2 * solo.c: the number-placing puzzle most popularly known as `Sudoku'.
6 * - reports from users are that `Trivial'-mode puzzles are still
7 * rather hard compared to newspapers' easy ones, so some better
8 * low-end difficulty grading would be nice
9 * + it's possible that really easy puzzles always have
10 * _several_ things you can do, so don't make you hunt too
11 * hard for the one deduction you can currently make
12 * + it's also possible that easy puzzles require fewer
13 * cross-eliminations: perhaps there's a higher incidence of
14 * things you can deduce by looking only at (say) rows,
15 * rather than things you have to check both rows and columns
17 * + but really, what I need to do is find some really easy
18 * puzzles and _play_ them, to see what's actually easy about
20 * + while I'm revamping this area, filling in the _last_
21 * number in a nearly-full row or column should certainly be
22 * permitted even at the lowest difficulty level.
23 * + also Owen noticed that `Basic' grids requiring numeric
24 * elimination are actually very hard, so I wonder if a
25 * difficulty gradation between that and positional-
26 * elimination-only might be in order
27 * + but it's not good to have _too_ many difficulty levels, or
28 * it'll take too long to randomly generate a given level.
30 * - it might still be nice to do some prioritisation on the
31 * removal of numbers from the grid
32 * + one possibility is to try to minimise the maximum number
33 * of filled squares in any block, which in particular ought
34 * to enforce never leaving a completely filled block in the
35 * puzzle as presented.
37 * - alternative interface modes
38 * + sudoku.com's Windows program has a palette of possible
39 * entries; you select a palette entry first and then click
40 * on the square you want it to go in, thus enabling
41 * mouse-only play. Useful for PDAs! I don't think it's
42 * actually incompatible with the current highlight-then-type
43 * approach: you _either_ highlight a palette entry and then
44 * click, _or_ you highlight a square and then type. At most
45 * one thing is ever highlighted at a time, so there's no way
47 * + then again, I don't actually like sudoku.com's interface;
48 * it's too much like a paint package whereas I prefer to
49 * think of Solo as a text editor.
50 * + another PDA-friendly possibility is a drag interface:
51 * _drag_ numbers from the palette into the grid squares.
52 * Thought experiments suggest I'd prefer that to the
53 * sudoku.com approach, but I haven't actually tried it.
57 * Solo puzzles need to be square overall (since each row and each
58 * column must contain one of every digit), but they need not be
59 * subdivided the same way internally. I am going to adopt a
60 * convention whereby I _always_ refer to `r' as the number of rows
61 * of _big_ divisions, and `c' as the number of columns of _big_
62 * divisions. Thus, a 2c by 3r puzzle looks something like this:
66 * ------+------ (Of course, you can't subdivide it the other way
67 * 1 4 5 | 6 3 2 or you'll get clashes; observe that the 4 in the
68 * 3 2 6 | 4 1 5 top left would conflict with the 4 in the second
69 * ------+------ box down on the left-hand side.)
73 * The need for a strong naming convention should now be clear:
74 * each small box is two rows of digits by three columns, while the
75 * overall puzzle has three rows of small boxes by two columns. So
76 * I will (hopefully) consistently use `r' to denote the number of
77 * rows _of small boxes_ (here 3), which is also the number of
78 * columns of digits in each small box; and `c' vice versa (here
81 * I'm also going to choose arbitrarily to list c first wherever
82 * possible: the above is a 2x3 puzzle, not a 3x2 one.
92 #ifdef STANDALONE_SOLVER
94 int solver_show_working;
100 * To save space, I store digits internally as unsigned char. This
101 * imposes a hard limit of 255 on the order of the puzzle. Since
102 * even a 5x5 takes unacceptably long to generate, I don't see this
103 * as a serious limitation unless something _really_ impressive
104 * happens in computing technology; but here's a typedef anyway for
105 * general good practice.
107 typedef unsigned char digit;
108 #define ORDER_MAX 255
110 #define PREFERRED_TILE_SIZE 32
111 #define TILE_SIZE (ds->tilesize)
112 #define BORDER (TILE_SIZE / 2)
114 #define FLASH_TIME 0.4F
116 enum { SYMM_NONE, SYMM_ROT2, SYMM_ROT4, SYMM_REF2, SYMM_REF2D, SYMM_REF4,
117 SYMM_REF4D, SYMM_REF8 };
119 enum { DIFF_BLOCK, DIFF_SIMPLE, DIFF_INTERSECT,
120 DIFF_SET, DIFF_RECURSIVE, DIFF_AMBIGUOUS, DIFF_IMPOSSIBLE };
134 int c, r, symm, diff;
140 unsigned char *pencil; /* c*r*c*r elements */
141 unsigned char *immutable; /* marks which digits are clues */
142 int completed, cheated;
145 static game_params *default_params(void)
147 game_params *ret = snew(game_params);
150 ret->symm = SYMM_ROT2; /* a plausible default */
151 ret->diff = DIFF_BLOCK; /* so is this */
156 static void free_params(game_params *params)
161 static game_params *dup_params(game_params *params)
163 game_params *ret = snew(game_params);
164 *ret = *params; /* structure copy */
168 static int game_fetch_preset(int i, char **name, game_params **params)
174 { "2x2 Trivial", { 2, 2, SYMM_ROT2, DIFF_BLOCK } },
175 { "2x3 Basic", { 2, 3, SYMM_ROT2, DIFF_SIMPLE } },
176 { "3x3 Trivial", { 3, 3, SYMM_ROT2, DIFF_BLOCK } },
177 { "3x3 Basic", { 3, 3, SYMM_ROT2, DIFF_SIMPLE } },
178 { "3x3 Intermediate", { 3, 3, SYMM_ROT2, DIFF_INTERSECT } },
179 { "3x3 Advanced", { 3, 3, SYMM_ROT2, DIFF_SET } },
180 { "3x3 Unreasonable", { 3, 3, SYMM_ROT2, DIFF_RECURSIVE } },
182 { "3x4 Basic", { 3, 4, SYMM_ROT2, DIFF_SIMPLE } },
183 { "4x4 Basic", { 4, 4, SYMM_ROT2, DIFF_SIMPLE } },
187 if (i < 0 || i >= lenof(presets))
190 *name = dupstr(presets[i].title);
191 *params = dup_params(&presets[i].params);
196 static void decode_params(game_params *ret, char const *string)
198 ret->c = ret->r = atoi(string);
199 while (*string && isdigit((unsigned char)*string)) string++;
200 if (*string == 'x') {
202 ret->r = atoi(string);
203 while (*string && isdigit((unsigned char)*string)) string++;
206 if (*string == 'r' || *string == 'm' || *string == 'a') {
209 if (*string == 'd') {
216 while (*string && isdigit((unsigned char)*string)) string++;
217 if (sc == 'm' && sn == 8)
218 ret->symm = SYMM_REF8;
219 if (sc == 'm' && sn == 4)
220 ret->symm = sd ? SYMM_REF4D : SYMM_REF4;
221 if (sc == 'm' && sn == 2)
222 ret->symm = sd ? SYMM_REF2D : SYMM_REF2;
223 if (sc == 'r' && sn == 4)
224 ret->symm = SYMM_ROT4;
225 if (sc == 'r' && sn == 2)
226 ret->symm = SYMM_ROT2;
228 ret->symm = SYMM_NONE;
229 } else if (*string == 'd') {
231 if (*string == 't') /* trivial */
232 string++, ret->diff = DIFF_BLOCK;
233 else if (*string == 'b') /* basic */
234 string++, ret->diff = DIFF_SIMPLE;
235 else if (*string == 'i') /* intermediate */
236 string++, ret->diff = DIFF_INTERSECT;
237 else if (*string == 'a') /* advanced */
238 string++, ret->diff = DIFF_SET;
239 else if (*string == 'u') /* unreasonable */
240 string++, ret->diff = DIFF_RECURSIVE;
242 string++; /* eat unknown character */
246 static char *encode_params(game_params *params, int full)
250 sprintf(str, "%dx%d", params->c, params->r);
252 switch (params->symm) {
253 case SYMM_REF8: strcat(str, "m8"); break;
254 case SYMM_REF4: strcat(str, "m4"); break;
255 case SYMM_REF4D: strcat(str, "md4"); break;
256 case SYMM_REF2: strcat(str, "m2"); break;
257 case SYMM_REF2D: strcat(str, "md2"); break;
258 case SYMM_ROT4: strcat(str, "r4"); break;
259 /* case SYMM_ROT2: strcat(str, "r2"); break; [default] */
260 case SYMM_NONE: strcat(str, "a"); break;
262 switch (params->diff) {
263 /* case DIFF_BLOCK: strcat(str, "dt"); break; [default] */
264 case DIFF_SIMPLE: strcat(str, "db"); break;
265 case DIFF_INTERSECT: strcat(str, "di"); break;
266 case DIFF_SET: strcat(str, "da"); break;
267 case DIFF_RECURSIVE: strcat(str, "du"); break;
273 static config_item *game_configure(game_params *params)
278 ret = snewn(5, config_item);
280 ret[0].name = "Columns of sub-blocks";
281 ret[0].type = C_STRING;
282 sprintf(buf, "%d", params->c);
283 ret[0].sval = dupstr(buf);
286 ret[1].name = "Rows of sub-blocks";
287 ret[1].type = C_STRING;
288 sprintf(buf, "%d", params->r);
289 ret[1].sval = dupstr(buf);
292 ret[2].name = "Symmetry";
293 ret[2].type = C_CHOICES;
294 ret[2].sval = ":None:2-way rotation:4-way rotation:2-way mirror:"
295 "2-way diagonal mirror:4-way mirror:4-way diagonal mirror:"
297 ret[2].ival = params->symm;
299 ret[3].name = "Difficulty";
300 ret[3].type = C_CHOICES;
301 ret[3].sval = ":Trivial:Basic:Intermediate:Advanced:Unreasonable";
302 ret[3].ival = params->diff;
312 static game_params *custom_params(config_item *cfg)
314 game_params *ret = snew(game_params);
316 ret->c = atoi(cfg[0].sval);
317 ret->r = atoi(cfg[1].sval);
318 ret->symm = cfg[2].ival;
319 ret->diff = cfg[3].ival;
324 static char *validate_params(game_params *params)
326 if (params->c < 2 || params->r < 2)
327 return "Both dimensions must be at least 2";
328 if (params->c > ORDER_MAX || params->r > ORDER_MAX)
329 return "Dimensions greater than "STR(ORDER_MAX)" are not supported";
333 /* ----------------------------------------------------------------------
334 * Full recursive Solo solver.
336 * The algorithm for this solver is shamelessly copied from a
337 * Python solver written by Andrew Wilkinson (which is GPLed, but
338 * I've reused only ideas and no code). It mostly just does the
339 * obvious recursive thing: pick an empty square, put one of the
340 * possible digits in it, recurse until all squares are filled,
341 * backtrack and change some choices if necessary.
343 * The clever bit is that every time it chooses which square to
344 * fill in next, it does so by counting the number of _possible_
345 * numbers that can go in each square, and it prioritises so that
346 * it picks a square with the _lowest_ number of possibilities. The
347 * idea is that filling in lots of the obvious bits (particularly
348 * any squares with only one possibility) will cut down on the list
349 * of possibilities for other squares and hence reduce the enormous
350 * search space as much as possible as early as possible.
352 * In practice the algorithm appeared to work very well; run on
353 * sample problems from the Times it completed in well under a
354 * second on my G5 even when written in Python, and given an empty
355 * grid (so that in principle it would enumerate _all_ solved
356 * grids!) it found the first valid solution just as quickly. So
357 * with a bit more randomisation I see no reason not to use this as
362 * Internal data structure used in solver to keep track of
365 struct rsolve_coord { int x, y, r; };
366 struct rsolve_usage {
367 int c, r, cr; /* cr == c*r */
368 /* grid is a copy of the input grid, modified as we go along */
370 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
372 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
374 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
376 /* This lists all the empty spaces remaining in the grid. */
377 struct rsolve_coord *spaces;
379 /* If we need randomisation in the solve, this is our random state. */
381 /* Number of solutions so far found, and maximum number we care about. */
386 * The real recursive step in the solving function.
388 static void rsolve_real(struct rsolve_usage *usage, digit *grid)
390 int c = usage->c, r = usage->r, cr = usage->cr;
391 int i, j, n, sx, sy, bestm, bestr;
395 * Firstly, check for completion! If there are no spaces left
396 * in the grid, we have a solution.
398 if (usage->nspaces == 0) {
401 * This is our first solution, so fill in the output grid.
403 memcpy(grid, usage->grid, cr * cr);
410 * Otherwise, there must be at least one space. Find the most
411 * constrained space, using the `r' field as a tie-breaker.
413 bestm = cr+1; /* so that any space will beat it */
416 for (j = 0; j < usage->nspaces; j++) {
417 int x = usage->spaces[j].x, y = usage->spaces[j].y;
421 * Find the number of digits that could go in this space.
424 for (n = 0; n < cr; n++)
425 if (!usage->row[y*cr+n] && !usage->col[x*cr+n] &&
426 !usage->blk[((y/c)*c+(x/r))*cr+n])
429 if (m < bestm || (m == bestm && usage->spaces[j].r < bestr)) {
431 bestr = usage->spaces[j].r;
439 * Swap that square into the final place in the spaces array,
440 * so that decrementing nspaces will remove it from the list.
442 if (i != usage->nspaces-1) {
443 struct rsolve_coord t;
444 t = usage->spaces[usage->nspaces-1];
445 usage->spaces[usage->nspaces-1] = usage->spaces[i];
446 usage->spaces[i] = t;
450 * Now we've decided which square to start our recursion at,
451 * simply go through all possible values, shuffling them
452 * randomly first if necessary.
454 digits = snewn(bestm, int);
456 for (n = 0; n < cr; n++)
457 if (!usage->row[sy*cr+n] && !usage->col[sx*cr+n] &&
458 !usage->blk[((sy/c)*c+(sx/r))*cr+n]) {
464 for (i = j; i > 1; i--) {
465 int p = random_upto(usage->rs, i);
468 digits[p] = digits[i-1];
474 /* And finally, go through the digit list and actually recurse. */
475 for (i = 0; i < j; i++) {
478 /* Update the usage structure to reflect the placing of this digit. */
479 usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
480 usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = TRUE;
481 usage->grid[sy*cr+sx] = n;
484 /* Call the solver recursively. */
485 rsolve_real(usage, grid);
488 * If we have seen as many solutions as we need, terminate
489 * all processing immediately.
491 if (usage->solns >= usage->maxsolns)
494 /* Revert the usage structure. */
495 usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
496 usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = FALSE;
497 usage->grid[sy*cr+sx] = 0;
505 * Entry point to solver. You give it dimensions and a starting
506 * grid, which is simply an array of N^4 digits. In that array, 0
507 * means an empty square, and 1..N mean a clue square.
509 * Return value is the number of solutions found; searching will
510 * stop after the provided `max'. (Thus, you can pass max==1 to
511 * indicate that you only care about finding _one_ solution, or
512 * max==2 to indicate that you want to know the difference between
513 * a unique and non-unique solution.) The input parameter `grid' is
514 * also filled in with the _first_ (or only) solution found by the
517 static int rsolve(int c, int r, digit *grid, random_state *rs, int max)
519 struct rsolve_usage *usage;
524 * Create an rsolve_usage structure.
526 usage = snew(struct rsolve_usage);
532 usage->grid = snewn(cr * cr, digit);
533 memcpy(usage->grid, grid, cr * cr);
535 usage->row = snewn(cr * cr, unsigned char);
536 usage->col = snewn(cr * cr, unsigned char);
537 usage->blk = snewn(cr * cr, unsigned char);
538 memset(usage->row, FALSE, cr * cr);
539 memset(usage->col, FALSE, cr * cr);
540 memset(usage->blk, FALSE, cr * cr);
542 usage->spaces = snewn(cr * cr, struct rsolve_coord);
546 usage->maxsolns = max;
551 * Now fill it in with data from the input grid.
553 for (y = 0; y < cr; y++) {
554 for (x = 0; x < cr; x++) {
555 int v = grid[y*cr+x];
557 usage->spaces[usage->nspaces].x = x;
558 usage->spaces[usage->nspaces].y = y;
560 usage->spaces[usage->nspaces].r = random_bits(rs, 31);
562 usage->spaces[usage->nspaces].r = usage->nspaces;
565 usage->row[y*cr+v-1] = TRUE;
566 usage->col[x*cr+v-1] = TRUE;
567 usage->blk[((y/c)*c+(x/r))*cr+v-1] = TRUE;
573 * Run the real recursive solving function.
575 rsolve_real(usage, grid);
579 * Clean up the usage structure now we have our answer.
581 sfree(usage->spaces);
594 /* ----------------------------------------------------------------------
595 * End of recursive solver code.
598 /* ----------------------------------------------------------------------
599 * Less capable non-recursive solver. This one is used to check
600 * solubility of a grid as we gradually remove numbers from it: by
601 * verifying a grid using this solver we can ensure it isn't _too_
602 * hard (e.g. does not actually require guessing and backtracking).
604 * It supports a variety of specific modes of reasoning. By
605 * enabling or disabling subsets of these modes we can arrange a
606 * range of difficulty levels.
610 * Modes of reasoning currently supported:
612 * - Positional elimination: a number must go in a particular
613 * square because all the other empty squares in a given
614 * row/col/blk are ruled out.
616 * - Numeric elimination: a square must have a particular number
617 * in because all the other numbers that could go in it are
620 * - Intersectional analysis: given two domains which overlap
621 * (hence one must be a block, and the other can be a row or
622 * col), if the possible locations for a particular number in
623 * one of the domains can be narrowed down to the overlap, then
624 * that number can be ruled out everywhere but the overlap in
625 * the other domain too.
627 * - Set elimination: if there is a subset of the empty squares
628 * within a domain such that the union of the possible numbers
629 * in that subset has the same size as the subset itself, then
630 * those numbers can be ruled out everywhere else in the domain.
631 * (For example, if there are five empty squares and the
632 * possible numbers in each are 12, 23, 13, 134 and 1345, then
633 * the first three empty squares form such a subset: the numbers
634 * 1, 2 and 3 _must_ be in those three squares in some
635 * permutation, and hence we can deduce none of them can be in
636 * the fourth or fifth squares.)
637 * + You can also see this the other way round, concentrating
638 * on numbers rather than squares: if there is a subset of
639 * the unplaced numbers within a domain such that the union
640 * of all their possible positions has the same size as the
641 * subset itself, then all other numbers can be ruled out for
642 * those positions. However, it turns out that this is
643 * exactly equivalent to the first formulation at all times:
644 * there is a 1-1 correspondence between suitable subsets of
645 * the unplaced numbers and suitable subsets of the unfilled
646 * places, found by taking the _complement_ of the union of
647 * the numbers' possible positions (or the spaces' possible
652 * Within this solver, I'm going to transform all y-coordinates by
653 * inverting the significance of the block number and the position
654 * within the block. That is, we will start with the top row of
655 * each block in order, then the second row of each block in order,
658 * This transformation has the enormous advantage that it means
659 * every row, column _and_ block is described by an arithmetic
660 * progression of coordinates within the cubic array, so that I can
661 * use the same very simple function to do blockwise, row-wise and
662 * column-wise elimination.
664 #define YTRANS(y) (((y)%c)*r+(y)/c)
665 #define YUNTRANS(y) (((y)%r)*c+(y)/r)
667 struct nsolve_usage {
670 * We set up a cubic array, indexed by x, y and digit; each
671 * element of this array is TRUE or FALSE according to whether
672 * or not that digit _could_ in principle go in that position.
674 * The way to index this array is cube[(x*cr+y)*cr+n-1].
675 * y-coordinates in here are transformed.
679 * This is the grid in which we write down our final
680 * deductions. y-coordinates in here are _not_ transformed.
684 * Now we keep track, at a slightly higher level, of what we
685 * have yet to work out, to prevent doing the same deduction
688 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
690 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
692 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
695 #define cubepos(x,y,n) (((x)*usage->cr+(y))*usage->cr+(n)-1)
696 #define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
699 * Function called when we are certain that a particular square has
700 * a particular number in it. The y-coordinate passed in here is
703 static void nsolve_place(struct nsolve_usage *usage, int x, int y, int n)
705 int c = usage->c, r = usage->r, cr = usage->cr;
711 * Rule out all other numbers in this square.
713 for (i = 1; i <= cr; i++)
718 * Rule out this number in all other positions in the row.
720 for (i = 0; i < cr; i++)
725 * Rule out this number in all other positions in the column.
727 for (i = 0; i < cr; i++)
732 * Rule out this number in all other positions in the block.
736 for (i = 0; i < r; i++)
737 for (j = 0; j < c; j++)
738 if (bx+i != x || by+j*r != y)
739 cube(bx+i,by+j*r,n) = FALSE;
742 * Enter the number in the result grid.
744 usage->grid[YUNTRANS(y)*cr+x] = n;
747 * Cross out this number from the list of numbers left to place
748 * in its row, its column and its block.
750 usage->row[y*cr+n-1] = usage->col[x*cr+n-1] =
751 usage->blk[((y%r)*c+(x/r))*cr+n-1] = TRUE;
754 static int nsolve_elim(struct nsolve_usage *usage, int start, int step
755 #ifdef STANDALONE_SOLVER
760 int c = usage->c, r = usage->r, cr = c*r;
764 * Count the number of set bits within this section of the
769 for (i = 0; i < cr; i++)
770 if (usage->cube[start+i*step]) {
784 if (!usage->grid[YUNTRANS(y)*cr+x]) {
785 #ifdef STANDALONE_SOLVER
786 if (solver_show_working) {
791 printf(":\n placing %d at (%d,%d)\n",
792 n, 1+x, 1+YUNTRANS(y));
795 nsolve_place(usage, x, y, n);
803 static int nsolve_intersect(struct nsolve_usage *usage,
804 int start1, int step1, int start2, int step2
805 #ifdef STANDALONE_SOLVER
810 int c = usage->c, r = usage->r, cr = c*r;
814 * Loop over the first domain and see if there's any set bit
815 * not also in the second.
817 for (i = 0; i < cr; i++) {
818 int p = start1+i*step1;
819 if (usage->cube[p] &&
820 !(p >= start2 && p < start2+cr*step2 &&
821 (p - start2) % step2 == 0))
822 return FALSE; /* there is, so we can't deduce */
826 * We have determined that all set bits in the first domain are
827 * within its overlap with the second. So loop over the second
828 * domain and remove all set bits that aren't also in that
829 * overlap; return TRUE iff we actually _did_ anything.
832 for (i = 0; i < cr; i++) {
833 int p = start2+i*step2;
834 if (usage->cube[p] &&
835 !(p >= start1 && p < start1+cr*step1 && (p - start1) % step1 == 0))
837 #ifdef STANDALONE_SOLVER
838 if (solver_show_working) {
854 printf(" ruling out %d at (%d,%d)\n",
855 pn, 1+px, 1+YUNTRANS(py));
858 ret = TRUE; /* we did something */
866 struct nsolve_scratch {
867 unsigned char *grid, *rowidx, *colidx, *set;
870 static int nsolve_set(struct nsolve_usage *usage,
871 struct nsolve_scratch *scratch,
872 int start, int step1, int step2
873 #ifdef STANDALONE_SOLVER
878 int c = usage->c, r = usage->r, cr = c*r;
880 unsigned char *grid = scratch->grid;
881 unsigned char *rowidx = scratch->rowidx;
882 unsigned char *colidx = scratch->colidx;
883 unsigned char *set = scratch->set;
886 * We are passed a cr-by-cr matrix of booleans. Our first job
887 * is to winnow it by finding any definite placements - i.e.
888 * any row with a solitary 1 - and discarding that row and the
889 * column containing the 1.
891 memset(rowidx, TRUE, cr);
892 memset(colidx, TRUE, cr);
893 for (i = 0; i < cr; i++) {
894 int count = 0, first = -1;
895 for (j = 0; j < cr; j++)
896 if (usage->cube[start+i*step1+j*step2])
900 * This condition actually marks a completely insoluble
901 * (i.e. internally inconsistent) puzzle. We return and
902 * report no progress made.
907 rowidx[i] = colidx[first] = FALSE;
911 * Convert each of rowidx/colidx from a list of 0s and 1s to a
912 * list of the indices of the 1s.
914 for (i = j = 0; i < cr; i++)
918 for (i = j = 0; i < cr; i++)
924 * And create the smaller matrix.
926 for (i = 0; i < n; i++)
927 for (j = 0; j < n; j++)
928 grid[i*cr+j] = usage->cube[start+rowidx[i]*step1+colidx[j]*step2];
931 * Having done that, we now have a matrix in which every row
932 * has at least two 1s in. Now we search to see if we can find
933 * a rectangle of zeroes (in the set-theoretic sense of
934 * `rectangle', i.e. a subset of rows crossed with a subset of
935 * columns) whose width and height add up to n.
942 * We have a candidate set. If its size is <=1 or >=n-1
943 * then we move on immediately.
945 if (count > 1 && count < n-1) {
947 * The number of rows we need is n-count. See if we can
948 * find that many rows which each have a zero in all
949 * the positions listed in `set'.
952 for (i = 0; i < n; i++) {
954 for (j = 0; j < n; j++)
955 if (set[j] && grid[i*cr+j]) {
964 * We expect never to be able to get _more_ than
965 * n-count suitable rows: this would imply that (for
966 * example) there are four numbers which between them
967 * have at most three possible positions, and hence it
968 * indicates a faulty deduction before this point or
971 assert(rows <= n - count);
972 if (rows >= n - count) {
973 int progress = FALSE;
976 * We've got one! Now, for each row which _doesn't_
977 * satisfy the criterion, eliminate all its set
978 * bits in the positions _not_ listed in `set'.
979 * Return TRUE (meaning progress has been made) if
980 * we successfully eliminated anything at all.
982 * This involves referring back through
983 * rowidx/colidx in order to work out which actual
984 * positions in the cube to meddle with.
986 for (i = 0; i < n; i++) {
988 for (j = 0; j < n; j++)
989 if (set[j] && grid[i*cr+j]) {
994 for (j = 0; j < n; j++)
995 if (!set[j] && grid[i*cr+j]) {
996 int fpos = (start+rowidx[i]*step1+
998 #ifdef STANDALONE_SOLVER
999 if (solver_show_working) {
1015 printf(" ruling out %d at (%d,%d)\n",
1016 pn, 1+px, 1+YUNTRANS(py));
1020 usage->cube[fpos] = FALSE;
1032 * Binary increment: change the rightmost 0 to a 1, and
1033 * change all 1s to the right of it to 0s.
1036 while (i > 0 && set[i-1])
1037 set[--i] = 0, count--;
1039 set[--i] = 1, count++;
1047 static struct nsolve_scratch *nsolve_new_scratch(struct nsolve_usage *usage)
1049 struct nsolve_scratch *scratch = snew(struct nsolve_scratch);
1051 scratch->grid = snewn(cr*cr, unsigned char);
1052 scratch->rowidx = snewn(cr, unsigned char);
1053 scratch->colidx = snewn(cr, unsigned char);
1054 scratch->set = snewn(cr, unsigned char);
1058 static void nsolve_free_scratch(struct nsolve_scratch *scratch)
1060 sfree(scratch->set);
1061 sfree(scratch->colidx);
1062 sfree(scratch->rowidx);
1063 sfree(scratch->grid);
1067 static int nsolve(int c, int r, digit *grid)
1069 struct nsolve_usage *usage;
1070 struct nsolve_scratch *scratch;
1073 int diff = DIFF_BLOCK;
1076 * Set up a usage structure as a clean slate (everything
1079 usage = snew(struct nsolve_usage);
1083 usage->cube = snewn(cr*cr*cr, unsigned char);
1084 usage->grid = grid; /* write straight back to the input */
1085 memset(usage->cube, TRUE, cr*cr*cr);
1087 usage->row = snewn(cr * cr, unsigned char);
1088 usage->col = snewn(cr * cr, unsigned char);
1089 usage->blk = snewn(cr * cr, unsigned char);
1090 memset(usage->row, FALSE, cr * cr);
1091 memset(usage->col, FALSE, cr * cr);
1092 memset(usage->blk, FALSE, cr * cr);
1094 scratch = nsolve_new_scratch(usage);
1097 * Place all the clue numbers we are given.
1099 for (x = 0; x < cr; x++)
1100 for (y = 0; y < cr; y++)
1102 nsolve_place(usage, x, YTRANS(y), grid[y*cr+x]);
1105 * Now loop over the grid repeatedly trying all permitted modes
1106 * of reasoning. The loop terminates if we complete an
1107 * iteration without making any progress; we then return
1108 * failure or success depending on whether the grid is full or
1113 * I'd like to write `continue;' inside each of the
1114 * following loops, so that the solver returns here after
1115 * making some progress. However, I can't specify that I
1116 * want to continue an outer loop rather than the innermost
1117 * one, so I'm apologetically resorting to a goto.
1122 * Blockwise positional elimination.
1124 for (x = 0; x < cr; x += r)
1125 for (y = 0; y < r; y++)
1126 for (n = 1; n <= cr; n++)
1127 if (!usage->blk[(y*c+(x/r))*cr+n-1] &&
1128 nsolve_elim(usage, cubepos(x,y,n), r*cr
1129 #ifdef STANDALONE_SOLVER
1130 , "positional elimination,"
1131 " block (%d,%d)", 1+x/r, 1+y
1134 diff = max(diff, DIFF_BLOCK);
1139 * Row-wise positional elimination.
1141 for (y = 0; y < cr; y++)
1142 for (n = 1; n <= cr; n++)
1143 if (!usage->row[y*cr+n-1] &&
1144 nsolve_elim(usage, cubepos(0,y,n), cr*cr
1145 #ifdef STANDALONE_SOLVER
1146 , "positional elimination,"
1147 " row %d", 1+YUNTRANS(y)
1150 diff = max(diff, DIFF_SIMPLE);
1154 * Column-wise positional elimination.
1156 for (x = 0; x < cr; x++)
1157 for (n = 1; n <= cr; n++)
1158 if (!usage->col[x*cr+n-1] &&
1159 nsolve_elim(usage, cubepos(x,0,n), cr
1160 #ifdef STANDALONE_SOLVER
1161 , "positional elimination," " column %d", 1+x
1164 diff = max(diff, DIFF_SIMPLE);
1169 * Numeric elimination.
1171 for (x = 0; x < cr; x++)
1172 for (y = 0; y < cr; y++)
1173 if (!usage->grid[YUNTRANS(y)*cr+x] &&
1174 nsolve_elim(usage, cubepos(x,y,1), 1
1175 #ifdef STANDALONE_SOLVER
1176 , "numeric elimination at (%d,%d)", 1+x,
1180 diff = max(diff, DIFF_SIMPLE);
1185 * Intersectional analysis, rows vs blocks.
1187 for (y = 0; y < cr; y++)
1188 for (x = 0; x < cr; x += r)
1189 for (n = 1; n <= cr; n++)
1190 if (!usage->row[y*cr+n-1] &&
1191 !usage->blk[((y%r)*c+(x/r))*cr+n-1] &&
1192 (nsolve_intersect(usage, cubepos(0,y,n), cr*cr,
1193 cubepos(x,y%r,n), r*cr
1194 #ifdef STANDALONE_SOLVER
1195 , "intersectional analysis,"
1196 " row %d vs block (%d,%d)",
1197 1+YUNTRANS(y), 1+x/r, 1+y%r
1200 nsolve_intersect(usage, cubepos(x,y%r,n), r*cr,
1201 cubepos(0,y,n), cr*cr
1202 #ifdef STANDALONE_SOLVER
1203 , "intersectional analysis,"
1204 " block (%d,%d) vs row %d",
1205 1+x/r, 1+y%r, 1+YUNTRANS(y)
1208 diff = max(diff, DIFF_INTERSECT);
1213 * Intersectional analysis, columns vs blocks.
1215 for (x = 0; x < cr; x++)
1216 for (y = 0; y < r; y++)
1217 for (n = 1; n <= cr; n++)
1218 if (!usage->col[x*cr+n-1] &&
1219 !usage->blk[(y*c+(x/r))*cr+n-1] &&
1220 (nsolve_intersect(usage, cubepos(x,0,n), cr,
1221 cubepos((x/r)*r,y,n), r*cr
1222 #ifdef STANDALONE_SOLVER
1223 , "intersectional analysis,"
1224 " column %d vs block (%d,%d)",
1228 nsolve_intersect(usage, cubepos((x/r)*r,y,n), r*cr,
1230 #ifdef STANDALONE_SOLVER
1231 , "intersectional analysis,"
1232 " block (%d,%d) vs column %d",
1236 diff = max(diff, DIFF_INTERSECT);
1241 * Blockwise set elimination.
1243 for (x = 0; x < cr; x += r)
1244 for (y = 0; y < r; y++)
1245 if (nsolve_set(usage, scratch, cubepos(x,y,1), r*cr, 1
1246 #ifdef STANDALONE_SOLVER
1247 , "set elimination, block (%d,%d)", 1+x/r, 1+y
1250 diff = max(diff, DIFF_SET);
1255 * Row-wise set elimination.
1257 for (y = 0; y < cr; y++)
1258 if (nsolve_set(usage, scratch, cubepos(0,y,1), cr*cr, 1
1259 #ifdef STANDALONE_SOLVER
1260 , "set elimination, row %d", 1+YUNTRANS(y)
1263 diff = max(diff, DIFF_SET);
1268 * Column-wise set elimination.
1270 for (x = 0; x < cr; x++)
1271 if (nsolve_set(usage, scratch, cubepos(x,0,1), cr, 1
1272 #ifdef STANDALONE_SOLVER
1273 , "set elimination, column %d", 1+x
1276 diff = max(diff, DIFF_SET);
1281 * If we reach here, we have made no deductions in this
1282 * iteration, so the algorithm terminates.
1287 nsolve_free_scratch(scratch);
1295 for (x = 0; x < cr; x++)
1296 for (y = 0; y < cr; y++)
1298 return DIFF_IMPOSSIBLE;
1302 /* ----------------------------------------------------------------------
1303 * End of non-recursive solver code.
1307 * Check whether a grid contains a valid complete puzzle.
1309 static int check_valid(int c, int r, digit *grid)
1312 unsigned char *used;
1315 used = snewn(cr, unsigned char);
1318 * Check that each row contains precisely one of everything.
1320 for (y = 0; y < cr; y++) {
1321 memset(used, FALSE, cr);
1322 for (x = 0; x < cr; x++)
1323 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
1324 used[grid[y*cr+x]-1] = TRUE;
1325 for (n = 0; n < cr; n++)
1333 * Check that each column contains precisely one of everything.
1335 for (x = 0; x < cr; x++) {
1336 memset(used, FALSE, cr);
1337 for (y = 0; y < cr; y++)
1338 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
1339 used[grid[y*cr+x]-1] = TRUE;
1340 for (n = 0; n < cr; n++)
1348 * Check that each block contains precisely one of everything.
1350 for (x = 0; x < cr; x += r) {
1351 for (y = 0; y < cr; y += c) {
1353 memset(used, FALSE, cr);
1354 for (xx = x; xx < x+r; xx++)
1355 for (yy = 0; yy < y+c; yy++)
1356 if (grid[yy*cr+xx] > 0 && grid[yy*cr+xx] <= cr)
1357 used[grid[yy*cr+xx]-1] = TRUE;
1358 for (n = 0; n < cr; n++)
1370 static int symmetries(game_params *params, int x, int y, int *output, int s)
1372 int c = params->c, r = params->r, cr = c*r;
1375 #define ADD(x,y) (*output++ = (x), *output++ = (y), i++)
1381 break; /* just x,y is all we need */
1383 ADD(cr - 1 - x, cr - 1 - y);
1388 ADD(cr - 1 - x, cr - 1 - y);
1399 ADD(cr - 1 - x, cr - 1 - y);
1403 ADD(cr - 1 - x, cr - 1 - y);
1404 ADD(cr - 1 - y, cr - 1 - x);
1409 ADD(cr - 1 - x, cr - 1 - y);
1413 ADD(cr - 1 - y, cr - 1 - x);
1422 static char *encode_solve_move(int cr, digit *grid)
1425 char *ret, *p, *sep;
1428 * It's surprisingly easy to work out _exactly_ how long this
1429 * string needs to be. To decimal-encode all the numbers from 1
1432 * - every number has a units digit; total is n.
1433 * - all numbers above 9 have a tens digit; total is max(n-9,0).
1434 * - all numbers above 99 have a hundreds digit; total is max(n-99,0).
1438 for (i = 1; i <= cr; i *= 10)
1439 len += max(cr - i + 1, 0);
1440 len += cr; /* don't forget the commas */
1441 len *= cr; /* there are cr rows of these */
1444 * Now len is one bigger than the total size of the
1445 * comma-separated numbers (because we counted an
1446 * additional leading comma). We need to have a leading S
1447 * and a trailing NUL, so we're off by one in total.
1451 ret = snewn(len, char);
1455 for (i = 0; i < cr*cr; i++) {
1456 p += sprintf(p, "%s%d", sep, grid[i]);
1460 assert(p - ret == len);
1465 static char *new_game_desc(game_params *params, random_state *rs,
1466 char **aux, int interactive)
1468 int c = params->c, r = params->r, cr = c*r;
1470 digit *grid, *grid2;
1471 struct xy { int x, y; } *locs;
1475 int coords[16], ncoords;
1476 int *symmclasses, nsymmclasses;
1477 int maxdiff, recursing;
1480 * Adjust the maximum difficulty level to be consistent with
1481 * the puzzle size: all 2x2 puzzles appear to be Trivial
1482 * (DIFF_BLOCK) so we cannot hold out for even a Basic
1483 * (DIFF_SIMPLE) one.
1485 maxdiff = params->diff;
1486 if (c == 2 && r == 2)
1487 maxdiff = DIFF_BLOCK;
1489 grid = snewn(area, digit);
1490 locs = snewn(area, struct xy);
1491 grid2 = snewn(area, digit);
1494 * Find the set of equivalence classes of squares permitted
1495 * by the selected symmetry. We do this by enumerating all
1496 * the grid squares which have no symmetric companion
1497 * sorting lower than themselves.
1500 symmclasses = snewn(cr * cr, int);
1504 for (y = 0; y < cr; y++)
1505 for (x = 0; x < cr; x++) {
1509 ncoords = symmetries(params, x, y, coords, params->symm);
1510 for (j = 0; j < ncoords; j++)
1511 if (coords[2*j+1]*cr+coords[2*j] < i)
1514 symmclasses[nsymmclasses++] = i;
1519 * Loop until we get a grid of the required difficulty. This is
1520 * nasty, but it seems to be unpleasantly hard to generate
1521 * difficult grids otherwise.
1525 * Start the recursive solver with an empty grid to generate a
1526 * random solved state.
1528 memset(grid, 0, area);
1529 ret = rsolve(c, r, grid, rs, 1);
1531 assert(check_valid(c, r, grid));
1534 * Save the solved grid in aux.
1538 * We might already have written *aux the last time we
1539 * went round this loop, in which case we should free
1540 * the old aux before overwriting it with the new one.
1546 *aux = encode_solve_move(cr, grid);
1550 * Now we have a solved grid, start removing things from it
1551 * while preserving solubility.
1558 * Iterate over the grid and enumerate all the filled
1559 * squares we could empty.
1563 for (i = 0; i < nsymmclasses; i++) {
1564 x = symmclasses[i] % cr;
1565 y = symmclasses[i] / cr;
1574 * Now shuffle that list.
1576 for (i = nlocs; i > 1; i--) {
1577 int p = random_upto(rs, i);
1579 struct xy t = locs[p];
1580 locs[p] = locs[i-1];
1586 * Now loop over the shuffled list and, for each element,
1587 * see whether removing that element (and its reflections)
1588 * from the grid will still leave the grid soluble by
1591 for (i = 0; i < nlocs; i++) {
1597 memcpy(grid2, grid, area);
1598 ncoords = symmetries(params, x, y, coords, params->symm);
1599 for (j = 0; j < ncoords; j++)
1600 grid2[coords[2*j+1]*cr+coords[2*j]] = 0;
1603 ret = (rsolve(c, r, grid2, NULL, 2) == 1);
1605 ret = (nsolve(c, r, grid2) <= maxdiff);
1608 for (j = 0; j < ncoords; j++)
1609 grid[coords[2*j+1]*cr+coords[2*j]] = 0;
1616 * There was nothing we could remove without
1617 * destroying solvability. If we're trying to
1618 * generate a recursion-only grid and haven't
1619 * switched over to rsolve yet, we now do;
1620 * otherwise we give up.
1622 if (maxdiff == DIFF_RECURSIVE && !recursing) {
1630 memcpy(grid2, grid, area);
1631 } while (nsolve(c, r, grid2) < maxdiff);
1639 * Now we have the grid as it will be presented to the user.
1640 * Encode it in a game desc.
1646 desc = snewn(5 * area, char);
1649 for (i = 0; i <= area; i++) {
1650 int n = (i < area ? grid[i] : -1);
1657 int c = 'a' - 1 + run;
1661 run -= c - ('a' - 1);
1665 * If there's a number in the very top left or
1666 * bottom right, there's no point putting an
1667 * unnecessary _ before or after it.
1669 if (p > desc && n > 0)
1673 p += sprintf(p, "%d", n);
1677 assert(p - desc < 5 * area);
1679 desc = sresize(desc, p - desc, char);
1687 static char *validate_desc(game_params *params, char *desc)
1689 int area = params->r * params->r * params->c * params->c;
1694 if (n >= 'a' && n <= 'z') {
1695 squares += n - 'a' + 1;
1696 } else if (n == '_') {
1698 } else if (n > '0' && n <= '9') {
1700 while (*desc >= '0' && *desc <= '9')
1703 return "Invalid character in game description";
1707 return "Not enough data to fill grid";
1710 return "Too much data to fit in grid";
1715 static game_state *new_game(midend_data *me, game_params *params, char *desc)
1717 game_state *state = snew(game_state);
1718 int c = params->c, r = params->r, cr = c*r, area = cr * cr;
1721 state->c = params->c;
1722 state->r = params->r;
1724 state->grid = snewn(area, digit);
1725 state->pencil = snewn(area * cr, unsigned char);
1726 memset(state->pencil, 0, area * cr);
1727 state->immutable = snewn(area, unsigned char);
1728 memset(state->immutable, FALSE, area);
1730 state->completed = state->cheated = FALSE;
1735 if (n >= 'a' && n <= 'z') {
1736 int run = n - 'a' + 1;
1737 assert(i + run <= area);
1739 state->grid[i++] = 0;
1740 } else if (n == '_') {
1742 } else if (n > '0' && n <= '9') {
1744 state->immutable[i] = TRUE;
1745 state->grid[i++] = atoi(desc-1);
1746 while (*desc >= '0' && *desc <= '9')
1749 assert(!"We can't get here");
1757 static game_state *dup_game(game_state *state)
1759 game_state *ret = snew(game_state);
1760 int c = state->c, r = state->r, cr = c*r, area = cr * cr;
1765 ret->grid = snewn(area, digit);
1766 memcpy(ret->grid, state->grid, area);
1768 ret->pencil = snewn(area * cr, unsigned char);
1769 memcpy(ret->pencil, state->pencil, area * cr);
1771 ret->immutable = snewn(area, unsigned char);
1772 memcpy(ret->immutable, state->immutable, area);
1774 ret->completed = state->completed;
1775 ret->cheated = state->cheated;
1780 static void free_game(game_state *state)
1782 sfree(state->immutable);
1783 sfree(state->pencil);
1788 static char *solve_game(game_state *state, game_state *currstate,
1789 char *ai, char **error)
1791 int c = state->c, r = state->r, cr = c*r;
1797 * If we already have the solution in ai, save ourselves some
1803 grid = snewn(cr*cr, digit);
1804 memcpy(grid, state->grid, cr*cr);
1805 rsolve_ret = rsolve(c, r, grid, NULL, 2);
1807 if (rsolve_ret != 1) {
1809 if (rsolve_ret == 0)
1810 *error = "No solution exists for this puzzle";
1812 *error = "Multiple solutions exist for this puzzle";
1816 ret = encode_solve_move(cr, grid);
1823 static char *grid_text_format(int c, int r, digit *grid)
1831 * There are cr lines of digits, plus r-1 lines of block
1832 * separators. Each line contains cr digits, cr-1 separating
1833 * spaces, and c-1 two-character block separators. Thus, the
1834 * total length of a line is 2*cr+2*c-3 (not counting the
1835 * newline), and there are cr+r-1 of them.
1837 maxlen = (cr+r-1) * (2*cr+2*c-2);
1838 ret = snewn(maxlen+1, char);
1841 for (y = 0; y < cr; y++) {
1842 for (x = 0; x < cr; x++) {
1843 int ch = grid[y * cr + x];
1853 if ((x+1) % r == 0) {
1860 if (y+1 < cr && (y+1) % c == 0) {
1861 for (x = 0; x < cr; x++) {
1865 if ((x+1) % r == 0) {
1875 assert(p - ret == maxlen);
1880 static char *game_text_format(game_state *state)
1882 return grid_text_format(state->c, state->r, state->grid);
1887 * These are the coordinates of the currently highlighted
1888 * square on the grid, or -1,-1 if there isn't one. When there
1889 * is, pressing a valid number or letter key or Space will
1890 * enter that number or letter in the grid.
1894 * This indicates whether the current highlight is a
1895 * pencil-mark one or a real one.
1900 static game_ui *new_ui(game_state *state)
1902 game_ui *ui = snew(game_ui);
1904 ui->hx = ui->hy = -1;
1910 static void free_ui(game_ui *ui)
1915 static char *encode_ui(game_ui *ui)
1920 static void decode_ui(game_ui *ui, char *encoding)
1924 static void game_changed_state(game_ui *ui, game_state *oldstate,
1925 game_state *newstate)
1927 int c = newstate->c, r = newstate->r, cr = c*r;
1929 * We prevent pencil-mode highlighting of a filled square. So
1930 * if the user has just filled in a square which we had a
1931 * pencil-mode highlight in (by Undo, or by Redo, or by Solve),
1932 * then we cancel the highlight.
1934 if (ui->hx >= 0 && ui->hy >= 0 && ui->hpencil &&
1935 newstate->grid[ui->hy * cr + ui->hx] != 0) {
1936 ui->hx = ui->hy = -1;
1940 struct game_drawstate {
1945 unsigned char *pencil;
1947 /* This is scratch space used within a single call to game_redraw. */
1951 static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
1952 int x, int y, int button)
1954 int c = state->c, r = state->r, cr = c*r;
1958 button &= ~MOD_MASK;
1960 tx = (x + TILE_SIZE - BORDER) / TILE_SIZE - 1;
1961 ty = (y + TILE_SIZE - BORDER) / TILE_SIZE - 1;
1963 if (tx >= 0 && tx < cr && ty >= 0 && ty < cr) {
1964 if (button == LEFT_BUTTON) {
1965 if (state->immutable[ty*cr+tx]) {
1966 ui->hx = ui->hy = -1;
1967 } else if (tx == ui->hx && ty == ui->hy && ui->hpencil == 0) {
1968 ui->hx = ui->hy = -1;
1974 return ""; /* UI activity occurred */
1976 if (button == RIGHT_BUTTON) {
1978 * Pencil-mode highlighting for non filled squares.
1980 if (state->grid[ty*cr+tx] == 0) {
1981 if (tx == ui->hx && ty == ui->hy && ui->hpencil) {
1982 ui->hx = ui->hy = -1;
1989 ui->hx = ui->hy = -1;
1991 return ""; /* UI activity occurred */
1995 if (ui->hx != -1 && ui->hy != -1 &&
1996 ((button >= '1' && button <= '9' && button - '0' <= cr) ||
1997 (button >= 'a' && button <= 'z' && button - 'a' + 10 <= cr) ||
1998 (button >= 'A' && button <= 'Z' && button - 'A' + 10 <= cr) ||
2000 int n = button - '0';
2001 if (button >= 'A' && button <= 'Z')
2002 n = button - 'A' + 10;
2003 if (button >= 'a' && button <= 'z')
2004 n = button - 'a' + 10;
2009 * Can't overwrite this square. In principle this shouldn't
2010 * happen anyway because we should never have even been
2011 * able to highlight the square, but it never hurts to be
2014 if (state->immutable[ui->hy*cr+ui->hx])
2018 * Can't make pencil marks in a filled square. In principle
2019 * this shouldn't happen anyway because we should never
2020 * have even been able to pencil-highlight the square, but
2021 * it never hurts to be careful.
2023 if (ui->hpencil && state->grid[ui->hy*cr+ui->hx])
2026 sprintf(buf, "%c%d,%d,%d",
2027 (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n);
2029 ui->hx = ui->hy = -1;
2037 static game_state *execute_move(game_state *from, char *move)
2039 int c = from->c, r = from->r, cr = c*r;
2043 if (move[0] == 'S') {
2046 ret = dup_game(from);
2047 ret->completed = ret->cheated = TRUE;
2050 for (n = 0; n < cr*cr; n++) {
2051 ret->grid[n] = atoi(p);
2053 if (!*p || ret->grid[n] < 1 || ret->grid[n] > cr) {
2058 while (*p && isdigit((unsigned char)*p)) p++;
2063 } else if ((move[0] == 'P' || move[0] == 'R') &&
2064 sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
2065 x >= 0 && x < cr && y >= 0 && y < cr && n >= 0 && n <= cr) {
2067 ret = dup_game(from);
2068 if (move[0] == 'P' && n > 0) {
2069 int index = (y*cr+x) * cr + (n-1);
2070 ret->pencil[index] = !ret->pencil[index];
2072 ret->grid[y*cr+x] = n;
2073 memset(ret->pencil + (y*cr+x)*cr, 0, cr);
2076 * We've made a real change to the grid. Check to see
2077 * if the game has been completed.
2079 if (!ret->completed && check_valid(c, r, ret->grid)) {
2080 ret->completed = TRUE;
2085 return NULL; /* couldn't parse move string */
2088 /* ----------------------------------------------------------------------
2092 #define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
2093 #define GETTILESIZE(cr, w) ( (double)(w-1) / (double)(cr+1) )
2095 static void game_compute_size(game_params *params, int tilesize,
2098 /* Ick: fake up `ds->tilesize' for macro expansion purposes */
2099 struct { int tilesize; } ads, *ds = &ads;
2100 ads.tilesize = tilesize;
2102 *x = SIZE(params->c * params->r);
2103 *y = SIZE(params->c * params->r);
2106 static void game_set_size(game_drawstate *ds, game_params *params,
2109 ds->tilesize = tilesize;
2112 static float *game_colours(frontend *fe, game_state *state, int *ncolours)
2114 float *ret = snewn(3 * NCOLOURS, float);
2116 frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
2118 ret[COL_GRID * 3 + 0] = 0.0F;
2119 ret[COL_GRID * 3 + 1] = 0.0F;
2120 ret[COL_GRID * 3 + 2] = 0.0F;
2122 ret[COL_CLUE * 3 + 0] = 0.0F;
2123 ret[COL_CLUE * 3 + 1] = 0.0F;
2124 ret[COL_CLUE * 3 + 2] = 0.0F;
2126 ret[COL_USER * 3 + 0] = 0.0F;
2127 ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
2128 ret[COL_USER * 3 + 2] = 0.0F;
2130 ret[COL_HIGHLIGHT * 3 + 0] = 0.85F * ret[COL_BACKGROUND * 3 + 0];
2131 ret[COL_HIGHLIGHT * 3 + 1] = 0.85F * ret[COL_BACKGROUND * 3 + 1];
2132 ret[COL_HIGHLIGHT * 3 + 2] = 0.85F * ret[COL_BACKGROUND * 3 + 2];
2134 ret[COL_ERROR * 3 + 0] = 1.0F;
2135 ret[COL_ERROR * 3 + 1] = 0.0F;
2136 ret[COL_ERROR * 3 + 2] = 0.0F;
2138 ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
2139 ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
2140 ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
2142 *ncolours = NCOLOURS;
2146 static game_drawstate *game_new_drawstate(game_state *state)
2148 struct game_drawstate *ds = snew(struct game_drawstate);
2149 int c = state->c, r = state->r, cr = c*r;
2151 ds->started = FALSE;
2155 ds->grid = snewn(cr*cr, digit);
2156 memset(ds->grid, 0, cr*cr);
2157 ds->pencil = snewn(cr*cr*cr, digit);
2158 memset(ds->pencil, 0, cr*cr*cr);
2159 ds->hl = snewn(cr*cr, unsigned char);
2160 memset(ds->hl, 0, cr*cr);
2161 ds->entered_items = snewn(cr*cr, int);
2162 ds->tilesize = 0; /* not decided yet */
2166 static void game_free_drawstate(game_drawstate *ds)
2171 sfree(ds->entered_items);
2175 static void draw_number(frontend *fe, game_drawstate *ds, game_state *state,
2176 int x, int y, int hl)
2178 int c = state->c, r = state->r, cr = c*r;
2183 if (ds->grid[y*cr+x] == state->grid[y*cr+x] &&
2184 ds->hl[y*cr+x] == hl &&
2185 !memcmp(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr))
2186 return; /* no change required */
2188 tx = BORDER + x * TILE_SIZE + 2;
2189 ty = BORDER + y * TILE_SIZE + 2;
2205 clip(fe, cx, cy, cw, ch);
2207 /* background needs erasing */
2208 draw_rect(fe, cx, cy, cw, ch, (hl & 15) == 1 ? COL_HIGHLIGHT : COL_BACKGROUND);
2210 /* pencil-mode highlight */
2211 if ((hl & 15) == 2) {
2215 coords[2] = cx+cw/2;
2218 coords[5] = cy+ch/2;
2219 draw_polygon(fe, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
2222 /* new number needs drawing? */
2223 if (state->grid[y*cr+x]) {
2225 str[0] = state->grid[y*cr+x] + '0';
2227 str[0] += 'a' - ('9'+1);
2228 draw_text(fe, tx + TILE_SIZE/2, ty + TILE_SIZE/2,
2229 FONT_VARIABLE, TILE_SIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
2230 state->immutable[y*cr+x] ? COL_CLUE : (hl & 16) ? COL_ERROR : COL_USER, str);
2233 int pw, ph, pmax, fontsize;
2235 /* count the pencil marks required */
2236 for (i = npencil = 0; i < cr; i++)
2237 if (state->pencil[(y*cr+x)*cr+i])
2241 * It's not sensible to arrange pencil marks in the same
2242 * layout as the squares within a block, because this leads
2243 * to the font being too small. Instead, we arrange pencil
2244 * marks in the nearest thing we can to a square layout,
2245 * and we adjust the square layout depending on the number
2246 * of pencil marks in the square.
2248 for (pw = 1; pw * pw < npencil; pw++);
2249 if (pw < 3) pw = 3; /* otherwise it just looks _silly_ */
2250 ph = (npencil + pw - 1) / pw;
2251 if (ph < 2) ph = 2; /* likewise */
2253 fontsize = TILE_SIZE/(pmax*(11-pmax)/8);
2255 for (i = j = 0; i < cr; i++)
2256 if (state->pencil[(y*cr+x)*cr+i]) {
2257 int dx = j % pw, dy = j / pw;
2262 str[0] += 'a' - ('9'+1);
2263 draw_text(fe, tx + (4*dx+3) * TILE_SIZE / (4*pw+2),
2264 ty + (4*dy+3) * TILE_SIZE / (4*ph+2),
2265 FONT_VARIABLE, fontsize,
2266 ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
2273 draw_update(fe, cx, cy, cw, ch);
2275 ds->grid[y*cr+x] = state->grid[y*cr+x];
2276 memcpy(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr);
2277 ds->hl[y*cr+x] = hl;
2280 static void game_redraw(frontend *fe, game_drawstate *ds, game_state *oldstate,
2281 game_state *state, int dir, game_ui *ui,
2282 float animtime, float flashtime)
2284 int c = state->c, r = state->r, cr = c*r;
2289 * The initial contents of the window are not guaranteed
2290 * and can vary with front ends. To be on the safe side,
2291 * all games should start by drawing a big
2292 * background-colour rectangle covering the whole window.
2294 draw_rect(fe, 0, 0, SIZE(cr), SIZE(cr), COL_BACKGROUND);
2299 for (x = 0; x <= cr; x++) {
2300 int thick = (x % r ? 0 : 1);
2301 draw_rect(fe, BORDER + x*TILE_SIZE - thick, BORDER-1,
2302 1+2*thick, cr*TILE_SIZE+3, COL_GRID);
2304 for (y = 0; y <= cr; y++) {
2305 int thick = (y % c ? 0 : 1);
2306 draw_rect(fe, BORDER-1, BORDER + y*TILE_SIZE - thick,
2307 cr*TILE_SIZE+3, 1+2*thick, COL_GRID);
2312 * This array is used to keep track of rows, columns and boxes
2313 * which contain a number more than once.
2315 for (x = 0; x < cr * cr; x++)
2316 ds->entered_items[x] = 0;
2317 for (x = 0; x < cr; x++)
2318 for (y = 0; y < cr; y++) {
2319 digit d = state->grid[y*cr+x];
2321 int box = (x/r)+(y/c)*c;
2322 ds->entered_items[x*cr+d-1] |= ((ds->entered_items[x*cr+d-1] & 1) << 1) | 1;
2323 ds->entered_items[y*cr+d-1] |= ((ds->entered_items[y*cr+d-1] & 4) << 1) | 4;
2324 ds->entered_items[box*cr+d-1] |= ((ds->entered_items[box*cr+d-1] & 16) << 1) | 16;
2329 * Draw any numbers which need redrawing.
2331 for (x = 0; x < cr; x++) {
2332 for (y = 0; y < cr; y++) {
2334 digit d = state->grid[y*cr+x];
2336 if (flashtime > 0 &&
2337 (flashtime <= FLASH_TIME/3 ||
2338 flashtime >= FLASH_TIME*2/3))
2341 /* Highlight active input areas. */
2342 if (x == ui->hx && y == ui->hy)
2343 highlight = ui->hpencil ? 2 : 1;
2345 /* Mark obvious errors (ie, numbers which occur more than once
2346 * in a single row, column, or box). */
2347 if (d && ((ds->entered_items[x*cr+d-1] & 2) ||
2348 (ds->entered_items[y*cr+d-1] & 8) ||
2349 (ds->entered_items[((x/r)+(y/c)*c)*cr+d-1] & 32)))
2352 draw_number(fe, ds, state, x, y, highlight);
2357 * Update the _entire_ grid if necessary.
2360 draw_update(fe, 0, 0, SIZE(cr), SIZE(cr));
2365 static float game_anim_length(game_state *oldstate, game_state *newstate,
2366 int dir, game_ui *ui)
2371 static float game_flash_length(game_state *oldstate, game_state *newstate,
2372 int dir, game_ui *ui)
2374 if (!oldstate->completed && newstate->completed &&
2375 !oldstate->cheated && !newstate->cheated)
2380 static int game_wants_statusbar(void)
2385 static int game_timing_state(game_state *state)
2391 #define thegame solo
2394 const struct game thegame = {
2395 "Solo", "games.solo",
2402 TRUE, game_configure, custom_params,
2410 TRUE, game_text_format,
2418 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
2421 game_free_drawstate,
2425 game_wants_statusbar,
2426 FALSE, game_timing_state,
2427 0, /* mouse_priorities */
2430 #ifdef STANDALONE_SOLVER
2433 * gcc -DSTANDALONE_SOLVER -o solosolver solo.c malloc.c
2436 void frontend_default_colour(frontend *fe, float *output) {}
2437 void draw_text(frontend *fe, int x, int y, int fonttype, int fontsize,
2438 int align, int colour, char *text) {}
2439 void draw_rect(frontend *fe, int x, int y, int w, int h, int colour) {}
2440 void draw_line(frontend *fe, int x1, int y1, int x2, int y2, int colour) {}
2441 void draw_polygon(frontend *fe, int *coords, int npoints,
2442 int fillcolour, int outlinecolour) {}
2443 void clip(frontend *fe, int x, int y, int w, int h) {}
2444 void unclip(frontend *fe) {}
2445 void start_draw(frontend *fe) {}
2446 void draw_update(frontend *fe, int x, int y, int w, int h) {}
2447 void end_draw(frontend *fe) {}
2448 unsigned long random_bits(random_state *state, int bits)
2449 { assert(!"Shouldn't get randomness"); return 0; }
2450 unsigned long random_upto(random_state *state, unsigned long limit)
2451 { assert(!"Shouldn't get randomness"); return 0; }
2453 void fatal(char *fmt, ...)
2457 fprintf(stderr, "fatal error: ");
2460 vfprintf(stderr, fmt, ap);
2463 fprintf(stderr, "\n");
2467 int main(int argc, char **argv)
2472 char *id = NULL, *desc, *err;
2476 while (--argc > 0) {
2478 if (!strcmp(p, "-r")) {
2480 } else if (!strcmp(p, "-n")) {
2482 } else if (!strcmp(p, "-v")) {
2483 solver_show_working = TRUE;
2485 } else if (!strcmp(p, "-g")) {
2488 } else if (*p == '-') {
2489 fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0]);
2497 fprintf(stderr, "usage: %s [-n | -r | -g | -v] <game_id>\n", argv[0]);
2501 desc = strchr(id, ':');
2503 fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
2508 p = default_params();
2509 decode_params(p, id);
2510 err = validate_desc(p, desc);
2512 fprintf(stderr, "%s: %s\n", argv[0], err);
2515 s = new_game(NULL, p, desc);
2518 int ret = rsolve(p->c, p->r, s->grid, NULL, 2);
2520 fprintf(stderr, "%s: rsolve: multiple solutions detected\n",
2524 int ret = nsolve(p->c, p->r, s->grid);
2526 if (ret == DIFF_IMPOSSIBLE) {
2528 * Now resort to rsolve to determine whether it's
2531 ret = rsolve(p->c, p->r, s->grid, NULL, 2);
2533 ret = DIFF_IMPOSSIBLE;
2535 ret = DIFF_RECURSIVE;
2537 ret = DIFF_AMBIGUOUS;
2539 printf("Difficulty rating: %s\n",
2540 ret==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)":
2541 ret==DIFF_SIMPLE ? "Basic (row/column/number elimination required)":
2542 ret==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)":
2543 ret==DIFF_SET ? "Advanced (set elimination required)":
2544 ret==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)":
2545 ret==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)":
2546 ret==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)":
2547 "INTERNAL ERROR: unrecognised difficulty code");
2551 printf("%s\n", grid_text_format(p->c, p->r, s->grid));