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;
125 /* Used in game_text_format(), so that it knows what type of
126 * grid it's trying to render as ASCII text. */
131 SOLVER_SOLVED, /* This is the only solution the solver could find */
132 SOLVER_MISTAKE, /* This is definitely not a solution */
133 SOLVER_AMBIGUOUS, /* This _might_ be an ambiguous solution */
134 SOLVER_INCOMPLETE /* This may be a partial solution */
137 /* ------ Solver state ------ */
138 typedef struct solver_state {
140 enum solver_status solver_status;
141 /* NB looplen is the number of dots that are joined together at a point, ie a
142 * looplen of 1 means there are no lines to a particular dot */
145 /* Difficulty level of solver. Used by solver functions that want to
146 * vary their behaviour depending on the requested difficulty level. */
152 char *face_yes_count;
154 char *dot_solved, *face_solved;
157 /* Information for Normal level deductions:
158 * For each dline, store a bitmask for whether we know:
159 * (bit 0) at least one is YES
160 * (bit 1) at most one is YES */
163 /* Hard level information */
168 * Difficulty levels. I do some macro ickery here to ensure that my
169 * enum and the various forms of my name list always match up.
172 #define DIFFLIST(A) \
177 #define ENUM(upper,title,lower) DIFF_ ## upper,
178 #define TITLE(upper,title,lower) #title,
179 #define ENCODE(upper,title,lower) #lower
180 #define CONFIG(upper,title,lower) ":" #title
181 enum { DIFFLIST(ENUM) DIFF_MAX };
182 static char const *const diffnames[] = { DIFFLIST(TITLE) };
183 static char const diffchars[] = DIFFLIST(ENCODE);
184 #define DIFFCONFIG DIFFLIST(CONFIG)
187 * Solver routines, sorted roughly in order of computational cost.
188 * The solver will run the faster deductions first, and slower deductions are
189 * only invoked when the faster deductions are unable to make progress.
190 * Each function is associated with a difficulty level, so that the generated
191 * puzzles are solvable by applying only the functions with the chosen
192 * difficulty level or lower.
194 #define SOLVERLIST(A) \
195 A(trivial_deductions, DIFF_EASY) \
196 A(dline_deductions, DIFF_NORMAL) \
197 A(linedsf_deductions, DIFF_HARD) \
198 A(loop_deductions, DIFF_EASY)
199 #define SOLVER_FN_DECL(fn,diff) static int fn(solver_state *);
200 #define SOLVER_FN(fn,diff) &fn,
201 #define SOLVER_DIFF(fn,diff) diff,
202 SOLVERLIST(SOLVER_FN_DECL)
203 static int (*(solver_fns[]))(solver_state *) = { SOLVERLIST(SOLVER_FN) };
204 static int const solver_diffs[] = { SOLVERLIST(SOLVER_DIFF) };
205 static const int NUM_SOLVERS = sizeof(solver_diffs)/sizeof(*solver_diffs);
213 /* line_drawstate is the same as line_state, but with the extra ERROR
214 * possibility. The drawing code copies line_state to line_drawstate,
215 * except in the case that the line is an error. */
216 enum line_state { LINE_YES, LINE_UNKNOWN, LINE_NO };
217 enum line_drawstate { DS_LINE_YES, DS_LINE_UNKNOWN,
218 DS_LINE_NO, DS_LINE_ERROR };
220 #define OPP(line_state) \
224 struct game_drawstate {
231 char *clue_satisfied;
234 static char *validate_desc(const game_params *params, const char *desc);
235 static int dot_order(const game_state* state, int i, char line_type);
236 static int face_order(const game_state* state, int i, char line_type);
237 static solver_state *solve_game_rec(const solver_state *sstate);
240 static void check_caches(const solver_state* sstate);
242 #define check_caches(s)
245 /* ------- List of grid generators ------- */
246 #define GRIDLIST(A) \
247 A(Squares,GRID_SQUARE,3,3) \
248 A(Triangular,GRID_TRIANGULAR,3,3) \
249 A(Honeycomb,GRID_HONEYCOMB,3,3) \
250 A(Snub-Square,GRID_SNUBSQUARE,3,3) \
251 A(Cairo,GRID_CAIRO,3,4) \
252 A(Great-Hexagonal,GRID_GREATHEXAGONAL,3,3) \
253 A(Octagonal,GRID_OCTAGONAL,3,3) \
254 A(Kites,GRID_KITE,3,3) \
255 A(Floret,GRID_FLORET,1,2) \
256 A(Dodecagonal,GRID_DODECAGONAL,2,2) \
257 A(Great-Dodecagonal,GRID_GREATDODECAGONAL,2,2) \
258 A(Penrose (kite/dart),GRID_PENROSE_P2,3,3) \
259 A(Penrose (rhombs),GRID_PENROSE_P3,3,3)
261 #define GRID_NAME(title,type,amin,omin) #title,
262 #define GRID_CONFIG(title,type,amin,omin) ":" #title
263 #define GRID_TYPE(title,type,amin,omin) type,
264 #define GRID_SIZES(title,type,amin,omin) \
266 "Width and height for this grid type must both be at least " #amin, \
267 "At least one of width and height for this grid type must be at least " #omin,},
268 static char const *const gridnames[] = { GRIDLIST(GRID_NAME) };
269 #define GRID_CONFIGS GRIDLIST(GRID_CONFIG)
270 static grid_type grid_types[] = { GRIDLIST(GRID_TYPE) };
271 #define NUM_GRID_TYPES (sizeof(grid_types) / sizeof(grid_types[0]))
272 static const struct {
275 } grid_size_limits[] = { GRIDLIST(GRID_SIZES) };
277 /* Generates a (dynamically allocated) new grid, according to the
278 * type and size requested in params. Does nothing if the grid is already
280 static grid *loopy_generate_grid(const game_params *params,
281 const char *grid_desc)
283 return grid_new(grid_types[params->type], params->w, params->h, grid_desc);
286 /* ----------------------------------------------------------------------
290 /* General constants */
291 #define PREFERRED_TILE_SIZE 32
292 #define BORDER(tilesize) ((tilesize) / 2)
293 #define FLASH_TIME 0.5F
295 #define BIT_SET(field, bit) ((field) & (1<<(bit)))
297 #define SET_BIT(field, bit) (BIT_SET(field, bit) ? FALSE : \
298 ((field) |= (1<<(bit)), TRUE))
300 #define CLEAR_BIT(field, bit) (BIT_SET(field, bit) ? \
301 ((field) &= ~(1<<(bit)), TRUE) : FALSE)
303 #define CLUE2CHAR(c) \
304 ((c < 0) ? ' ' : c < 10 ? c + '0' : c - 10 + 'A')
306 /* ----------------------------------------------------------------------
307 * General struct manipulation and other straightforward code
310 static game_state *dup_game(const game_state *state)
312 game_state *ret = snew(game_state);
314 ret->game_grid = state->game_grid;
315 ret->game_grid->refcount++;
317 ret->solved = state->solved;
318 ret->cheated = state->cheated;
320 ret->clues = snewn(state->game_grid->num_faces, signed char);
321 memcpy(ret->clues, state->clues, state->game_grid->num_faces);
323 ret->lines = snewn(state->game_grid->num_edges, char);
324 memcpy(ret->lines, state->lines, state->game_grid->num_edges);
326 ret->line_errors = snewn(state->game_grid->num_edges, unsigned char);
327 memcpy(ret->line_errors, state->line_errors, state->game_grid->num_edges);
329 ret->grid_type = state->grid_type;
333 static void free_game(game_state *state)
336 grid_free(state->game_grid);
339 sfree(state->line_errors);
344 static solver_state *new_solver_state(const game_state *state, int diff) {
346 int num_dots = state->game_grid->num_dots;
347 int num_faces = state->game_grid->num_faces;
348 int num_edges = state->game_grid->num_edges;
349 solver_state *ret = snew(solver_state);
351 ret->state = dup_game(state);
353 ret->solver_status = SOLVER_INCOMPLETE;
356 ret->dotdsf = snew_dsf(num_dots);
357 ret->looplen = snewn(num_dots, int);
359 for (i = 0; i < num_dots; i++) {
363 ret->dot_solved = snewn(num_dots, char);
364 ret->face_solved = snewn(num_faces, char);
365 memset(ret->dot_solved, FALSE, num_dots);
366 memset(ret->face_solved, FALSE, num_faces);
368 ret->dot_yes_count = snewn(num_dots, char);
369 memset(ret->dot_yes_count, 0, num_dots);
370 ret->dot_no_count = snewn(num_dots, char);
371 memset(ret->dot_no_count, 0, num_dots);
372 ret->face_yes_count = snewn(num_faces, char);
373 memset(ret->face_yes_count, 0, num_faces);
374 ret->face_no_count = snewn(num_faces, char);
375 memset(ret->face_no_count, 0, num_faces);
377 if (diff < DIFF_NORMAL) {
380 ret->dlines = snewn(2*num_edges, char);
381 memset(ret->dlines, 0, 2*num_edges);
384 if (diff < DIFF_HARD) {
387 ret->linedsf = snew_dsf(state->game_grid->num_edges);
393 static void free_solver_state(solver_state *sstate) {
395 free_game(sstate->state);
396 sfree(sstate->dotdsf);
397 sfree(sstate->looplen);
398 sfree(sstate->dot_solved);
399 sfree(sstate->face_solved);
400 sfree(sstate->dot_yes_count);
401 sfree(sstate->dot_no_count);
402 sfree(sstate->face_yes_count);
403 sfree(sstate->face_no_count);
405 /* OK, because sfree(NULL) is a no-op */
406 sfree(sstate->dlines);
407 sfree(sstate->linedsf);
413 static solver_state *dup_solver_state(const solver_state *sstate) {
414 game_state *state = sstate->state;
415 int num_dots = state->game_grid->num_dots;
416 int num_faces = state->game_grid->num_faces;
417 int num_edges = state->game_grid->num_edges;
418 solver_state *ret = snew(solver_state);
420 ret->state = state = dup_game(sstate->state);
422 ret->solver_status = sstate->solver_status;
423 ret->diff = sstate->diff;
425 ret->dotdsf = snewn(num_dots, int);
426 ret->looplen = snewn(num_dots, int);
427 memcpy(ret->dotdsf, sstate->dotdsf,
428 num_dots * sizeof(int));
429 memcpy(ret->looplen, sstate->looplen,
430 num_dots * sizeof(int));
432 ret->dot_solved = snewn(num_dots, char);
433 ret->face_solved = snewn(num_faces, char);
434 memcpy(ret->dot_solved, sstate->dot_solved, num_dots);
435 memcpy(ret->face_solved, sstate->face_solved, num_faces);
437 ret->dot_yes_count = snewn(num_dots, char);
438 memcpy(ret->dot_yes_count, sstate->dot_yes_count, num_dots);
439 ret->dot_no_count = snewn(num_dots, char);
440 memcpy(ret->dot_no_count, sstate->dot_no_count, num_dots);
442 ret->face_yes_count = snewn(num_faces, char);
443 memcpy(ret->face_yes_count, sstate->face_yes_count, num_faces);
444 ret->face_no_count = snewn(num_faces, char);
445 memcpy(ret->face_no_count, sstate->face_no_count, num_faces);
447 if (sstate->dlines) {
448 ret->dlines = snewn(2*num_edges, char);
449 memcpy(ret->dlines, sstate->dlines,
455 if (sstate->linedsf) {
456 ret->linedsf = snewn(num_edges, int);
457 memcpy(ret->linedsf, sstate->linedsf,
458 num_edges * sizeof(int));
466 static game_params *default_params(void)
468 game_params *ret = snew(game_params);
477 ret->diff = DIFF_EASY;
483 static game_params *dup_params(const game_params *params)
485 game_params *ret = snew(game_params);
487 *ret = *params; /* structure copy */
491 static const game_params presets[] = {
493 { 7, 7, DIFF_EASY, 0 },
494 { 7, 7, DIFF_NORMAL, 0 },
495 { 7, 7, DIFF_HARD, 0 },
496 { 7, 7, DIFF_HARD, 1 },
497 { 7, 7, DIFF_HARD, 2 },
498 { 5, 5, DIFF_HARD, 3 },
499 { 7, 7, DIFF_HARD, 4 },
500 { 5, 4, DIFF_HARD, 5 },
501 { 5, 5, DIFF_HARD, 6 },
502 { 5, 5, DIFF_HARD, 7 },
503 { 3, 3, DIFF_HARD, 8 },
504 { 3, 3, DIFF_HARD, 9 },
505 { 3, 3, DIFF_HARD, 10 },
506 { 6, 6, DIFF_HARD, 11 },
507 { 6, 6, DIFF_HARD, 12 },
509 { 7, 7, DIFF_EASY, 0 },
510 { 10, 10, DIFF_EASY, 0 },
511 { 7, 7, DIFF_NORMAL, 0 },
512 { 10, 10, DIFF_NORMAL, 0 },
513 { 7, 7, DIFF_HARD, 0 },
514 { 10, 10, DIFF_HARD, 0 },
515 { 10, 10, DIFF_HARD, 1 },
516 { 12, 10, DIFF_HARD, 2 },
517 { 7, 7, DIFF_HARD, 3 },
518 { 9, 9, DIFF_HARD, 4 },
519 { 5, 4, DIFF_HARD, 5 },
520 { 7, 7, DIFF_HARD, 6 },
521 { 5, 5, DIFF_HARD, 7 },
522 { 5, 5, DIFF_HARD, 8 },
523 { 5, 4, DIFF_HARD, 9 },
524 { 5, 4, DIFF_HARD, 10 },
525 { 10, 10, DIFF_HARD, 11 },
526 { 10, 10, DIFF_HARD, 12 }
530 static int game_fetch_preset(int i, char **name, game_params **params)
535 if (i < 0 || i >= lenof(presets))
538 tmppar = snew(game_params);
539 *tmppar = presets[i];
541 sprintf(buf, "%dx%d %s - %s", tmppar->h, tmppar->w,
542 gridnames[tmppar->type], diffnames[tmppar->diff]);
548 static void free_params(game_params *params)
553 static void decode_params(game_params *params, char const *string)
555 params->h = params->w = atoi(string);
556 params->diff = DIFF_EASY;
557 while (*string && isdigit((unsigned char)*string)) string++;
558 if (*string == 'x') {
560 params->h = atoi(string);
561 while (*string && isdigit((unsigned char)*string)) string++;
563 if (*string == 't') {
565 params->type = atoi(string);
566 while (*string && isdigit((unsigned char)*string)) string++;
568 if (*string == 'd') {
571 for (i = 0; i < DIFF_MAX; i++)
572 if (*string == diffchars[i])
574 if (*string) string++;
578 static char *encode_params(const game_params *params, int full)
581 sprintf(str, "%dx%dt%d", params->w, params->h, params->type);
583 sprintf(str + strlen(str), "d%c", diffchars[params->diff]);
587 static config_item *game_configure(const game_params *params)
592 ret = snewn(5, config_item);
594 ret[0].name = "Width";
595 ret[0].type = C_STRING;
596 sprintf(buf, "%d", params->w);
597 ret[0].sval = dupstr(buf);
600 ret[1].name = "Height";
601 ret[1].type = C_STRING;
602 sprintf(buf, "%d", params->h);
603 ret[1].sval = dupstr(buf);
606 ret[2].name = "Grid type";
607 ret[2].type = C_CHOICES;
608 ret[2].sval = GRID_CONFIGS;
609 ret[2].ival = params->type;
611 ret[3].name = "Difficulty";
612 ret[3].type = C_CHOICES;
613 ret[3].sval = DIFFCONFIG;
614 ret[3].ival = params->diff;
624 static game_params *custom_params(const config_item *cfg)
626 game_params *ret = snew(game_params);
628 ret->w = atoi(cfg[0].sval);
629 ret->h = atoi(cfg[1].sval);
630 ret->type = cfg[2].ival;
631 ret->diff = cfg[3].ival;
636 static char *validate_params(const game_params *params, int full)
638 if (params->type < 0 || params->type >= NUM_GRID_TYPES)
639 return "Illegal grid type";
640 if (params->w < grid_size_limits[params->type].amin ||
641 params->h < grid_size_limits[params->type].amin)
642 return grid_size_limits[params->type].aerr;
643 if (params->w < grid_size_limits[params->type].omin &&
644 params->h < grid_size_limits[params->type].omin)
645 return grid_size_limits[params->type].oerr;
648 * This shouldn't be able to happen at all, since decode_params
649 * and custom_params will never generate anything that isn't
652 assert(params->diff < DIFF_MAX);
657 /* Returns a newly allocated string describing the current puzzle */
658 static char *state_to_text(const game_state *state)
660 grid *g = state->game_grid;
662 int num_faces = g->num_faces;
663 char *description = snewn(num_faces + 1, char);
664 char *dp = description;
668 for (i = 0; i < num_faces; i++) {
669 if (state->clues[i] < 0) {
670 if (empty_count > 25) {
671 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
677 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
680 dp += sprintf(dp, "%c", (int)CLUE2CHAR(state->clues[i]));
685 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
687 retval = dupstr(description);
693 #define GRID_DESC_SEP '_'
695 /* Splits up a (optional) grid_desc from the game desc. Returns the
696 * grid_desc (which needs freeing) and updates the desc pointer to
697 * start of real desc, or returns NULL if no desc. */
698 static char *extract_grid_desc(const char **desc)
700 char *sep = strchr(*desc, GRID_DESC_SEP), *gd;
703 if (!sep) return NULL;
705 gd_len = sep - (*desc);
706 gd = snewn(gd_len+1, char);
707 memcpy(gd, *desc, gd_len);
715 /* We require that the params pass the test in validate_params and that the
716 * description fills the entire game area */
717 static char *validate_desc(const game_params *params, const char *desc)
721 char *grid_desc, *ret;
723 /* It's pretty inefficient to do this just for validation. All we need to
724 * know is the precise number of faces. */
725 grid_desc = extract_grid_desc(&desc);
726 ret = grid_validate_desc(grid_types[params->type], params->w, params->h, grid_desc);
729 g = loopy_generate_grid(params, grid_desc);
730 if (grid_desc) sfree(grid_desc);
732 for (; *desc; ++desc) {
733 if ((*desc >= '0' && *desc <= '9') || (*desc >= 'A' && *desc <= 'Z')) {
738 count += *desc - 'a' + 1;
741 return "Unknown character in description";
744 if (count < g->num_faces)
745 return "Description too short for board size";
746 if (count > g->num_faces)
747 return "Description too long for board size";
754 /* Sums the lengths of the numbers in range [0,n) */
755 /* See equivalent function in solo.c for justification of this. */
756 static int len_0_to_n(int n)
758 int len = 1; /* Counting 0 as a bit of a special case */
761 for (i = 1; i < n; i *= 10) {
762 len += max(n - i, 0);
768 static char *encode_solve_move(const game_state *state)
773 int num_edges = state->game_grid->num_edges;
775 /* This is going to return a string representing the moves needed to set
776 * every line in a grid to be the same as the ones in 'state'. The exact
777 * length of this string is predictable. */
779 len = 1; /* Count the 'S' prefix */
780 /* Numbers in all lines */
781 len += len_0_to_n(num_edges);
782 /* For each line we also have a letter */
785 ret = snewn(len + 1, char);
788 p += sprintf(p, "S");
790 for (i = 0; i < num_edges; i++) {
791 switch (state->lines[i]) {
793 p += sprintf(p, "%dy", i);
796 p += sprintf(p, "%dn", i);
801 /* No point in doing sums like that if they're going to be wrong */
802 assert(strlen(ret) <= (size_t)len);
806 static game_ui *new_ui(const game_state *state)
811 static void free_ui(game_ui *ui)
815 static char *encode_ui(const game_ui *ui)
820 static void decode_ui(game_ui *ui, const char *encoding)
824 static void game_changed_state(game_ui *ui, const game_state *oldstate,
825 const game_state *newstate)
829 static void game_compute_size(const game_params *params, int tilesize,
832 int grid_width, grid_height, rendered_width, rendered_height;
835 grid_compute_size(grid_types[params->type], params->w, params->h,
836 &g_tilesize, &grid_width, &grid_height);
838 /* multiply first to minimise rounding error on integer division */
839 rendered_width = grid_width * tilesize / g_tilesize;
840 rendered_height = grid_height * tilesize / g_tilesize;
841 *x = rendered_width + 2 * BORDER(tilesize) + 1;
842 *y = rendered_height + 2 * BORDER(tilesize) + 1;
845 static void game_set_size(drawing *dr, game_drawstate *ds,
846 const game_params *params, int tilesize)
848 ds->tilesize = tilesize;
851 static float *game_colours(frontend *fe, int *ncolours)
853 float *ret = snewn(3 * NCOLOURS, float);
855 frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
857 ret[COL_FOREGROUND * 3 + 0] = 0.0F;
858 ret[COL_FOREGROUND * 3 + 1] = 0.0F;
859 ret[COL_FOREGROUND * 3 + 2] = 0.0F;
862 * We want COL_LINEUNKNOWN to be a yellow which is a bit darker
863 * than the background. (I previously set it to 0.8,0.8,0, but
864 * found that this went badly with the 0.8,0.8,0.8 favoured as a
865 * background by the Java frontend.)
867 ret[COL_LINEUNKNOWN * 3 + 0] = ret[COL_BACKGROUND * 3 + 0] * 0.9F;
868 ret[COL_LINEUNKNOWN * 3 + 1] = ret[COL_BACKGROUND * 3 + 1] * 0.9F;
869 ret[COL_LINEUNKNOWN * 3 + 2] = 0.0F;
871 ret[COL_HIGHLIGHT * 3 + 0] = 1.0F;
872 ret[COL_HIGHLIGHT * 3 + 1] = 1.0F;
873 ret[COL_HIGHLIGHT * 3 + 2] = 1.0F;
875 ret[COL_MISTAKE * 3 + 0] = 1.0F;
876 ret[COL_MISTAKE * 3 + 1] = 0.0F;
877 ret[COL_MISTAKE * 3 + 2] = 0.0F;
879 ret[COL_SATISFIED * 3 + 0] = 0.0F;
880 ret[COL_SATISFIED * 3 + 1] = 0.0F;
881 ret[COL_SATISFIED * 3 + 2] = 0.0F;
883 /* We want the faint lines to be a bit darker than the background.
884 * Except if the background is pretty dark already; then it ought to be a
885 * bit lighter. Oy vey.
887 ret[COL_FAINT * 3 + 0] = ret[COL_BACKGROUND * 3 + 0] * 0.9F;
888 ret[COL_FAINT * 3 + 1] = ret[COL_BACKGROUND * 3 + 1] * 0.9F;
889 ret[COL_FAINT * 3 + 2] = ret[COL_BACKGROUND * 3 + 2] * 0.9F;
891 *ncolours = NCOLOURS;
895 static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
897 struct game_drawstate *ds = snew(struct game_drawstate);
898 int num_faces = state->game_grid->num_faces;
899 int num_edges = state->game_grid->num_edges;
904 ds->lines = snewn(num_edges, char);
905 ds->clue_error = snewn(num_faces, char);
906 ds->clue_satisfied = snewn(num_faces, char);
907 ds->textx = snewn(num_faces, int);
908 ds->texty = snewn(num_faces, int);
911 memset(ds->lines, LINE_UNKNOWN, num_edges);
912 memset(ds->clue_error, 0, num_faces);
913 memset(ds->clue_satisfied, 0, num_faces);
914 for (i = 0; i < num_faces; i++)
915 ds->textx[i] = ds->texty[i] = -1;
920 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
924 sfree(ds->clue_error);
925 sfree(ds->clue_satisfied);
930 static int game_timing_state(const game_state *state, game_ui *ui)
935 static float game_anim_length(const game_state *oldstate,
936 const game_state *newstate, int dir, game_ui *ui)
941 static int game_can_format_as_text_now(const game_params *params)
943 if (params->type != 0)
948 static char *game_text_format(const game_state *state)
954 grid *g = state->game_grid;
957 assert(state->grid_type == 0);
959 /* Work out the basic size unit */
960 f = g->faces; /* first face */
961 assert(f->order == 4);
962 /* The dots are ordered clockwise, so the two opposite
963 * corners are guaranteed to span the square */
964 cell_size = abs(f->dots[0]->x - f->dots[2]->x);
966 w = (g->highest_x - g->lowest_x) / cell_size;
967 h = (g->highest_y - g->lowest_y) / cell_size;
969 /* Create a blank "canvas" to "draw" on */
972 ret = snewn(W * H + 1, char);
973 for (y = 0; y < H; y++) {
974 for (x = 0; x < W-1; x++) {
977 ret[y*W + W-1] = '\n';
981 /* Fill in edge info */
982 for (i = 0; i < g->num_edges; i++) {
983 grid_edge *e = g->edges + i;
984 /* Cell coordinates, from (0,0) to (w-1,h-1) */
985 int x1 = (e->dot1->x - g->lowest_x) / cell_size;
986 int x2 = (e->dot2->x - g->lowest_x) / cell_size;
987 int y1 = (e->dot1->y - g->lowest_y) / cell_size;
988 int y2 = (e->dot2->y - g->lowest_y) / cell_size;
989 /* Midpoint, in canvas coordinates (canvas coordinates are just twice
990 * cell coordinates) */
993 switch (state->lines[i]) {
995 ret[y*W + x] = (y1 == y2) ? '-' : '|';
1001 break; /* already a space */
1003 assert(!"Illegal line state");
1008 for (i = 0; i < g->num_faces; i++) {
1012 assert(f->order == 4);
1013 /* Cell coordinates, from (0,0) to (w-1,h-1) */
1014 x1 = (f->dots[0]->x - g->lowest_x) / cell_size;
1015 x2 = (f->dots[2]->x - g->lowest_x) / cell_size;
1016 y1 = (f->dots[0]->y - g->lowest_y) / cell_size;
1017 y2 = (f->dots[2]->y - g->lowest_y) / cell_size;
1018 /* Midpoint, in canvas coordinates */
1021 ret[y*W + x] = CLUE2CHAR(state->clues[i]);
1026 /* ----------------------------------------------------------------------
1031 static void check_caches(const solver_state* sstate)
1034 const game_state *state = sstate->state;
1035 const grid *g = state->game_grid;
1037 for (i = 0; i < g->num_dots; i++) {
1038 assert(dot_order(state, i, LINE_YES) == sstate->dot_yes_count[i]);
1039 assert(dot_order(state, i, LINE_NO) == sstate->dot_no_count[i]);
1042 for (i = 0; i < g->num_faces; i++) {
1043 assert(face_order(state, i, LINE_YES) == sstate->face_yes_count[i]);
1044 assert(face_order(state, i, LINE_NO) == sstate->face_no_count[i]);
1049 #define check_caches(s) \
1051 fprintf(stderr, "check_caches at line %d\n", __LINE__); \
1055 #endif /* DEBUG_CACHES */
1057 /* ----------------------------------------------------------------------
1058 * Solver utility functions
1061 /* Sets the line (with index i) to the new state 'line_new', and updates
1062 * the cached counts of any affected faces and dots.
1063 * Returns TRUE if this actually changed the line's state. */
1064 static int solver_set_line(solver_state *sstate, int i,
1065 enum line_state line_new
1067 , const char *reason
1071 game_state *state = sstate->state;
1075 assert(line_new != LINE_UNKNOWN);
1077 check_caches(sstate);
1079 if (state->lines[i] == line_new) {
1080 return FALSE; /* nothing changed */
1082 state->lines[i] = line_new;
1085 fprintf(stderr, "solver: set line [%d] to %s (%s)\n",
1086 i, line_new == LINE_YES ? "YES" : "NO",
1090 g = state->game_grid;
1093 /* Update the cache for both dots and both faces affected by this. */
1094 if (line_new == LINE_YES) {
1095 sstate->dot_yes_count[e->dot1 - g->dots]++;
1096 sstate->dot_yes_count[e->dot2 - g->dots]++;
1098 sstate->face_yes_count[e->face1 - g->faces]++;
1101 sstate->face_yes_count[e->face2 - g->faces]++;
1104 sstate->dot_no_count[e->dot1 - g->dots]++;
1105 sstate->dot_no_count[e->dot2 - g->dots]++;
1107 sstate->face_no_count[e->face1 - g->faces]++;
1110 sstate->face_no_count[e->face2 - g->faces]++;
1114 check_caches(sstate);
1119 #define solver_set_line(a, b, c) \
1120 solver_set_line(a, b, c, __FUNCTION__)
1124 * Merge two dots due to the existence of an edge between them.
1125 * Updates the dsf tracking equivalence classes, and keeps track of
1126 * the length of path each dot is currently a part of.
1127 * Returns TRUE if the dots were already linked, ie if they are part of a
1128 * closed loop, and false otherwise.
1130 static int merge_dots(solver_state *sstate, int edge_index)
1133 grid *g = sstate->state->game_grid;
1134 grid_edge *e = g->edges + edge_index;
1136 i = e->dot1 - g->dots;
1137 j = e->dot2 - g->dots;
1139 i = dsf_canonify(sstate->dotdsf, i);
1140 j = dsf_canonify(sstate->dotdsf, j);
1145 len = sstate->looplen[i] + sstate->looplen[j];
1146 dsf_merge(sstate->dotdsf, i, j);
1147 i = dsf_canonify(sstate->dotdsf, i);
1148 sstate->looplen[i] = len;
1153 /* Merge two lines because the solver has deduced that they must be either
1154 * identical or opposite. Returns TRUE if this is new information, otherwise
1156 static int merge_lines(solver_state *sstate, int i, int j, int inverse
1158 , const char *reason
1164 assert(i < sstate->state->game_grid->num_edges);
1165 assert(j < sstate->state->game_grid->num_edges);
1167 i = edsf_canonify(sstate->linedsf, i, &inv_tmp);
1169 j = edsf_canonify(sstate->linedsf, j, &inv_tmp);
1172 edsf_merge(sstate->linedsf, i, j, inverse);
1176 fprintf(stderr, "%s [%d] [%d] %s(%s)\n",
1178 inverse ? "inverse " : "", reason);
1185 #define merge_lines(a, b, c, d) \
1186 merge_lines(a, b, c, d, __FUNCTION__)
1189 /* Count the number of lines of a particular type currently going into the
1191 static int dot_order(const game_state* state, int dot, char line_type)
1194 grid *g = state->game_grid;
1195 grid_dot *d = g->dots + dot;
1198 for (i = 0; i < d->order; i++) {
1199 grid_edge *e = d->edges[i];
1200 if (state->lines[e - g->edges] == line_type)
1206 /* Count the number of lines of a particular type currently surrounding the
1208 static int face_order(const game_state* state, int face, char line_type)
1211 grid *g = state->game_grid;
1212 grid_face *f = g->faces + face;
1215 for (i = 0; i < f->order; i++) {
1216 grid_edge *e = f->edges[i];
1217 if (state->lines[e - g->edges] == line_type)
1223 /* Set all lines bordering a dot of type old_type to type new_type
1224 * Return value tells caller whether this function actually did anything */
1225 static int dot_setall(solver_state *sstate, int dot,
1226 char old_type, char new_type)
1228 int retval = FALSE, r;
1229 game_state *state = sstate->state;
1234 if (old_type == new_type)
1237 g = state->game_grid;
1240 for (i = 0; i < d->order; i++) {
1241 int line_index = d->edges[i] - g->edges;
1242 if (state->lines[line_index] == old_type) {
1243 r = solver_set_line(sstate, line_index, new_type);
1251 /* Set all lines bordering a face of type old_type to type new_type */
1252 static int face_setall(solver_state *sstate, int face,
1253 char old_type, char new_type)
1255 int retval = FALSE, r;
1256 game_state *state = sstate->state;
1261 if (old_type == new_type)
1264 g = state->game_grid;
1265 f = g->faces + face;
1267 for (i = 0; i < f->order; i++) {
1268 int line_index = f->edges[i] - g->edges;
1269 if (state->lines[line_index] == old_type) {
1270 r = solver_set_line(sstate, line_index, new_type);
1278 /* ----------------------------------------------------------------------
1279 * Loop generation and clue removal
1282 static void add_full_clues(game_state *state, random_state *rs)
1284 signed char *clues = state->clues;
1285 grid *g = state->game_grid;
1286 char *board = snewn(g->num_faces, char);
1289 generate_loop(g, board, rs, NULL, NULL);
1291 /* Fill out all the clues by initialising to 0, then iterating over
1292 * all edges and incrementing each clue as we find edges that border
1293 * between BLACK/WHITE faces. While we're at it, we verify that the
1294 * algorithm does work, and there aren't any GREY faces still there. */
1295 memset(clues, 0, g->num_faces);
1296 for (i = 0; i < g->num_edges; i++) {
1297 grid_edge *e = g->edges + i;
1298 grid_face *f1 = e->face1;
1299 grid_face *f2 = e->face2;
1300 enum face_colour c1 = FACE_COLOUR(f1);
1301 enum face_colour c2 = FACE_COLOUR(f2);
1302 assert(c1 != FACE_GREY);
1303 assert(c2 != FACE_GREY);
1305 if (f1) clues[f1 - g->faces]++;
1306 if (f2) clues[f2 - g->faces]++;
1313 static int game_has_unique_soln(const game_state *state, int diff)
1316 solver_state *sstate_new;
1317 solver_state *sstate = new_solver_state((game_state *)state, diff);
1319 sstate_new = solve_game_rec(sstate);
1321 assert(sstate_new->solver_status != SOLVER_MISTAKE);
1322 ret = (sstate_new->solver_status == SOLVER_SOLVED);
1324 free_solver_state(sstate_new);
1325 free_solver_state(sstate);
1331 /* Remove clues one at a time at random. */
1332 static game_state *remove_clues(game_state *state, random_state *rs,
1336 int num_faces = state->game_grid->num_faces;
1337 game_state *ret = dup_game(state), *saved_ret;
1340 /* We need to remove some clues. We'll do this by forming a list of all
1341 * available clues, shuffling it, then going along one at a
1342 * time clearing each clue in turn for which doing so doesn't render the
1343 * board unsolvable. */
1344 face_list = snewn(num_faces, int);
1345 for (n = 0; n < num_faces; ++n) {
1349 shuffle(face_list, num_faces, sizeof(int), rs);
1351 for (n = 0; n < num_faces; ++n) {
1352 saved_ret = dup_game(ret);
1353 ret->clues[face_list[n]] = -1;
1355 if (game_has_unique_soln(ret, diff)) {
1356 free_game(saved_ret);
1368 static char *new_game_desc(const game_params *params, random_state *rs,
1369 char **aux, int interactive)
1371 /* solution and description both use run-length encoding in obvious ways */
1372 char *retval, *game_desc, *grid_desc;
1374 game_state *state = snew(game_state);
1375 game_state *state_new;
1377 grid_desc = grid_new_desc(grid_types[params->type], params->w, params->h, rs);
1378 state->game_grid = g = loopy_generate_grid(params, grid_desc);
1380 state->clues = snewn(g->num_faces, signed char);
1381 state->lines = snewn(g->num_edges, char);
1382 state->line_errors = snewn(g->num_edges, unsigned char);
1384 state->grid_type = params->type;
1388 memset(state->lines, LINE_UNKNOWN, g->num_edges);
1389 memset(state->line_errors, 0, g->num_edges);
1391 state->solved = state->cheated = FALSE;
1393 /* Get a new random solvable board with all its clues filled in. Yes, this
1394 * can loop for ever if the params are suitably unfavourable, but
1395 * preventing games smaller than 4x4 seems to stop this happening */
1397 add_full_clues(state, rs);
1398 } while (!game_has_unique_soln(state, params->diff));
1400 state_new = remove_clues(state, rs, params->diff);
1405 if (params->diff > 0 && game_has_unique_soln(state, params->diff-1)) {
1407 fprintf(stderr, "Rejecting board, it is too easy\n");
1409 goto newboard_please;
1412 game_desc = state_to_text(state);
1417 retval = snewn(strlen(grid_desc) + 1 + strlen(game_desc) + 1, char);
1418 sprintf(retval, "%s%c%s", grid_desc, (int)GRID_DESC_SEP, game_desc);
1425 assert(!validate_desc(params, retval));
1430 static game_state *new_game(midend *me, const game_params *params,
1434 game_state *state = snew(game_state);
1435 int empties_to_make = 0;
1440 int num_faces, num_edges;
1442 grid_desc = extract_grid_desc(&desc);
1443 state->game_grid = g = loopy_generate_grid(params, grid_desc);
1444 if (grid_desc) sfree(grid_desc);
1448 num_faces = g->num_faces;
1449 num_edges = g->num_edges;
1451 state->clues = snewn(num_faces, signed char);
1452 state->lines = snewn(num_edges, char);
1453 state->line_errors = snewn(num_edges, unsigned char);
1455 state->solved = state->cheated = FALSE;
1457 state->grid_type = params->type;
1459 for (i = 0; i < num_faces; i++) {
1460 if (empties_to_make) {
1462 state->clues[i] = -1;
1468 n2 = *dp - 'A' + 10;
1469 if (n >= 0 && n < 10) {
1470 state->clues[i] = n;
1471 } else if (n2 >= 10 && n2 < 36) {
1472 state->clues[i] = n2;
1476 state->clues[i] = -1;
1477 empties_to_make = n - 1;
1482 memset(state->lines, LINE_UNKNOWN, num_edges);
1483 memset(state->line_errors, 0, num_edges);
1487 /* Calculates the line_errors data, and checks if the current state is a
1489 static int check_completion(game_state *state)
1491 grid *g = state->game_grid;
1493 int *dsf, *component_state;
1494 int nsilly, nloop, npath, largest_comp, largest_size;
1495 enum { COMP_NONE, COMP_LOOP, COMP_PATH, COMP_SILLY, COMP_EMPTY };
1497 memset(state->line_errors, 0, g->num_edges);
1500 * Find loops in the grid, and determine whether the puzzle is
1503 * Loopy is a bit more complicated than most puzzles that care
1504 * about loop detection. In most of them, loops are simply
1505 * _forbidden_; so the obviously right way to do
1506 * error-highlighting during play is to light up a graph edge red
1507 * iff it is part of a loop, which is exactly what the centralised
1508 * findloop.c makes easy.
1510 * But Loopy is unusual in that you're _supposed_ to be making a
1511 * loop - and yet _some_ loops are not the right loop. So we need
1512 * to be more discriminating, by identifying loops one by one and
1513 * then thinking about which ones to highlight, and so findloop.c
1514 * isn't quite the right tool for the job in this case.
1516 * Worse still, consider situations in which the grid contains a
1517 * loop and also some non-loop edges: there are some cases like
1518 * this in which the user's intuitive expectation would be to
1519 * highlight the loop (if you're only about half way through the
1520 * puzzle and have accidentally made a little loop in some corner
1521 * of the grid), and others in which they'd be more likely to
1522 * expect you to highlight the non-loop edges (if you've just
1523 * closed off a whole loop that you thought was the entire
1524 * solution, but forgot some disconnected edges in a corner
1525 * somewhere). So while it's easy enough to check whether the
1526 * solution is _right_, highlighting the wrong parts is a tricky
1527 * problem for this puzzle!
1529 * I'd quite like, in some situations, to identify the largest
1530 * loop among the player's YES edges, and then light up everything
1531 * other than that. But finding the longest cycle in a graph is an
1532 * NP-complete problem (because, in particular, it must return a
1533 * Hamilton cycle if one exists).
1535 * However, I think we can make the problem tractable by
1536 * exercising the Puzzles principle that it isn't absolutely
1537 * necessary to highlight _all_ errors: the key point is that by
1538 * the time the user has filled in the whole grid, they should
1539 * either have seen a completion flash, or have _some_ error
1540 * highlight showing them why the solution isn't right. So in
1541 * principle it would be *just about* good enough to highlight
1542 * just one error in the whole grid, if there was really no better
1543 * way. But we'd like to highlight as many errors as possible.
1545 * In this case, I think the simple approach is to make use of the
1546 * fact that no vertex may have degree > 2, and that's really
1547 * simple to detect. So the plan goes like this:
1549 * - Form the dsf of connected components of the graph vertices.
1551 * - Highlight an error at any vertex with degree > 2. (It so
1552 * happens that we do this by lighting up all the edges
1553 * incident to that vertex, but that's an output detail.)
1555 * - Any component that contains such a vertex is now excluded
1556 * from further consideration, because it already has a
1559 * - The remaining components have no vertex with degree > 2, and
1560 * hence they all consist of either a simple loop, or a simple
1561 * path with two endpoints.
1563 * - If the sensible components are all paths, or if there's
1564 * exactly one of them and it is a loop, then highlight no
1565 * further edge errors. (The former case is normal during play,
1566 * and the latter is a potentially solved puzzle.)
1568 * - Otherwise - if there is more than one sensible component
1569 * _and_ at least one of them is a loop - find the largest of
1570 * the sensible components, leave that one unhighlighted, and
1571 * light the rest up in red.
1574 dsf = snew_dsf(g->num_dots);
1576 /* Build the dsf. */
1577 for (i = 0; i < g->num_edges; i++) {
1578 if (state->lines[i] == LINE_YES) {
1579 grid_edge *e = g->edges + i;
1580 int d1 = e->dot1 - g->dots, d2 = e->dot2 - g->dots;
1581 dsf_merge(dsf, d1, d2);
1585 /* Initialise a state variable for each connected component. */
1586 component_state = snewn(g->num_dots, int);
1587 for (i = 0; i < g->num_dots; i++) {
1588 if (dsf_canonify(dsf, i) == i)
1589 component_state[i] = COMP_LOOP;
1591 component_state[i] = COMP_NONE;
1594 /* Check for dots with degree > 3. Here we also spot dots of
1595 * degree 1 in which the user has marked all the non-edges as
1596 * LINE_NO, because those are also clear vertex-level errors, so
1597 * we give them the same treatment of excluding their connected
1598 * component from the subsequent loop analysis. */
1599 for (i = 0; i < g->num_dots; i++) {
1600 int comp = dsf_canonify(dsf, i);
1601 int yes = dot_order(state, i, LINE_YES);
1602 int unknown = dot_order(state, i, LINE_UNKNOWN);
1603 if ((yes == 1 && unknown == 0) || (yes >= 3)) {
1604 /* violation, so mark all YES edges as errors */
1605 grid_dot *d = g->dots + i;
1607 for (j = 0; j < d->order; j++) {
1608 int e = d->edges[j] - g->edges;
1609 if (state->lines[e] == LINE_YES)
1610 state->line_errors[e] = TRUE;
1612 /* And mark this component as not worthy of further
1614 component_state[comp] = COMP_SILLY;
1616 } else if (yes == 0) {
1617 /* A completely isolated dot must also be excluded it from
1618 * the subsequent loop highlighting pass, but we tag it
1619 * with a different enum value to avoid it counting
1620 * towards the components that inhibit returning a win
1622 component_state[comp] = COMP_EMPTY;
1623 } else if (yes == 1) {
1624 /* A dot with degree 1 that didn't fall into the 'clearly
1625 * erroneous' case above indicates that this connected
1626 * component will be a path rather than a loop - unless
1627 * something worse elsewhere in the component has
1628 * classified it as silly. */
1629 if (component_state[comp] != COMP_SILLY)
1630 component_state[comp] = COMP_PATH;
1634 /* Count up the components. Also, find the largest sensible
1635 * component. (Tie-breaking condition is derived from the order of
1636 * vertices in the grid data structure, which is fairly arbitrary
1637 * but at least stays stable throughout the game.) */
1638 nsilly = nloop = npath = 0;
1639 largest_comp = largest_size = -1;
1640 for (i = 0; i < g->num_dots; i++) {
1641 if (component_state[i] == COMP_SILLY) {
1643 } else if (component_state[i] == COMP_PATH ||
1644 component_state[i] == COMP_LOOP) {
1647 if (component_state[i] == COMP_PATH)
1649 else if (component_state[i] == COMP_LOOP)
1652 if ((this_size = dsf_size(dsf, i)) > largest_size) {
1654 largest_size = this_size;
1659 if (nloop > 0 && nloop + npath > 1) {
1661 * If there are at least two sensible components including at
1662 * least one loop, highlight all edges in every sensible
1663 * component that is not the largest one.
1665 for (i = 0; i < g->num_edges; i++) {
1666 if (state->lines[i] == LINE_YES) {
1667 grid_edge *e = g->edges + i;
1668 int d1 = e->dot1 - g->dots; /* either endpoint is good enough */
1669 int comp = dsf_canonify(dsf, d1);
1670 if (component_state[comp] != COMP_SILLY &&
1671 comp != largest_comp)
1672 state->line_errors[i] = TRUE;
1677 if (nloop == 1 && npath == 0 && nsilly == 0) {
1679 * If there is exactly one component and it is a loop, then
1680 * the puzzle is potentially complete, so check the clues.
1684 for (i = 0; i < g->num_faces; i++) {
1685 int c = state->clues[i];
1686 if (c >= 0 && face_order(state, i, LINE_YES) != c) {
1695 sfree(component_state);
1701 /* ----------------------------------------------------------------------
1704 * Our solver modes operate as follows. Each mode also uses the modes above it.
1707 * Just implement the rules of the game.
1709 * Normal and Tricky Modes
1710 * For each (adjacent) pair of lines through each dot we store a bit for
1711 * whether at least one of them is on and whether at most one is on. (If we
1712 * know both or neither is on that's already stored more directly.)
1715 * Use edsf data structure to make equivalence classes of lines that are
1716 * known identical to or opposite to one another.
1721 * For general grids, we consider "dlines" to be pairs of lines joined
1722 * at a dot. The lines must be adjacent around the dot, so we can think of
1723 * a dline as being a dot+face combination. Or, a dot+edge combination where
1724 * the second edge is taken to be the next clockwise edge from the dot.
1725 * Original loopy code didn't have this extra restriction of the lines being
1726 * adjacent. From my tests with square grids, this extra restriction seems to
1727 * take little, if anything, away from the quality of the puzzles.
1728 * A dline can be uniquely identified by an edge/dot combination, given that
1729 * a dline-pair always goes clockwise around its common dot. The edge/dot
1730 * combination can be represented by an edge/bool combination - if bool is
1731 * TRUE, use edge->dot1 else use edge->dot2. So the total number of dlines is
1732 * exactly twice the number of edges in the grid - although the dlines
1733 * spanning the infinite face are not all that useful to the solver.
1734 * Note that, by convention, a dline goes clockwise around its common dot,
1735 * which means the dline goes anti-clockwise around its common face.
1738 /* Helper functions for obtaining an index into an array of dlines, given
1739 * various information. We assume the grid layout conventions about how
1740 * the various lists are interleaved - see grid_make_consistent() for
1743 /* i points to the first edge of the dline pair, reading clockwise around
1745 static int dline_index_from_dot(grid *g, grid_dot *d, int i)
1747 grid_edge *e = d->edges[i];
1752 if (i2 == d->order) i2 = 0;
1755 ret = 2 * (e - g->edges) + ((e->dot1 == d) ? 1 : 0);
1757 printf("dline_index_from_dot: d=%d,i=%d, edges [%d,%d] - %d\n",
1758 (int)(d - g->dots), i, (int)(e - g->edges),
1759 (int)(e2 - g->edges), ret);
1763 /* i points to the second edge of the dline pair, reading clockwise around
1764 * the face. That is, the edges of the dline, starting at edge{i}, read
1765 * anti-clockwise around the face. By layout conventions, the common dot
1766 * of the dline will be f->dots[i] */
1767 static int dline_index_from_face(grid *g, grid_face *f, int i)
1769 grid_edge *e = f->edges[i];
1770 grid_dot *d = f->dots[i];
1775 if (i2 < 0) i2 += f->order;
1778 ret = 2 * (e - g->edges) + ((e->dot1 == d) ? 1 : 0);
1780 printf("dline_index_from_face: f=%d,i=%d, edges [%d,%d] - %d\n",
1781 (int)(f - g->faces), i, (int)(e - g->edges),
1782 (int)(e2 - g->edges), ret);
1786 static int is_atleastone(const char *dline_array, int index)
1788 return BIT_SET(dline_array[index], 0);
1790 static int set_atleastone(char *dline_array, int index)
1792 return SET_BIT(dline_array[index], 0);
1794 static int is_atmostone(const char *dline_array, int index)
1796 return BIT_SET(dline_array[index], 1);
1798 static int set_atmostone(char *dline_array, int index)
1800 return SET_BIT(dline_array[index], 1);
1803 static void array_setall(char *array, char from, char to, int len)
1805 char *p = array, *p_old = p;
1806 int len_remaining = len;
1808 while ((p = memchr(p, from, len_remaining))) {
1810 len_remaining -= p - p_old;
1815 /* Helper, called when doing dline dot deductions, in the case where we
1816 * have 4 UNKNOWNs, and two of them (adjacent) have *exactly* one YES between
1817 * them (because of dline atmostone/atleastone).
1818 * On entry, edge points to the first of these two UNKNOWNs. This function
1819 * will find the opposite UNKNOWNS (if they are adjacent to one another)
1820 * and set their corresponding dline to atleastone. (Setting atmostone
1821 * already happens in earlier dline deductions) */
1822 static int dline_set_opp_atleastone(solver_state *sstate,
1823 grid_dot *d, int edge)
1825 game_state *state = sstate->state;
1826 grid *g = state->game_grid;
1829 for (opp = 0; opp < N; opp++) {
1830 int opp_dline_index;
1831 if (opp == edge || opp == edge+1 || opp == edge-1)
1833 if (opp == 0 && edge == N-1)
1835 if (opp == N-1 && edge == 0)
1838 if (opp2 == N) opp2 = 0;
1839 /* Check if opp, opp2 point to LINE_UNKNOWNs */
1840 if (state->lines[d->edges[opp] - g->edges] != LINE_UNKNOWN)
1842 if (state->lines[d->edges[opp2] - g->edges] != LINE_UNKNOWN)
1844 /* Found opposite UNKNOWNS and they're next to each other */
1845 opp_dline_index = dline_index_from_dot(g, d, opp);
1846 return set_atleastone(sstate->dlines, opp_dline_index);
1852 /* Set pairs of lines around this face which are known to be identical, to
1853 * the given line_state */
1854 static int face_setall_identical(solver_state *sstate, int face_index,
1855 enum line_state line_new)
1857 /* can[dir] contains the canonical line associated with the line in
1858 * direction dir from the square in question. Similarly inv[dir] is
1859 * whether or not the line in question is inverse to its canonical
1862 game_state *state = sstate->state;
1863 grid *g = state->game_grid;
1864 grid_face *f = g->faces + face_index;
1867 int can1, can2, inv1, inv2;
1869 for (i = 0; i < N; i++) {
1870 int line1_index = f->edges[i] - g->edges;
1871 if (state->lines[line1_index] != LINE_UNKNOWN)
1873 for (j = i + 1; j < N; j++) {
1874 int line2_index = f->edges[j] - g->edges;
1875 if (state->lines[line2_index] != LINE_UNKNOWN)
1878 /* Found two UNKNOWNS */
1879 can1 = edsf_canonify(sstate->linedsf, line1_index, &inv1);
1880 can2 = edsf_canonify(sstate->linedsf, line2_index, &inv2);
1881 if (can1 == can2 && inv1 == inv2) {
1882 solver_set_line(sstate, line1_index, line_new);
1883 solver_set_line(sstate, line2_index, line_new);
1890 /* Given a dot or face, and a count of LINE_UNKNOWNs, find them and
1891 * return the edge indices into e. */
1892 static void find_unknowns(game_state *state,
1893 grid_edge **edge_list, /* Edge list to search (from a face or a dot) */
1894 int expected_count, /* Number of UNKNOWNs (comes from solver's cache) */
1895 int *e /* Returned edge indices */)
1898 grid *g = state->game_grid;
1899 while (c < expected_count) {
1900 int line_index = *edge_list - g->edges;
1901 if (state->lines[line_index] == LINE_UNKNOWN) {
1909 /* If we have a list of edges, and we know whether the number of YESs should
1910 * be odd or even, and there are only a few UNKNOWNs, we can do some simple
1911 * linedsf deductions. This can be used for both face and dot deductions.
1912 * Returns the difficulty level of the next solver that should be used,
1913 * or DIFF_MAX if no progress was made. */
1914 static int parity_deductions(solver_state *sstate,
1915 grid_edge **edge_list, /* Edge list (from a face or a dot) */
1916 int total_parity, /* Expected number of YESs modulo 2 (either 0 or 1) */
1919 game_state *state = sstate->state;
1920 int diff = DIFF_MAX;
1921 int *linedsf = sstate->linedsf;
1923 if (unknown_count == 2) {
1924 /* Lines are known alike/opposite, depending on inv. */
1926 find_unknowns(state, edge_list, 2, e);
1927 if (merge_lines(sstate, e[0], e[1], total_parity))
1928 diff = min(diff, DIFF_HARD);
1929 } else if (unknown_count == 3) {
1931 int can[3]; /* canonical edges */
1932 int inv[3]; /* whether can[x] is inverse to e[x] */
1933 find_unknowns(state, edge_list, 3, e);
1934 can[0] = edsf_canonify(linedsf, e[0], inv);
1935 can[1] = edsf_canonify(linedsf, e[1], inv+1);
1936 can[2] = edsf_canonify(linedsf, e[2], inv+2);
1937 if (can[0] == can[1]) {
1938 if (solver_set_line(sstate, e[2], (total_parity^inv[0]^inv[1]) ?
1939 LINE_YES : LINE_NO))
1940 diff = min(diff, DIFF_EASY);
1942 if (can[0] == can[2]) {
1943 if (solver_set_line(sstate, e[1], (total_parity^inv[0]^inv[2]) ?
1944 LINE_YES : LINE_NO))
1945 diff = min(diff, DIFF_EASY);
1947 if (can[1] == can[2]) {
1948 if (solver_set_line(sstate, e[0], (total_parity^inv[1]^inv[2]) ?
1949 LINE_YES : LINE_NO))
1950 diff = min(diff, DIFF_EASY);
1952 } else if (unknown_count == 4) {
1954 int can[4]; /* canonical edges */
1955 int inv[4]; /* whether can[x] is inverse to e[x] */
1956 find_unknowns(state, edge_list, 4, e);
1957 can[0] = edsf_canonify(linedsf, e[0], inv);
1958 can[1] = edsf_canonify(linedsf, e[1], inv+1);
1959 can[2] = edsf_canonify(linedsf, e[2], inv+2);
1960 can[3] = edsf_canonify(linedsf, e[3], inv+3);
1961 if (can[0] == can[1]) {
1962 if (merge_lines(sstate, e[2], e[3], total_parity^inv[0]^inv[1]))
1963 diff = min(diff, DIFF_HARD);
1964 } else if (can[0] == can[2]) {
1965 if (merge_lines(sstate, e[1], e[3], total_parity^inv[0]^inv[2]))
1966 diff = min(diff, DIFF_HARD);
1967 } else if (can[0] == can[3]) {
1968 if (merge_lines(sstate, e[1], e[2], total_parity^inv[0]^inv[3]))
1969 diff = min(diff, DIFF_HARD);
1970 } else if (can[1] == can[2]) {
1971 if (merge_lines(sstate, e[0], e[3], total_parity^inv[1]^inv[2]))
1972 diff = min(diff, DIFF_HARD);
1973 } else if (can[1] == can[3]) {
1974 if (merge_lines(sstate, e[0], e[2], total_parity^inv[1]^inv[3]))
1975 diff = min(diff, DIFF_HARD);
1976 } else if (can[2] == can[3]) {
1977 if (merge_lines(sstate, e[0], e[1], total_parity^inv[2]^inv[3]))
1978 diff = min(diff, DIFF_HARD);
1986 * These are the main solver functions.
1988 * Their return values are diff values corresponding to the lowest mode solver
1989 * that would notice the work that they have done. For example if the normal
1990 * mode solver adds actual lines or crosses, it will return DIFF_EASY as the
1991 * easy mode solver might be able to make progress using that. It doesn't make
1992 * sense for one of them to return a diff value higher than that of the
1995 * Each function returns the lowest value it can, as early as possible, in
1996 * order to try and pass as much work as possible back to the lower level
1997 * solvers which progress more quickly.
2000 /* PROPOSED NEW DESIGN:
2001 * We have a work queue consisting of 'events' notifying us that something has
2002 * happened that a particular solver mode might be interested in. For example
2003 * the hard mode solver might do something that helps the normal mode solver at
2004 * dot [x,y] in which case it will enqueue an event recording this fact. Then
2005 * we pull events off the work queue, and hand each in turn to the solver that
2006 * is interested in them. If a solver reports that it failed we pass the same
2007 * event on to progressively more advanced solvers and the loop detector. Once
2008 * we've exhausted an event, or it has helped us progress, we drop it and
2009 * continue to the next one. The events are sorted first in order of solver
2010 * complexity (easy first) then order of insertion (oldest first).
2011 * Once we run out of events we loop over each permitted solver in turn
2012 * (easiest first) until either a deduction is made (and an event therefore
2013 * emerges) or no further deductions can be made (in which case we've failed).
2016 * * How do we 'loop over' a solver when both dots and squares are concerned.
2017 * Answer: first all squares then all dots.
2020 static int trivial_deductions(solver_state *sstate)
2022 int i, current_yes, current_no;
2023 game_state *state = sstate->state;
2024 grid *g = state->game_grid;
2025 int diff = DIFF_MAX;
2027 /* Per-face deductions */
2028 for (i = 0; i < g->num_faces; i++) {
2029 grid_face *f = g->faces + i;
2031 if (sstate->face_solved[i])
2034 current_yes = sstate->face_yes_count[i];
2035 current_no = sstate->face_no_count[i];
2037 if (current_yes + current_no == f->order) {
2038 sstate->face_solved[i] = TRUE;
2042 if (state->clues[i] < 0)
2046 * This code checks whether the numeric clue on a face is so
2047 * large as to permit all its remaining LINE_UNKNOWNs to be
2048 * filled in as LINE_YES, or alternatively so small as to
2049 * permit them all to be filled in as LINE_NO.
2052 if (state->clues[i] < current_yes) {
2053 sstate->solver_status = SOLVER_MISTAKE;
2056 if (state->clues[i] == current_yes) {
2057 if (face_setall(sstate, i, LINE_UNKNOWN, LINE_NO))
2058 diff = min(diff, DIFF_EASY);
2059 sstate->face_solved[i] = TRUE;
2063 if (f->order - state->clues[i] < current_no) {
2064 sstate->solver_status = SOLVER_MISTAKE;
2067 if (f->order - state->clues[i] == current_no) {
2068 if (face_setall(sstate, i, LINE_UNKNOWN, LINE_YES))
2069 diff = min(diff, DIFF_EASY);
2070 sstate->face_solved[i] = TRUE;
2074 if (f->order - state->clues[i] == current_no + 1 &&
2075 f->order - current_yes - current_no > 2) {
2077 * One small refinement to the above: we also look for any
2078 * adjacent pair of LINE_UNKNOWNs around the face with
2079 * some LINE_YES incident on it from elsewhere. If we find
2080 * one, then we know that pair of LINE_UNKNOWNs can't
2081 * _both_ be LINE_YES, and hence that pushes us one line
2082 * closer to being able to determine all the rest.
2084 int j, k, e1, e2, e, d;
2086 for (j = 0; j < f->order; j++) {
2087 e1 = f->edges[j] - g->edges;
2088 e2 = f->edges[j+1 < f->order ? j+1 : 0] - g->edges;
2090 if (g->edges[e1].dot1 == g->edges[e2].dot1 ||
2091 g->edges[e1].dot1 == g->edges[e2].dot2) {
2092 d = g->edges[e1].dot1 - g->dots;
2094 assert(g->edges[e1].dot2 == g->edges[e2].dot1 ||
2095 g->edges[e1].dot2 == g->edges[e2].dot2);
2096 d = g->edges[e1].dot2 - g->dots;
2099 if (state->lines[e1] == LINE_UNKNOWN &&
2100 state->lines[e2] == LINE_UNKNOWN) {
2101 for (k = 0; k < g->dots[d].order; k++) {
2102 int e = g->dots[d].edges[k] - g->edges;
2103 if (state->lines[e] == LINE_YES)
2104 goto found; /* multi-level break */
2112 * If we get here, we've found such a pair of edges, and
2113 * they're e1 and e2.
2115 for (j = 0; j < f->order; j++) {
2116 e = f->edges[j] - g->edges;
2117 if (state->lines[e] == LINE_UNKNOWN && e != e1 && e != e2) {
2118 int r = solver_set_line(sstate, e, LINE_YES);
2120 diff = min(diff, DIFF_EASY);
2126 check_caches(sstate);
2128 /* Per-dot deductions */
2129 for (i = 0; i < g->num_dots; i++) {
2130 grid_dot *d = g->dots + i;
2131 int yes, no, unknown;
2133 if (sstate->dot_solved[i])
2136 yes = sstate->dot_yes_count[i];
2137 no = sstate->dot_no_count[i];
2138 unknown = d->order - yes - no;
2142 sstate->dot_solved[i] = TRUE;
2143 } else if (unknown == 1) {
2144 dot_setall(sstate, i, LINE_UNKNOWN, LINE_NO);
2145 diff = min(diff, DIFF_EASY);
2146 sstate->dot_solved[i] = TRUE;
2148 } else if (yes == 1) {
2150 sstate->solver_status = SOLVER_MISTAKE;
2152 } else if (unknown == 1) {
2153 dot_setall(sstate, i, LINE_UNKNOWN, LINE_YES);
2154 diff = min(diff, DIFF_EASY);
2156 } else if (yes == 2) {
2158 dot_setall(sstate, i, LINE_UNKNOWN, LINE_NO);
2159 diff = min(diff, DIFF_EASY);
2161 sstate->dot_solved[i] = TRUE;
2163 sstate->solver_status = SOLVER_MISTAKE;
2168 check_caches(sstate);
2173 static int dline_deductions(solver_state *sstate)
2175 game_state *state = sstate->state;
2176 grid *g = state->game_grid;
2177 char *dlines = sstate->dlines;
2179 int diff = DIFF_MAX;
2181 /* ------ Face deductions ------ */
2183 /* Given a set of dline atmostone/atleastone constraints, need to figure
2184 * out if we can deduce any further info. For more general faces than
2185 * squares, this turns out to be a tricky problem.
2186 * The approach taken here is to define (per face) NxN matrices:
2187 * "maxs" and "mins".
2188 * The entries maxs(j,k) and mins(j,k) define the upper and lower limits
2189 * for the possible number of edges that are YES between positions j and k
2190 * going clockwise around the face. Can think of j and k as marking dots
2191 * around the face (recall the labelling scheme: edge0 joins dot0 to dot1,
2192 * edge1 joins dot1 to dot2 etc).
2193 * Trivially, mins(j,j) = maxs(j,j) = 0, and we don't even bother storing
2194 * these. mins(j,j+1) and maxs(j,j+1) are determined by whether edge{j}
2195 * is YES, NO or UNKNOWN. mins(j,j+2) and maxs(j,j+2) are related to
2196 * the dline atmostone/atleastone status for edges j and j+1.
2198 * Then we calculate the remaining entries recursively. We definitely
2200 * mins(j,k) >= { mins(j,u) + mins(u,k) } for any u between j and k.
2201 * This is because any valid placement of YESs between j and k must give
2202 * a valid placement between j and u, and also between u and k.
2203 * I believe it's sufficient to use just the two values of u:
2204 * j+1 and j+2. Seems to work well in practice - the bounds we compute
2205 * are rigorous, even if they might not be best-possible.
2207 * Once we have maxs and mins calculated, we can make inferences about
2208 * each dline{j,j+1} by looking at the possible complementary edge-counts
2209 * mins(j+2,j) and maxs(j+2,j) and comparing these with the face clue.
2210 * As well as dlines, we can make similar inferences about single edges.
2211 * For example, consider a pentagon with clue 3, and we know at most one
2212 * of (edge0, edge1) is YES, and at most one of (edge2, edge3) is YES.
2213 * We could then deduce edge4 is YES, because maxs(0,4) would be 2, so
2214 * that final edge would have to be YES to make the count up to 3.
2217 /* Much quicker to allocate arrays on the stack than the heap, so
2218 * define the largest possible face size, and base our array allocations
2219 * on that. We check this with an assertion, in case someone decides to
2220 * make a grid which has larger faces than this. Note, this algorithm
2221 * could get quite expensive if there are many large faces. */
2222 #define MAX_FACE_SIZE 12
2224 for (i = 0; i < g->num_faces; i++) {
2225 int maxs[MAX_FACE_SIZE][MAX_FACE_SIZE];
2226 int mins[MAX_FACE_SIZE][MAX_FACE_SIZE];
2227 grid_face *f = g->faces + i;
2230 int clue = state->clues[i];
2231 assert(N <= MAX_FACE_SIZE);
2232 if (sstate->face_solved[i])
2234 if (clue < 0) continue;
2236 /* Calculate the (j,j+1) entries */
2237 for (j = 0; j < N; j++) {
2238 int edge_index = f->edges[j] - g->edges;
2240 enum line_state line1 = state->lines[edge_index];
2241 enum line_state line2;
2245 maxs[j][k] = (line1 == LINE_NO) ? 0 : 1;
2246 mins[j][k] = (line1 == LINE_YES) ? 1 : 0;
2247 /* Calculate the (j,j+2) entries */
2248 dline_index = dline_index_from_face(g, f, k);
2249 edge_index = f->edges[k] - g->edges;
2250 line2 = state->lines[edge_index];
2256 if (line1 == LINE_NO) tmp--;
2257 if (line2 == LINE_NO) tmp--;
2258 if (tmp == 2 && is_atmostone(dlines, dline_index))
2264 if (line1 == LINE_YES) tmp++;
2265 if (line2 == LINE_YES) tmp++;
2266 if (tmp == 0 && is_atleastone(dlines, dline_index))
2271 /* Calculate the (j,j+m) entries for m between 3 and N-1 */
2272 for (m = 3; m < N; m++) {
2273 for (j = 0; j < N; j++) {
2281 maxs[j][k] = maxs[j][u] + maxs[u][k];
2282 mins[j][k] = mins[j][u] + mins[u][k];
2283 tmp = maxs[j][v] + maxs[v][k];
2284 maxs[j][k] = min(maxs[j][k], tmp);
2285 tmp = mins[j][v] + mins[v][k];
2286 mins[j][k] = max(mins[j][k], tmp);
2290 /* See if we can make any deductions */
2291 for (j = 0; j < N; j++) {
2293 grid_edge *e = f->edges[j];
2294 int line_index = e - g->edges;
2297 if (state->lines[line_index] != LINE_UNKNOWN)
2302 /* minimum YESs in the complement of this edge */
2303 if (mins[k][j] > clue) {
2304 sstate->solver_status = SOLVER_MISTAKE;
2307 if (mins[k][j] == clue) {
2308 /* setting this edge to YES would make at least
2309 * (clue+1) edges - contradiction */
2310 solver_set_line(sstate, line_index, LINE_NO);
2311 diff = min(diff, DIFF_EASY);
2313 if (maxs[k][j] < clue - 1) {
2314 sstate->solver_status = SOLVER_MISTAKE;
2317 if (maxs[k][j] == clue - 1) {
2318 /* Only way to satisfy the clue is to set edge{j} as YES */
2319 solver_set_line(sstate, line_index, LINE_YES);
2320 diff = min(diff, DIFF_EASY);
2323 /* More advanced deduction that allows propagation along diagonal
2324 * chains of faces connected by dots, for example, 3-2-...-2-3
2325 * in square grids. */
2326 if (sstate->diff >= DIFF_TRICKY) {
2327 /* Now see if we can make dline deduction for edges{j,j+1} */
2329 if (state->lines[e - g->edges] != LINE_UNKNOWN)
2330 /* Only worth doing this for an UNKNOWN,UNKNOWN pair.
2331 * Dlines where one of the edges is known, are handled in the
2335 dline_index = dline_index_from_face(g, f, k);
2339 /* minimum YESs in the complement of this dline */
2340 if (mins[k][j] > clue - 2) {
2341 /* Adding 2 YESs would break the clue */
2342 if (set_atmostone(dlines, dline_index))
2343 diff = min(diff, DIFF_NORMAL);
2345 /* maximum YESs in the complement of this dline */
2346 if (maxs[k][j] < clue) {
2347 /* Adding 2 NOs would mean not enough YESs */
2348 if (set_atleastone(dlines, dline_index))
2349 diff = min(diff, DIFF_NORMAL);
2355 if (diff < DIFF_NORMAL)
2358 /* ------ Dot deductions ------ */
2360 for (i = 0; i < g->num_dots; i++) {
2361 grid_dot *d = g->dots + i;
2363 int yes, no, unknown;
2365 if (sstate->dot_solved[i])
2367 yes = sstate->dot_yes_count[i];
2368 no = sstate->dot_no_count[i];
2369 unknown = N - yes - no;
2371 for (j = 0; j < N; j++) {
2374 int line1_index, line2_index;
2375 enum line_state line1, line2;
2378 dline_index = dline_index_from_dot(g, d, j);
2379 line1_index = d->edges[j] - g->edges;
2380 line2_index = d->edges[k] - g->edges;
2381 line1 = state->lines[line1_index];
2382 line2 = state->lines[line2_index];
2384 /* Infer dline state from line state */
2385 if (line1 == LINE_NO || line2 == LINE_NO) {
2386 if (set_atmostone(dlines, dline_index))
2387 diff = min(diff, DIFF_NORMAL);
2389 if (line1 == LINE_YES || line2 == LINE_YES) {
2390 if (set_atleastone(dlines, dline_index))
2391 diff = min(diff, DIFF_NORMAL);
2393 /* Infer line state from dline state */
2394 if (is_atmostone(dlines, dline_index)) {
2395 if (line1 == LINE_YES && line2 == LINE_UNKNOWN) {
2396 solver_set_line(sstate, line2_index, LINE_NO);
2397 diff = min(diff, DIFF_EASY);
2399 if (line2 == LINE_YES && line1 == LINE_UNKNOWN) {
2400 solver_set_line(sstate, line1_index, LINE_NO);
2401 diff = min(diff, DIFF_EASY);
2404 if (is_atleastone(dlines, dline_index)) {
2405 if (line1 == LINE_NO && line2 == LINE_UNKNOWN) {
2406 solver_set_line(sstate, line2_index, LINE_YES);
2407 diff = min(diff, DIFF_EASY);
2409 if (line2 == LINE_NO && line1 == LINE_UNKNOWN) {
2410 solver_set_line(sstate, line1_index, LINE_YES);
2411 diff = min(diff, DIFF_EASY);
2414 /* Deductions that depend on the numbers of lines.
2415 * Only bother if both lines are UNKNOWN, otherwise the
2416 * easy-mode solver (or deductions above) would have taken
2418 if (line1 != LINE_UNKNOWN || line2 != LINE_UNKNOWN)
2421 if (yes == 0 && unknown == 2) {
2422 /* Both these unknowns must be identical. If we know
2423 * atmostone or atleastone, we can make progress. */
2424 if (is_atmostone(dlines, dline_index)) {
2425 solver_set_line(sstate, line1_index, LINE_NO);
2426 solver_set_line(sstate, line2_index, LINE_NO);
2427 diff = min(diff, DIFF_EASY);
2429 if (is_atleastone(dlines, dline_index)) {
2430 solver_set_line(sstate, line1_index, LINE_YES);
2431 solver_set_line(sstate, line2_index, LINE_YES);
2432 diff = min(diff, DIFF_EASY);
2436 if (set_atmostone(dlines, dline_index))
2437 diff = min(diff, DIFF_NORMAL);
2439 if (set_atleastone(dlines, dline_index))
2440 diff = min(diff, DIFF_NORMAL);
2444 /* More advanced deduction that allows propagation along diagonal
2445 * chains of faces connected by dots, for example: 3-2-...-2-3
2446 * in square grids. */
2447 if (sstate->diff >= DIFF_TRICKY) {
2448 /* If we have atleastone set for this dline, infer
2449 * atmostone for each "opposite" dline (that is, each
2450 * dline without edges in common with this one).
2451 * Again, this test is only worth doing if both these
2452 * lines are UNKNOWN. For if one of these lines were YES,
2453 * the (yes == 1) test above would kick in instead. */
2454 if (is_atleastone(dlines, dline_index)) {
2456 for (opp = 0; opp < N; opp++) {
2457 int opp_dline_index;
2458 if (opp == j || opp == j+1 || opp == j-1)
2460 if (j == 0 && opp == N-1)
2462 if (j == N-1 && opp == 0)
2464 opp_dline_index = dline_index_from_dot(g, d, opp);
2465 if (set_atmostone(dlines, opp_dline_index))
2466 diff = min(diff, DIFF_NORMAL);
2468 if (yes == 0 && is_atmostone(dlines, dline_index)) {
2469 /* This dline has *exactly* one YES and there are no
2470 * other YESs. This allows more deductions. */
2472 /* Third unknown must be YES */
2473 for (opp = 0; opp < N; opp++) {
2475 if (opp == j || opp == k)
2477 opp_index = d->edges[opp] - g->edges;
2478 if (state->lines[opp_index] == LINE_UNKNOWN) {
2479 solver_set_line(sstate, opp_index,
2481 diff = min(diff, DIFF_EASY);
2484 } else if (unknown == 4) {
2485 /* Exactly one of opposite UNKNOWNS is YES. We've
2486 * already set atmostone, so set atleastone as
2489 if (dline_set_opp_atleastone(sstate, d, j))
2490 diff = min(diff, DIFF_NORMAL);
2500 static int linedsf_deductions(solver_state *sstate)
2502 game_state *state = sstate->state;
2503 grid *g = state->game_grid;
2504 char *dlines = sstate->dlines;
2506 int diff = DIFF_MAX;
2509 /* ------ Face deductions ------ */
2511 /* A fully-general linedsf deduction seems overly complicated
2512 * (I suspect the problem is NP-complete, though in practice it might just
2513 * be doable because faces are limited in size).
2514 * For simplicity, we only consider *pairs* of LINE_UNKNOWNS that are
2515 * known to be identical. If setting them both to YES (or NO) would break
2516 * the clue, set them to NO (or YES). */
2518 for (i = 0; i < g->num_faces; i++) {
2519 int N, yes, no, unknown;
2522 if (sstate->face_solved[i])
2524 clue = state->clues[i];
2528 N = g->faces[i].order;
2529 yes = sstate->face_yes_count[i];
2530 if (yes + 1 == clue) {
2531 if (face_setall_identical(sstate, i, LINE_NO))
2532 diff = min(diff, DIFF_EASY);
2534 no = sstate->face_no_count[i];
2535 if (no + 1 == N - clue) {
2536 if (face_setall_identical(sstate, i, LINE_YES))
2537 diff = min(diff, DIFF_EASY);
2540 /* Reload YES count, it might have changed */
2541 yes = sstate->face_yes_count[i];
2542 unknown = N - no - yes;
2544 /* Deductions with small number of LINE_UNKNOWNs, based on overall
2545 * parity of lines. */
2546 diff_tmp = parity_deductions(sstate, g->faces[i].edges,
2547 (clue - yes) % 2, unknown);
2548 diff = min(diff, diff_tmp);
2551 /* ------ Dot deductions ------ */
2552 for (i = 0; i < g->num_dots; i++) {
2553 grid_dot *d = g->dots + i;
2556 int yes, no, unknown;
2557 /* Go through dlines, and do any dline<->linedsf deductions wherever
2558 * we find two UNKNOWNS. */
2559 for (j = 0; j < N; j++) {
2560 int dline_index = dline_index_from_dot(g, d, j);
2563 int can1, can2, inv1, inv2;
2565 line1_index = d->edges[j] - g->edges;
2566 if (state->lines[line1_index] != LINE_UNKNOWN)
2569 if (j2 == N) j2 = 0;
2570 line2_index = d->edges[j2] - g->edges;
2571 if (state->lines[line2_index] != LINE_UNKNOWN)
2573 /* Infer dline flags from linedsf */
2574 can1 = edsf_canonify(sstate->linedsf, line1_index, &inv1);
2575 can2 = edsf_canonify(sstate->linedsf, line2_index, &inv2);
2576 if (can1 == can2 && inv1 != inv2) {
2577 /* These are opposites, so set dline atmostone/atleastone */
2578 if (set_atmostone(dlines, dline_index))
2579 diff = min(diff, DIFF_NORMAL);
2580 if (set_atleastone(dlines, dline_index))
2581 diff = min(diff, DIFF_NORMAL);
2584 /* Infer linedsf from dline flags */
2585 if (is_atmostone(dlines, dline_index)
2586 && is_atleastone(dlines, dline_index)) {
2587 if (merge_lines(sstate, line1_index, line2_index, 1))
2588 diff = min(diff, DIFF_HARD);
2592 /* Deductions with small number of LINE_UNKNOWNs, based on overall
2593 * parity of lines. */
2594 yes = sstate->dot_yes_count[i];
2595 no = sstate->dot_no_count[i];
2596 unknown = N - yes - no;
2597 diff_tmp = parity_deductions(sstate, d->edges,
2599 diff = min(diff, diff_tmp);
2602 /* ------ Edge dsf deductions ------ */
2604 /* If the state of a line is known, deduce the state of its canonical line
2605 * too, and vice versa. */
2606 for (i = 0; i < g->num_edges; i++) {
2609 can = edsf_canonify(sstate->linedsf, i, &inv);
2612 s = sstate->state->lines[can];
2613 if (s != LINE_UNKNOWN) {
2614 if (solver_set_line(sstate, i, inv ? OPP(s) : s))
2615 diff = min(diff, DIFF_EASY);
2617 s = sstate->state->lines[i];
2618 if (s != LINE_UNKNOWN) {
2619 if (solver_set_line(sstate, can, inv ? OPP(s) : s))
2620 diff = min(diff, DIFF_EASY);
2628 static int loop_deductions(solver_state *sstate)
2630 int edgecount = 0, clues = 0, satclues = 0, sm1clues = 0;
2631 game_state *state = sstate->state;
2632 grid *g = state->game_grid;
2633 int shortest_chainlen = g->num_dots;
2634 int loop_found = FALSE;
2636 int progress = FALSE;
2640 * Go through the grid and update for all the new edges.
2641 * Since merge_dots() is idempotent, the simplest way to
2642 * do this is just to update for _all_ the edges.
2643 * Also, while we're here, we count the edges.
2645 for (i = 0; i < g->num_edges; i++) {
2646 if (state->lines[i] == LINE_YES) {
2647 loop_found |= merge_dots(sstate, i);
2653 * Count the clues, count the satisfied clues, and count the
2654 * satisfied-minus-one clues.
2656 for (i = 0; i < g->num_faces; i++) {
2657 int c = state->clues[i];
2659 int o = sstate->face_yes_count[i];
2668 for (i = 0; i < g->num_dots; ++i) {
2670 sstate->looplen[dsf_canonify(sstate->dotdsf, i)];
2671 if (dots_connected > 1)
2672 shortest_chainlen = min(shortest_chainlen, dots_connected);
2675 assert(sstate->solver_status == SOLVER_INCOMPLETE);
2677 if (satclues == clues && shortest_chainlen == edgecount) {
2678 sstate->solver_status = SOLVER_SOLVED;
2679 /* This discovery clearly counts as progress, even if we haven't
2680 * just added any lines or anything */
2682 goto finished_loop_deductionsing;
2686 * Now go through looking for LINE_UNKNOWN edges which
2687 * connect two dots that are already in the same
2688 * equivalence class. If we find one, test to see if the
2689 * loop it would create is a solution.
2691 for (i = 0; i < g->num_edges; i++) {
2692 grid_edge *e = g->edges + i;
2693 int d1 = e->dot1 - g->dots;
2694 int d2 = e->dot2 - g->dots;
2696 if (state->lines[i] != LINE_UNKNOWN)
2699 eqclass = dsf_canonify(sstate->dotdsf, d1);
2700 if (eqclass != dsf_canonify(sstate->dotdsf, d2))
2703 val = LINE_NO; /* loop is bad until proven otherwise */
2706 * This edge would form a loop. Next
2707 * question: how long would the loop be?
2708 * Would it equal the total number of edges
2709 * (plus the one we'd be adding if we added
2712 if (sstate->looplen[eqclass] == edgecount + 1) {
2716 * This edge would form a loop which
2717 * took in all the edges in the entire
2718 * grid. So now we need to work out
2719 * whether it would be a valid solution
2720 * to the puzzle, which means we have to
2721 * check if it satisfies all the clues.
2722 * This means that every clue must be
2723 * either satisfied or satisfied-minus-
2724 * 1, and also that the number of
2725 * satisfied-minus-1 clues must be at
2726 * most two and they must lie on either
2727 * side of this edge.
2731 int f = e->face1 - g->faces;
2732 int c = state->clues[f];
2733 if (c >= 0 && sstate->face_yes_count[f] == c - 1)
2737 int f = e->face2 - g->faces;
2738 int c = state->clues[f];
2739 if (c >= 0 && sstate->face_yes_count[f] == c - 1)
2742 if (sm1clues == sm1_nearby &&
2743 sm1clues + satclues == clues) {
2744 val = LINE_YES; /* loop is good! */
2749 * Right. Now we know that adding this edge
2750 * would form a loop, and we know whether
2751 * that loop would be a viable solution or
2754 * If adding this edge produces a solution,
2755 * then we know we've found _a_ solution but
2756 * we don't know that it's _the_ solution -
2757 * if it were provably the solution then
2758 * we'd have deduced this edge some time ago
2759 * without the need to do loop detection. So
2760 * in this state we return SOLVER_AMBIGUOUS,
2761 * which has the effect that hitting Solve
2762 * on a user-provided puzzle will fill in a
2763 * solution but using the solver to
2764 * construct new puzzles won't consider this
2765 * a reasonable deduction for the user to
2768 progress = solver_set_line(sstate, i, val);
2769 assert(progress == TRUE);
2770 if (val == LINE_YES) {
2771 sstate->solver_status = SOLVER_AMBIGUOUS;
2772 goto finished_loop_deductionsing;
2776 finished_loop_deductionsing:
2777 return progress ? DIFF_EASY : DIFF_MAX;
2780 /* This will return a dynamically allocated solver_state containing the (more)
2782 static solver_state *solve_game_rec(const solver_state *sstate_start)
2784 solver_state *sstate;
2786 /* Index of the solver we should call next. */
2789 /* As a speed-optimisation, we avoid re-running solvers that we know
2790 * won't make any progress. This happens when a high-difficulty
2791 * solver makes a deduction that can only help other high-difficulty
2793 * For example: if a new 'dline' flag is set by dline_deductions, the
2794 * trivial_deductions solver cannot do anything with this information.
2795 * If we've already run the trivial_deductions solver (because it's
2796 * earlier in the list), there's no point running it again.
2798 * Therefore: if a solver is earlier in the list than "threshold_index",
2799 * we don't bother running it if it's difficulty level is less than
2802 int threshold_diff = 0;
2803 int threshold_index = 0;
2805 sstate = dup_solver_state(sstate_start);
2807 check_caches(sstate);
2809 while (i < NUM_SOLVERS) {
2810 if (sstate->solver_status == SOLVER_MISTAKE)
2812 if (sstate->solver_status == SOLVER_SOLVED ||
2813 sstate->solver_status == SOLVER_AMBIGUOUS) {
2814 /* solver finished */
2818 if ((solver_diffs[i] >= threshold_diff || i >= threshold_index)
2819 && solver_diffs[i] <= sstate->diff) {
2820 /* current_solver is eligible, so use it */
2821 int next_diff = solver_fns[i](sstate);
2822 if (next_diff != DIFF_MAX) {
2823 /* solver made progress, so use new thresholds and
2824 * start again at top of list. */
2825 threshold_diff = next_diff;
2826 threshold_index = i;
2831 /* current_solver is ineligible, or failed to make progress, so
2832 * go to the next solver in the list */
2836 if (sstate->solver_status == SOLVER_SOLVED ||
2837 sstate->solver_status == SOLVER_AMBIGUOUS) {
2838 /* s/LINE_UNKNOWN/LINE_NO/g */
2839 array_setall(sstate->state->lines, LINE_UNKNOWN, LINE_NO,
2840 sstate->state->game_grid->num_edges);
2847 static char *solve_game(const game_state *state, const game_state *currstate,
2848 const char *aux, char **error)
2851 solver_state *sstate, *new_sstate;
2853 sstate = new_solver_state(state, DIFF_MAX);
2854 new_sstate = solve_game_rec(sstate);
2856 if (new_sstate->solver_status == SOLVER_SOLVED) {
2857 soln = encode_solve_move(new_sstate->state);
2858 } else if (new_sstate->solver_status == SOLVER_AMBIGUOUS) {
2859 soln = encode_solve_move(new_sstate->state);
2860 /**error = "Solver found ambiguous solutions"; */
2862 soln = encode_solve_move(new_sstate->state);
2863 /**error = "Solver failed"; */
2866 free_solver_state(new_sstate);
2867 free_solver_state(sstate);
2872 /* ----------------------------------------------------------------------
2873 * Drawing and mouse-handling
2876 static char *interpret_move(const game_state *state, game_ui *ui,
2877 const game_drawstate *ds,
2878 int x, int y, int button)
2880 grid *g = state->game_grid;
2884 char button_char = ' ';
2885 enum line_state old_state;
2887 button &= ~MOD_MASK;
2889 /* Convert mouse-click (x,y) to grid coordinates */
2890 x -= BORDER(ds->tilesize);
2891 y -= BORDER(ds->tilesize);
2892 x = x * g->tilesize / ds->tilesize;
2893 y = y * g->tilesize / ds->tilesize;
2897 e = grid_nearest_edge(g, x, y);
2903 /* I think it's only possible to play this game with mouse clicks, sorry */
2904 /* Maybe will add mouse drag support some time */
2905 old_state = state->lines[i];
2909 switch (old_state) {
2927 switch (old_state) {
2946 sprintf(buf, "%d%c", i, (int)button_char);
2952 static game_state *execute_move(const game_state *state, const char *move)
2955 game_state *newstate = dup_game(state);
2957 if (move[0] == 'S') {
2959 newstate->cheated = TRUE;
2964 if (i < 0 || i >= newstate->game_grid->num_edges)
2966 move += strspn(move, "1234567890");
2967 switch (*(move++)) {
2969 newstate->lines[i] = LINE_YES;
2972 newstate->lines[i] = LINE_NO;
2975 newstate->lines[i] = LINE_UNKNOWN;
2983 * Check for completion.
2985 if (check_completion(newstate))
2986 newstate->solved = TRUE;
2991 free_game(newstate);
2995 /* ----------------------------------------------------------------------
2999 /* Convert from grid coordinates to screen coordinates */
3000 static void grid_to_screen(const game_drawstate *ds, const grid *g,
3001 int grid_x, int grid_y, int *x, int *y)
3003 *x = grid_x - g->lowest_x;
3004 *y = grid_y - g->lowest_y;
3005 *x = *x * ds->tilesize / g->tilesize;
3006 *y = *y * ds->tilesize / g->tilesize;
3007 *x += BORDER(ds->tilesize);
3008 *y += BORDER(ds->tilesize);
3011 /* Returns (into x,y) position of centre of face for rendering the text clue.
3013 static void face_text_pos(const game_drawstate *ds, const grid *g,
3014 grid_face *f, int *xret, int *yret)
3016 int faceindex = f - g->faces;
3019 * Return the cached position for this face, if we've already
3022 if (ds->textx[faceindex] >= 0) {
3023 *xret = ds->textx[faceindex];
3024 *yret = ds->texty[faceindex];
3029 * Otherwise, use the incentre computed by grid.c and convert it
3030 * to screen coordinates.
3032 grid_find_incentre(f);
3033 grid_to_screen(ds, g, f->ix, f->iy,
3034 &ds->textx[faceindex], &ds->texty[faceindex]);
3036 *xret = ds->textx[faceindex];
3037 *yret = ds->texty[faceindex];
3040 static void face_text_bbox(game_drawstate *ds, grid *g, grid_face *f,
3041 int *x, int *y, int *w, int *h)
3044 face_text_pos(ds, g, f, &xx, &yy);
3046 /* There seems to be a certain amount of trial-and-error involved
3047 * in working out the correct bounding-box for the text. */
3049 *x = xx - ds->tilesize/4 - 1;
3050 *y = yy - ds->tilesize/4 - 3;
3051 *w = ds->tilesize/2 + 2;
3052 *h = ds->tilesize/2 + 5;
3055 static void game_redraw_clue(drawing *dr, game_drawstate *ds,
3056 const game_state *state, int i)
3058 grid *g = state->game_grid;
3059 grid_face *f = g->faces + i;
3063 sprintf(c, "%d", state->clues[i]);
3065 face_text_pos(ds, g, f, &x, &y);
3067 FONT_VARIABLE, ds->tilesize/2,
3068 ALIGN_VCENTRE | ALIGN_HCENTRE,
3069 ds->clue_error[i] ? COL_MISTAKE :
3070 ds->clue_satisfied[i] ? COL_SATISFIED : COL_FOREGROUND, c);
3073 static void edge_bbox(game_drawstate *ds, grid *g, grid_edge *e,
3074 int *x, int *y, int *w, int *h)
3076 int x1 = e->dot1->x;
3077 int y1 = e->dot1->y;
3078 int x2 = e->dot2->x;
3079 int y2 = e->dot2->y;
3080 int xmin, xmax, ymin, ymax;
3082 grid_to_screen(ds, g, x1, y1, &x1, &y1);
3083 grid_to_screen(ds, g, x2, y2, &x2, &y2);
3084 /* Allow extra margin for dots, and thickness of lines */
3085 xmin = min(x1, x2) - 2;
3086 xmax = max(x1, x2) + 2;
3087 ymin = min(y1, y2) - 2;
3088 ymax = max(y1, y2) + 2;
3092 *w = xmax - xmin + 1;
3093 *h = ymax - ymin + 1;
3096 static void dot_bbox(game_drawstate *ds, grid *g, grid_dot *d,
3097 int *x, int *y, int *w, int *h)
3101 grid_to_screen(ds, g, d->x, d->y, &x1, &y1);
3109 static const int loopy_line_redraw_phases[] = {
3110 COL_FAINT, COL_LINEUNKNOWN, COL_FOREGROUND, COL_HIGHLIGHT, COL_MISTAKE
3112 #define NPHASES lenof(loopy_line_redraw_phases)
3114 static void game_redraw_line(drawing *dr, game_drawstate *ds,
3115 const game_state *state, int i, int phase)
3117 grid *g = state->game_grid;
3118 grid_edge *e = g->edges + i;
3122 if (state->line_errors[i])
3123 line_colour = COL_MISTAKE;
3124 else if (state->lines[i] == LINE_UNKNOWN)
3125 line_colour = COL_LINEUNKNOWN;
3126 else if (state->lines[i] == LINE_NO)
3127 line_colour = COL_FAINT;
3128 else if (ds->flashing)
3129 line_colour = COL_HIGHLIGHT;
3131 line_colour = COL_FOREGROUND;
3132 if (line_colour != loopy_line_redraw_phases[phase])
3135 /* Convert from grid to screen coordinates */
3136 grid_to_screen(ds, g, e->dot1->x, e->dot1->y, &x1, &y1);
3137 grid_to_screen(ds, g, e->dot2->x, e->dot2->y, &x2, &y2);
3139 if (line_colour == COL_FAINT) {
3140 static int draw_faint_lines = -1;
3141 if (draw_faint_lines < 0) {
3142 char *env = getenv("LOOPY_FAINT_LINES");
3143 draw_faint_lines = (!env || (env[0] == 'y' ||
3146 if (draw_faint_lines)
3147 draw_line(dr, x1, y1, x2, y2, line_colour);
3149 draw_thick_line(dr, 3.0,
3156 static void game_redraw_dot(drawing *dr, game_drawstate *ds,
3157 const game_state *state, int i)
3159 grid *g = state->game_grid;
3160 grid_dot *d = g->dots + i;
3163 grid_to_screen(ds, g, d->x, d->y, &x, &y);
3164 draw_circle(dr, x, y, 2, COL_FOREGROUND, COL_FOREGROUND);
3167 static int boxes_intersect(int x0, int y0, int w0, int h0,
3168 int x1, int y1, int w1, int h1)
3171 * Two intervals intersect iff neither is wholly on one side of
3172 * the other. Two boxes intersect iff their horizontal and
3173 * vertical intervals both intersect.
3175 return (x0 < x1+w1 && x1 < x0+w0 && y0 < y1+h1 && y1 < y0+h0);
3178 static void game_redraw_in_rect(drawing *dr, game_drawstate *ds,
3179 const game_state *state,
3180 int x, int y, int w, int h)
3182 grid *g = state->game_grid;
3186 clip(dr, x, y, w, h);
3187 draw_rect(dr, x, y, w, h, COL_BACKGROUND);
3189 for (i = 0; i < g->num_faces; i++) {
3190 if (state->clues[i] >= 0) {
3191 face_text_bbox(ds, g, &g->faces[i], &bx, &by, &bw, &bh);
3192 if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
3193 game_redraw_clue(dr, ds, state, i);
3196 for (phase = 0; phase < NPHASES; phase++) {
3197 for (i = 0; i < g->num_edges; i++) {
3198 edge_bbox(ds, g, &g->edges[i], &bx, &by, &bw, &bh);
3199 if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
3200 game_redraw_line(dr, ds, state, i, phase);
3203 for (i = 0; i < g->num_dots; i++) {
3204 dot_bbox(ds, g, &g->dots[i], &bx, &by, &bw, &bh);
3205 if (boxes_intersect(x, y, w, h, bx, by, bw, bh))
3206 game_redraw_dot(dr, ds, state, i);
3210 draw_update(dr, x, y, w, h);
3213 static void game_redraw(drawing *dr, game_drawstate *ds,
3214 const game_state *oldstate, const game_state *state,
3215 int dir, const game_ui *ui,
3216 float animtime, float flashtime)
3218 #define REDRAW_OBJECTS_LIMIT 16 /* Somewhat arbitrary tradeoff */
3220 grid *g = state->game_grid;
3221 int border = BORDER(ds->tilesize);
3224 int redraw_everything = FALSE;
3226 int edges[REDRAW_OBJECTS_LIMIT], nedges = 0;
3227 int faces[REDRAW_OBJECTS_LIMIT], nfaces = 0;
3229 /* Redrawing is somewhat involved.
3231 * An update can theoretically affect an arbitrary number of edges
3232 * (consider, for example, completing or breaking a cycle which doesn't
3233 * satisfy all the clues -- we'll switch many edges between error and
3234 * normal states). On the other hand, redrawing the whole grid takes a
3235 * while, making the game feel sluggish, and many updates are actually
3236 * quite well localized.
3238 * This redraw algorithm attempts to cope with both situations gracefully
3239 * and correctly. For localized changes, we set a clip rectangle, fill
3240 * it with background, and then redraw (a plausible but conservative
3241 * guess at) the objects which intersect the rectangle; if several
3242 * objects need redrawing, we'll do them individually. However, if lots
3243 * of objects are affected, we'll just redraw everything.
3245 * The reason for all of this is that it's just not safe to do the redraw
3246 * piecemeal. If you try to draw an antialiased diagonal line over
3247 * itself, you get a slightly thicker antialiased diagonal line, which
3248 * looks rather ugly after a while.
3250 * So, we take two passes over the grid. The first attempts to work out
3251 * what needs doing, and the second actually does it.
3255 redraw_everything = TRUE;
3257 * But we must still go through the upcoming loops, so that we
3258 * set up stuff in ds correctly for the initial redraw.
3262 /* First, trundle through the faces. */
3263 for (i = 0; i < g->num_faces; i++) {
3264 grid_face *f = g->faces + i;
3265 int sides = f->order;
3268 int n = state->clues[i];
3272 clue_mistake = (face_order(state, i, LINE_YES) > n ||
3273 face_order(state, i, LINE_NO ) > (sides-n));
3274 clue_satisfied = (face_order(state, i, LINE_YES) == n &&
3275 face_order(state, i, LINE_NO ) == (sides-n));
3277 if (clue_mistake != ds->clue_error[i] ||
3278 clue_satisfied != ds->clue_satisfied[i]) {
3279 ds->clue_error[i] = clue_mistake;
3280 ds->clue_satisfied[i] = clue_satisfied;
3281 if (nfaces == REDRAW_OBJECTS_LIMIT)
3282 redraw_everything = TRUE;
3284 faces[nfaces++] = i;
3288 /* Work out what the flash state needs to be. */
3289 if (flashtime > 0 &&
3290 (flashtime <= FLASH_TIME/3 ||
3291 flashtime >= FLASH_TIME*2/3)) {
3292 flash_changed = !ds->flashing;
3293 ds->flashing = TRUE;
3295 flash_changed = ds->flashing;
3296 ds->flashing = FALSE;
3299 /* Now, trundle through the edges. */
3300 for (i = 0; i < g->num_edges; i++) {
3302 state->line_errors[i] ? DS_LINE_ERROR : state->lines[i];
3303 if (new_ds != ds->lines[i] ||
3304 (flash_changed && state->lines[i] == LINE_YES)) {
3305 ds->lines[i] = new_ds;
3306 if (nedges == REDRAW_OBJECTS_LIMIT)
3307 redraw_everything = TRUE;
3309 edges[nedges++] = i;
3313 /* Pass one is now done. Now we do the actual drawing. */
3314 if (redraw_everything) {
3315 int grid_width = g->highest_x - g->lowest_x;
3316 int grid_height = g->highest_y - g->lowest_y;
3317 int w = grid_width * ds->tilesize / g->tilesize;
3318 int h = grid_height * ds->tilesize / g->tilesize;
3320 game_redraw_in_rect(dr, ds, state,
3321 0, 0, w + 2*border + 1, h + 2*border + 1);
3324 /* Right. Now we roll up our sleeves. */
3326 for (i = 0; i < nfaces; i++) {
3327 grid_face *f = g->faces + faces[i];
3330 face_text_bbox(ds, g, f, &x, &y, &w, &h);
3331 game_redraw_in_rect(dr, ds, state, x, y, w, h);
3334 for (i = 0; i < nedges; i++) {
3335 grid_edge *e = g->edges + edges[i];
3338 edge_bbox(ds, g, e, &x, &y, &w, &h);
3339 game_redraw_in_rect(dr, ds, state, x, y, w, h);
3346 static float game_flash_length(const game_state *oldstate,
3347 const game_state *newstate, int dir, game_ui *ui)
3349 if (!oldstate->solved && newstate->solved &&
3350 !oldstate->cheated && !newstate->cheated) {
3357 static int game_status(const game_state *state)
3359 return state->solved ? +1 : 0;
3362 static void game_print_size(const game_params *params, float *x, float *y)
3367 * I'll use 7mm "squares" by default.
3369 game_compute_size(params, 700, &pw, &ph);
3374 static void game_print(drawing *dr, const game_state *state, int tilesize)
3376 int ink = print_mono_colour(dr, 0);
3378 game_drawstate ads, *ds = &ads;
3379 grid *g = state->game_grid;
3381 ds->tilesize = tilesize;
3382 ds->textx = snewn(g->num_faces, int);
3383 ds->texty = snewn(g->num_faces, int);
3384 for (i = 0; i < g->num_faces; i++)
3385 ds->textx[i] = ds->texty[i] = -1;
3387 for (i = 0; i < g->num_dots; i++) {
3389 grid_to_screen(ds, g, g->dots[i].x, g->dots[i].y, &x, &y);
3390 draw_circle(dr, x, y, ds->tilesize / 15, ink, ink);
3396 for (i = 0; i < g->num_faces; i++) {
3397 grid_face *f = g->faces + i;
3398 int clue = state->clues[i];
3402 sprintf(c, "%d", state->clues[i]);
3403 face_text_pos(ds, g, f, &x, &y);
3405 FONT_VARIABLE, ds->tilesize / 2,
3406 ALIGN_VCENTRE | ALIGN_HCENTRE, ink, c);
3413 for (i = 0; i < g->num_edges; i++) {
3414 int thickness = (state->lines[i] == LINE_YES) ? 30 : 150;
3415 grid_edge *e = g->edges + i;
3417 grid_to_screen(ds, g, e->dot1->x, e->dot1->y, &x1, &y1);
3418 grid_to_screen(ds, g, e->dot2->x, e->dot2->y, &x2, &y2);
3419 if (state->lines[i] == LINE_YES)
3421 /* (dx, dy) points from (x1, y1) to (x2, y2).
3422 * The line is then "fattened" in a perpendicular
3423 * direction to create a thin rectangle. */
3424 double d = sqrt(SQ((double)x1 - x2) + SQ((double)y1 - y2));
3425 double dx = (x2 - x1) / d;
3426 double dy = (y2 - y1) / d;
3429 dx = (dx * ds->tilesize) / thickness;
3430 dy = (dy * ds->tilesize) / thickness;
3431 points[0] = x1 + (int)dy;
3432 points[1] = y1 - (int)dx;
3433 points[2] = x1 - (int)dy;
3434 points[3] = y1 + (int)dx;
3435 points[4] = x2 - (int)dy;
3436 points[5] = y2 + (int)dx;
3437 points[6] = x2 + (int)dy;
3438 points[7] = y2 - (int)dx;
3439 draw_polygon(dr, points, 4, ink, ink);
3443 /* Draw a dotted line */
3446 for (j = 1; j < divisions; j++) {
3447 /* Weighted average */
3448 int x = (x1 * (divisions -j) + x2 * j) / divisions;
3449 int y = (y1 * (divisions -j) + y2 * j) / divisions;
3450 draw_circle(dr, x, y, ds->tilesize / thickness, ink, ink);
3460 #define thegame loopy
3463 const struct game thegame = {
3464 "Loopy", "games.loopy", "loopy",
3471 TRUE, game_configure, custom_params,
3479 TRUE, game_can_format_as_text_now, game_text_format,
3487 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
3490 game_free_drawstate,
3495 TRUE, FALSE, game_print_size, game_print,
3496 FALSE /* wants_statusbar */,
3497 FALSE, game_timing_state,
3498 0, /* mouse_priorities */
3501 #ifdef STANDALONE_SOLVER
3504 * Half-hearted standalone solver. It can't output the solution to
3505 * anything but a square puzzle, and it can't log the deductions
3506 * it makes either. But it can solve square puzzles, and more
3507 * importantly it can use its solver to grade the difficulty of
3508 * any puzzle you give it.
3513 int main(int argc, char **argv)
3517 char *id = NULL, *desc, *err;
3520 #if 0 /* verbose solver not supported here (yet) */
3521 int really_verbose = FALSE;
3524 while (--argc > 0) {
3526 #if 0 /* verbose solver not supported here (yet) */
3527 if (!strcmp(p, "-v")) {
3528 really_verbose = TRUE;
3531 if (!strcmp(p, "-g")) {
3533 } else if (*p == '-') {
3534 fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
3542 fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
3546 desc = strchr(id, ':');
3548 fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
3553 p = default_params();
3554 decode_params(p, id);
3555 err = validate_desc(p, desc);
3557 fprintf(stderr, "%s: %s\n", argv[0], err);
3560 s = new_game(NULL, p, desc);
3563 * When solving an Easy puzzle, we don't want to bother the
3564 * user with Hard-level deductions. For this reason, we grade
3565 * the puzzle internally before doing anything else.
3567 ret = -1; /* placate optimiser */
3568 for (diff = 0; diff < DIFF_MAX; diff++) {
3569 solver_state *sstate_new;
3570 solver_state *sstate = new_solver_state((game_state *)s, diff);
3572 sstate_new = solve_game_rec(sstate);
3574 if (sstate_new->solver_status == SOLVER_MISTAKE)
3576 else if (sstate_new->solver_status == SOLVER_SOLVED)
3581 free_solver_state(sstate_new);
3582 free_solver_state(sstate);
3588 if (diff == DIFF_MAX) {
3590 printf("Difficulty rating: harder than Hard, or ambiguous\n");
3592 printf("Unable to find a unique solution\n");
3596 printf("Difficulty rating: impossible (no solution exists)\n");
3598 printf("Difficulty rating: %s\n", diffnames[diff]);
3600 solver_state *sstate_new;
3601 solver_state *sstate = new_solver_state((game_state *)s, diff);
3603 /* If we supported a verbose solver, we'd set verbosity here */
3605 sstate_new = solve_game_rec(sstate);
3607 if (sstate_new->solver_status == SOLVER_MISTAKE)
3608 printf("Puzzle is inconsistent\n");
3610 assert(sstate_new->solver_status == SOLVER_SOLVED);
3611 if (s->grid_type == 0) {
3612 fputs(game_text_format(sstate_new->state), stdout);
3614 printf("Unable to output non-square grids\n");
3618 free_solver_state(sstate_new);
3619 free_solver_state(sstate);
3628 /* vim: set shiftwidth=4 tabstop=8: */