edges[e1].dot2 - g->dots;
2163 if (state->lines[e1] == LINE_UNKNOWN &&
2164 state->lines[e2] == LINE_UNKNOWN) {
2165 for (k = 0; k < g->dots[d].order; k++) {
2166 int e = g->dots[d].edges[k] - g->edges;
2167 if (state->lines[e] == LINE_YES)
2168 goto found; /* multi-level break */
2176 * If we get here, we've found such a pair of edges, and
2177 * they're e1 and e2.
2179 for (j = 0; j < f->order; j++) {
2180 e = f->edges[j] - g->edges;
2181 if (state->lines[e] == LINE_UNKNOWN && e != e1 && e != e2) {
2182 int r = solver_set_line(sstate, e, LINE_YES);
2184 diff = min(diff, DIFF_EASY);
2190 check_caches(sstate);
2192 /* Per-dot deductions */
2193 for (i = 0; i < g->num_dots; i++) {
2194 grid_dot *d = g->dots + i;
2195 int yes, no, unknown;
2197 if (sstate->dot_solved[i])
2200 yes = sstate->dot_yes_count[i];
2201 no = sstate->dot_no_count[i];
2202 unknown = d->order - yes - no;
2206 sstate->dot_solved[i] = TRUE;
2207 } else if (unknown == 1) {
2208 dot_setall(sstate, i, LINE_UNKNOWN, LINE_NO);
2209 diff = min(diff, DIFF_EASY);
2210 sstate->dot_solved[i] = TRUE;
2212 } else if (yes == 1) {
2214 sstate->solver_status = SOLVER_MISTAKE;
2216 } else if (unknown == 1) {
2217 dot_setall(sstate, i, LINE_UNKNOWN, LINE_YES);
2218 diff = min(diff, DIFF_EASY);
2220 } else if (yes == 2) {
2222 dot_setall(sstate, i, LINE_UNKNOWN, LINE_NO);
2223 diff = min(diff, DIFF_EASY);
2225 sstate->dot_solved[i] = TRUE;
2227 sstate->solver_status = SOLVER_MISTAKE;
2232 check_caches(sstate);
2237 static int dline_deductions(solver_state *sstate)
2239 game_state *state = sstate->state;
2240 grid *g = state->game_grid;
2241 char *dlines = sstate->dlines;
2243 int diff = DIFF_MAX;
2245 /* ------ Face deductions ------ */
2247 /* Given a set of dline atmostone/atleastone constraints, need to figure
2248 * out if we can deduce any further info. For more general faces than
2249 * squares, this turns out to be a tricky problem.
2250 * The approach taken here is to define (per face) NxN matrices:
2251 * "maxs" and "mins".
2252 * The entries maxs(j,k) and mins(j,k) define the upper and lower limits
2253 * for the possible number of edges that are YES between positions j and k
2254 * going clockwise around the face. Can think of j and k as marking dots
2255 * around the face (recall the labelling scheme: edge0 joins dot0 to dot1,
2256 * edge1 joins dot1 to dot2 etc).
2257 * Trivially, mins(j,j) = maxs(j,j) = 0, and we don't even bother storing
2258 * these. mins(j,j+1) and maxs(j,j+1) are determined by whether edge{j}
2259 * is YES, NO or UNKNOWN. mins(j,j+2) and maxs(j,j+2) are related to
2260 * the dline atmostone/atleastone status for edges j and j+1.
2262 * Then we calculate the remaining entries recursively. We definitely
2264 * mins(j,k) >= { mins(j,u) + mins(u,k) } for any u between j and k.
2265 * This is because any valid placement of YESs between j and k must give
2266 * a valid placement between j and u, and also between u and k.
2267 * I believe it's sufficient to use just the two values of u:
2268 * j+1 and j+2. Seems to work well in practice - the bounds we compute
2269 * are rigorous, even if they might not be best-possible.
2271 * Once we have maxs and mins calculated, we can make inferences about
2272 * each dline{j,j+1} by looking at the possible complementary edge-counts
2273 * mins(j+2,j) and maxs(j+2,j) and comparing these with the face clue.
2274 * As well as dlines, we can make similar inferences about single edges.
2275 * For example, consider a pentagon with clue 3, and we know at most one
2276 * of (edge0, edge1) is YES, and at most one of (edge2, edge3) is YES.
2277 * We could then deduce edge4 is YES, because maxs(0,4) would be 2, so
2278 * that final edge would have to be YES to make the count up to 3.
2281 /* Much quicker to allocate arrays on the stack than the heap, so
2282 * define the largest possible face size, and base our array allocations
2283 * on that. We check this with an assertion, in case someone decides to
2284 * make a grid which has larger faces than this. Note, this algorithm
2285 * could get quite expensive if there are many large faces. */
2286 #define MAX_FACE_SIZE 12
2288 for (i = 0; i < g->num_faces; i++) {
2289 int maxs[MAX_FACE_SIZE][MAX_FACE_SIZE];
2290 int mins[MAX_FACE_SIZE][MAX_FACE_SIZE];
2291 grid_face *f = g->faces + i;
2294 int clue = state->clues[i];
2295 assert(N <= MAX_FACE_SIZE);
2296 if (sstate->face_solved[i])
2298 if (clue < 0) continue;
2300 /* Calculate the (j,j+1) entries */
2301 for (j = 0; j < N; j++) {
2302 int edge_index = f->edges[j] - g->edges;
2304 enum line_state line1 = state->lines[edge_index];
2305 enum line_state line2;
2309 maxs[j][k] = (line1 == LINE_NO) ? 0 : 1;
2310 mins[j][k] = (line1 == LINE_YES) ? 1 : 0;
2311 /* Calculate the (j,j+2) entries */
2312 dline_index = dline_index_from_face(g, f, k);
2313 edge_index = f->edges[k] - g->edges;
2314 line2 = state->lines[edge_index];
2320 if (line1 == LINE_NO) tmp--;
2321 if (line2 == LINE_NO) tmp--;
2322 if (tmp == 2 && is_atmostone(dlines, dline_index))
2328 if (line1 == LINE_YES) tmp++;
2329 if (line2 == LINE_YES) tmp++;
2330 if (tmp == 0 && is_atleastone(dlines, dline_index))
2335 /* Calculate the (j,j+m) entries for m between 3 and N-1 */
2336 for (m = 3; m < N; m++) {
2337 for (j = 0; j < N; j++) {
2345 maxs[j][k] = maxs[j][u] + maxs[u][k];
2346 mins[j][k] = mins[j][u] + mins[u][k];
2347 tmp = maxs[j][v] + maxs[v][k];
2348 maxs[j][k] = min(maxs[j][k], tmp);
2349 tmp = mins[j][v] + mins[v][k];
2350 mins[j][k] = max(mins[j][k], tmp);
2354 /* See if we can make any deductions */
2355 for (j = 0; j < N; j++) {
2357 grid_edge *e = f->edges[j];
2358 int line_index = e - g->edges;
2361 if (state->lines[line_index] != LINE_UNKNOWN)
2366 /* minimum YESs in the complement of this edge */
2367 if (mins[k][j] > clue) {
2368 sstate->solver_status = SOLVER_MISTAKE;
2371 if (mins[k][j] == clue) {
2372 /* setting this edge to YES would make at least
2373 * (clue+1) edges - contradiction */
2374 solver_set_line(sstate, line_index, LINE_NO);
2375 diff = min(diff, DIFF_EASY);
2377 if (maxs[k][j] < clue - 1) {
2378 sstate->solver_status = SOLVER_MISTAKE;
2381 if (maxs[k][j] == clue - 1) {
2382 /* Only way to satisfy the clue is to set edge{j} as YES */
2383 solver_set_line(sstate, line_index, LINE_YES);
2384 diff = min(diff, DIFF_EASY);
2387 /* More advanced deduction that allows propagation along diagonal
2388 * chains of faces connected by dots, for example, 3-2-...-2-3
2389 * in square grids. */
2390 if (sstate->diff >= DIFF_TRICKY) {
2391 /* Now see if we can make dline deduction for edges{j,j+1} */
2393 if (state->lines[e - g->edges] != LINE_UNKNOWN)
2394 /* Only worth doing this for an UNKNOWN,UNKNOWN pair.
2395 * Dlines where one of the edges is known, are handled in the
2399 dline_index = dline_index_from_face(g, f, k);
2403 /* minimum YESs in the complement of this dline */
2404 if (mins[k][j] > clue - 2) {
2405 /* Adding 2 YESs would break the clue */
2406 if (set_atmostone(dlines, dline_index))
2407 diff = min(diff, DIFF_NORMAL);
2409 /* maximum YESs in the complement of this dline */
2410 if (maxs[k][j] < clue) {
2411 /* Adding 2 NOs would mean not enough YESs */
2412 if (set_atleastone(dlines, dline_index))
2413 diff = min(diff, DIFF_NORMAL);
2419 if (diff < DIFF_NORMAL)
2422 /* ------ Dot deductions ------ */
2424 for (i = 0; i < g->num_dots; i++) {
2425 grid_dot *d = g->dots + i;
2427 int yes, no, unknown;
2429 if (sstate->dot_solved[i])
2431 yes = sstate->dot_yes_count[i];
2432 no = sstate->dot_no_count[i];
2433 unknown = N - yes - no;
2435 for (j = 0; j < N; j++) {
2438 int line1_index, line2_index;
2439 enum line_state line1, line2;
2442 dline_index = dline_index_from_dot(g, d, j);
2443 line1_index = d->edges[j] - g->edges;
2444 line2_index = d->edges[k] - g->edges;
2445 line1 = state->lines[line1_index];
2446 line2 = state->lines[line2_index];
2448 /* Infer dline state from line state */
2449 if (line1 == LINE_NO || line2 == LINE_NO) {
2450 if (set_atmostone(dlines, dline_index))
2451 diff = min(diff, DIFF_NORMAL);
2453 if (line1 == LINE_YES || line2 == LINE_YES) {
2454 if (set_atleastone(dlines, dline_index))
2455 diff = min(diff, DIFF_NORMAL);
2457 /* Infer line state from dline state */
2458 if (is_atmostone(dlines, dline_index)) {
2459 if (line1 == LINE_YES && line2 == LINE_UNKNOWN) {
2460 solver_set_line(sstate, line2_index, LINE_NO);
2461 diff = min(diff, DIFF_EASY);
2463 if (line2 == LINE_YES && line1 == LINE_UNKNOWN) {
2464 solver_set_line(sstate, line1_index, LINE_NO);
2465 diff = min(diff, DIFF_EASY);
2468 if (is_atleastone(dlines, dline_index)) {
2469 if (line1 == LINE_NO && line2 == LINE_UNKNOWN) {
2470 solver_set_line(sstate, line2_index, LINE_YES);
2471 diff = min(diff, DIFF_EASY);
2473 if (line2 == LINE_NO && line1 == LINE_UNKNOWN) {
2474 solver_set_line(sstate, line1_index, LINE_YES);
2475 diff = min(diff, DIFF_EASY);
2478 /* Deductions that depend on the numbers of lines.
2479 * Only bother if both lines are UNKNOWN, otherwise the
2480 * easy-mode solver (or deductions above) would have taken
2482 if (line1 != LINE_UNKNOWN || line2 != LINE_UNKNOWN)
2485 if (yes == 0 && unknown == 2) {
2486 /* Both these unknowns must be identical. If we know
2487 * atmostone or atleastone, we can make progress. */
2488 if (is_atmostone(dlines, dline_index)) {
2489 solver_set_line(sstate, line1_index, LINE_NO);
2490 solver_set_line(sstate, line2_index, LINE_NO);
2491 diff = min(diff, DIFF_EASY);
2493 if (is_atleastone(dlines, dline_index)) {
2494 solver_set_line(sstate, line1_index, LINE_YES);
2495 solver_set_line(sstate, line2_index, LINE_YES);
2496 diff = min(diff, DIFF_EASY);
2500 if (set_atmostone(dlines, dline_index))
2501 diff = min(diff, DIFF_NORMAL);
2503 if (set_atleastone(dlines, dline_index))
2504 diff = min(diff, DIFF_NORMAL);
2508 /* More advanced deduction that allows propagation along diagonal
2509 * chains of faces connected by dots, for example: 3-2-...-2-3
2510 * in square grids. */
2511 if (sstate->diff >= DIFF_TRICKY) {
2512 /* If we have atleastone set for this dline, infer
2513 * atmostone for each "opposite" dline (that is, each
2514 * dline without edges in common with this one).
2515 * Again, this test is only worth doing if both these
2516 * lines are UNKNOWN. For if one of these lines were YES,
2517 * the (yes == 1) test above would kick in instead. */
2518 if (is_atleastone(dlines, dline_index)) {
2520 for (opp = 0; opp < N; opp++) {
2521 int opp_dline_index;
2522 if (opp == j || opp == j+1 || opp == j-1)
2524 if (j == 0 && opp == N-1)
2526 if (j == N-1 && opp == 0)
2528 opp_dline_index = dline_index_from_dot(g, d, opp);
2529 if (set_atmostone(dlines, opp_dline_index))
2530 diff = min(diff, DIFF_NORMAL);
2532 if (yes == 0 && is_atmostone(dlines, dline_index)) {
2533 /* This dline has *exactly* one YES and there are no
2534 * other YESs. This allows more deductions. */
2536 /* Third unknown must be YES */
2537 for (opp = 0; opp < N; opp++) {
2539 if (opp == j || opp == k)
2541 opp_index = d->edges[opp] - g->edges;
2542 if (state->lines[opp_index] == LINE_UNKNOWN) {
2543 solver_set_line(sstate, opp_index,
2545 diff = min(diff, DIFF_EASY);
2548 } else if (unknown == 4) {
2549 /* Exactly one of opposite UNKNOWNS is YES. We've
2550 * already set atmostone, so set atleastone as
2553 if (dline_set_opp_atleastone(sstate, d, j))
2554 diff = min(diff, DIFF_NORMAL);
2564 static int linedsf_deductions(solver_state *sstate)
2566 game_state *state = sstate->state;
2567 grid *g = state->game_grid;
2568 char *dlines = sstate->dlines;
2570 int diff = DIFF_MAX;
2573 /* ------ Face deductions ------ */
2575 /* A fully-general linedsf deduction seems overly complicated
2576 * (I suspect the problem is NP-complete, though in practice it might just
2577 * be doable because faces are limited in size).
2578 * For simplicity, we only consider *pairs* of LINE_UNKNOWNS that are
2579 * known to be identical. If setting them both to YES (or NO) would break
2580 * the clue, set them to NO (or YES). */
2582 for (i = 0; i < g->num_faces; i++) {
2583 int N, yes, no, unknown;
2586 if (sstate->face_solved[i])
2588 clue = state->clues[i];
2592 N = g->faces[i].order;
2593 yes = sstate->face_yes_count[i];
2594 if (yes + 1 == clue) {
2595 if (face_setall_identical(sstate, i, LINE_NO))
2596 diff = min(diff, DIFF_EASY);
2598 no = sstate->face_no_count[i];
2599 if (no + 1 == N - clue) {
2600 if (face_setall_identical(sstate, i, LINE_YES))
2601 diff = min(diff, DIFF_EASY);
2604 /* Reload YES count, it might have changed */
2605 yes = sstate->face_yes_count[i];
2606 unknown = N - no - yes;
2608 /* Deductions with small number of LINE_UNKNOWNs, based on overall
2609 * parity of lines. */
2610 diff_tmp = parity_deductions(sstate, g->faces[i].edges,
2611 (clue - yes) % 2, unknown);
2612 diff = min(diff, diff_tmp);
2615 /* ------ Dot deductions ------ */
2616 for (i = 0; i < g->num_dots; i++) {
2617 grid_dot *d = g->dots + i;
2620 int yes, no, unknown;
2621 /* Go through dlines, and do any dline<->linedsf deductions wherever
2622 * we find two UNKNOWNS. */
2623 for (j = 0; j < N; j++) {
2624 int dline_index = dline_index_from_dot(g, d, j);
2627 int can1, can2, inv1, inv2;
2629 line1_index = d->edges[j] - g->edges;
2630 if (state->lines[line1_index] != LINE_UNKNOWN)
2633 if (j2 == N) j2 = 0;
2634 line2_index = d->edges[j2] - g->edges;
2635 if (state->lines[line2_index] != LINE_UNKNOWN)
2637 /* Infer dline flags from linedsf */
2638 can1 = edsf_canonify(sstate->linedsf, line1_index, &inv1);
2639 can2 = edsf_canonify(sstate->linedsf, line2_index, &inv2);
2640 if (can1 == can2 && inv1 != inv2) {
2641 /* These are opposites, so set dline atmostone/atleastone */
2642 if (set_atmostone(dlines, dline_index))
2643 diff = min(diff, DIFF_NORMAL);
2644 if (set_atleastone(dlines, dline_index))
2645 diff = min(diff, DIFF_NORMAL);
2648 /* Infer linedsf from dline flags */
2649 if (is_atmostone(dlines, dline_index)
2650 && is_atleastone(dlines, dline_index)) {
2651 if (merge_lines(sstate, line1_index, line2_index, 1))
2652 diff = min(diff, DIFF_HARD);
2656 /* Deductions with small number of LINE_UNKNOWNs, based on overall
2657 * parity of lines. */
2658 yes = sstate->dot_yes_count[i];
2659 no = sstate->dot_no_count[i];
2660 unknown = N - yes - no;
2661 diff_tmp = parity_deductions(sstate, d->edges,
2663 diff = min(diff, diff_tmp);
2666 /* ------ Edge dsf deductions ------ */
2668 /* If the state of a line is known, deduce the state of its canonical line
2669 * too, and vice versa. */
2670 for (i = 0; i < g->num_edges; i++) {
2673 can = edsf_canonify(sstate->linedsf, i, &inv);
2676 s = sstate->state->lines[can];
2677 if (s != LINE_UNKNOWN) {
2678 if (solver_set_line(sstate, i, inv ? OPP(s) : s))
2679 diff = min(diff, DIFF_EASY);
2681 s = sstate->state->lines[i];
2682 if (s != LINE_UNKNOWN) {
2683 if (solver_set_line(sstate, can, inv ? OPP(s) : s))
2684 diff = min(diff, DIFF_EASY);
2692 static int loop_deductions(solver_state *sstate)
2694 int edgecount = 0, clues = 0, satclues = 0, sm1clues = 0;
2695 game_state *state = sstate->state;
2696 grid *g = state->game_grid;
2697 int shortest_chainlen = g->num_dots;
2698 int loop_found = FALSE;
2700 int progress = FALSE;
2704 * Go through the grid and update for all the new edges.
2705 * Since merge_dots() is idempotent, the simplest way to
2706 * do this is just to update for _all_ the edges.
2707 * Also, while we're here, we count the edges.
2709 for (i = 0; i < g->num_edges; i++) {
2710 if (state->lines[i] == LINE_YES) {
2711 loop_found |= merge_dots(sstate, i);
2717 * Count the clues, count the satisfied clues, and count the
2718 * satisfied-minus-one clues.
2720 for (i = 0; i < g->num_faces; i++) {
2721 int c = state->clues[i];
2723 int o = sstate->face_yes_count[i];
2732 for (i = 0; i < g->num_dots; ++i) {
2734 sstate->looplen[dsf_canonify(sstate->dotdsf, i)];
2735 if (dots_connected > 1)
2736 shortest_chainlen = min(shortest_chainlen, dots_connected);
2739 assert(sstate->solver_status == SOLVER_INCOMPLETE);
2741 if (satclues == clues && shortest_chainlen == edgecount) {
2742 sstate->solver_status = SOLVER_SOLVED;
2743 /* This discovery clearly counts as progress, even if we haven't
2744 * just added any lines or anything */
2746 goto finished_loop_deductionsing;
2750 * Now go through looking for LINE_UNKNOWN edges which
2751 * connect two dots that are already in the same
2752 * equivalence class. If we find one, test to see if the
2753 * loop it would create is a solution.
2755 for (i = 0; i < g->num_edges; i++) {
2756 grid_edge *e = g->edges + i;
2757 int d1 = e->dot1 - g->dots;
2758 int d2 = e->dot2 - g->dots;
2760 if (state->lines[i] != LINE_UNKNOWN)
2763 eqclass = dsf_canonify(sstate->dotdsf, d1);
2764 if (eqclass != dsf_canonify(sstate->dotdsf, d2))
2767 val = LINE_NO; /* loop is bad until proven otherwise */
2770 * This edge would form a loop. Next
2771 * question: how long would the loop be?
2772 * Would it equal the total number of edges
2773 * (plus the one we'd be adding if we added
2776 if (sstate->looplen[eqclass] == edgecount + 1) {
2780 * This edge would form a loop which
2781 * took in all the edges in the entire
2782 * grid. So now we need to work out
2783 * whether it would be a valid solution
2784 * to the puzzle, which means we have to
2785 * check if it satisfies all the clues.
2786 * This means that every clue must be
2787 * either satisfied or satisfied-minus-
2788 * 1, and also that the number of
2789 * satisfied-minus-1 clues must be at
2790 * most two and they must lie on either
2791 * side of this edge.
2795 int f = e->face1 - g->faces;
2796 int c = state->clues[f];
2797 if (c >= 0 && sstate->face_yes_count[f] == c - 1)
2801 int f = e->face2 - g->faces;
2802 int c = state->clues[f];
2803 if (c >= 0 && sstate->face_yes_count[f] == c - 1)
2806 if (sm1clues == sm1_nearby &&
2807 sm1clues + satclues == clues) {
2808 val = LINE_YES; /* loop is good! */
2813 * Right. Now we know that adding this edge
2814 * would form a loop, and we know whether
2815 * that loop would be a viable solution or
2818 * If adding this edge produces a solution,
2819 * then we know we've found _a_ solution but
2820 * we don't know that it's _the_ solution -
2821 * if it were provably the solution then
2822 * we'd have deduced this edge some time ago
2823 * without the need to do loop detection. So
2824 * in this state we return SOLVER_AMBIGUOUS,
2825 * which has the effect that hitting Solve
2826 * on a user-provided puzzle will fill in a
2827 * solution but using the solver to
2828 * construct new puzzles won't consider this
2829 * a reasonable deduction for the user to
2832 progress = solver_set_line(sstate, i, val);
2833 assert(progress == TRUE);
2834 if (val == LINE_YES) {
2835 sstate->solver_status = SOLVER_AMBIGUOUS;
2836 goto finished_loop_deductionsing;
2840 finished_loop_deductionsing:
2841 return progress ? DIFF_EASY : DIFF_MAX;
2844 /* This will return a dynamically allocated solver_state containing the (more)
2846 static solver_state *solve_game_rec(const solver_state *sstate_start)
2848 solver_state *sstate;
2850 /* Index of the solver we should call next. */
2853 /* As a speed-optimisation, we avoid re-running solvers that we know
2854 * won't make any progress. This happens when a high-difficulty
2855 * solver makes a deduction that can only help other high-difficulty
2857 * For example: if a new 'dline' flag is set by dline_deductions, the
2858 * trivial_deductions solver cannot do anything with this information.
2859 * If we've already run the trivial_deductions solver (because it's
2860 * earlier in the list), there's no point running it again.
2862 * Therefore: if a solver is earlier in the list than "threshold_index",
2863 * we don't bother running it if it's difficulty level is less than
2866 int threshold_diff = 0;
2867 int threshold_index = 0;
2869 sstate = dup_solver_state(sstate_start);
2871 check_caches(sstate);
2873 while (i < NUM_SOLVERS) {
2874 if (sstate->solver_status == SOLVER_MISTAKE)
2876 if (sstate->solver_status == SOLVER_SOLVED ||
2877 sstate->solver_status == SOLVER_AMBIGUOUS) {
2878 /* solver finished */
2882 if ((solver_diffs[i] >= threshold_diff || i >= threshold_index)
2883 && solver_diffs[i] <= sstate->diff) {
2884 /* current_solver is eligible, so use it */
2885 int next_diff = solver_fns[i](sstate);
2886 if (next_diff != DIFF_MAX) {
2887 /* solver made progress, so use new thresholds and
2888 * start again at top of list. */
2889 threshold_diff = next_diff;
2890 threshold_index = i;
2895 /* current_solver is ineligible, or failed to make progress, so
2896 * go to the next solver in the list */
2900 if (sstate->solver_status == SOLVER_SOLVED ||
2901 sstate->solver_status == SOLVER_AMBIGUOUS) {
2902 /* s/LINE_UNKNOWN/LINE_NO/g */
2903 array_setall(sstate->state->lines, LINE_UNKNOWN, LINE_NO,
2904 sstate->state->game_grid->num_edges);
2911 static char *solve_game(const game_state *state, const game_state *currstate,
2912 const char *aux, const char **error)
2915 solver_state *sstate, *new_sstate;
2917 sstate = new_solver_state(state, DIFF_MAX);
2918 new_sstate = solve_game_rec(sstate);
2920 if (new_sstate->solver_status == SOLVER_SOLVED) {
2921 soln = encode_solve_move(new_sstate->state);
2922 } else if (new_sstate->solver_status == SOLVER_AMBIGUOUS) {
2923 soln = encode_solve_move(new_sstate->state);
2924 /**error = "Solver found ambiguous solutions"; */
2926 soln = encode_solve_move(new_sstate->state);
2927 /**error = "Solver failed"; */
2930 free_solver_state(new_sstate);
2931 free_solver_state(sstate);
2936 /* ----------------------------------------------------------------------
2937 * Drawing and mouse-handling
2940 static char *interpret_move(const game_state *state, game_ui *ui,
2941 const game_drawstate *ds,
2942 int x, int y, int button)
2944 grid *g = state->game_grid;
2948 int movelen, movesize;
2949 char button_char = ' ';
2950 enum line_state old_state;
2952 button &= ~MOD_MASK;
2954 /* Convert mouse-click (x,y) to grid coordinates */
2955 x -= BORDER(ds->tilesize);
2956 y -= BORDER(ds->tilesize);
2957 x = x * g->tilesize / ds->tilesize;
2958 y = y * g->tilesize / ds->tilesize;
2962 e = grid_nearest_edge(g, x, y);
2968 /* I think it's only possible to play this game with mouse clicks, sorry */
2969 /* Maybe will add mouse drag support some time */
2970 old_state = state->lines[i];
2974 switch (old_state) {
2992 switch (old_state) {
3012 movebuf = snewn(movesize, char);
3013 movelen = sprintf(movebuf, "%d%c", i, (int)button_char);
3015 static enum { OFF, FIXED, ADAPTIVE, DUNNO } autofollow = DUNNO;
3016 if (autofollow == DUNNO) {
3017 const char *env = getenv("LOOPY_AUTOFOLLOW");
3018 if (env && !strcmp(env, "off"))
3020 else if (env && !strcmp(env, "fixed"))
3022 else if (env && !strcmp(env, "adaptive"))
3023 autofollow = ADAPTIVE;
3028 if (autofollow != OFF) {
3030 for (dotid = 0; dotid < 2; dotid++) {
3031 grid_dot *dot = (dotid == 0 ? e->dot1 : e->dot2);
3032 grid_edge *e_this = e;
3036 grid_edge *e_next = NULL;
3038 for (j = n_found = 0; j < dot->order; j++) {
3039 grid_edge *e_candidate = dot->edges[j];
3040 int i_candidate = e_candidate - g->edges;
3041 if (e_candidate != e_this &&
3042 (autofollow == FIXED ||
3043 state->lines[i] == LINE_NO ||
3044 state->lines[i_candidate] != LINE_NO)) {
3045 e_next = e_candidate;
3051 state->lines[e_next - g->edges] != state->lines[i])
3056 * Special case: we might have come all the
3057 * way round a loop and found our way back to
3058 * the same edge we started from. In that
3059 * situation, we must terminate not only this
3060 * while loop, but the 'for' outside it that
3061 * was tracing in both directions from the
3062 * starting edge, because if we let it trace
3063 * in the second direction then we'll only
3064 * find ourself traversing the same loop in
3065 * the other order and generate an encoded
3066 * move string that mentions the same set of
3069 goto autofollow_done;
3072 dot = (e_next->dot1 != dot ? e_next->dot1 : e_next->dot2);
3073 if (movelen > movesize - 40) {
3074 movesize = movesize * 5 / 4 + 128;
3075 movebuf = sresize(movebuf, movesize, char);
3078 movelen += sprintf(movebuf+movelen, "%d%c",
3079 (int)(e_this - g->edges), button_char);
3086 return sresize(movebuf, movelen+1, char);
3089 static game_state *execute_move(const game_state *state, const char *move)
3092 game_state *newstate = dup_game(state);
3094 if (move[0] == 'S') {
3096 newstate->cheated = TRUE;
3101 if (i < 0 || i >= newstate->game_grid->num_edges)
3103 move += strspn(move, "1234567890");
3104 switch (*(move++)) {
3106 newstate->lines[i] = LINE_YES;
3109 newstate->lines[i] = LINE_NO;
3112 newstate->lines[i] = LINE_UNKNOWN;
3120 * Check for completion.
3122 if (check_completion(newstate))
3123 newstate->solved = TRUE;
3128 free_game(newstate);
3132 /* ----------------------------------------------------------------------
3136 /* Convert from grid coordinates to screen coordinates */
3137 static void grid_to_screen(const game_drawstate *ds, const grid *g,
3138 int grid_x, int grid_y, int *x, int *y)
3140 *x = grid_x - g->lowest_x;
3141 *y = grid_y - g->lowest_y;
3142 *x = *x * ds->tilesize / g->tilesize;
3143 *y = *y * ds->tilesize / g->tilesize;
3144 *x += BORDER(ds->tilesize);
3145 *y += BORDER(ds->tilesize);
3148 /* Returns (into x,y) position of centre of face for rendering the text clue.
3150 static void face_text_pos(const game_drawstate *ds, const grid *g,
3151 grid_face *f, int *xret, int *yret)
3153 int faceindex = f - g->faces;
3156 * Return the cached position for this face, if we've already
3159 if (ds->textx[faceindex] >= 0) {
3160 *xret = ds->textx[faceindex];
3161 *yret = ds->texty[faceindex];
3166 * Otherwise, use the incentre computed by grid.c and convert it
3167 * to screen coordinates.
3169 grid_find_incentre(f);
3170 grid_to_screen(ds, g, f->ix, f->iy,
3171 &ds->textx[faceindex], &ds->texty[faceindex]);
3173 *xret = ds->textx[faceindex];
3174 *yret = ds->texty[faceindex];
3177 static void face_text_bbox(game_drawstate *ds, grid *g, grid_face *f,
3178 int *x, int *y, int *w, int *h)
3181 face_text_pos(ds, g, f, &xx, &yy);
3183 /* There seems to be a certain amount of trial-and-error involved
3184 * in working out the correct bounding-box for the text. */
3186 *x = xx - ds->tilesize/4 - 1;
3187 *y = yy - ds->tilesize/4 - 3;
3188 *w = ds->tilesize/2 + 2;
3189 *h = ds->tilesize/2 + 5;
3192 static void game_redraw_clue(drawing *dr, game_drawstate *ds,
3193 const game_state *state, int i)
3195 grid *g = state->game_grid;
3196 grid_face *f = g->faces + i;
3200 sprintf(c, "%d", state->clues[i]);
3202 face_text_pos(ds, g, f, &x, &y);
3204 FONT_VARIABLE, ds->tilesize/2,
3205 ALIGN_VCENTRE | ALIGN_HCENTRE,
3206 ds->clue_error[i] ? COL_MISTAKE :
3207 ds->clue_satisfied[i] ? COL_SATISFIED : COL_FOREGROUND, c);
3210 static void edge_bbox(game_drawstate *ds, grid *g, grid_edge *e,
3211 int *x, int *y, int *w, int *h)
3213 int x1 = e->dot1->x;
3214 int y1 = e->dot1->y;
3215 int x2 = e->dot2->x;
3216 int y2 = e->dot2->y;
3217 int xmin, xmax, ymin, ymax;
3219 grid_to_screen(ds, g, x1, y1, &x1, &y1);
3220 grid_to_screen(ds, g, x2, y2, &x2, &y2);
3221 /* Allow extra margin for dots, and thickness of lines */
3222 xmin = min(x1, x2) - 2;
3223 xmax = max(x1, x2) + 2;
3224 ymin = min(y1, y2) - 2;
3225 ymax = max(y1, y2) + 2;
3229 *w = xmax - xmin + 1;
3230 *h = ymax - ymin + 1;
3233 static void dot_bbox(game_drawstate *ds, grid *g, grid_dot *d,
3234 int *x, int *y, int *w, int *h)
3238 grid_to_screen(ds, g, d->x, d->y, &x1, &y1);
3246 static const int loopy_line_redraw_phases[] = {
3247 COL_FAINT, COL_LINEUNKNOWN, COL_FOREGROUND, COL_HIGHLIGHT, COL_MISTAKE
3249 #define NPHASES lenof(loopy_line_redraw_phases)
3251 static void game_redraw_line(drawing *dr, game_drawstate *ds,
3252 const game_state *state, int i, int phase)
3254 grid *g = state->game_grid;
3255 grid_edge *e = g->edges + i;
3259 if (state->line_errors[i])
3260 line_colour = COL_MISTAKE;
3261 else if (state->lines[i] == LINE_UNKNOWN)
3262 line_colour = COL_LINEUNKNOWN;
3263 else if (state->lines[i] == LINE_NO)
3264 line_colour = COL_FAINT;
3265 else if (ds->flashing)
3266 line_colour = COL_HIGHLIGHT;
3268 line_colour = COL_FOREGROUND;
3269 if (line_colour != loopy_line_redraw_phases[phase])
3272 /* Convert from grid to screen coordinates */
3273 grid_to_screen(ds, g, e->dot1->x, e->dot1->y, &x1, &y1);
3274 grid_to_screen(ds, g, e->dot2->x, e->dot2->y, &x2, &y2);
3276 if (line_colour == COL_FAINT) {
3277 static int draw_faint_lines = -1;
3278 if (draw_faint_lines < 0) {
3279 char *env = getenv("LOOPY_FAINT_LINES");
3280 draw_faint_lines = (!env || (env[0] == 'y' ||
3283 if (draw_faint_lines)
3284 draw_line(dr, x1, y1, x2, y2, line_colour);
3286 draw_thick_line(dr, 3.0,
3293 static void game_redraw_dot(drawing *dr, game_drawstate *ds,
3294 const game_state *state, int i)
3296 grid *g = state->game_grid;
3297 grid_dot *d = g->dots + i;
3300 grid_to_screen(ds, g, d->x, d->y, &x, &y);
3301 draw_circle(dr, x, y, 2, COL_FOREGROUND, COL_FOREGROUND);
3304 static int boxes_intersect(int x0, int y0, int w0, int h0,
3305 int x1, int y1, int w1, int h1)
3308 * Two intervals intersect iff neither is wholly on one side of
3309 * the other. Two boxes intersect iff their horizontal and
3310 * vertical intervals both intersect.
3312 return (x0 < x1+w1 && x1 < x0+w0 && y0 < y1+h1 && y1 < y0+h0);
3315 static void game_redraw_in_rect(drawing *dr, game_drawstate *ds,
3316 const game_state *state,
3317 int x, int y, int w, int h)
3319 grid *g = state->game_grid;
3323 clip(dr, x, y, w, h);
3324 draw_rect(dr, x, y, w, h, COL_BACKGROUND);
3326 for (i = 0; i < g->num_faces; i++) {
3327 if (state->clues[i] >= 0) {
3328 face_text_bbox(ds, g, &g->faces[i], &bx, &by, &bw, &bh);
3329 if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
3330 game_redraw_clue(dr, ds, state, i);
3333 for (phase = 0; phase < NPHASES; phase++) {
3334 for (i = 0; i < g->num_edges; i++) {
3335 edge_bbox(ds, g, &g->edges[i], &bx, &by, &bw, &bh);
3336 if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
3337 game_redraw_line(dr, ds, state, i, phase);
3340 for (i = 0; i < g->num_dots; i++) {
3341 dot_bbox(ds, g, &g->dots[i], &bx, &by, &bw, &bh);
3342 if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
3343 game_redraw_dot(dr, ds, state, i);
3347 draw_update(dr, x, y, w, h);
3350 static void game_redraw(drawing *dr, game_drawstate *ds,
3351 const game_state *oldstate, const game_state *state,
3352 int dir, const game_ui *ui,
3353 float animtime, float flashtime)
3355 #define REDRAW_OBJECTS_LIMIT 16 /* Somewhat arbitrary tradeoff */
3357 grid *g = state->game_grid;
3358 int border = BORDER(ds->tilesize);
3361 int redraw_everything = FALSE;
3363 int edges[REDRAW_OBJECTS_LIMIT], nedges = 0;
3364 int faces[REDRAW_OBJECTS_LIMIT], nfaces = 0;
3366 /* Redrawing is somewhat involved.
3368 * An update can theoretically affect an arbitrary number of edges
3369 * (consider, for example, completing or breaking a cycle which doesn't
3370 * satisfy all the clues -- we'll switch many edges between error and
3371 * normal states). On the other hand, redrawing the whole grid takes a
3372 * while, making the game feel sluggish, and many updates are actually
3373 * quite well localized.
3375 * This redraw algorithm attempts to cope with both situations gracefully
3376 * and correctly. For localized changes, we set a clip rectangle, fill
3377 * it with background, and then redraw (a plausible but conservative
3378 * guess at) the objects which intersect the rectangle; if several
3379 * objects need redrawing, we'll do them individually. However, if lots
3380 * of objects are affected, we'll just redraw everything.
3382 * The reason for all of this is that it's just not safe to do the redraw
3383 * piecemeal. If you try to draw an antialiased diagonal line over
3384 * itself, you get a slightly thicker antialiased diagonal line, which
3385 * looks rather ugly after a while.
3387 * So, we take two passes over the grid. The first attempts to work out
3388 * what needs doing, and the second actually does it.
3392 redraw_everything = TRUE;
3394 * But we must still go through the upcoming loops, so that we
3395 * set up stuff in ds correctly for the initial redraw.
3399 /* First, trundle through the faces. */
3400 for (i = 0; i < g->num_faces; i++) {
3401 grid_face *f = g->faces + i;
3402 int sides = f->order;
3403 int yes_order, no_order;
3406 int n = state->clues[i];
3410 yes_order = face_order(state, i, LINE_YES);
3411 if (state->exactly_one_loop) {
3413 * Special case: if the set of LINE_YES edges in the grid
3414 * consists of exactly one loop and nothing else, then we
3415 * switch to treating LINE_UNKNOWN the same as LINE_NO for
3416 * purposes of clue checking.
3418 * This is because some people like to play Loopy without
3419 * using the right-click, i.e. never setting anything to
3420 * LINE_NO. Without this special case, if a person playing
3421 * in that style fills in what they think is a correct
3422 * solution loop but in fact it has an underfilled clue,
3423 * then we will display no victory flash and also no error
3424 * highlight explaining why not. With this special case,
3425 * we light up underfilled clues at the instant the loop
3426 * is closed. (Of course, *overfilled* clues are fine
3429 * (It might still be considered unfortunate that we can't
3430 * warn this style of player any earlier, if they make a
3431 * mistake very near the beginning which doesn't show up
3432 * until they close the last edge of the loop. One other
3433 * thing we _could_ do here is to treat any LINE_UNKNOWN
3434 * as LINE_NO if either of its endpoints has yes-degree 2,
3435 * reflecting the fact that setting that line to YES would
3436 * be an obvious error. But I don't think even that could
3437 * catch _all_ clue errors in a timely manner; I think
3438 * there are some that won't be displayed until the loop
3439 * is filled in, even so, and there's no way to avoid that
3440 * with complete reliability except to switch to being a
3441 * player who sets things to LINE_NO.)
3443 no_order = sides - yes_order;
3445 no_order = face_order(state, i, LINE_NO);
3448 clue_mistake = (yes_order > n || no_order > (sides-n));
3449 clue_satisfied = (yes_order == n && no_order == (sides-n));
3451 if (clue_mistake != ds->clue_error[i] ||
3452 clue_satisfied != ds->clue_satisfied[i]) {
3453 ds->clue_error[i] = clue_mistake;
3454 ds->clue_satisfied[i] = clue_satisfied;
3455 if (nfaces == REDRAW_OBJECTS_LIMIT)
3456 redraw_everything = TRUE;
3458 faces[nfaces++] = i;
3462 /* Work out what the flash state needs to be. */
3463 if (flashtime > 0 &&
3464 (flashtime <= FLASH_TIME/3 ||
3465 flashtime >= FLASH_TIME*2/3)) {
3466 flash_changed = !ds->flashing;
3467 ds->flashing = TRUE;
3469 flash_changed = ds->flashing;
3470 ds->flashing = FALSE;
3473 /* Now, trundle through the edges. */
3474 for (i = 0; i < g->num_edges; i++) {
3476 state->line_errors[i] ? DS_LINE_ERROR : state->lines[i];
3477 if (new_ds != ds->lines[i] ||
3478 (flash_changed && state->lines[i] == LINE_YES)) {
3479 ds->lines[i] = new_ds;
3480 if (nedges == REDRAW_OBJECTS_LIMIT)
3481 redraw_everything = TRUE;
3483 edges[nedges++] = i;
3487 /* Pass one is now done. Now we do the actual drawing. */
3488 if (redraw_everything) {
3489 int grid_width = g->highest_x - g->lowest_x;
3490 int grid_height = g->highest_y - g->lowest_y;
3491 int w = grid_width * ds->tilesize / g->tilesize;
3492 int h = grid_height * ds->tilesize / g->tilesize;
3494 game_redraw_in_rect(dr, ds, state,
3495 0, 0, w + 2*border + 1, h + 2*border + 1);
3498 /* Right. Now we roll up our sleeves. */
3500 for (i = 0; i < nfaces; i++) {
3501 grid_face *f = g->faces + faces[i];
3504 face_text_bbox(ds, g, f, &x, &y, &w, &h);
3505 game_redraw_in_rect(dr, ds, state, x, y, w, h);
3508 for (i = 0; i < nedges; i++) {
3509 grid_edge *e = g->edges + edges[i];
3512 edge_bbox(ds, g, e, &x, &y, &w, &h);
3513 game_redraw_in_rect(dr, ds, state, x, y, w, h);
3520 static float game_flash_length(const game_state *oldstate,
3521 const game_state *newstate, int dir, game_ui *ui)
3523 if (!oldstate->solved && newstate->solved &&
3524 !oldstate->cheated && !newstate->cheated) {
3531 static int game_status(const game_state *state)
3533 return state->solved ? +1 : 0;
3536 static void game_print_size(const game_params *params, float *x, float *y)
3541 * I'll use 7mm "squares" by default.
3543 game_compute_size(params, 700, &pw, &ph);
3548 static void game_print(drawing *dr, const game_state *state, int tilesize)
3550 int ink = print_mono_colour(dr, 0);
3552 game_drawstate ads, *ds = &ads;
3553 grid *g = state->game_grid;
3555 ds->tilesize = tilesize;
3556 ds->textx = snewn(g->num_faces, int);
3557 ds->texty = snewn(g->num_faces, int);
3558 for (i = 0; i < g->num_faces; i++)
3559 ds->textx[i] = ds->texty[i] = -1;
3561 for (i = 0; i < g->num_dots; i++) {
3563 grid_to_screen(ds, g, g->dots[i].x, g->dots[i].y, &x, &y);
3564 draw_circle(dr, x, y, ds->tilesize / 15, ink, ink);
3570 for (i = 0; i < g->num_faces; i++) {
3571 grid_face *f = g->faces + i;
3572 int clue = state->clues[i];
3576 sprintf(c, "%d", state->clues[i]);
3577 face_text_pos(ds, g, f, &x, &y);
3579 FONT_VARIABLE, ds->tilesize / 2,
3580 ALIGN_VCENTRE | ALIGN_HCENTRE, ink, c);
3587 for (i = 0; i < g->num_edges; i++) {
3588 int thickness = (state->lines[i] == LINE_YES) ? 30 : 150;
3589 grid_edge *e = g->edges + i;
3591 grid_to_screen(ds, g, e->dot1->x, e->dot1->y, &x1, &y1);
3592 grid_to_screen(ds, g, e->dot2->x, e->dot2->y, &x2, &y2);
3593 if (state->lines[i] == LINE_YES)
3595 /* (dx, dy) points from (x1, y1) to (x2, y2).
3596 * The line is then "fattened" in a perpendicular
3597 * direction to create a thin rectangle. */
3598 double d = sqrt(SQ((double)x1 - x2) + SQ((double)y1 - y2));
3599 double dx = (x2 - x1) / d;
3600 double dy = (y2 - y1) / d;
3603 dx = (dx * ds->tilesize) / thickness;
3604 dy = (dy * ds->tilesize) / thickness;
3605 points[0] = x1 + (int)dy;
3606 points[1] = y1 - (int)dx;
3607 points[2] = x1 - (int)dy;
3608 points[3] = y1 + (int)dx;
3609 points[4] = x2 - (int)dy;
3610 points[5] = y2 + (int)dx;
3611 points[6] = x2 + (int)dy;
3612 points[7] = y2 - (int)dx;
3613 draw_polygon(dr, points, 4, ink, ink);
3617 /* Draw a dotted line */
3620 for (j = 1; j < divisions; j++) {
3621 /* Weighted average */
3622 int x = (x1 * (divisions -j) + x2 * j) / divisions;
3623 int y = (y1 * (divisions -j) + y2 * j) / divisions;
3624 draw_circle(dr, x, y, ds->tilesize / thickness, ink, ink);
3634 #define thegame loopy
3637 const struct game thegame = {
3638 "Loopy", "games.loopy", "loopy",
3640 NULL, game_preset_menu,
3645 TRUE, game_configure, custom_params,
3653 TRUE, game_can_format_as_text_now, game_text_format,
3661 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
3664 game_free_drawstate,
3669 TRUE, FALSE, game_print_size, game_print,
3670 FALSE /* wants_statusbar */,
3671 FALSE, game_timing_state,
3672 0, /* mouse_priorities */
3675 #ifdef STANDALONE_SOLVER
3678 * Half-hearted standalone solver. It can't output the solution to
3679 * anything but a square puzzle, and it can't log the deductions
3680 * it makes either. But it can solve square puzzles, and more
3681 * importantly it can use its solver to grade the difficulty of
3682 * any puzzle you give it.
3687 int main(int argc, char **argv)
3691 char *id = NULL, *desc;
3695 #if 0 /* verbose solver not supported here (yet) */
3696 int really_verbose = FALSE;
3699 while (--argc > 0) {
3701 #if 0 /* verbose solver not supported here (yet) */
3702 if (!strcmp(p, "-v")) {
3703 really_verbose = TRUE;
3706 if (!strcmp(p, "-g")) {
3708 } else if (*p == '-') {
3709 fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
3717 fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
3721 desc = strchr(id, ':');
3723 fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
3728 p = default_params();
3729 decode_params(p, id);
3730 err = validate_desc(p, desc);
3732 fprintf(stderr, "%s: %s\n", argv[0], err);
3735 s = new_game(NULL, p, desc);
3738 * When solving an Easy puzzle, we don't want to bother the
3739 * user with Hard-level deductions. For this reason, we grade
3740 * the puzzle internally before doing anything else.
3742 ret = -1; /* placate optimiser */
3743 for (diff = 0; diff < DIFF_MAX; diff++) {
3744 solver_state *sstate_new;
3745 solver_state *sstate = new_solver_state((game_state *)s, diff);
3747 sstate_new = solve_game_rec(sstate);
3749 if (sstate_new->solver_status == SOLVER_MISTAKE)
3751 else if (sstate_new->solver_status == SOLVER_SOLVED)
3756 free_solver_state(sstate_new);
3757 free_solver_state(sstate);
3763 if (diff == DIFF_MAX) {
3765 printf("Difficulty rating: harder than Hard, or ambiguous\n");
3767 printf("Unable to find a unique solution\n");
3771 printf("Difficulty rating: impossible (no solution exists)\n");
3773 printf("Difficulty rating: %s\n", diffnames[diff]);
3775 solver_state *sstate_new;
3776 solver_state *sstate = new_solver_state((game_state *)s, diff);
3778 /* If we supported a verbose solver, we'd set verbosity here */
3780 sstate_new = solve_game_rec(sstate);
3782 if (sstate_new->solver_status == SOLVER_MISTAKE)
3783 printf("Puzzle is inconsistent\n");
3785 assert(sstate_new->solver_status == SOLVER_SOLVED);
3786 if (s->grid_type == 0) {
3787 fputs(game_text_format(sstate_new->state), stdout);
3789 printf("Unable to output non-square grids\n");
3793 free_solver_state(sstate_new);
3794 free_solver_state(sstate);
3803 /* vim: set shiftwidth=4 tabstop=8: */