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.
86 /* Debugging options */
94 /* ----------------------------------------------------------------------
95 * Struct, enum and function declarations
111 /* Put -1 in a face that doesn't get a clue */
114 /* Array of line states, to store whether each line is
115 * YES, NO or UNKNOWN */
118 unsigned char *line_errors;
123 /* Used in game_text_format(), so that it knows what type of
124 * grid it's trying to render as ASCII text. */
129 SOLVER_SOLVED, /* This is the only solution the solver could find */
130 SOLVER_MISTAKE, /* This is definitely not a solution */
131 SOLVER_AMBIGUOUS, /* This _might_ be an ambiguous solution */
132 SOLVER_INCOMPLETE /* This may be a partial solution */
135 /* ------ Solver state ------ */
136 typedef struct normal {
137 /* For each dline, store a bitmask for whether we know:
138 * (bit 0) at least one is YES
139 * (bit 1) at most one is YES */
143 typedef struct hard {
147 typedef struct solver_state {
149 enum solver_status solver_status;
150 /* NB looplen is the number of dots that are joined together at a point, ie a
151 * looplen of 1 means there are no lines to a particular dot */
157 char *face_yes_count;
159 char *dot_solved, *face_solved;
162 normal_mode_state *normal;
163 hard_mode_state *hard;
167 * Difficulty levels. I do some macro ickery here to ensure that my
168 * enum and the various forms of my name list always match up.
171 #define DIFFLIST(A) \
172 A(EASY,Easy,e,easy_mode_deductions) \
173 A(NORMAL,Normal,n,normal_mode_deductions) \
174 A(HARD,Hard,h,hard_mode_deductions)
175 #define ENUM(upper,title,lower,fn) DIFF_ ## upper,
176 #define TITLE(upper,title,lower,fn) #title,
177 #define ENCODE(upper,title,lower,fn) #lower
178 #define CONFIG(upper,title,lower,fn) ":" #title
179 #define SOLVER_FN_DECL(upper,title,lower,fn) static int fn(solver_state *);
180 #define SOLVER_FN(upper,title,lower,fn) &fn,
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)
185 DIFFLIST(SOLVER_FN_DECL)
186 static int (*(solver_fns[]))(solver_state *) = { DIFFLIST(SOLVER_FN) };
193 /* Grid generation is expensive, so keep a (ref-counted) reference to the
194 * grid for these parameters, and only generate when required. */
198 /* line_drawstate is the same as line_state, but with the extra ERROR
199 * possibility. The drawing code copies line_state to line_drawstate,
200 * except in the case that the line is an error. */
201 enum line_state { LINE_YES, LINE_UNKNOWN, LINE_NO };
202 enum line_drawstate { DS_LINE_YES, DS_LINE_UNKNOWN,
203 DS_LINE_NO, DS_LINE_ERROR };
205 #define OPP(line_state) \
209 struct game_drawstate {
215 char *clue_satisfied;
218 static char *validate_desc(game_params *params, char *desc);
219 static int dot_order(const game_state* state, int i, char line_type);
220 static int face_order(const game_state* state, int i, char line_type);
221 static solver_state *solve_game_rec(const solver_state *sstate,
225 static void check_caches(const solver_state* sstate);
227 #define check_caches(s)
230 /* ------- List of grid generators ------- */
231 #define GRIDLIST(A) \
232 A(Squares,grid_new_square,3,3) \
233 A(Triangular,grid_new_triangular,3,3) \
234 A(Honeycomb,grid_new_honeycomb,3,3) \
235 A(Snub-Square,grid_new_snubsquare,3,3) \
236 A(Cairo,grid_new_cairo,3,4) \
237 A(Great-Hexagonal,grid_new_greathexagonal,3,3) \
238 A(Octagonal,grid_new_octagonal,3,3) \
239 A(Kites,grid_new_kites,3,3)
241 #define GRID_NAME(title,fn,amin,omin) #title,
242 #define GRID_CONFIG(title,fn,amin,omin) ":" #title
243 #define GRID_FN(title,fn,amin,omin) &fn,
244 #define GRID_SIZES(title,fn,amin,omin) \
246 "Width and height for this grid type must both be at least " #amin, \
247 "At least one of width and height for this grid type must be at least " #omin,},
248 static char const *const gridnames[] = { GRIDLIST(GRID_NAME) };
249 #define GRID_CONFIGS GRIDLIST(GRID_CONFIG)
250 static grid * (*(grid_fns[]))(int w, int h) = { GRIDLIST(GRID_FN) };
251 #define NUM_GRID_TYPES (sizeof(grid_fns) / sizeof(grid_fns[0]))
252 static const struct {
255 } grid_size_limits[] = { GRIDLIST(GRID_SIZES) };
257 /* Generates a (dynamically allocated) new grid, according to the
258 * type and size requested in params. Does nothing if the grid is already
259 * generated. The allocated grid is owned by the params object, and will be
260 * freed in free_params(). */
261 static void params_generate_grid(game_params *params)
263 if (!params->game_grid) {
264 params->game_grid = grid_fns[params->type](params->w, params->h);
268 /* ----------------------------------------------------------------------
272 /* General constants */
273 #define PREFERRED_TILE_SIZE 32
274 #define BORDER(tilesize) ((tilesize) / 2)
275 #define FLASH_TIME 0.5F
277 #define BIT_SET(field, bit) ((field) & (1<<(bit)))
279 #define SET_BIT(field, bit) (BIT_SET(field, bit) ? FALSE : \
280 ((field) |= (1<<(bit)), TRUE))
282 #define CLEAR_BIT(field, bit) (BIT_SET(field, bit) ? \
283 ((field) &= ~(1<<(bit)), TRUE) : FALSE)
285 #define CLUE2CHAR(c) \
286 ((c < 0) ? ' ' : c + '0')
288 /* ----------------------------------------------------------------------
289 * General struct manipulation and other straightforward code
292 static game_state *dup_game(game_state *state)
294 game_state *ret = snew(game_state);
296 ret->game_grid = state->game_grid;
297 ret->game_grid->refcount++;
299 ret->solved = state->solved;
300 ret->cheated = state->cheated;
302 ret->clues = snewn(state->game_grid->num_faces, signed char);
303 memcpy(ret->clues, state->clues, state->game_grid->num_faces);
305 ret->lines = snewn(state->game_grid->num_edges, char);
306 memcpy(ret->lines, state->lines, state->game_grid->num_edges);
308 ret->line_errors = snewn(state->game_grid->num_edges, unsigned char);
309 memcpy(ret->line_errors, state->line_errors, state->game_grid->num_edges);
311 ret->grid_type = state->grid_type;
315 static void free_game(game_state *state)
318 grid_free(state->game_grid);
321 sfree(state->line_errors);
326 static solver_state *new_solver_state(game_state *state, int diff) {
328 int num_dots = state->game_grid->num_dots;
329 int num_faces = state->game_grid->num_faces;
330 int num_edges = state->game_grid->num_edges;
331 solver_state *ret = snew(solver_state);
333 ret->state = dup_game(state);
335 ret->solver_status = SOLVER_INCOMPLETE;
337 ret->dotdsf = snew_dsf(num_dots);
338 ret->looplen = snewn(num_dots, int);
340 for (i = 0; i < num_dots; i++) {
344 ret->dot_solved = snewn(num_dots, char);
345 ret->face_solved = snewn(num_faces, char);
346 memset(ret->dot_solved, FALSE, num_dots);
347 memset(ret->face_solved, FALSE, num_faces);
349 ret->dot_yes_count = snewn(num_dots, char);
350 memset(ret->dot_yes_count, 0, num_dots);
351 ret->dot_no_count = snewn(num_dots, char);
352 memset(ret->dot_no_count, 0, num_dots);
353 ret->face_yes_count = snewn(num_faces, char);
354 memset(ret->face_yes_count, 0, num_faces);
355 ret->face_no_count = snewn(num_faces, char);
356 memset(ret->face_no_count, 0, num_faces);
358 if (diff < DIFF_NORMAL) {
361 ret->normal = snew(normal_mode_state);
362 ret->normal->dlines = snewn(2*num_edges, char);
363 memset(ret->normal->dlines, 0, 2*num_edges);
366 if (diff < DIFF_HARD) {
369 ret->hard = snew(hard_mode_state);
370 ret->hard->linedsf = snew_dsf(state->game_grid->num_edges);
376 static void free_solver_state(solver_state *sstate) {
378 free_game(sstate->state);
379 sfree(sstate->dotdsf);
380 sfree(sstate->looplen);
381 sfree(sstate->dot_solved);
382 sfree(sstate->face_solved);
383 sfree(sstate->dot_yes_count);
384 sfree(sstate->dot_no_count);
385 sfree(sstate->face_yes_count);
386 sfree(sstate->face_no_count);
388 if (sstate->normal) {
389 sfree(sstate->normal->dlines);
390 sfree(sstate->normal);
394 sfree(sstate->hard->linedsf);
402 static solver_state *dup_solver_state(const solver_state *sstate) {
403 game_state *state = sstate->state;
404 int num_dots = state->game_grid->num_dots;
405 int num_faces = state->game_grid->num_faces;
406 int num_edges = state->game_grid->num_edges;
407 solver_state *ret = snew(solver_state);
409 ret->state = state = dup_game(sstate->state);
411 ret->solver_status = sstate->solver_status;
413 ret->dotdsf = snewn(num_dots, int);
414 ret->looplen = snewn(num_dots, int);
415 memcpy(ret->dotdsf, sstate->dotdsf,
416 num_dots * sizeof(int));
417 memcpy(ret->looplen, sstate->looplen,
418 num_dots * sizeof(int));
420 ret->dot_solved = snewn(num_dots, char);
421 ret->face_solved = snewn(num_faces, char);
422 memcpy(ret->dot_solved, sstate->dot_solved, num_dots);
423 memcpy(ret->face_solved, sstate->face_solved, num_faces);
425 ret->dot_yes_count = snewn(num_dots, char);
426 memcpy(ret->dot_yes_count, sstate->dot_yes_count, num_dots);
427 ret->dot_no_count = snewn(num_dots, char);
428 memcpy(ret->dot_no_count, sstate->dot_no_count, num_dots);
430 ret->face_yes_count = snewn(num_faces, char);
431 memcpy(ret->face_yes_count, sstate->face_yes_count, num_faces);
432 ret->face_no_count = snewn(num_faces, char);
433 memcpy(ret->face_no_count, sstate->face_no_count, num_faces);
435 if (sstate->normal) {
436 ret->normal = snew(normal_mode_state);
437 ret->normal->dlines = snewn(2*num_edges, char);
438 memcpy(ret->normal->dlines, sstate->normal->dlines,
445 ret->hard = snew(hard_mode_state);
446 ret->hard->linedsf = snewn(num_edges, int);
447 memcpy(ret->hard->linedsf, sstate->hard->linedsf,
448 num_edges * sizeof(int));
456 static game_params *default_params(void)
458 game_params *ret = snew(game_params);
467 ret->diff = DIFF_EASY;
470 ret->game_grid = NULL;
475 static game_params *dup_params(game_params *params)
477 game_params *ret = snew(game_params);
479 *ret = *params; /* structure copy */
480 if (ret->game_grid) {
481 ret->game_grid->refcount++;
486 static const game_params presets[] = {
488 { 7, 7, DIFF_EASY, 0, NULL },
489 { 7, 7, DIFF_NORMAL, 0, NULL },
490 { 7, 7, DIFF_HARD, 0, NULL },
491 { 7, 7, DIFF_HARD, 1, NULL },
492 { 7, 7, DIFF_HARD, 2, NULL },
493 { 5, 5, DIFF_HARD, 3, NULL },
494 { 7, 7, DIFF_HARD, 4, NULL },
495 { 5, 4, DIFF_HARD, 5, NULL },
496 { 5, 5, DIFF_HARD, 6, NULL },
497 { 5, 5, DIFF_HARD, 7, NULL },
499 { 7, 7, DIFF_EASY, 0, NULL },
500 { 10, 10, DIFF_EASY, 0, NULL },
501 { 7, 7, DIFF_NORMAL, 0, NULL },
502 { 10, 10, DIFF_NORMAL, 0, NULL },
503 { 7, 7, DIFF_HARD, 0, NULL },
504 { 10, 10, DIFF_HARD, 0, NULL },
505 { 10, 10, DIFF_HARD, 1, NULL },
506 { 12, 10, DIFF_HARD, 2, NULL },
507 { 7, 7, DIFF_HARD, 3, NULL },
508 { 9, 9, DIFF_HARD, 4, NULL },
509 { 5, 4, DIFF_HARD, 5, NULL },
510 { 7, 7, DIFF_HARD, 6, NULL },
511 { 5, 5, DIFF_HARD, 7, NULL },
515 static int game_fetch_preset(int i, char **name, game_params **params)
520 if (i < 0 || i >= lenof(presets))
523 tmppar = snew(game_params);
524 *tmppar = presets[i];
526 sprintf(buf, "%dx%d %s - %s", tmppar->h, tmppar->w,
527 gridnames[tmppar->type], diffnames[tmppar->diff]);
533 static void free_params(game_params *params)
535 if (params->game_grid) {
536 grid_free(params->game_grid);
541 static void decode_params(game_params *params, char const *string)
543 if (params->game_grid) {
544 grid_free(params->game_grid);
545 params->game_grid = NULL;
547 params->h = params->w = atoi(string);
548 params->diff = DIFF_EASY;
549 while (*string && isdigit((unsigned char)*string)) string++;
550 if (*string == 'x') {
552 params->h = atoi(string);
553 while (*string && isdigit((unsigned char)*string)) string++;
555 if (*string == 't') {
557 params->type = atoi(string);
558 while (*string && isdigit((unsigned char)*string)) string++;
560 if (*string == 'd') {
563 for (i = 0; i < DIFF_MAX; i++)
564 if (*string == diffchars[i])
566 if (*string) string++;
570 static char *encode_params(game_params *params, int full)
573 sprintf(str, "%dx%dt%d", params->w, params->h, params->type);
575 sprintf(str + strlen(str), "d%c", diffchars[params->diff]);
579 static config_item *game_configure(game_params *params)
584 ret = snewn(5, config_item);
586 ret[0].name = "Width";
587 ret[0].type = C_STRING;
588 sprintf(buf, "%d", params->w);
589 ret[0].sval = dupstr(buf);
592 ret[1].name = "Height";
593 ret[1].type = C_STRING;
594 sprintf(buf, "%d", params->h);
595 ret[1].sval = dupstr(buf);
598 ret[2].name = "Grid type";
599 ret[2].type = C_CHOICES;
600 ret[2].sval = GRID_CONFIGS;
601 ret[2].ival = params->type;
603 ret[3].name = "Difficulty";
604 ret[3].type = C_CHOICES;
605 ret[3].sval = DIFFCONFIG;
606 ret[3].ival = params->diff;
616 static game_params *custom_params(config_item *cfg)
618 game_params *ret = snew(game_params);
620 ret->w = atoi(cfg[0].sval);
621 ret->h = atoi(cfg[1].sval);
622 ret->type = cfg[2].ival;
623 ret->diff = cfg[3].ival;
625 ret->game_grid = NULL;
629 static char *validate_params(game_params *params, int full)
631 if (params->type < 0 || params->type >= NUM_GRID_TYPES)
632 return "Illegal grid type";
633 if (params->w < grid_size_limits[params->type].amin ||
634 params->h < grid_size_limits[params->type].amin)
635 return grid_size_limits[params->type].aerr;
636 if (params->w < grid_size_limits[params->type].omin &&
637 params->h < grid_size_limits[params->type].omin)
638 return grid_size_limits[params->type].oerr;
641 * This shouldn't be able to happen at all, since decode_params
642 * and custom_params will never generate anything that isn't
645 assert(params->diff < DIFF_MAX);
650 /* Returns a newly allocated string describing the current puzzle */
651 static char *state_to_text(const game_state *state)
653 grid *g = state->game_grid;
655 int num_faces = g->num_faces;
656 char *description = snewn(num_faces + 1, char);
657 char *dp = description;
661 for (i = 0; i < num_faces; i++) {
662 if (state->clues[i] < 0) {
663 if (empty_count > 25) {
664 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
670 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
673 dp += sprintf(dp, "%c", (int)CLUE2CHAR(state->clues[i]));
678 dp += sprintf(dp, "%c", (int)(empty_count + 'a' - 1));
680 retval = dupstr(description);
686 /* We require that the params pass the test in validate_params and that the
687 * description fills the entire game area */
688 static char *validate_desc(game_params *params, char *desc)
692 params_generate_grid(params);
693 g = params->game_grid;
695 for (; *desc; ++desc) {
696 if (*desc >= '0' && *desc <= '9') {
701 count += *desc - 'a' + 1;
704 return "Unknown character in description";
707 if (count < g->num_faces)
708 return "Description too short for board size";
709 if (count > g->num_faces)
710 return "Description too long for board size";
715 /* Sums the lengths of the numbers in range [0,n) */
716 /* See equivalent function in solo.c for justification of this. */
717 static int len_0_to_n(int n)
719 int len = 1; /* Counting 0 as a bit of a special case */
722 for (i = 1; i < n; i *= 10) {
723 len += max(n - i, 0);
729 static char *encode_solve_move(const game_state *state)
734 int num_edges = state->game_grid->num_edges;
736 /* This is going to return a string representing the moves needed to set
737 * every line in a grid to be the same as the ones in 'state'. The exact
738 * length of this string is predictable. */
740 len = 1; /* Count the 'S' prefix */
741 /* Numbers in all lines */
742 len += len_0_to_n(num_edges);
743 /* For each line we also have a letter */
746 ret = snewn(len + 1, char);
749 p += sprintf(p, "S");
751 for (i = 0; i < num_edges; i++) {
752 switch (state->lines[i]) {
754 p += sprintf(p, "%dy", i);
757 p += sprintf(p, "%dn", i);
762 /* No point in doing sums like that if they're going to be wrong */
763 assert(strlen(ret) <= (size_t)len);
767 static game_ui *new_ui(game_state *state)
772 static void free_ui(game_ui *ui)
776 static char *encode_ui(game_ui *ui)
781 static void decode_ui(game_ui *ui, char *encoding)
785 static void game_changed_state(game_ui *ui, game_state *oldstate,
786 game_state *newstate)
790 static void game_compute_size(game_params *params, int tilesize,
794 int grid_width, grid_height, rendered_width, rendered_height;
796 params_generate_grid(params);
797 g = params->game_grid;
798 grid_width = g->highest_x - g->lowest_x;
799 grid_height = g->highest_y - g->lowest_y;
800 /* multiply first to minimise rounding error on integer division */
801 rendered_width = grid_width * tilesize / g->tilesize;
802 rendered_height = grid_height * tilesize / g->tilesize;
803 *x = rendered_width + 2 * BORDER(tilesize) + 1;
804 *y = rendered_height + 2 * BORDER(tilesize) + 1;
807 static void game_set_size(drawing *dr, game_drawstate *ds,
808 game_params *params, int tilesize)
810 ds->tilesize = tilesize;
813 static float *game_colours(frontend *fe, int *ncolours)
815 float *ret = snewn(4 * NCOLOURS, float);
817 frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
819 ret[COL_FOREGROUND * 3 + 0] = 0.0F;
820 ret[COL_FOREGROUND * 3 + 1] = 0.0F;
821 ret[COL_FOREGROUND * 3 + 2] = 0.0F;
823 ret[COL_LINEUNKNOWN * 3 + 0] = 0.8F;
824 ret[COL_LINEUNKNOWN * 3 + 1] = 0.8F;
825 ret[COL_LINEUNKNOWN * 3 + 2] = 0.0F;
827 ret[COL_HIGHLIGHT * 3 + 0] = 1.0F;
828 ret[COL_HIGHLIGHT * 3 + 1] = 1.0F;
829 ret[COL_HIGHLIGHT * 3 + 2] = 1.0F;
831 ret[COL_MISTAKE * 3 + 0] = 1.0F;
832 ret[COL_MISTAKE * 3 + 1] = 0.0F;
833 ret[COL_MISTAKE * 3 + 2] = 0.0F;
835 ret[COL_SATISFIED * 3 + 0] = 0.0F;
836 ret[COL_SATISFIED * 3 + 1] = 0.0F;
837 ret[COL_SATISFIED * 3 + 2] = 0.0F;
839 *ncolours = NCOLOURS;
843 static game_drawstate *game_new_drawstate(drawing *dr, game_state *state)
845 struct game_drawstate *ds = snew(struct game_drawstate);
846 int num_faces = state->game_grid->num_faces;
847 int num_edges = state->game_grid->num_edges;
851 ds->lines = snewn(num_edges, char);
852 ds->clue_error = snewn(num_faces, char);
853 ds->clue_satisfied = snewn(num_faces, char);
856 memset(ds->lines, LINE_UNKNOWN, num_edges);
857 memset(ds->clue_error, 0, num_faces);
858 memset(ds->clue_satisfied, 0, num_faces);
863 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
865 sfree(ds->clue_error);
866 sfree(ds->clue_satisfied);
871 static int game_timing_state(game_state *state, game_ui *ui)
876 static float game_anim_length(game_state *oldstate, game_state *newstate,
877 int dir, game_ui *ui)
882 static int game_can_format_as_text_now(game_params *params)
884 if (params->type != 0)
889 static char *game_text_format(game_state *state)
895 grid *g = state->game_grid;
898 assert(state->grid_type == 0);
900 /* Work out the basic size unit */
901 f = g->faces; /* first face */
902 assert(f->order == 4);
903 /* The dots are ordered clockwise, so the two opposite
904 * corners are guaranteed to span the square */
905 cell_size = abs(f->dots[0]->x - f->dots[2]->x);
907 w = (g->highest_x - g->lowest_x) / cell_size;
908 h = (g->highest_y - g->lowest_y) / cell_size;
910 /* Create a blank "canvas" to "draw" on */
913 ret = snewn(W * H + 1, char);
914 for (y = 0; y < H; y++) {
915 for (x = 0; x < W-1; x++) {
918 ret[y*W + W-1] = '\n';
922 /* Fill in edge info */
923 for (i = 0; i < g->num_edges; i++) {
924 grid_edge *e = g->edges + i;
925 /* Cell coordinates, from (0,0) to (w-1,h-1) */
926 int x1 = (e->dot1->x - g->lowest_x) / cell_size;
927 int x2 = (e->dot2->x - g->lowest_x) / cell_size;
928 int y1 = (e->dot1->y - g->lowest_y) / cell_size;
929 int y2 = (e->dot2->y - g->lowest_y) / cell_size;
930 /* Midpoint, in canvas coordinates (canvas coordinates are just twice
931 * cell coordinates) */
934 switch (state->lines[i]) {
936 ret[y*W + x] = (y1 == y2) ? '-' : '|';
942 break; /* already a space */
944 assert(!"Illegal line state");
949 for (i = 0; i < g->num_faces; i++) {
953 assert(f->order == 4);
954 /* Cell coordinates, from (0,0) to (w-1,h-1) */
955 x1 = (f->dots[0]->x - g->lowest_x) / cell_size;
956 x2 = (f->dots[2]->x - g->lowest_x) / cell_size;
957 y1 = (f->dots[0]->y - g->lowest_y) / cell_size;
958 y2 = (f->dots[2]->y - g->lowest_y) / cell_size;
959 /* Midpoint, in canvas coordinates */
962 ret[y*W + x] = CLUE2CHAR(state->clues[i]);
967 /* ----------------------------------------------------------------------
972 static void check_caches(const solver_state* sstate)
975 const game_state *state = sstate->state;
976 const grid *g = state->game_grid;
978 for (i = 0; i < g->num_dots; i++) {
979 assert(dot_order(state, i, LINE_YES) == sstate->dot_yes_count[i]);
980 assert(dot_order(state, i, LINE_NO) == sstate->dot_no_count[i]);
983 for (i = 0; i < g->num_faces; i++) {
984 assert(face_order(state, i, LINE_YES) == sstate->face_yes_count[i]);
985 assert(face_order(state, i, LINE_NO) == sstate->face_no_count[i]);
990 #define check_caches(s) \
992 fprintf(stderr, "check_caches at line %d\n", __LINE__); \
996 #endif /* DEBUG_CACHES */
998 /* ----------------------------------------------------------------------
999 * Solver utility functions
1002 /* Sets the line (with index i) to the new state 'line_new', and updates
1003 * the cached counts of any affected faces and dots.
1004 * Returns TRUE if this actually changed the line's state. */
1005 static int solver_set_line(solver_state *sstate, int i,
1006 enum line_state line_new
1008 , const char *reason
1012 game_state *state = sstate->state;
1016 assert(line_new != LINE_UNKNOWN);
1018 check_caches(sstate);
1020 if (state->lines[i] == line_new) {
1021 return FALSE; /* nothing changed */
1023 state->lines[i] = line_new;
1026 fprintf(stderr, "solver: set line [%d] to %s (%s)\n",
1027 i, line_new == LINE_YES ? "YES" : "NO",
1031 g = state->game_grid;
1034 /* Update the cache for both dots and both faces affected by this. */
1035 if (line_new == LINE_YES) {
1036 sstate->dot_yes_count[e->dot1 - g->dots]++;
1037 sstate->dot_yes_count[e->dot2 - g->dots]++;
1039 sstate->face_yes_count[e->face1 - g->faces]++;
1042 sstate->face_yes_count[e->face2 - g->faces]++;
1045 sstate->dot_no_count[e->dot1 - g->dots]++;
1046 sstate->dot_no_count[e->dot2 - g->dots]++;
1048 sstate->face_no_count[e->face1 - g->faces]++;
1051 sstate->face_no_count[e->face2 - g->faces]++;
1055 check_caches(sstate);
1060 #define solver_set_line(a, b, c) \
1061 solver_set_line(a, b, c, __FUNCTION__)
1065 * Merge two dots due to the existence of an edge between them.
1066 * Updates the dsf tracking equivalence classes, and keeps track of
1067 * the length of path each dot is currently a part of.
1068 * Returns TRUE if the dots were already linked, ie if they are part of a
1069 * closed loop, and false otherwise.
1071 static int merge_dots(solver_state *sstate, int edge_index)
1074 grid *g = sstate->state->game_grid;
1075 grid_edge *e = g->edges + edge_index;
1077 i = e->dot1 - g->dots;
1078 j = e->dot2 - g->dots;
1080 i = dsf_canonify(sstate->dotdsf, i);
1081 j = dsf_canonify(sstate->dotdsf, j);
1086 len = sstate->looplen[i] + sstate->looplen[j];
1087 dsf_merge(sstate->dotdsf, i, j);
1088 i = dsf_canonify(sstate->dotdsf, i);
1089 sstate->looplen[i] = len;
1094 /* Merge two lines because the solver has deduced that they must be either
1095 * identical or opposite. Returns TRUE if this is new information, otherwise
1097 static int merge_lines(solver_state *sstate, int i, int j, int inverse
1099 , const char *reason
1105 assert(i < sstate->state->game_grid->num_edges);
1106 assert(j < sstate->state->game_grid->num_edges);
1108 i = edsf_canonify(sstate->hard->linedsf, i, &inv_tmp);
1110 j = edsf_canonify(sstate->hard->linedsf, j, &inv_tmp);
1113 edsf_merge(sstate->hard->linedsf, i, j, inverse);
1117 fprintf(stderr, "%s [%d] [%d] %s(%s)\n",
1119 inverse ? "inverse " : "", reason);
1126 #define merge_lines(a, b, c, d) \
1127 merge_lines(a, b, c, d, __FUNCTION__)
1130 /* Count the number of lines of a particular type currently going into the
1132 static int dot_order(const game_state* state, int dot, char line_type)
1135 grid *g = state->game_grid;
1136 grid_dot *d = g->dots + dot;
1139 for (i = 0; i < d->order; i++) {
1140 grid_edge *e = d->edges[i];
1141 if (state->lines[e - g->edges] == line_type)
1147 /* Count the number of lines of a particular type currently surrounding the
1149 static int face_order(const game_state* state, int face, char line_type)
1152 grid *g = state->game_grid;
1153 grid_face *f = g->faces + face;
1156 for (i = 0; i < f->order; i++) {
1157 grid_edge *e = f->edges[i];
1158 if (state->lines[e - g->edges] == line_type)
1164 /* Set all lines bordering a dot of type old_type to type new_type
1165 * Return value tells caller whether this function actually did anything */
1166 static int dot_setall(solver_state *sstate, int dot,
1167 char old_type, char new_type)
1169 int retval = FALSE, r;
1170 game_state *state = sstate->state;
1175 if (old_type == new_type)
1178 g = state->game_grid;
1181 for (i = 0; i < d->order; i++) {
1182 int line_index = d->edges[i] - g->edges;
1183 if (state->lines[line_index] == old_type) {
1184 r = solver_set_line(sstate, line_index, new_type);
1192 /* Set all lines bordering a face of type old_type to type new_type */
1193 static int face_setall(solver_state *sstate, int face,
1194 char old_type, char new_type)
1196 int retval = FALSE, r;
1197 game_state *state = sstate->state;
1202 if (old_type == new_type)
1205 g = state->game_grid;
1206 f = g->faces + face;
1208 for (i = 0; i < f->order; i++) {
1209 int line_index = f->edges[i] - g->edges;
1210 if (state->lines[line_index] == old_type) {
1211 r = solver_set_line(sstate, line_index, new_type);
1219 /* ----------------------------------------------------------------------
1220 * Loop generation and clue removal
1223 /* We're going to store lists of current candidate faces for colouring black
1225 * Each face gets a 'score', which tells us how adding that face right
1226 * now would affect the curliness of the solution loop. We're trying to
1227 * maximise that quantity so will bias our random selection of faces to
1228 * colour those with high scores */
1232 unsigned long random;
1233 /* No need to store a grid_face* here. The 'face_scores' array will
1234 * be a list of 'face_score' objects, one for each face of the grid, so
1235 * the position (index) within the 'face_scores' array will determine
1236 * which face corresponds to a particular face_score.
1237 * Having a single 'face_scores' array for all faces simplifies memory
1238 * management, and probably improves performance, because we don't have to
1239 * malloc/free each individual face_score, and we don't have to maintain
1240 * a mapping from grid_face* pointers to face_score* pointers.
1244 static int generic_sort_cmpfn(void *v1, void *v2, size_t offset)
1246 struct face_score *f1 = v1;
1247 struct face_score *f2 = v2;
1250 r = *(int *)((char *)f2 + offset) - *(int *)((char *)f1 + offset);
1255 if (f1->random < f2->random)
1257 else if (f1->random > f2->random)
1261 * It's _just_ possible that two faces might have been given
1262 * the same random value. In that situation, fall back to
1263 * comparing based on the positions within the face_scores list.
1264 * This introduces a tiny directional bias, but not a significant one.
1269 static int white_sort_cmpfn(void *v1, void *v2)
1271 return generic_sort_cmpfn(v1, v2, offsetof(struct face_score,white_score));
1274 static int black_sort_cmpfn(void *v1, void *v2)
1276 return generic_sort_cmpfn(v1, v2, offsetof(struct face_score,black_score));
1279 enum face_colour { FACE_WHITE, FACE_GREY, FACE_BLACK };
1281 /* face should be of type grid_face* here. */
1282 #define FACE_COLOUR(face) \
1283 ( (face) == NULL ? FACE_BLACK : \
1284 board[(face) - g->faces] )
1286 /* 'board' is an array of these enums, indicating which faces are
1287 * currently black/white/grey. 'colour' is FACE_WHITE or FACE_BLACK.
1288 * Returns whether it's legal to colour the given face with this colour. */
1289 static int can_colour_face(grid *g, char* board, int face_index,
1290 enum face_colour colour)
1293 grid_face *test_face = g->faces + face_index;
1294 grid_face *starting_face, *current_face;
1296 int current_state, s; /* booleans: equal or not-equal to 'colour' */
1297 int found_same_coloured_neighbour = FALSE;
1298 assert(board[face_index] != colour);
1300 /* Can only consider a face for colouring if it's adjacent to a face
1301 * with the same colour. */
1302 for (i = 0; i < test_face->order; i++) {
1303 grid_edge *e = test_face->edges[i];
1304 grid_face *f = (e->face1 == test_face) ? e->face2 : e->face1;
1305 if (FACE_COLOUR(f) == colour) {
1306 found_same_coloured_neighbour = TRUE;
1310 if (!found_same_coloured_neighbour)
1313 /* Need to avoid creating a loop of faces of this colour around some
1314 * differently-coloured faces.
1315 * Also need to avoid meeting a same-coloured face at a corner, with
1316 * other-coloured faces in between. Here's a simple test that (I believe)
1317 * takes care of both these conditions:
1319 * Take the circular path formed by this face's edges, and inflate it
1320 * slightly outwards. Imagine walking around this path and consider
1321 * the faces that you visit in sequence. This will include all faces
1322 * touching the given face, either along an edge or just at a corner.
1323 * Count the number of 'colour'/not-'colour' transitions you encounter, as
1324 * you walk along the complete loop. This will obviously turn out to be
1326 * If 0, we're either in the middle of an "island" of this colour (should
1327 * be impossible as we're not supposed to create black or white loops),
1328 * or we're about to start a new island - also not allowed.
1329 * If 4 or greater, there are too many separate coloured regions touching
1330 * this face, and colouring it would create a loop or a corner-violation.
1331 * The only allowed case is when the count is exactly 2. */
1333 /* i points to a dot around the test face.
1334 * j points to a face around the i^th dot.
1335 * The current face will always be:
1336 * test_face->dots[i]->faces[j]
1337 * We assume dots go clockwise around the test face,
1338 * and faces go clockwise around dots. */
1340 starting_face = test_face->dots[0]->faces[0];
1341 if (starting_face == test_face) {
1343 starting_face = test_face->dots[0]->faces[1];
1345 current_face = starting_face;
1347 current_state = (FACE_COLOUR(current_face) == colour);
1350 /* Advance to next face.
1351 * Need to loop here because it might take several goes to
1355 if (j == test_face->dots[i]->order)
1358 if (test_face->dots[i]->faces[j] == test_face) {
1359 /* Advance to next dot round test_face, then
1360 * find current_face around new dot
1361 * and advance to the next face clockwise */
1363 if (i == test_face->order)
1365 for (j = 0; j < test_face->dots[i]->order; j++) {
1366 if (test_face->dots[i]->faces[j] == current_face)
1369 /* Must actually find current_face around new dot,
1370 * or else something's wrong with the grid. */
1371 assert(j != test_face->dots[i]->order);
1372 /* Found, so advance to next face and try again */
1377 /* (i,j) are now advanced to next face */
1378 current_face = test_face->dots[i]->faces[j];
1379 s = (FACE_COLOUR(current_face) == colour);
1380 if (s != current_state) {
1383 if (transitions > 2)
1384 return FALSE; /* no point in continuing */
1386 } while (current_face != starting_face);
1388 return (transitions == 2) ? TRUE : FALSE;
1391 /* Count the number of neighbours of 'face', having colour 'colour' */
1392 static int face_num_neighbours(grid *g, char *board, grid_face *face,
1393 enum face_colour colour)
1395 int colour_count = 0;
1399 for (i = 0; i < face->order; i++) {
1401 f = (e->face1 == face) ? e->face2 : e->face1;
1402 if (FACE_COLOUR(f) == colour)
1405 return colour_count;
1408 /* The 'score' of a face reflects its current desirability for selection
1409 * as the next face to colour white or black. We want to encourage moving
1410 * into grey areas and increasing loopiness, so we give scores according to
1411 * how many of the face's neighbours are currently coloured the same as the
1412 * proposed colour. */
1413 static int face_score(grid *g, char *board, grid_face *face,
1414 enum face_colour colour)
1416 /* Simple formula: score = 0 - num. same-coloured neighbours,
1417 * so a higher score means fewer same-coloured neighbours. */
1418 return -face_num_neighbours(g, board, face, colour);
1421 /* Generate a new complete set of clues for the given game_state.
1422 * The method is to generate a WHITE/BLACK colouring of all the faces,
1423 * such that the WHITE faces will define the inside of the path, and the
1424 * BLACK faces define the outside.
1425 * To do this, we initially colour all faces GREY. The infinite space outside
1426 * the grid is coloured BLACK, and we choose a random face to colour WHITE.
1427 * Then we gradually grow the BLACK and the WHITE regions, eliminating GREY
1428 * faces, until the grid is filled with BLACK/WHITE. As we grow the regions,
1429 * we avoid creating loops of a single colour, to preserve the topological
1430 * shape of the WHITE and BLACK regions.
1431 * We also try to make the boundary as loopy and twisty as possible, to avoid
1432 * generating paths that are uninteresting.
1433 * The algorithm works by choosing a BLACK/WHITE colour, then choosing a GREY
1434 * face that can be coloured with that colour (without violating the
1435 * topological shape of that region). It's not obvious, but I think this
1436 * algorithm is guaranteed to terminate without leaving any GREY faces behind.
1437 * Indeed, if there are any GREY faces at all, both the WHITE and BLACK
1438 * regions can be grown.
1439 * This is checked using assert()ions, and I haven't seen any failures yet.
1441 * Hand-wavy proof: imagine what can go wrong...
1443 * Could the white faces get completely cut off by the black faces, and still
1444 * leave some grey faces remaining?
1445 * No, because then the black faces would form a loop around both the white
1446 * faces and the grey faces, which is disallowed because we continually
1447 * maintain the correct topological shape of the black region.
1448 * Similarly, the black faces can never get cut off by the white faces. That
1449 * means both the WHITE and BLACK regions always have some room to grow into
1451 * Could it be that we can't colour some GREY face, because there are too many
1452 * WHITE/BLACK transitions as we walk round the face? (see the
1453 * can_colour_face() function for details)
1454 * No. Imagine otherwise, and we see WHITE/BLACK/WHITE/BLACK as we walk
1455 * around the face. The two WHITE faces would be connected by a WHITE path,
1456 * and the BLACK faces would be connected by a BLACK path. These paths would
1457 * have to cross, which is impossible.
1458 * Another thing that could go wrong: perhaps we can't find any GREY face to
1459 * colour WHITE, because it would create a loop-violation or a corner-violation
1460 * with the other WHITE faces?
1461 * This is a little bit tricky to prove impossible. Imagine you have such a
1462 * GREY face (that is, if you coloured it WHITE, you would create a WHITE loop
1463 * or corner violation).
1464 * That would cut all the non-white area into two blobs. One of those blobs
1465 * must be free of BLACK faces (because the BLACK stuff is a connected blob).
1466 * So we have a connected GREY area, completely surrounded by WHITE
1467 * (including the GREY face we've tentatively coloured WHITE).
1468 * A well-known result in graph theory says that you can always find a GREY
1469 * face whose removal leaves the remaining GREY area connected. And it says
1470 * there are at least two such faces, so we can always choose the one that
1471 * isn't the "tentative" GREY face. Colouring that face WHITE leaves
1472 * everything nice and connected, including that "tentative" GREY face which
1473 * acts as a gateway to the rest of the non-WHITE grid.
1475 static void add_full_clues(game_state *state, random_state *rs)
1477 signed char *clues = state->clues;
1479 grid *g = state->game_grid;
1481 int num_faces = g->num_faces;
1482 struct face_score *face_scores; /* Array of face_score objects */
1483 struct face_score *fs; /* Points somewhere in the above list */
1484 struct grid_face *cur_face;
1485 tree234 *lightable_faces_sorted;
1486 tree234 *darkable_faces_sorted;
1490 board = snewn(num_faces, char);
1493 memset(board, FACE_GREY, num_faces);
1495 /* Create and initialise the list of face_scores */
1496 face_scores = snewn(num_faces, struct face_score);
1497 for (i = 0; i < num_faces; i++) {
1498 face_scores[i].random = random_bits(rs, 31);
1501 /* Colour a random, finite face white. The infinite face is implicitly
1502 * coloured black. Together, they will seed the random growth process
1503 * for the black and white areas. */
1504 i = random_upto(rs, num_faces);
1505 board[i] = FACE_WHITE;
1507 /* We need a way of favouring faces that will increase our loopiness.
1508 * We do this by maintaining a list of all candidate faces sorted by
1509 * their score and choose randomly from that with appropriate skew.
1510 * In order to avoid consistently biasing towards particular faces, we
1511 * need the sort order _within_ each group of scores to be completely
1512 * random. But it would be abusing the hospitality of the tree234 data
1513 * structure if our comparison function were nondeterministic :-). So with
1514 * each face we associate a random number that does not change during a
1515 * particular run of the generator, and use that as a secondary sort key.
1516 * Yes, this means we will be biased towards particular random faces in
1517 * any one run but that doesn't actually matter. */
1519 lightable_faces_sorted = newtree234(white_sort_cmpfn);
1520 darkable_faces_sorted = newtree234(black_sort_cmpfn);
1522 /* Initialise the lists of lightable and darkable faces. This is
1523 * slightly different from the code inside the while-loop, because we need
1524 * to check every face of the board (the grid structure does not keep a
1525 * list of the infinite face's neighbours). */
1526 for (i = 0; i < num_faces; i++) {
1527 grid_face *f = g->faces + i;
1528 struct face_score *fs = face_scores + i;
1529 if (board[i] != FACE_GREY) continue;
1530 /* We need the full colourability check here, it's not enough simply
1531 * to check neighbourhood. On some grids, a neighbour of the infinite
1532 * face is not necessarily darkable. */
1533 if (can_colour_face(g, board, i, FACE_BLACK)) {
1534 fs->black_score = face_score(g, board, f, FACE_BLACK);
1535 add234(darkable_faces_sorted, fs);
1537 if (can_colour_face(g, board, i, FACE_WHITE)) {
1538 fs->white_score = face_score(g, board, f, FACE_WHITE);
1539 add234(lightable_faces_sorted, fs);
1543 /* Colour faces one at a time until no more faces are colourable. */
1546 enum face_colour colour;
1547 struct face_score *fs_white, *fs_black;
1548 int c_lightable = count234(lightable_faces_sorted);
1549 int c_darkable = count234(darkable_faces_sorted);
1550 if (c_lightable == 0) {
1551 /* No more lightable faces. Because of how the algorithm
1552 * works, there should be no more darkable faces either. */
1553 assert(c_darkable == 0);
1557 fs_white = (struct face_score *)index234(lightable_faces_sorted, 0);
1558 fs_black = (struct face_score *)index234(darkable_faces_sorted, 0);
1560 /* Choose a colour, and colour the best available face
1561 * with that colour. */
1562 colour = random_upto(rs, 2) ? FACE_WHITE : FACE_BLACK;
1564 if (colour == FACE_WHITE)
1569 i = fs - face_scores;
1570 assert(board[i] == FACE_GREY);
1573 /* Remove this newly-coloured face from the lists. These lists should
1574 * only contain grey faces. */
1575 del234(lightable_faces_sorted, fs);
1576 del234(darkable_faces_sorted, fs);
1578 /* Remember which face we've just coloured */
1579 cur_face = g->faces + i;
1581 /* The face we've just coloured potentially affects the colourability
1582 * and the scores of any neighbouring faces (touching at a corner or
1583 * edge). So the search needs to be conducted around all faces
1584 * touching the one we've just lit. Iterate over its corners, then
1585 * over each corner's faces. For each such face, we remove it from
1586 * the lists, recalculate any scores, then add it back to the lists
1587 * (depending on whether it is lightable, darkable or both). */
1588 for (i = 0; i < cur_face->order; i++) {
1589 grid_dot *d = cur_face->dots[i];
1590 for (j = 0; j < d->order; j++) {
1591 grid_face *f = d->faces[j];
1592 int fi; /* face index of f */
1599 /* If the face is already coloured, it won't be on our
1600 * lightable/darkable lists anyway, so we can skip it without
1601 * bothering with the removal step. */
1602 if (FACE_COLOUR(f) != FACE_GREY) continue;
1604 /* Find the face index and face_score* corresponding to f */
1606 fs = face_scores + fi;
1608 /* Remove from lightable list if it's in there. We do this,
1609 * even if it is still lightable, because the score might
1610 * be different, and we need to remove-then-add to maintain
1611 * correct sort order. */
1612 del234(lightable_faces_sorted, fs);
1613 if (can_colour_face(g, board, fi, FACE_WHITE)) {
1614 fs->white_score = face_score(g, board, f, FACE_WHITE);
1615 add234(lightable_faces_sorted, fs);
1617 /* Do the same for darkable list. */
1618 del234(darkable_faces_sorted, fs);
1619 if (can_colour_face(g, board, fi, FACE_BLACK)) {
1620 fs->black_score = face_score(g, board, f, FACE_BLACK);
1621 add234(darkable_faces_sorted, fs);
1628 freetree234(lightable_faces_sorted);
1629 freetree234(darkable_faces_sorted);
1632 /* The next step requires a shuffled list of all faces */
1633 face_list = snewn(num_faces, int);
1634 for (i = 0; i < num_faces; ++i) {
1637 shuffle(face_list, num_faces, sizeof(int), rs);
1639 /* The above loop-generation algorithm can often leave large clumps
1640 * of faces of one colour. In extreme cases, the resulting path can be
1641 * degenerate and not very satisfying to solve.
1642 * This next step alleviates this problem:
1643 * Go through the shuffled list, and flip the colour of any face we can
1644 * legally flip, and which is adjacent to only one face of the opposite
1645 * colour - this tends to grow 'tendrils' into any clumps.
1646 * Repeat until we can find no more faces to flip. This will
1647 * eventually terminate, because each flip increases the loop's
1648 * perimeter, which cannot increase for ever.
1649 * The resulting path will have maximal loopiness (in the sense that it
1650 * cannot be improved "locally". Unfortunately, this allows a player to
1651 * make some illicit deductions. To combat this (and make the path more
1652 * interesting), we do one final pass making random flips. */
1654 /* Set to TRUE for final pass */
1655 do_random_pass = FALSE;
1658 /* Remember whether a flip occurred during this pass */
1659 int flipped = FALSE;
1661 for (i = 0; i < num_faces; ++i) {
1662 int j = face_list[i];
1663 enum face_colour opp =
1664 (board[j] == FACE_WHITE) ? FACE_BLACK : FACE_WHITE;
1665 if (can_colour_face(g, board, j, opp)) {
1666 grid_face *face = g->faces +j;
1667 if (do_random_pass) {
1668 /* final random pass */
1669 if (!random_upto(rs, 10))
1672 /* normal pass - flip when neighbour count is 1 */
1673 if (face_num_neighbours(g, board, face, opp) == 1) {
1681 if (do_random_pass) break;
1682 if (!flipped) do_random_pass = TRUE;
1687 /* Fill out all the clues by initialising to 0, then iterating over
1688 * all edges and incrementing each clue as we find edges that border
1689 * between BLACK/WHITE faces. While we're at it, we verify that the
1690 * algorithm does work, and there aren't any GREY faces still there. */
1691 memset(clues, 0, num_faces);
1692 for (i = 0; i < g->num_edges; i++) {
1693 grid_edge *e = g->edges + i;
1694 grid_face *f1 = e->face1;
1695 grid_face *f2 = e->face2;
1696 enum face_colour c1 = FACE_COLOUR(f1);
1697 enum face_colour c2 = FACE_COLOUR(f2);
1698 assert(c1 != FACE_GREY);
1699 assert(c2 != FACE_GREY);
1701 if (f1) clues[f1 - g->faces]++;
1702 if (f2) clues[f2 - g->faces]++;
1710 static int game_has_unique_soln(const game_state *state, int diff)
1713 solver_state *sstate_new;
1714 solver_state *sstate = new_solver_state((game_state *)state, diff);
1716 sstate_new = solve_game_rec(sstate, diff);
1718 assert(sstate_new->solver_status != SOLVER_MISTAKE);
1719 ret = (sstate_new->solver_status == SOLVER_SOLVED);
1721 free_solver_state(sstate_new);
1722 free_solver_state(sstate);
1728 /* Remove clues one at a time at random. */
1729 static game_state *remove_clues(game_state *state, random_state *rs,
1733 int num_faces = state->game_grid->num_faces;
1734 game_state *ret = dup_game(state), *saved_ret;
1737 /* We need to remove some clues. We'll do this by forming a list of all
1738 * available clues, shuffling it, then going along one at a
1739 * time clearing each clue in turn for which doing so doesn't render the
1740 * board unsolvable. */
1741 face_list = snewn(num_faces, int);
1742 for (n = 0; n < num_faces; ++n) {
1746 shuffle(face_list, num_faces, sizeof(int), rs);
1748 for (n = 0; n < num_faces; ++n) {
1749 saved_ret = dup_game(ret);
1750 ret->clues[face_list[n]] = -1;
1752 if (game_has_unique_soln(ret, diff)) {
1753 free_game(saved_ret);
1765 static char *new_game_desc(game_params *params, random_state *rs,
1766 char **aux, int interactive)
1768 /* solution and description both use run-length encoding in obvious ways */
1771 game_state *state = snew(game_state);
1772 game_state *state_new;
1773 params_generate_grid(params);
1774 state->game_grid = g = params->game_grid;
1776 state->clues = snewn(g->num_faces, signed char);
1777 state->lines = snewn(g->num_edges, char);
1778 state->line_errors = snewn(g->num_edges, unsigned char);
1780 state->grid_type = params->type;
1784 memset(state->lines, LINE_UNKNOWN, g->num_edges);
1785 memset(state->line_errors, 0, g->num_edges);
1787 state->solved = state->cheated = FALSE;
1789 /* Get a new random solvable board with all its clues filled in. Yes, this
1790 * can loop for ever if the params are suitably unfavourable, but
1791 * preventing games smaller than 4x4 seems to stop this happening */
1793 add_full_clues(state, rs);
1794 } while (!game_has_unique_soln(state, params->diff));
1796 state_new = remove_clues(state, rs, params->diff);
1801 if (params->diff > 0 && game_has_unique_soln(state, params->diff-1)) {
1803 fprintf(stderr, "Rejecting board, it is too easy\n");
1805 goto newboard_please;
1808 retval = state_to_text(state);
1812 assert(!validate_desc(params, retval));
1817 static game_state *new_game(midend *me, game_params *params, char *desc)
1820 game_state *state = snew(game_state);
1821 int empties_to_make = 0;
1823 const char *dp = desc;
1825 int num_faces, num_edges;
1827 params_generate_grid(params);
1828 state->game_grid = g = params->game_grid;
1830 num_faces = g->num_faces;
1831 num_edges = g->num_edges;
1833 state->clues = snewn(num_faces, signed char);
1834 state->lines = snewn(num_edges, char);
1835 state->line_errors = snewn(num_edges, unsigned char);
1837 state->solved = state->cheated = FALSE;
1839 state->grid_type = params->type;
1841 for (i = 0; i < num_faces; i++) {
1842 if (empties_to_make) {
1844 state->clues[i] = -1;
1850 if (n >= 0 && n < 10) {
1851 state->clues[i] = n;
1855 state->clues[i] = -1;
1856 empties_to_make = n - 1;
1861 memset(state->lines, LINE_UNKNOWN, num_edges);
1862 memset(state->line_errors, 0, num_edges);
1866 /* Calculates the line_errors data, and checks if the current state is a
1868 static int check_completion(game_state *state)
1870 grid *g = state->game_grid;
1872 int num_faces = g->num_faces;
1874 int infinite_area, finite_area;
1875 int loops_found = 0;
1876 int found_edge_not_in_loop = FALSE;
1878 memset(state->line_errors, 0, g->num_edges);
1880 /* LL implementation of SGT's idea:
1881 * A loop will partition the grid into an inside and an outside.
1882 * If there is more than one loop, the grid will be partitioned into
1883 * even more distinct regions. We can therefore track equivalence of
1884 * faces, by saying that two faces are equivalent when there is a non-YES
1885 * edge between them.
1886 * We could keep track of the number of connected components, by counting
1887 * the number of dsf-merges that aren't no-ops.
1888 * But we're only interested in 3 separate cases:
1889 * no loops, one loop, more than one loop.
1891 * No loops: all faces are equivalent to the infinite face.
1892 * One loop: only two equivalence classes - finite and infinite.
1893 * >= 2 loops: there are 2 distinct finite regions.
1895 * So we simply make two passes through all the edges.
1896 * In the first pass, we dsf-merge the two faces bordering each non-YES
1898 * In the second pass, we look for YES-edges bordering:
1899 * a) two non-equivalent faces.
1900 * b) two non-equivalent faces, and one of them is part of a different
1901 * finite area from the first finite area we've seen.
1903 * An occurrence of a) means there is at least one loop.
1904 * An occurrence of b) means there is more than one loop.
1905 * Edges satisfying a) are marked as errors.
1907 * While we're at it, we set a flag if we find a YES edge that is not
1909 * This information will help decide, if there's a single loop, whether it
1910 * is a candidate for being a solution (that is, all YES edges are part of
1913 * If there is a candidate loop, we then go through all clues and check
1914 * they are all satisfied. If so, we have found a solution and we can
1915 * unmark all line_errors.
1918 /* Infinite face is at the end - its index is num_faces.
1919 * This macro is just to make this obvious! */
1920 #define INF_FACE num_faces
1921 dsf = snewn(num_faces + 1, int);
1922 dsf_init(dsf, num_faces + 1);
1925 for (i = 0; i < g->num_edges; i++) {
1926 grid_edge *e = g->edges + i;
1927 int f1 = e->face1 ? e->face1 - g->faces : INF_FACE;
1928 int f2 = e->face2 ? e->face2 - g->faces : INF_FACE;
1929 if (state->lines[i] != LINE_YES)
1930 dsf_merge(dsf, f1, f2);
1934 infinite_area = dsf_canonify(dsf, INF_FACE);
1936 for (i = 0; i < g->num_edges; i++) {
1937 grid_edge *e = g->edges + i;
1938 int f1 = e->face1 ? e->face1 - g->faces : INF_FACE;
1939 int can1 = dsf_canonify(dsf, f1);
1940 int f2 = e->face2 ? e->face2 - g->faces : INF_FACE;
1941 int can2 = dsf_canonify(dsf, f2);
1942 if (state->lines[i] != LINE_YES) continue;
1945 /* Faces are equivalent, so this edge not part of a loop */
1946 found_edge_not_in_loop = TRUE;
1949 state->line_errors[i] = TRUE;
1950 if (loops_found == 0) loops_found = 1;
1952 /* Don't bother with further checks if we've already found 2 loops */
1953 if (loops_found == 2) continue;
1955 if (finite_area == -1) {
1956 /* Found our first finite area */
1957 if (can1 != infinite_area)
1963 /* Have we found a second area? */
1964 if (finite_area != -1) {
1965 if (can1 != infinite_area && can1 != finite_area) {
1969 if (can2 != infinite_area && can2 != finite_area) {
1976 printf("loops_found = %d\n", loops_found);
1977 printf("found_edge_not_in_loop = %s\n",
1978 found_edge_not_in_loop ? "TRUE" : "FALSE");
1981 sfree(dsf); /* No longer need the dsf */
1983 /* Have we found a candidate loop? */
1984 if (loops_found == 1 && !found_edge_not_in_loop) {
1985 /* Yes, so check all clues are satisfied */
1986 int found_clue_violation = FALSE;
1987 for (i = 0; i < num_faces; i++) {
1988 int c = state->clues[i];
1990 if (face_order(state, i, LINE_YES) != c) {
1991 found_clue_violation = TRUE;
1997 if (!found_clue_violation) {
1998 /* The loop is good */
1999 memset(state->line_errors, 0, g->num_edges);
2000 return TRUE; /* No need to bother checking for dot violations */
2004 /* Check for dot violations */
2005 for (i = 0; i < g->num_dots; i++) {
2006 int yes = dot_order(state, i, LINE_YES);
2007 int unknown = dot_order(state, i, LINE_UNKNOWN);
2008 if ((yes == 1 && unknown == 0) || (yes >= 3)) {
2009 /* violation, so mark all YES edges as errors */
2010 grid_dot *d = g->dots + i;
2012 for (j = 0; j < d->order; j++) {
2013 int e = d->edges[j] - g->edges;
2014 if (state->lines[e] == LINE_YES)
2015 state->line_errors[e] = TRUE;
2022 /* ----------------------------------------------------------------------
2025 * Our solver modes operate as follows. Each mode also uses the modes above it.
2028 * Just implement the rules of the game.
2031 * For each (adjacent) pair of lines through each dot we store a bit for
2032 * whether at least one of them is on and whether at most one is on. (If we
2033 * know both or neither is on that's already stored more directly.)
2036 * Use edsf data structure to make equivalence classes of lines that are
2037 * known identical to or opposite to one another.
2042 * For general grids, we consider "dlines" to be pairs of lines joined
2043 * at a dot. The lines must be adjacent around the dot, so we can think of
2044 * a dline as being a dot+face combination. Or, a dot+edge combination where
2045 * the second edge is taken to be the next clockwise edge from the dot.
2046 * Original loopy code didn't have this extra restriction of the lines being
2047 * adjacent. From my tests with square grids, this extra restriction seems to
2048 * take little, if anything, away from the quality of the puzzles.
2049 * A dline can be uniquely identified by an edge/dot combination, given that
2050 * a dline-pair always goes clockwise around its common dot. The edge/dot
2051 * combination can be represented by an edge/bool combination - if bool is
2052 * TRUE, use edge->dot1 else use edge->dot2. So the total number of dlines is
2053 * exactly twice the number of edges in the grid - although the dlines
2054 * spanning the infinite face are not all that useful to the solver.
2055 * Note that, by convention, a dline goes clockwise around its common dot,
2056 * which means the dline goes anti-clockwise around its common face.
2059 /* Helper functions for obtaining an index into an array of dlines, given
2060 * various information. We assume the grid layout conventions about how
2061 * the various lists are interleaved - see grid_make_consistent() for
2064 /* i points to the first edge of the dline pair, reading clockwise around
2066 static int dline_index_from_dot(grid *g, grid_dot *d, int i)
2068 grid_edge *e = d->edges[i];
2073 if (i2 == d->order) i2 = 0;
2076 ret = 2 * (e - g->edges) + ((e->dot1 == d) ? 1 : 0);
2078 printf("dline_index_from_dot: d=%d,i=%d, edges [%d,%d] - %d\n",
2079 (int)(d - g->dots), i, (int)(e - g->edges),
2080 (int)(e2 - g->edges), ret);
2084 /* i points to the second edge of the dline pair, reading clockwise around
2085 * the face. That is, the edges of the dline, starting at edge{i}, read
2086 * anti-clockwise around the face. By layout conventions, the common dot
2087 * of the dline will be f->dots[i] */
2088 static int dline_index_from_face(grid *g, grid_face *f, int i)
2090 grid_edge *e = f->edges[i];
2091 grid_dot *d = f->dots[i];
2096 if (i2 < 0) i2 += f->order;
2099 ret = 2 * (e - g->edges) + ((e->dot1 == d) ? 1 : 0);
2101 printf("dline_index_from_face: f=%d,i=%d, edges [%d,%d] - %d\n",
2102 (int)(f - g->faces), i, (int)(e - g->edges),
2103 (int)(e2 - g->edges), ret);
2107 static int is_atleastone(const char *dline_array, int index)
2109 return BIT_SET(dline_array[index], 0);
2111 static int set_atleastone(char *dline_array, int index)
2113 return SET_BIT(dline_array[index], 0);
2115 static int is_atmostone(const char *dline_array, int index)
2117 return BIT_SET(dline_array[index], 1);
2119 static int set_atmostone(char *dline_array, int index)
2121 return SET_BIT(dline_array[index], 1);
2124 static void array_setall(char *array, char from, char to, int len)
2126 char *p = array, *p_old = p;
2127 int len_remaining = len;
2129 while ((p = memchr(p, from, len_remaining))) {
2131 len_remaining -= p - p_old;
2136 /* Helper, called when doing dline dot deductions, in the case where we
2137 * have 4 UNKNOWNs, and two of them (adjacent) have *exactly* one YES between
2138 * them (because of dline atmostone/atleastone).
2139 * On entry, edge points to the first of these two UNKNOWNs. This function
2140 * will find the opposite UNKNOWNS (if they are adjacent to one another)
2141 * and set their corresponding dline to atleastone. (Setting atmostone
2142 * already happens in earlier dline deductions) */
2143 static int dline_set_opp_atleastone(solver_state *sstate,
2144 grid_dot *d, int edge)
2146 game_state *state = sstate->state;
2147 grid *g = state->game_grid;
2150 for (opp = 0; opp < N; opp++) {
2151 int opp_dline_index;
2152 if (opp == edge || opp == edge+1 || opp == edge-1)
2154 if (opp == 0 && edge == N-1)
2156 if (opp == N-1 && edge == 0)
2159 if (opp2 == N) opp2 = 0;
2160 /* Check if opp, opp2 point to LINE_UNKNOWNs */
2161 if (state->lines[d->edges[opp] - g->edges] != LINE_UNKNOWN)
2163 if (state->lines[d->edges[opp2] - g->edges] != LINE_UNKNOWN)
2165 /* Found opposite UNKNOWNS and they're next to each other */
2166 opp_dline_index = dline_index_from_dot(g, d, opp);
2167 return set_atleastone(sstate->normal->dlines, opp_dline_index);
2173 /* Set pairs of lines around this face which are known to be identical, to
2174 * the given line_state */
2175 static int face_setall_identical(solver_state *sstate, int face_index,
2176 enum line_state line_new)
2178 /* can[dir] contains the canonical line associated with the line in
2179 * direction dir from the square in question. Similarly inv[dir] is
2180 * whether or not the line in question is inverse to its canonical
2183 game_state *state = sstate->state;
2184 grid *g = state->game_grid;
2185 grid_face *f = g->faces + face_index;
2188 int can1, can2, inv1, inv2;
2190 for (i = 0; i < N; i++) {
2191 int line1_index = f->edges[i] - g->edges;
2192 if (state->lines[line1_index] != LINE_UNKNOWN)
2194 for (j = i + 1; j < N; j++) {
2195 int line2_index = f->edges[j] - g->edges;
2196 if (state->lines[line2_index] != LINE_UNKNOWN)
2199 /* Found two UNKNOWNS */
2200 can1 = edsf_canonify(sstate->hard->linedsf, line1_index, &inv1);
2201 can2 = edsf_canonify(sstate->hard->linedsf, line2_index, &inv2);
2202 if (can1 == can2 && inv1 == inv2) {
2203 solver_set_line(sstate, line1_index, line_new);
2204 solver_set_line(sstate, line2_index, line_new);
2211 /* Given a dot or face, and a count of LINE_UNKNOWNs, find them and
2212 * return the edge indices into e. */
2213 static void find_unknowns(game_state *state,
2214 grid_edge **edge_list, /* Edge list to search (from a face or a dot) */
2215 int expected_count, /* Number of UNKNOWNs (comes from solver's cache) */
2216 int *e /* Returned edge indices */)
2219 grid *g = state->game_grid;
2220 while (c < expected_count) {
2221 int line_index = *edge_list - g->edges;
2222 if (state->lines[line_index] == LINE_UNKNOWN) {
2230 /* If we have a list of edges, and we know whether the number of YESs should
2231 * be odd or even, and there are only a few UNKNOWNs, we can do some simple
2232 * linedsf deductions. This can be used for both face and dot deductions.
2233 * Returns the difficulty level of the next solver that should be used,
2234 * or DIFF_MAX if no progress was made. */
2235 static int parity_deductions(solver_state *sstate,
2236 grid_edge **edge_list, /* Edge list (from a face or a dot) */
2237 int total_parity, /* Expected number of YESs modulo 2 (either 0 or 1) */
2240 game_state *state = sstate->state;
2241 int diff = DIFF_MAX;
2242 int *linedsf = sstate->hard->linedsf;
2244 if (unknown_count == 2) {
2245 /* Lines are known alike/opposite, depending on inv. */
2247 find_unknowns(state, edge_list, 2, e);
2248 if (merge_lines(sstate, e[0], e[1], total_parity))
2249 diff = min(diff, DIFF_HARD);
2250 } else if (unknown_count == 3) {
2252 int can[3]; /* canonical edges */
2253 int inv[3]; /* whether can[x] is inverse to e[x] */
2254 find_unknowns(state, edge_list, 3, e);
2255 can[0] = edsf_canonify(linedsf, e[0], inv);
2256 can[1] = edsf_canonify(linedsf, e[1], inv+1);
2257 can[2] = edsf_canonify(linedsf, e[2], inv+2);
2258 if (can[0] == can[1]) {
2259 if (solver_set_line(sstate, e[2], (total_parity^inv[0]^inv[1]) ?
2260 LINE_YES : LINE_NO))
2261 diff = min(diff, DIFF_EASY);
2263 if (can[0] == can[2]) {
2264 if (solver_set_line(sstate, e[1], (total_parity^inv[0]^inv[2]) ?
2265 LINE_YES : LINE_NO))
2266 diff = min(diff, DIFF_EASY);
2268 if (can[1] == can[2]) {
2269 if (solver_set_line(sstate, e[0], (total_parity^inv[1]^inv[2]) ?
2270 LINE_YES : LINE_NO))
2271 diff = min(diff, DIFF_EASY);
2273 } else if (unknown_count == 4) {
2275 int can[4]; /* canonical edges */
2276 int inv[4]; /* whether can[x] is inverse to e[x] */
2277 find_unknowns(state, edge_list, 4, e);
2278 can[0] = edsf_canonify(linedsf, e[0], inv);
2279 can[1] = edsf_canonify(linedsf, e[1], inv+1);
2280 can[2] = edsf_canonify(linedsf, e[2], inv+2);
2281 can[3] = edsf_canonify(linedsf, e[3], inv+3);
2282 if (can[0] == can[1]) {
2283 if (merge_lines(sstate, e[2], e[3], total_parity^inv[0]^inv[1]))
2284 diff = min(diff, DIFF_HARD);
2285 } else if (can[0] == can[2]) {
2286 if (merge_lines(sstate, e[1], e[3], total_parity^inv[0]^inv[2]))
2287 diff = min(diff, DIFF_HARD);
2288 } else if (can[0] == can[3]) {
2289 if (merge_lines(sstate, e[1], e[2], total_parity^inv[0]^inv[3]))
2290 diff = min(diff, DIFF_HARD);
2291 } else if (can[1] == can[2]) {
2292 if (merge_lines(sstate, e[0], e[3], total_parity^inv[1]^inv[2]))
2293 diff = min(diff, DIFF_HARD);
2294 } else if (can[1] == can[3]) {
2295 if (merge_lines(sstate, e[0], e[2], total_parity^inv[1]^inv[3]))
2296 diff = min(diff, DIFF_HARD);
2297 } else if (can[2] == can[3]) {
2298 if (merge_lines(sstate, e[0], e[1], total_parity^inv[2]^inv[3]))
2299 diff = min(diff, DIFF_HARD);
2307 * These are the main solver functions.
2309 * Their return values are diff values corresponding to the lowest mode solver
2310 * that would notice the work that they have done. For example if the normal
2311 * mode solver adds actual lines or crosses, it will return DIFF_EASY as the
2312 * easy mode solver might be able to make progress using that. It doesn't make
2313 * sense for one of them to return a diff value higher than that of the
2316 * Each function returns the lowest value it can, as early as possible, in
2317 * order to try and pass as much work as possible back to the lower level
2318 * solvers which progress more quickly.
2321 /* PROPOSED NEW DESIGN:
2322 * We have a work queue consisting of 'events' notifying us that something has
2323 * happened that a particular solver mode might be interested in. For example
2324 * the hard mode solver might do something that helps the normal mode solver at
2325 * dot [x,y] in which case it will enqueue an event recording this fact. Then
2326 * we pull events off the work queue, and hand each in turn to the solver that
2327 * is interested in them. If a solver reports that it failed we pass the same
2328 * event on to progressively more advanced solvers and the loop detector. Once
2329 * we've exhausted an event, or it has helped us progress, we drop it and
2330 * continue to the next one. The events are sorted first in order of solver
2331 * complexity (easy first) then order of insertion (oldest first).
2332 * Once we run out of events we loop over each permitted solver in turn
2333 * (easiest first) until either a deduction is made (and an event therefore
2334 * emerges) or no further deductions can be made (in which case we've failed).
2337 * * How do we 'loop over' a solver when both dots and squares are concerned.
2338 * Answer: first all squares then all dots.
2341 static int easy_mode_deductions(solver_state *sstate)
2343 int i, current_yes, current_no;
2344 game_state *state = sstate->state;
2345 grid *g = state->game_grid;
2346 int diff = DIFF_MAX;
2348 /* Per-face deductions */
2349 for (i = 0; i < g->num_faces; i++) {
2350 grid_face *f = g->faces + i;
2352 if (sstate->face_solved[i])
2355 current_yes = sstate->face_yes_count[i];
2356 current_no = sstate->face_no_count[i];
2358 if (current_yes + current_no == f->order) {
2359 sstate->face_solved[i] = TRUE;
2363 if (state->clues[i] < 0)
2366 if (state->clues[i] < current_yes) {
2367 sstate->solver_status = SOLVER_MISTAKE;
2370 if (state->clues[i] == current_yes) {
2371 if (face_setall(sstate, i, LINE_UNKNOWN, LINE_NO))
2372 diff = min(diff, DIFF_EASY);
2373 sstate->face_solved[i] = TRUE;
2377 if (f->order - state->clues[i] < current_no) {
2378 sstate->solver_status = SOLVER_MISTAKE;
2381 if (f->order - state->clues[i] == current_no) {
2382 if (face_setall(sstate, i, LINE_UNKNOWN, LINE_YES))
2383 diff = min(diff, DIFF_EASY);
2384 sstate->face_solved[i] = TRUE;
2389 check_caches(sstate);
2391 /* Per-dot deductions */
2392 for (i = 0; i < g->num_dots; i++) {
2393 grid_dot *d = g->dots + i;
2394 int yes, no, unknown;
2396 if (sstate->dot_solved[i])
2399 yes = sstate->dot_yes_count[i];
2400 no = sstate->dot_no_count[i];
2401 unknown = d->order - yes - no;
2405 sstate->dot_solved[i] = TRUE;
2406 } else if (unknown == 1) {
2407 dot_setall(sstate, i, LINE_UNKNOWN, LINE_NO);
2408 diff = min(diff, DIFF_EASY);
2409 sstate->dot_solved[i] = TRUE;
2411 } else if (yes == 1) {
2413 sstate->solver_status = SOLVER_MISTAKE;
2415 } else if (unknown == 1) {
2416 dot_setall(sstate, i, LINE_UNKNOWN, LINE_YES);
2417 diff = min(diff, DIFF_EASY);
2419 } else if (yes == 2) {
2421 dot_setall(sstate, i, LINE_UNKNOWN, LINE_NO);
2422 diff = min(diff, DIFF_EASY);
2424 sstate->dot_solved[i] = TRUE;
2426 sstate->solver_status = SOLVER_MISTAKE;
2431 check_caches(sstate);
2436 static int normal_mode_deductions(solver_state *sstate)
2438 game_state *state = sstate->state;
2439 grid *g = state->game_grid;
2440 char *dlines = sstate->normal->dlines;
2442 int diff = DIFF_MAX;
2444 /* ------ Face deductions ------ */
2446 /* Given a set of dline atmostone/atleastone constraints, need to figure
2447 * out if we can deduce any further info. For more general faces than
2448 * squares, this turns out to be a tricky problem.
2449 * The approach taken here is to define (per face) NxN matrices:
2450 * "maxs" and "mins".
2451 * The entries maxs(j,k) and mins(j,k) define the upper and lower limits
2452 * for the possible number of edges that are YES between positions j and k
2453 * going clockwise around the face. Can think of j and k as marking dots
2454 * around the face (recall the labelling scheme: edge0 joins dot0 to dot1,
2455 * edge1 joins dot1 to dot2 etc).
2456 * Trivially, mins(j,j) = maxs(j,j) = 0, and we don't even bother storing
2457 * these. mins(j,j+1) and maxs(j,j+1) are determined by whether edge{j}
2458 * is YES, NO or UNKNOWN. mins(j,j+2) and maxs(j,j+2) are related to
2459 * the dline atmostone/atleastone status for edges j and j+1.
2461 * Then we calculate the remaining entries recursively. We definitely
2463 * mins(j,k) >= { mins(j,u) + mins(u,k) } for any u between j and k.
2464 * This is because any valid placement of YESs between j and k must give
2465 * a valid placement between j and u, and also between u and k.
2466 * I believe it's sufficient to use just the two values of u:
2467 * j+1 and j+2. Seems to work well in practice - the bounds we compute
2468 * are rigorous, even if they might not be best-possible.
2470 * Once we have maxs and mins calculated, we can make inferences about
2471 * each dline{j,j+1} by looking at the possible complementary edge-counts
2472 * mins(j+2,j) and maxs(j+2,j) and comparing these with the face clue.
2473 * As well as dlines, we can make similar inferences about single edges.
2474 * For example, consider a pentagon with clue 3, and we know at most one
2475 * of (edge0, edge1) is YES, and at most one of (edge2, edge3) is YES.
2476 * We could then deduce edge4 is YES, because maxs(0,4) would be 2, so
2477 * that final edge would have to be YES to make the count up to 3.
2480 /* Much quicker to allocate arrays on the stack than the heap, so
2481 * define the largest possible face size, and base our array allocations
2482 * on that. We check this with an assertion, in case someone decides to
2483 * make a grid which has larger faces than this. Note, this algorithm
2484 * could get quite expensive if there are many large faces. */
2485 #define MAX_FACE_SIZE 8
2487 for (i = 0; i < g->num_faces; i++) {
2488 int maxs[MAX_FACE_SIZE][MAX_FACE_SIZE];
2489 int mins[MAX_FACE_SIZE][MAX_FACE_SIZE];
2490 grid_face *f = g->faces + i;
2493 int clue = state->clues[i];
2494 assert(N <= MAX_FACE_SIZE);
2495 if (sstate->face_solved[i])
2497 if (clue < 0) continue;
2499 /* Calculate the (j,j+1) entries */
2500 for (j = 0; j < N; j++) {
2501 int edge_index = f->edges[j] - g->edges;
2503 enum line_state line1 = state->lines[edge_index];
2504 enum line_state line2;
2508 maxs[j][k] = (line1 == LINE_NO) ? 0 : 1;
2509 mins[j][k] = (line1 == LINE_YES) ? 1 : 0;
2510 /* Calculate the (j,j+2) entries */
2511 dline_index = dline_index_from_face(g, f, k);
2512 edge_index = f->edges[k] - g->edges;
2513 line2 = state->lines[edge_index];
2519 if (line1 == LINE_NO) tmp--;
2520 if (line2 == LINE_NO) tmp--;
2521 if (tmp == 2 && is_atmostone(dlines, dline_index))
2527 if (line1 == LINE_YES) tmp++;
2528 if (line2 == LINE_YES) tmp++;
2529 if (tmp == 0 && is_atleastone(dlines, dline_index))
2534 /* Calculate the (j,j+m) entries for m between 3 and N-1 */
2535 for (m = 3; m < N; m++) {
2536 for (j = 0; j < N; j++) {
2544 maxs[j][k] = maxs[j][u] + maxs[u][k];
2545 mins[j][k] = mins[j][u] + mins[u][k];
2546 tmp = maxs[j][v] + maxs[v][k];
2547 maxs[j][k] = min(maxs[j][k], tmp);
2548 tmp = mins[j][v] + mins[v][k];
2549 mins[j][k] = max(mins[j][k], tmp);
2553 /* See if we can make any deductions */
2554 for (j = 0; j < N; j++) {
2556 grid_edge *e = f->edges[j];
2557 int line_index = e - g->edges;
2560 if (state->lines[line_index] != LINE_UNKNOWN)
2565 /* minimum YESs in the complement of this edge */
2566 if (mins[k][j] > clue) {
2567 sstate->solver_status = SOLVER_MISTAKE;
2570 if (mins[k][j] == clue) {
2571 /* setting this edge to YES would make at least
2572 * (clue+1) edges - contradiction */
2573 solver_set_line(sstate, line_index, LINE_NO);
2574 diff = min(diff, DIFF_EASY);
2576 if (maxs[k][j] < clue - 1) {
2577 sstate->solver_status = SOLVER_MISTAKE;
2580 if (maxs[k][j] == clue - 1) {
2581 /* Only way to satisfy the clue is to set edge{j} as YES */
2582 solver_set_line(sstate, line_index, LINE_YES);
2583 diff = min(diff, DIFF_EASY);
2586 /* Now see if we can make dline deduction for edges{j,j+1} */
2588 if (state->lines[e - g->edges] != LINE_UNKNOWN)
2589 /* Only worth doing this for an UNKNOWN,UNKNOWN pair.
2590 * Dlines where one of the edges is known, are handled in the
2594 dline_index = dline_index_from_face(g, f, k);
2598 /* minimum YESs in the complement of this dline */
2599 if (mins[k][j] > clue - 2) {
2600 /* Adding 2 YESs would break the clue */
2601 if (set_atmostone(dlines, dline_index))
2602 diff = min(diff, DIFF_NORMAL);
2604 /* maximum YESs in the complement of this dline */
2605 if (maxs[k][j] < clue) {
2606 /* Adding 2 NOs would mean not enough YESs */
2607 if (set_atleastone(dlines, dline_index))
2608 diff = min(diff, DIFF_NORMAL);
2613 if (diff < DIFF_NORMAL)
2616 /* ------ Dot deductions ------ */
2618 for (i = 0; i < g->num_dots; i++) {
2619 grid_dot *d = g->dots + i;
2621 int yes, no, unknown;
2623 if (sstate->dot_solved[i])
2625 yes = sstate->dot_yes_count[i];
2626 no = sstate->dot_no_count[i];
2627 unknown = N - yes - no;
2629 for (j = 0; j < N; j++) {
2632 int line1_index, line2_index;
2633 enum line_state line1, line2;
2636 dline_index = dline_index_from_dot(g, d, j);
2637 line1_index = d->edges[j] - g->edges;
2638 line2_index = d->edges[k] - g->edges;
2639 line1 = state->lines[line1_index];
2640 line2 = state->lines[line2_index];
2642 /* Infer dline state from line state */
2643 if (line1 == LINE_NO || line2 == LINE_NO) {
2644 if (set_atmostone(dlines, dline_index))
2645 diff = min(diff, DIFF_NORMAL);
2647 if (line1 == LINE_YES || line2 == LINE_YES) {
2648 if (set_atleastone(dlines, dline_index))
2649 diff = min(diff, DIFF_NORMAL);
2651 /* Infer line state from dline state */
2652 if (is_atmostone(dlines, dline_index)) {
2653 if (line1 == LINE_YES && line2 == LINE_UNKNOWN) {
2654 solver_set_line(sstate, line2_index, LINE_NO);
2655 diff = min(diff, DIFF_EASY);
2657 if (line2 == LINE_YES && line1 == LINE_UNKNOWN) {
2658 solver_set_line(sstate, line1_index, LINE_NO);
2659 diff = min(diff, DIFF_EASY);
2662 if (is_atleastone(dlines, dline_index)) {
2663 if (line1 == LINE_NO && line2 == LINE_UNKNOWN) {
2664 solver_set_line(sstate, line2_index, LINE_YES);
2665 diff = min(diff, DIFF_EASY);
2667 if (line2 == LINE_NO && line1 == LINE_UNKNOWN) {
2668 solver_set_line(sstate, line1_index, LINE_YES);
2669 diff = min(diff, DIFF_EASY);
2672 /* Deductions that depend on the numbers of lines.
2673 * Only bother if both lines are UNKNOWN, otherwise the
2674 * easy-mode solver (or deductions above) would have taken
2676 if (line1 != LINE_UNKNOWN || line2 != LINE_UNKNOWN)
2679 if (yes == 0 && unknown == 2) {
2680 /* Both these unknowns must be identical. If we know
2681 * atmostone or atleastone, we can make progress. */
2682 if (is_atmostone(dlines, dline_index)) {
2683 solver_set_line(sstate, line1_index, LINE_NO);
2684 solver_set_line(sstate, line2_index, LINE_NO);
2685 diff = min(diff, DIFF_EASY);
2687 if (is_atleastone(dlines, dline_index)) {
2688 solver_set_line(sstate, line1_index, LINE_YES);
2689 solver_set_line(sstate, line2_index, LINE_YES);
2690 diff = min(diff, DIFF_EASY);
2694 if (set_atmostone(dlines, dline_index))
2695 diff = min(diff, DIFF_NORMAL);
2697 if (set_atleastone(dlines, dline_index))
2698 diff = min(diff, DIFF_NORMAL);
2702 /* If we have atleastone set for this dline, infer
2703 * atmostone for each "opposite" dline (that is, each
2704 * dline without edges in common with this one).
2705 * Again, this test is only worth doing if both these
2706 * lines are UNKNOWN. For if one of these lines were YES,
2707 * the (yes == 1) test above would kick in instead. */
2708 if (is_atleastone(dlines, dline_index)) {
2710 for (opp = 0; opp < N; opp++) {
2711 int opp_dline_index;
2712 if (opp == j || opp == j+1 || opp == j-1)
2714 if (j == 0 && opp == N-1)
2716 if (j == N-1 && opp == 0)
2718 opp_dline_index = dline_index_from_dot(g, d, opp);
2719 if (set_atmostone(dlines, opp_dline_index))
2720 diff = min(diff, DIFF_NORMAL);
2723 if (yes == 0 && is_atmostone(dlines, dline_index)) {
2724 /* This dline has *exactly* one YES and there are no
2725 * other YESs. This allows more deductions. */
2727 /* Third unknown must be YES */
2728 for (opp = 0; opp < N; opp++) {
2730 if (opp == j || opp == k)
2732 opp_index = d->edges[opp] - g->edges;
2733 if (state->lines[opp_index] == LINE_UNKNOWN) {
2734 solver_set_line(sstate, opp_index, LINE_YES);
2735 diff = min(diff, DIFF_EASY);
2738 } else if (unknown == 4) {
2739 /* Exactly one of opposite UNKNOWNS is YES. We've
2740 * already set atmostone, so set atleastone as well.
2742 if (dline_set_opp_atleastone(sstate, d, j))
2743 diff = min(diff, DIFF_NORMAL);
2752 static int hard_mode_deductions(solver_state *sstate)
2754 game_state *state = sstate->state;
2755 grid *g = state->game_grid;
2756 char *dlines = sstate->normal->dlines;
2758 int diff = DIFF_MAX;
2761 /* ------ Face deductions ------ */
2763 /* A fully-general linedsf deduction seems overly complicated
2764 * (I suspect the problem is NP-complete, though in practice it might just
2765 * be doable because faces are limited in size).
2766 * For simplicity, we only consider *pairs* of LINE_UNKNOWNS that are
2767 * known to be identical. If setting them both to YES (or NO) would break
2768 * the clue, set them to NO (or YES). */
2770 for (i = 0; i < g->num_faces; i++) {
2771 int N, yes, no, unknown;
2774 if (sstate->face_solved[i])
2776 clue = state->clues[i];
2780 N = g->faces[i].order;
2781 yes = sstate->face_yes_count[i];
2782 if (yes + 1 == clue) {
2783 if (face_setall_identical(sstate, i, LINE_NO))
2784 diff = min(diff, DIFF_EASY);
2786 no = sstate->face_no_count[i];
2787 if (no + 1 == N - clue) {
2788 if (face_setall_identical(sstate, i, LINE_YES))
2789 diff = min(diff, DIFF_EASY);
2792 /* Reload YES count, it might have changed */
2793 yes = sstate->face_yes_count[i];
2794 unknown = N - no - yes;
2796 /* Deductions with small number of LINE_UNKNOWNs, based on overall
2797 * parity of lines. */
2798 diff_tmp = parity_deductions(sstate, g->faces[i].edges,
2799 (clue - yes) % 2, unknown);
2800 diff = min(diff, diff_tmp);
2803 /* ------ Dot deductions ------ */
2804 for (i = 0; i < g->num_dots; i++) {
2805 grid_dot *d = g->dots + i;
2808 int yes, no, unknown;
2809 /* Go through dlines, and do any dline<->linedsf deductions wherever
2810 * we find two UNKNOWNS. */
2811 for (j = 0; j < N; j++) {
2812 int dline_index = dline_index_from_dot(g, d, j);
2815 int can1, can2, inv1, inv2;
2817 line1_index = d->edges[j] - g->edges;
2818 if (state->lines[line1_index] != LINE_UNKNOWN)
2821 if (j2 == N) j2 = 0;
2822 line2_index = d->edges[j2] - g->edges;
2823 if (state->lines[line2_index] != LINE_UNKNOWN)
2825 /* Infer dline flags from linedsf */
2826 can1 = edsf_canonify(sstate->hard->linedsf, line1_index, &inv1);
2827 can2 = edsf_canonify(sstate->hard->linedsf, line2_index, &inv2);
2828 if (can1 == can2 && inv1 != inv2) {
2829 /* These are opposites, so set dline atmostone/atleastone */
2830 if (set_atmostone(dlines, dline_index))
2831 diff = min(diff, DIFF_NORMAL);
2832 if (set_atleastone(dlines, dline_index))
2833 diff = min(diff, DIFF_NORMAL);
2836 /* Infer linedsf from dline flags */
2837 if (is_atmostone(dlines, dline_index)
2838 && is_atleastone(dlines, dline_index)) {
2839 if (merge_lines(sstate, line1_index, line2_index, 1))
2840 diff = min(diff, DIFF_HARD);
2844 /* Deductions with small number of LINE_UNKNOWNs, based on overall
2845 * parity of lines. */
2846 yes = sstate->dot_yes_count[i];
2847 no = sstate->dot_no_count[i];
2848 unknown = N - yes - no;
2849 diff_tmp = parity_deductions(sstate, d->edges,
2851 diff = min(diff, diff_tmp);
2854 /* ------ Edge dsf deductions ------ */
2856 /* If the state of a line is known, deduce the state of its canonical line
2857 * too, and vice versa. */
2858 for (i = 0; i < g->num_edges; i++) {
2861 can = edsf_canonify(sstate->hard->linedsf, i, &inv);
2864 s = sstate->state->lines[can];
2865 if (s != LINE_UNKNOWN) {
2866 if (solver_set_line(sstate, i, inv ? OPP(s) : s))
2867 diff = min(diff, DIFF_EASY);
2869 s = sstate->state->lines[i];
2870 if (s != LINE_UNKNOWN) {
2871 if (solver_set_line(sstate, can, inv ? OPP(s) : s))
2872 diff = min(diff, DIFF_EASY);
2880 static int loop_deductions(solver_state *sstate)
2882 int edgecount = 0, clues = 0, satclues = 0, sm1clues = 0;
2883 game_state *state = sstate->state;
2884 grid *g = state->game_grid;
2885 int shortest_chainlen = g->num_dots;
2886 int loop_found = FALSE;
2888 int progress = FALSE;
2892 * Go through the grid and update for all the new edges.
2893 * Since merge_dots() is idempotent, the simplest way to
2894 * do this is just to update for _all_ the edges.
2895 * Also, while we're here, we count the edges.
2897 for (i = 0; i < g->num_edges; i++) {
2898 if (state->lines[i] == LINE_YES) {
2899 loop_found |= merge_dots(sstate, i);
2905 * Count the clues, count the satisfied clues, and count the
2906 * satisfied-minus-one clues.
2908 for (i = 0; i < g->num_faces; i++) {
2909 int c = state->clues[i];
2911 int o = sstate->face_yes_count[i];
2920 for (i = 0; i < g->num_dots; ++i) {
2922 sstate->looplen[dsf_canonify(sstate->dotdsf, i)];
2923 if (dots_connected > 1)
2924 shortest_chainlen = min(shortest_chainlen, dots_connected);
2927 assert(sstate->solver_status == SOLVER_INCOMPLETE);
2929 if (satclues == clues && shortest_chainlen == edgecount) {
2930 sstate->solver_status = SOLVER_SOLVED;
2931 /* This discovery clearly counts as progress, even if we haven't
2932 * just added any lines or anything */
2934 goto finished_loop_deductionsing;
2938 * Now go through looking for LINE_UNKNOWN edges which
2939 * connect two dots that are already in the same
2940 * equivalence class. If we find one, test to see if the
2941 * loop it would create is a solution.
2943 for (i = 0; i < g->num_edges; i++) {
2944 grid_edge *e = g->edges + i;
2945 int d1 = e->dot1 - g->dots;
2946 int d2 = e->dot2 - g->dots;
2948 if (state->lines[i] != LINE_UNKNOWN)
2951 eqclass = dsf_canonify(sstate->dotdsf, d1);
2952 if (eqclass != dsf_canonify(sstate->dotdsf, d2))
2955 val = LINE_NO; /* loop is bad until proven otherwise */
2958 * This edge would form a loop. Next
2959 * question: how long would the loop be?
2960 * Would it equal the total number of edges
2961 * (plus the one we'd be adding if we added
2964 if (sstate->looplen[eqclass] == edgecount + 1) {
2968 * This edge would form a loop which
2969 * took in all the edges in the entire
2970 * grid. So now we need to work out
2971 * whether it would be a valid solution
2972 * to the puzzle, which means we have to
2973 * check if it satisfies all the clues.
2974 * This means that every clue must be
2975 * either satisfied or satisfied-minus-
2976 * 1, and also that the number of
2977 * satisfied-minus-1 clues must be at
2978 * most two and they must lie on either
2979 * side of this edge.
2983 int f = e->face1 - g->faces;
2984 int c = state->clues[f];
2985 if (c >= 0 && sstate->face_yes_count[f] == c - 1)
2989 int f = e->face2 - g->faces;
2990 int c = state->clues[f];
2991 if (c >= 0 && sstate->face_yes_count[f] == c - 1)
2994 if (sm1clues == sm1_nearby &&
2995 sm1clues + satclues == clues) {
2996 val = LINE_YES; /* loop is good! */
3001 * Right. Now we know that adding this edge
3002 * would form a loop, and we know whether
3003 * that loop would be a viable solution or
3006 * If adding this edge produces a solution,
3007 * then we know we've found _a_ solution but
3008 * we don't know that it's _the_ solution -
3009 * if it were provably the solution then
3010 * we'd have deduced this edge some time ago
3011 * without the need to do loop detection. So
3012 * in this state we return SOLVER_AMBIGUOUS,
3013 * which has the effect that hitting Solve
3014 * on a user-provided puzzle will fill in a
3015 * solution but using the solver to
3016 * construct new puzzles won't consider this
3017 * a reasonable deduction for the user to
3020 progress = solver_set_line(sstate, i, val);
3021 assert(progress == TRUE);
3022 if (val == LINE_YES) {
3023 sstate->solver_status = SOLVER_AMBIGUOUS;
3024 goto finished_loop_deductionsing;
3028 finished_loop_deductionsing:
3029 return progress ? DIFF_EASY : DIFF_MAX;
3032 /* This will return a dynamically allocated solver_state containing the (more)
3034 static solver_state *solve_game_rec(const solver_state *sstate_start,
3037 solver_state *sstate, *sstate_saved;
3038 int solver_progress;
3041 /* Indicates which solver we should call next. This is a sensible starting
3043 int current_solver = DIFF_EASY, next_solver;
3044 sstate = dup_solver_state(sstate_start);
3046 /* Cache the values of some variables for readability */
3047 state = sstate->state;
3049 sstate_saved = NULL;
3051 solver_progress = FALSE;
3053 check_caches(sstate);
3056 if (sstate->solver_status == SOLVER_MISTAKE)
3059 next_solver = solver_fns[current_solver](sstate);
3061 if (next_solver == DIFF_MAX) {
3062 if (current_solver < diff && current_solver + 1 < DIFF_MAX) {
3063 /* Try next beefier solver */
3064 next_solver = current_solver + 1;
3066 next_solver = loop_deductions(sstate);
3070 if (sstate->solver_status == SOLVER_SOLVED ||
3071 sstate->solver_status == SOLVER_AMBIGUOUS) {
3072 /* fprintf(stderr, "Solver completed\n"); */
3076 /* Once we've looped over all permitted solvers then the loop
3077 * deductions without making any progress, we'll exit this while loop */
3078 current_solver = next_solver;
3079 } while (current_solver < DIFF_MAX);
3081 if (sstate->solver_status == SOLVER_SOLVED ||
3082 sstate->solver_status == SOLVER_AMBIGUOUS) {
3083 /* s/LINE_UNKNOWN/LINE_NO/g */
3084 array_setall(sstate->state->lines, LINE_UNKNOWN, LINE_NO,
3085 sstate->state->game_grid->num_edges);
3092 static char *solve_game(game_state *state, game_state *currstate,
3093 char *aux, char **error)
3096 solver_state *sstate, *new_sstate;
3098 sstate = new_solver_state(state, DIFF_MAX);
3099 new_sstate = solve_game_rec(sstate, DIFF_MAX);
3101 if (new_sstate->solver_status == SOLVER_SOLVED) {
3102 soln = encode_solve_move(new_sstate->state);
3103 } else if (new_sstate->solver_status == SOLVER_AMBIGUOUS) {
3104 soln = encode_solve_move(new_sstate->state);
3105 /**error = "Solver found ambiguous solutions"; */
3107 soln = encode_solve_move(new_sstate->state);
3108 /**error = "Solver failed"; */
3111 free_solver_state(new_sstate);
3112 free_solver_state(sstate);
3117 /* ----------------------------------------------------------------------
3118 * Drawing and mouse-handling
3121 static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
3122 int x, int y, int button)
3124 grid *g = state->game_grid;
3128 char button_char = ' ';
3129 enum line_state old_state;
3131 button &= ~MOD_MASK;
3133 /* Convert mouse-click (x,y) to grid coordinates */
3134 x -= BORDER(ds->tilesize);
3135 y -= BORDER(ds->tilesize);
3136 x = x * g->tilesize / ds->tilesize;
3137 y = y * g->tilesize / ds->tilesize;
3141 e = grid_nearest_edge(g, x, y);
3147 /* I think it's only possible to play this game with mouse clicks, sorry */
3148 /* Maybe will add mouse drag support some time */
3149 old_state = state->lines[i];
3153 switch (old_state) {
3167 switch (old_state) {
3182 sprintf(buf, "%d%c", i, (int)button_char);
3188 static game_state *execute_move(game_state *state, char *move)
3191 game_state *newstate = dup_game(state);
3193 if (move[0] == 'S') {
3195 newstate->cheated = TRUE;
3200 move += strspn(move, "1234567890");
3201 switch (*(move++)) {
3203 newstate->lines[i] = LINE_YES;
3206 newstate->lines[i] = LINE_NO;
3209 newstate->lines[i] = LINE_UNKNOWN;
3217 * Check for completion.
3219 if (check_completion(newstate))
3220 newstate->solved = TRUE;
3225 free_game(newstate);
3229 /* ----------------------------------------------------------------------
3233 /* Convert from grid coordinates to screen coordinates */
3234 static void grid_to_screen(const game_drawstate *ds, const grid *g,
3235 int grid_x, int grid_y, int *x, int *y)
3237 *x = grid_x - g->lowest_x;
3238 *y = grid_y - g->lowest_y;
3239 *x = *x * ds->tilesize / g->tilesize;
3240 *y = *y * ds->tilesize / g->tilesize;
3241 *x += BORDER(ds->tilesize);
3242 *y += BORDER(ds->tilesize);
3245 /* Returns (into x,y) position of centre of face for rendering the text clue.
3247 static void face_text_pos(const game_drawstate *ds, const grid *g,
3248 const grid_face *f, int *x, int *y)
3252 /* Simplest solution is the centroid. Might not work in some cases. */
3254 /* Another algorithm to look into:
3255 * Find the midpoints of the sides, find the bounding-box,
3256 * then take the centre of that. */
3258 /* Best solution probably involves incentres (inscribed circles) */
3260 int sx = 0, sy = 0; /* sums */
3261 for (i = 0; i < f->order; i++) {
3262 grid_dot *d = f->dots[i];
3269 /* convert to screen coordinates */
3270 grid_to_screen(ds, g, sx, sy, x, y);
3273 static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
3274 game_state *state, int dir, game_ui *ui,
3275 float animtime, float flashtime)
3277 grid *g = state->game_grid;
3278 int border = BORDER(ds->tilesize);
3281 int line_colour, flash_changed;
3287 * The initial contents of the window are not guaranteed and
3288 * can vary with front ends. To be on the safe side, all games
3289 * should start by drawing a big background-colour rectangle
3290 * covering the whole window.
3292 int grid_width = g->highest_x - g->lowest_x;
3293 int grid_height = g->highest_y - g->lowest_y;
3294 int w = grid_width * ds->tilesize / g->tilesize;
3295 int h = grid_height * ds->tilesize / g->tilesize;
3296 draw_rect(dr, 0, 0, w + 2 * border + 1, h + 2 * border + 1,
3300 for (i = 0; i < g->num_faces; i++) {
3304 c[0] = CLUE2CHAR(state->clues[i]);
3307 face_text_pos(ds, g, f, &x, &y);
3308 draw_text(dr, x, y, FONT_VARIABLE, ds->tilesize/2,
3309 ALIGN_VCENTRE | ALIGN_HCENTRE, COL_FOREGROUND, c);
3311 draw_update(dr, 0, 0, w + 2 * border, h + 2 * border);
3314 if (flashtime > 0 &&
3315 (flashtime <= FLASH_TIME/3 ||
3316 flashtime >= FLASH_TIME*2/3)) {
3317 flash_changed = !ds->flashing;
3318 ds->flashing = TRUE;
3320 flash_changed = ds->flashing;
3321 ds->flashing = FALSE;
3324 /* Some platforms may perform anti-aliasing, which may prevent clean
3325 * repainting of lines when the colour is changed.
3326 * If a line needs to be over-drawn in a different colour, erase a
3327 * bounding-box around the line, then flag all nearby objects for redraw.
3330 const char redraw_flag = (char)(1<<7);
3331 for (i = 0; i < g->num_edges; i++) {
3332 char prev_ds = (ds->lines[i] & ~redraw_flag);
3333 char new_ds = state->lines[i];
3334 if (state->line_errors[i])
3335 new_ds = DS_LINE_ERROR;
3337 /* If we're changing state, AND
3338 * the previous state was a coloured line */
3339 if ((prev_ds != new_ds) && (prev_ds != LINE_NO)) {
3340 grid_edge *e = g->edges + i;
3341 int x1 = e->dot1->x;
3342 int y1 = e->dot1->y;
3343 int x2 = e->dot2->x;
3344 int y2 = e->dot2->y;
3345 int xmin, xmax, ymin, ymax;
3347 grid_to_screen(ds, g, x1, y1, &x1, &y1);
3348 grid_to_screen(ds, g, x2, y2, &x2, &y2);
3349 /* Allow extra margin for dots, and thickness of lines */
3350 xmin = min(x1, x2) - 2;
3351 xmax = max(x1, x2) + 2;
3352 ymin = min(y1, y2) - 2;
3353 ymax = max(y1, y2) + 2;
3354 /* For testing, I find it helpful to change COL_BACKGROUND
3355 * to COL_SATISFIED here. */
3356 draw_rect(dr, xmin, ymin, xmax - xmin + 1, ymax - ymin + 1,
3358 draw_update(dr, xmin, ymin, xmax - xmin + 1, ymax - ymin + 1);
3360 /* Mark nearby lines for redraw */
3361 for (j = 0; j < e->dot1->order; j++)
3362 ds->lines[e->dot1->edges[j] - g->edges] |= redraw_flag;
3363 for (j = 0; j < e->dot2->order; j++)
3364 ds->lines[e->dot2->edges[j] - g->edges] |= redraw_flag;
3365 /* Mark nearby clues for redraw. Use a value that is
3366 * neither TRUE nor FALSE for this. */
3368 ds->clue_error[e->face1 - g->faces] = 2;
3370 ds->clue_error[e->face2 - g->faces] = 2;
3375 /* Redraw clue colours if necessary */
3376 for (i = 0; i < g->num_faces; i++) {
3377 grid_face *f = g->faces + i;
3378 int sides = f->order;
3380 n = state->clues[i];
3384 c[0] = CLUE2CHAR(n);
3387 clue_mistake = (face_order(state, i, LINE_YES) > n ||
3388 face_order(state, i, LINE_NO ) > (sides-n));
3390 clue_satisfied = (face_order(state, i, LINE_YES) == n &&
3391 face_order(state, i, LINE_NO ) == (sides-n));
3393 if (clue_mistake != ds->clue_error[i]
3394 || clue_satisfied != ds->clue_satisfied[i]) {
3396 face_text_pos(ds, g, f, &x, &y);
3397 /* There seems to be a certain amount of trial-and-error
3398 * involved in working out the correct bounding-box for
3400 draw_rect(dr, x - ds->tilesize/4 - 1, y - ds->tilesize/4 - 3,
3401 ds->tilesize/2 + 2, ds->tilesize/2 + 5,
3404 FONT_VARIABLE, ds->tilesize/2,
3405 ALIGN_VCENTRE | ALIGN_HCENTRE,
3406 clue_mistake ? COL_MISTAKE :
3407 clue_satisfied ? COL_SATISFIED : COL_FOREGROUND, c);
3408 draw_update(dr, x - ds->tilesize/4 - 1, y - ds->tilesize/4 - 3,
3409 ds->tilesize/2 + 2, ds->tilesize/2 + 5);
3411 ds->clue_error[i] = clue_mistake;
3412 ds->clue_satisfied[i] = clue_satisfied;
3414 /* Sometimes, the bounding-box encroaches into the surrounding
3415 * lines (particularly if the window is resized fairly small).
3416 * So redraw them. */
3417 for (j = 0; j < f->order; j++)
3418 ds->lines[f->edges[j] - g->edges] = -1;
3423 for (i = 0; i < g->num_edges; i++) {
3424 grid_edge *e = g->edges + i;
3426 int xmin, ymin, xmax, ymax;
3427 char new_ds, need_draw;
3428 new_ds = state->lines[i];
3429 if (state->line_errors[i])
3430 new_ds = DS_LINE_ERROR;
3431 need_draw = (new_ds != ds->lines[i]) ? TRUE : FALSE;
3432 if (flash_changed && (state->lines[i] == LINE_YES))
3435 need_draw = TRUE; /* draw everything at the start */
3436 ds->lines[i] = new_ds;
3439 if (state->line_errors[i])
3440 line_colour = COL_MISTAKE;
3441 else if (state->lines[i] == LINE_UNKNOWN)
3442 line_colour = COL_LINEUNKNOWN;
3443 else if (state->lines[i] == LINE_NO)
3444 line_colour = COL_BACKGROUND;
3445 else if (ds->flashing)
3446 line_colour = COL_HIGHLIGHT;
3448 line_colour = COL_FOREGROUND;
3450 /* Convert from grid to screen coordinates */
3451 grid_to_screen(ds, g, e->dot1->x, e->dot1->y, &x1, &y1);
3452 grid_to_screen(ds, g, e->dot2->x, e->dot2->y, &x2, &y2);
3459 if (line_colour != COL_BACKGROUND) {
3460 /* (dx, dy) points roughly from (x1, y1) to (x2, y2).
3461 * The line is then "fattened" in a (roughly) perpendicular
3462 * direction to create a thin rectangle. */
3463 int dx = (x1 > x2) ? -1 : ((x1 < x2) ? 1 : 0);
3464 int dy = (y1 > y2) ? -1 : ((y1 < y2) ? 1 : 0);
3466 points[0] = x1 + dy;
3467 points[1] = y1 - dx;
3468 points[2] = x1 - dy;
3469 points[3] = y1 + dx;
3470 points[4] = x2 - dy;
3471 points[5] = y2 + dx;
3472 points[6] = x2 + dy;
3473 points[7] = y2 - dx;
3474 draw_polygon(dr, points, 4, line_colour, line_colour);
3477 /* Draw dots at ends of the line */
3478 draw_circle(dr, x1, y1, 2, COL_FOREGROUND, COL_FOREGROUND);
3479 draw_circle(dr, x2, y2, 2, COL_FOREGROUND, COL_FOREGROUND);
3481 draw_update(dr, xmin-2, ymin-2, xmax - xmin + 4, ymax - ymin + 4);
3486 for (i = 0; i < g->num_dots; i++) {
3487 grid_dot *d = g->dots + i;
3489 grid_to_screen(ds, g, d->x, d->y, &x, &y);
3490 draw_circle(dr, x, y, 2, COL_FOREGROUND, COL_FOREGROUND);
3496 static float game_flash_length(game_state *oldstate, game_state *newstate,
3497 int dir, game_ui *ui)
3499 if (!oldstate->solved && newstate->solved &&
3500 !oldstate->cheated && !newstate->cheated) {
3507 static void game_print_size(game_params *params, float *x, float *y)
3512 * I'll use 7mm "squares" by default.
3514 game_compute_size(params, 700, &pw, &ph);
3519 static void game_print(drawing *dr, game_state *state, int tilesize)
3521 int ink = print_mono_colour(dr, 0);
3523 game_drawstate ads, *ds = &ads;
3524 grid *g = state->game_grid;
3526 game_set_size(dr, ds, NULL, tilesize);
3528 for (i = 0; i < g->num_dots; i++) {
3530 grid_to_screen(ds, g, g->dots[i].x, g->dots[i].y, &x, &y);
3531 draw_circle(dr, x, y, ds->tilesize / 15, ink, ink);
3537 for (i = 0; i < g->num_faces; i++) {
3538 grid_face *f = g->faces + i;
3539 int clue = state->clues[i];
3543 c[0] = CLUE2CHAR(clue);
3545 face_text_pos(ds, g, f, &x, &y);
3547 FONT_VARIABLE, ds->tilesize / 2,
3548 ALIGN_VCENTRE | ALIGN_HCENTRE, ink, c);
3555 for (i = 0; i < g->num_edges; i++) {
3556 int thickness = (state->lines[i] == LINE_YES) ? 30 : 150;
3557 grid_edge *e = g->edges + i;
3559 grid_to_screen(ds, g, e->dot1->x, e->dot1->y, &x1, &y1);
3560 grid_to_screen(ds, g, e->dot2->x, e->dot2->y, &x2, &y2);
3561 if (state->lines[i] == LINE_YES)
3563 /* (dx, dy) points from (x1, y1) to (x2, y2).
3564 * The line is then "fattened" in a perpendicular
3565 * direction to create a thin rectangle. */
3566 double d = sqrt(SQ((double)x1 - x2) + SQ((double)y1 - y2));
3567 double dx = (x2 - x1) / d;
3568 double dy = (y2 - y1) / d;
3571 dx = (dx * ds->tilesize) / thickness;
3572 dy = (dy * ds->tilesize) / thickness;
3573 points[0] = x1 + (int)dy;
3574 points[1] = y1 - (int)dx;
3575 points[2] = x1 - (int)dy;
3576 points[3] = y1 + (int)dx;
3577 points[4] = x2 - (int)dy;
3578 points[5] = y2 + (int)dx;
3579 points[6] = x2 + (int)dy;
3580 points[7] = y2 - (int)dx;
3581 draw_polygon(dr, points, 4, ink, ink);
3585 /* Draw a dotted line */
3588 for (j = 1; j < divisions; j++) {
3589 /* Weighted average */
3590 int x = (x1 * (divisions -j) + x2 * j) / divisions;
3591 int y = (y1 * (divisions -j) + y2 * j) / divisions;
3592 draw_circle(dr, x, y, ds->tilesize / thickness, ink, ink);
3599 #define thegame loopy
3602 const struct game thegame = {
3603 "Loopy", "games.loopy", "loopy",
3610 TRUE, game_configure, custom_params,
3618 TRUE, game_can_format_as_text_now, game_text_format,
3626 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
3629 game_free_drawstate,
3633 TRUE, FALSE, game_print_size, game_print,
3634 FALSE /* wants_statusbar */,
3635 FALSE, game_timing_state,
3636 0, /* mouse_priorities */