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_REF4 };
118 enum { DIFF_BLOCK, DIFF_SIMPLE, DIFF_INTERSECT,
119 DIFF_SET, DIFF_RECURSIVE, DIFF_AMBIGUOUS, DIFF_IMPOSSIBLE };
133 int c, r, symm, diff;
139 unsigned char *pencil; /* c*r*c*r elements */
140 unsigned char *immutable; /* marks which digits are clues */
141 int completed, cheated;
144 static game_params *default_params(void)
146 game_params *ret = snew(game_params);
149 ret->symm = SYMM_ROT2; /* a plausible default */
150 ret->diff = DIFF_BLOCK; /* so is this */
155 static void free_params(game_params *params)
160 static game_params *dup_params(game_params *params)
162 game_params *ret = snew(game_params);
163 *ret = *params; /* structure copy */
167 static int game_fetch_preset(int i, char **name, game_params **params)
173 { "2x2 Trivial", { 2, 2, SYMM_ROT2, DIFF_BLOCK } },
174 { "2x3 Basic", { 2, 3, SYMM_ROT2, DIFF_SIMPLE } },
175 { "3x3 Trivial", { 3, 3, SYMM_ROT2, DIFF_BLOCK } },
176 { "3x3 Basic", { 3, 3, SYMM_ROT2, DIFF_SIMPLE } },
177 { "3x3 Intermediate", { 3, 3, SYMM_ROT2, DIFF_INTERSECT } },
178 { "3x3 Advanced", { 3, 3, SYMM_ROT2, DIFF_SET } },
179 { "3x3 Unreasonable", { 3, 3, SYMM_ROT2, DIFF_RECURSIVE } },
181 { "3x4 Basic", { 3, 4, SYMM_ROT2, DIFF_SIMPLE } },
182 { "4x4 Basic", { 4, 4, SYMM_ROT2, DIFF_SIMPLE } },
186 if (i < 0 || i >= lenof(presets))
189 *name = dupstr(presets[i].title);
190 *params = dup_params(&presets[i].params);
195 static void decode_params(game_params *ret, char const *string)
197 ret->c = ret->r = atoi(string);
198 while (*string && isdigit((unsigned char)*string)) string++;
199 if (*string == 'x') {
201 ret->r = atoi(string);
202 while (*string && isdigit((unsigned char)*string)) string++;
205 if (*string == 'r' || *string == 'm' || *string == 'a') {
209 while (*string && isdigit((unsigned char)*string)) string++;
210 if (sc == 'm' && sn == 4)
211 ret->symm = SYMM_REF4;
212 if (sc == 'r' && sn == 4)
213 ret->symm = SYMM_ROT4;
214 if (sc == 'r' && sn == 2)
215 ret->symm = SYMM_ROT2;
217 ret->symm = SYMM_NONE;
218 } else if (*string == 'd') {
220 if (*string == 't') /* trivial */
221 string++, ret->diff = DIFF_BLOCK;
222 else if (*string == 'b') /* basic */
223 string++, ret->diff = DIFF_SIMPLE;
224 else if (*string == 'i') /* intermediate */
225 string++, ret->diff = DIFF_INTERSECT;
226 else if (*string == 'a') /* advanced */
227 string++, ret->diff = DIFF_SET;
228 else if (*string == 'u') /* unreasonable */
229 string++, ret->diff = DIFF_RECURSIVE;
231 string++; /* eat unknown character */
235 static char *encode_params(game_params *params, int full)
239 sprintf(str, "%dx%d", params->c, params->r);
241 switch (params->symm) {
242 case SYMM_REF4: strcat(str, "m4"); break;
243 case SYMM_ROT4: strcat(str, "r4"); break;
244 /* case SYMM_ROT2: strcat(str, "r2"); break; [default] */
245 case SYMM_NONE: strcat(str, "a"); break;
247 switch (params->diff) {
248 /* case DIFF_BLOCK: strcat(str, "dt"); break; [default] */
249 case DIFF_SIMPLE: strcat(str, "db"); break;
250 case DIFF_INTERSECT: strcat(str, "di"); break;
251 case DIFF_SET: strcat(str, "da"); break;
252 case DIFF_RECURSIVE: strcat(str, "du"); break;
258 static config_item *game_configure(game_params *params)
263 ret = snewn(5, config_item);
265 ret[0].name = "Columns of sub-blocks";
266 ret[0].type = C_STRING;
267 sprintf(buf, "%d", params->c);
268 ret[0].sval = dupstr(buf);
271 ret[1].name = "Rows of sub-blocks";
272 ret[1].type = C_STRING;
273 sprintf(buf, "%d", params->r);
274 ret[1].sval = dupstr(buf);
277 ret[2].name = "Symmetry";
278 ret[2].type = C_CHOICES;
279 ret[2].sval = ":None:2-way rotation:4-way rotation:4-way mirror";
280 ret[2].ival = params->symm;
282 ret[3].name = "Difficulty";
283 ret[3].type = C_CHOICES;
284 ret[3].sval = ":Trivial:Basic:Intermediate:Advanced:Unreasonable";
285 ret[3].ival = params->diff;
295 static game_params *custom_params(config_item *cfg)
297 game_params *ret = snew(game_params);
299 ret->c = atoi(cfg[0].sval);
300 ret->r = atoi(cfg[1].sval);
301 ret->symm = cfg[2].ival;
302 ret->diff = cfg[3].ival;
307 static char *validate_params(game_params *params)
309 if (params->c < 2 || params->r < 2)
310 return "Both dimensions must be at least 2";
311 if (params->c > ORDER_MAX || params->r > ORDER_MAX)
312 return "Dimensions greater than "STR(ORDER_MAX)" are not supported";
316 /* ----------------------------------------------------------------------
317 * Full recursive Solo solver.
319 * The algorithm for this solver is shamelessly copied from a
320 * Python solver written by Andrew Wilkinson (which is GPLed, but
321 * I've reused only ideas and no code). It mostly just does the
322 * obvious recursive thing: pick an empty square, put one of the
323 * possible digits in it, recurse until all squares are filled,
324 * backtrack and change some choices if necessary.
326 * The clever bit is that every time it chooses which square to
327 * fill in next, it does so by counting the number of _possible_
328 * numbers that can go in each square, and it prioritises so that
329 * it picks a square with the _lowest_ number of possibilities. The
330 * idea is that filling in lots of the obvious bits (particularly
331 * any squares with only one possibility) will cut down on the list
332 * of possibilities for other squares and hence reduce the enormous
333 * search space as much as possible as early as possible.
335 * In practice the algorithm appeared to work very well; run on
336 * sample problems from the Times it completed in well under a
337 * second on my G5 even when written in Python, and given an empty
338 * grid (so that in principle it would enumerate _all_ solved
339 * grids!) it found the first valid solution just as quickly. So
340 * with a bit more randomisation I see no reason not to use this as
345 * Internal data structure used in solver to keep track of
348 struct rsolve_coord { int x, y, r; };
349 struct rsolve_usage {
350 int c, r, cr; /* cr == c*r */
351 /* grid is a copy of the input grid, modified as we go along */
353 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
355 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
357 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
359 /* This lists all the empty spaces remaining in the grid. */
360 struct rsolve_coord *spaces;
362 /* If we need randomisation in the solve, this is our random state. */
364 /* Number of solutions so far found, and maximum number we care about. */
369 * The real recursive step in the solving function.
371 static void rsolve_real(struct rsolve_usage *usage, digit *grid)
373 int c = usage->c, r = usage->r, cr = usage->cr;
374 int i, j, n, sx, sy, bestm, bestr;
378 * Firstly, check for completion! If there are no spaces left
379 * in the grid, we have a solution.
381 if (usage->nspaces == 0) {
384 * This is our first solution, so fill in the output grid.
386 memcpy(grid, usage->grid, cr * cr);
393 * Otherwise, there must be at least one space. Find the most
394 * constrained space, using the `r' field as a tie-breaker.
396 bestm = cr+1; /* so that any space will beat it */
399 for (j = 0; j < usage->nspaces; j++) {
400 int x = usage->spaces[j].x, y = usage->spaces[j].y;
404 * Find the number of digits that could go in this space.
407 for (n = 0; n < cr; n++)
408 if (!usage->row[y*cr+n] && !usage->col[x*cr+n] &&
409 !usage->blk[((y/c)*c+(x/r))*cr+n])
412 if (m < bestm || (m == bestm && usage->spaces[j].r < bestr)) {
414 bestr = usage->spaces[j].r;
422 * Swap that square into the final place in the spaces array,
423 * so that decrementing nspaces will remove it from the list.
425 if (i != usage->nspaces-1) {
426 struct rsolve_coord t;
427 t = usage->spaces[usage->nspaces-1];
428 usage->spaces[usage->nspaces-1] = usage->spaces[i];
429 usage->spaces[i] = t;
433 * Now we've decided which square to start our recursion at,
434 * simply go through all possible values, shuffling them
435 * randomly first if necessary.
437 digits = snewn(bestm, int);
439 for (n = 0; n < cr; n++)
440 if (!usage->row[sy*cr+n] && !usage->col[sx*cr+n] &&
441 !usage->blk[((sy/c)*c+(sx/r))*cr+n]) {
447 for (i = j; i > 1; i--) {
448 int p = random_upto(usage->rs, i);
451 digits[p] = digits[i-1];
457 /* And finally, go through the digit list and actually recurse. */
458 for (i = 0; i < j; i++) {
461 /* Update the usage structure to reflect the placing of this digit. */
462 usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
463 usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = TRUE;
464 usage->grid[sy*cr+sx] = n;
467 /* Call the solver recursively. */
468 rsolve_real(usage, grid);
471 * If we have seen as many solutions as we need, terminate
472 * all processing immediately.
474 if (usage->solns >= usage->maxsolns)
477 /* Revert the usage structure. */
478 usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
479 usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = FALSE;
480 usage->grid[sy*cr+sx] = 0;
488 * Entry point to solver. You give it dimensions and a starting
489 * grid, which is simply an array of N^4 digits. In that array, 0
490 * means an empty square, and 1..N mean a clue square.
492 * Return value is the number of solutions found; searching will
493 * stop after the provided `max'. (Thus, you can pass max==1 to
494 * indicate that you only care about finding _one_ solution, or
495 * max==2 to indicate that you want to know the difference between
496 * a unique and non-unique solution.) The input parameter `grid' is
497 * also filled in with the _first_ (or only) solution found by the
500 static int rsolve(int c, int r, digit *grid, random_state *rs, int max)
502 struct rsolve_usage *usage;
507 * Create an rsolve_usage structure.
509 usage = snew(struct rsolve_usage);
515 usage->grid = snewn(cr * cr, digit);
516 memcpy(usage->grid, grid, cr * cr);
518 usage->row = snewn(cr * cr, unsigned char);
519 usage->col = snewn(cr * cr, unsigned char);
520 usage->blk = snewn(cr * cr, unsigned char);
521 memset(usage->row, FALSE, cr * cr);
522 memset(usage->col, FALSE, cr * cr);
523 memset(usage->blk, FALSE, cr * cr);
525 usage->spaces = snewn(cr * cr, struct rsolve_coord);
529 usage->maxsolns = max;
534 * Now fill it in with data from the input grid.
536 for (y = 0; y < cr; y++) {
537 for (x = 0; x < cr; x++) {
538 int v = grid[y*cr+x];
540 usage->spaces[usage->nspaces].x = x;
541 usage->spaces[usage->nspaces].y = y;
543 usage->spaces[usage->nspaces].r = random_bits(rs, 31);
545 usage->spaces[usage->nspaces].r = usage->nspaces;
548 usage->row[y*cr+v-1] = TRUE;
549 usage->col[x*cr+v-1] = TRUE;
550 usage->blk[((y/c)*c+(x/r))*cr+v-1] = TRUE;
556 * Run the real recursive solving function.
558 rsolve_real(usage, grid);
562 * Clean up the usage structure now we have our answer.
564 sfree(usage->spaces);
577 /* ----------------------------------------------------------------------
578 * End of recursive solver code.
581 /* ----------------------------------------------------------------------
582 * Less capable non-recursive solver. This one is used to check
583 * solubility of a grid as we gradually remove numbers from it: by
584 * verifying a grid using this solver we can ensure it isn't _too_
585 * hard (e.g. does not actually require guessing and backtracking).
587 * It supports a variety of specific modes of reasoning. By
588 * enabling or disabling subsets of these modes we can arrange a
589 * range of difficulty levels.
593 * Modes of reasoning currently supported:
595 * - Positional elimination: a number must go in a particular
596 * square because all the other empty squares in a given
597 * row/col/blk are ruled out.
599 * - Numeric elimination: a square must have a particular number
600 * in because all the other numbers that could go in it are
603 * - Intersectional analysis: given two domains which overlap
604 * (hence one must be a block, and the other can be a row or
605 * col), if the possible locations for a particular number in
606 * one of the domains can be narrowed down to the overlap, then
607 * that number can be ruled out everywhere but the overlap in
608 * the other domain too.
610 * - Set elimination: if there is a subset of the empty squares
611 * within a domain such that the union of the possible numbers
612 * in that subset has the same size as the subset itself, then
613 * those numbers can be ruled out everywhere else in the domain.
614 * (For example, if there are five empty squares and the
615 * possible numbers in each are 12, 23, 13, 134 and 1345, then
616 * the first three empty squares form such a subset: the numbers
617 * 1, 2 and 3 _must_ be in those three squares in some
618 * permutation, and hence we can deduce none of them can be in
619 * the fourth or fifth squares.)
620 * + You can also see this the other way round, concentrating
621 * on numbers rather than squares: if there is a subset of
622 * the unplaced numbers within a domain such that the union
623 * of all their possible positions has the same size as the
624 * subset itself, then all other numbers can be ruled out for
625 * those positions. However, it turns out that this is
626 * exactly equivalent to the first formulation at all times:
627 * there is a 1-1 correspondence between suitable subsets of
628 * the unplaced numbers and suitable subsets of the unfilled
629 * places, found by taking the _complement_ of the union of
630 * the numbers' possible positions (or the spaces' possible
635 * Within this solver, I'm going to transform all y-coordinates by
636 * inverting the significance of the block number and the position
637 * within the block. That is, we will start with the top row of
638 * each block in order, then the second row of each block in order,
641 * This transformation has the enormous advantage that it means
642 * every row, column _and_ block is described by an arithmetic
643 * progression of coordinates within the cubic array, so that I can
644 * use the same very simple function to do blockwise, row-wise and
645 * column-wise elimination.
647 #define YTRANS(y) (((y)%c)*r+(y)/c)
648 #define YUNTRANS(y) (((y)%r)*c+(y)/r)
650 struct nsolve_usage {
653 * We set up a cubic array, indexed by x, y and digit; each
654 * element of this array is TRUE or FALSE according to whether
655 * or not that digit _could_ in principle go in that position.
657 * The way to index this array is cube[(x*cr+y)*cr+n-1].
658 * y-coordinates in here are transformed.
662 * This is the grid in which we write down our final
663 * deductions. y-coordinates in here are _not_ transformed.
667 * Now we keep track, at a slightly higher level, of what we
668 * have yet to work out, to prevent doing the same deduction
671 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
673 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
675 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
678 #define cubepos(x,y,n) (((x)*usage->cr+(y))*usage->cr+(n)-1)
679 #define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
682 * Function called when we are certain that a particular square has
683 * a particular number in it. The y-coordinate passed in here is
686 static void nsolve_place(struct nsolve_usage *usage, int x, int y, int n)
688 int c = usage->c, r = usage->r, cr = usage->cr;
694 * Rule out all other numbers in this square.
696 for (i = 1; i <= cr; i++)
701 * Rule out this number in all other positions in the row.
703 for (i = 0; i < cr; i++)
708 * Rule out this number in all other positions in the column.
710 for (i = 0; i < cr; i++)
715 * Rule out this number in all other positions in the block.
719 for (i = 0; i < r; i++)
720 for (j = 0; j < c; j++)
721 if (bx+i != x || by+j*r != y)
722 cube(bx+i,by+j*r,n) = FALSE;
725 * Enter the number in the result grid.
727 usage->grid[YUNTRANS(y)*cr+x] = n;
730 * Cross out this number from the list of numbers left to place
731 * in its row, its column and its block.
733 usage->row[y*cr+n-1] = usage->col[x*cr+n-1] =
734 usage->blk[((y%r)*c+(x/r))*cr+n-1] = TRUE;
737 static int nsolve_elim(struct nsolve_usage *usage, int start, int step
738 #ifdef STANDALONE_SOLVER
743 int c = usage->c, r = usage->r, cr = c*r;
747 * Count the number of set bits within this section of the
752 for (i = 0; i < cr; i++)
753 if (usage->cube[start+i*step]) {
767 if (!usage->grid[YUNTRANS(y)*cr+x]) {
768 #ifdef STANDALONE_SOLVER
769 if (solver_show_working) {
774 printf(":\n placing %d at (%d,%d)\n",
775 n, 1+x, 1+YUNTRANS(y));
778 nsolve_place(usage, x, y, n);
786 static int nsolve_intersect(struct nsolve_usage *usage,
787 int start1, int step1, int start2, int step2
788 #ifdef STANDALONE_SOLVER
793 int c = usage->c, r = usage->r, cr = c*r;
797 * Loop over the first domain and see if there's any set bit
798 * not also in the second.
800 for (i = 0; i < cr; i++) {
801 int p = start1+i*step1;
802 if (usage->cube[p] &&
803 !(p >= start2 && p < start2+cr*step2 &&
804 (p - start2) % step2 == 0))
805 return FALSE; /* there is, so we can't deduce */
809 * We have determined that all set bits in the first domain are
810 * within its overlap with the second. So loop over the second
811 * domain and remove all set bits that aren't also in that
812 * overlap; return TRUE iff we actually _did_ anything.
815 for (i = 0; i < cr; i++) {
816 int p = start2+i*step2;
817 if (usage->cube[p] &&
818 !(p >= start1 && p < start1+cr*step1 && (p - start1) % step1 == 0))
820 #ifdef STANDALONE_SOLVER
821 if (solver_show_working) {
837 printf(" ruling out %d at (%d,%d)\n",
838 pn, 1+px, 1+YUNTRANS(py));
841 ret = TRUE; /* we did something */
849 struct nsolve_scratch {
850 unsigned char *grid, *rowidx, *colidx, *set;
853 static int nsolve_set(struct nsolve_usage *usage,
854 struct nsolve_scratch *scratch,
855 int start, int step1, int step2
856 #ifdef STANDALONE_SOLVER
861 int c = usage->c, r = usage->r, cr = c*r;
863 unsigned char *grid = scratch->grid;
864 unsigned char *rowidx = scratch->rowidx;
865 unsigned char *colidx = scratch->colidx;
866 unsigned char *set = scratch->set;
869 * We are passed a cr-by-cr matrix of booleans. Our first job
870 * is to winnow it by finding any definite placements - i.e.
871 * any row with a solitary 1 - and discarding that row and the
872 * column containing the 1.
874 memset(rowidx, TRUE, cr);
875 memset(colidx, TRUE, cr);
876 for (i = 0; i < cr; i++) {
877 int count = 0, first = -1;
878 for (j = 0; j < cr; j++)
879 if (usage->cube[start+i*step1+j*step2])
883 * This condition actually marks a completely insoluble
884 * (i.e. internally inconsistent) puzzle. We return and
885 * report no progress made.
890 rowidx[i] = colidx[first] = FALSE;
894 * Convert each of rowidx/colidx from a list of 0s and 1s to a
895 * list of the indices of the 1s.
897 for (i = j = 0; i < cr; i++)
901 for (i = j = 0; i < cr; i++)
907 * And create the smaller matrix.
909 for (i = 0; i < n; i++)
910 for (j = 0; j < n; j++)
911 grid[i*cr+j] = usage->cube[start+rowidx[i]*step1+colidx[j]*step2];
914 * Having done that, we now have a matrix in which every row
915 * has at least two 1s in. Now we search to see if we can find
916 * a rectangle of zeroes (in the set-theoretic sense of
917 * `rectangle', i.e. a subset of rows crossed with a subset of
918 * columns) whose width and height add up to n.
925 * We have a candidate set. If its size is <=1 or >=n-1
926 * then we move on immediately.
928 if (count > 1 && count < n-1) {
930 * The number of rows we need is n-count. See if we can
931 * find that many rows which each have a zero in all
932 * the positions listed in `set'.
935 for (i = 0; i < n; i++) {
937 for (j = 0; j < n; j++)
938 if (set[j] && grid[i*cr+j]) {
947 * We expect never to be able to get _more_ than
948 * n-count suitable rows: this would imply that (for
949 * example) there are four numbers which between them
950 * have at most three possible positions, and hence it
951 * indicates a faulty deduction before this point or
954 assert(rows <= n - count);
955 if (rows >= n - count) {
956 int progress = FALSE;
959 * We've got one! Now, for each row which _doesn't_
960 * satisfy the criterion, eliminate all its set
961 * bits in the positions _not_ listed in `set'.
962 * Return TRUE (meaning progress has been made) if
963 * we successfully eliminated anything at all.
965 * This involves referring back through
966 * rowidx/colidx in order to work out which actual
967 * positions in the cube to meddle with.
969 for (i = 0; i < n; i++) {
971 for (j = 0; j < n; j++)
972 if (set[j] && grid[i*cr+j]) {
977 for (j = 0; j < n; j++)
978 if (!set[j] && grid[i*cr+j]) {
979 int fpos = (start+rowidx[i]*step1+
981 #ifdef STANDALONE_SOLVER
982 if (solver_show_working) {
998 printf(" ruling out %d at (%d,%d)\n",
999 pn, 1+px, 1+YUNTRANS(py));
1003 usage->cube[fpos] = FALSE;
1015 * Binary increment: change the rightmost 0 to a 1, and
1016 * change all 1s to the right of it to 0s.
1019 while (i > 0 && set[i-1])
1020 set[--i] = 0, count--;
1022 set[--i] = 1, count++;
1030 static struct nsolve_scratch *nsolve_new_scratch(struct nsolve_usage *usage)
1032 struct nsolve_scratch *scratch = snew(struct nsolve_scratch);
1034 scratch->grid = snewn(cr*cr, unsigned char);
1035 scratch->rowidx = snewn(cr, unsigned char);
1036 scratch->colidx = snewn(cr, unsigned char);
1037 scratch->set = snewn(cr, unsigned char);
1041 static void nsolve_free_scratch(struct nsolve_scratch *scratch)
1043 sfree(scratch->set);
1044 sfree(scratch->colidx);
1045 sfree(scratch->rowidx);
1046 sfree(scratch->grid);
1050 static int nsolve(int c, int r, digit *grid)
1052 struct nsolve_usage *usage;
1053 struct nsolve_scratch *scratch;
1056 int diff = DIFF_BLOCK;
1059 * Set up a usage structure as a clean slate (everything
1062 usage = snew(struct nsolve_usage);
1066 usage->cube = snewn(cr*cr*cr, unsigned char);
1067 usage->grid = grid; /* write straight back to the input */
1068 memset(usage->cube, TRUE, cr*cr*cr);
1070 usage->row = snewn(cr * cr, unsigned char);
1071 usage->col = snewn(cr * cr, unsigned char);
1072 usage->blk = snewn(cr * cr, unsigned char);
1073 memset(usage->row, FALSE, cr * cr);
1074 memset(usage->col, FALSE, cr * cr);
1075 memset(usage->blk, FALSE, cr * cr);
1077 scratch = nsolve_new_scratch(usage);
1080 * Place all the clue numbers we are given.
1082 for (x = 0; x < cr; x++)
1083 for (y = 0; y < cr; y++)
1085 nsolve_place(usage, x, YTRANS(y), grid[y*cr+x]);
1088 * Now loop over the grid repeatedly trying all permitted modes
1089 * of reasoning. The loop terminates if we complete an
1090 * iteration without making any progress; we then return
1091 * failure or success depending on whether the grid is full or
1096 * I'd like to write `continue;' inside each of the
1097 * following loops, so that the solver returns here after
1098 * making some progress. However, I can't specify that I
1099 * want to continue an outer loop rather than the innermost
1100 * one, so I'm apologetically resorting to a goto.
1105 * Blockwise positional elimination.
1107 for (x = 0; x < cr; x += r)
1108 for (y = 0; y < r; y++)
1109 for (n = 1; n <= cr; n++)
1110 if (!usage->blk[(y*c+(x/r))*cr+n-1] &&
1111 nsolve_elim(usage, cubepos(x,y,n), r*cr
1112 #ifdef STANDALONE_SOLVER
1113 , "positional elimination,"
1114 " block (%d,%d)", 1+x/r, 1+y
1117 diff = max(diff, DIFF_BLOCK);
1122 * Row-wise positional elimination.
1124 for (y = 0; y < cr; y++)
1125 for (n = 1; n <= cr; n++)
1126 if (!usage->row[y*cr+n-1] &&
1127 nsolve_elim(usage, cubepos(0,y,n), cr*cr
1128 #ifdef STANDALONE_SOLVER
1129 , "positional elimination,"
1130 " row %d", 1+YUNTRANS(y)
1133 diff = max(diff, DIFF_SIMPLE);
1137 * Column-wise positional elimination.
1139 for (x = 0; x < cr; x++)
1140 for (n = 1; n <= cr; n++)
1141 if (!usage->col[x*cr+n-1] &&
1142 nsolve_elim(usage, cubepos(x,0,n), cr
1143 #ifdef STANDALONE_SOLVER
1144 , "positional elimination," " column %d", 1+x
1147 diff = max(diff, DIFF_SIMPLE);
1152 * Numeric elimination.
1154 for (x = 0; x < cr; x++)
1155 for (y = 0; y < cr; y++)
1156 if (!usage->grid[YUNTRANS(y)*cr+x] &&
1157 nsolve_elim(usage, cubepos(x,y,1), 1
1158 #ifdef STANDALONE_SOLVER
1159 , "numeric elimination at (%d,%d)", 1+x,
1163 diff = max(diff, DIFF_SIMPLE);
1168 * Intersectional analysis, rows vs blocks.
1170 for (y = 0; y < cr; y++)
1171 for (x = 0; x < cr; x += r)
1172 for (n = 1; n <= cr; n++)
1173 if (!usage->row[y*cr+n-1] &&
1174 !usage->blk[((y%r)*c+(x/r))*cr+n-1] &&
1175 (nsolve_intersect(usage, cubepos(0,y,n), cr*cr,
1176 cubepos(x,y%r,n), r*cr
1177 #ifdef STANDALONE_SOLVER
1178 , "intersectional analysis,"
1179 " row %d vs block (%d,%d)",
1180 1+YUNTRANS(y), 1+x/r, 1+y%r
1183 nsolve_intersect(usage, cubepos(x,y%r,n), r*cr,
1184 cubepos(0,y,n), cr*cr
1185 #ifdef STANDALONE_SOLVER
1186 , "intersectional analysis,"
1187 " block (%d,%d) vs row %d",
1188 1+x/r, 1+y%r, 1+YUNTRANS(y)
1191 diff = max(diff, DIFF_INTERSECT);
1196 * Intersectional analysis, columns vs blocks.
1198 for (x = 0; x < cr; x++)
1199 for (y = 0; y < r; y++)
1200 for (n = 1; n <= cr; n++)
1201 if (!usage->col[x*cr+n-1] &&
1202 !usage->blk[(y*c+(x/r))*cr+n-1] &&
1203 (nsolve_intersect(usage, cubepos(x,0,n), cr,
1204 cubepos((x/r)*r,y,n), r*cr
1205 #ifdef STANDALONE_SOLVER
1206 , "intersectional analysis,"
1207 " column %d vs block (%d,%d)",
1211 nsolve_intersect(usage, cubepos((x/r)*r,y,n), r*cr,
1213 #ifdef STANDALONE_SOLVER
1214 , "intersectional analysis,"
1215 " block (%d,%d) vs column %d",
1219 diff = max(diff, DIFF_INTERSECT);
1224 * Blockwise set elimination.
1226 for (x = 0; x < cr; x += r)
1227 for (y = 0; y < r; y++)
1228 if (nsolve_set(usage, scratch, cubepos(x,y,1), r*cr, 1
1229 #ifdef STANDALONE_SOLVER
1230 , "set elimination, block (%d,%d)", 1+x/r, 1+y
1233 diff = max(diff, DIFF_SET);
1238 * Row-wise set elimination.
1240 for (y = 0; y < cr; y++)
1241 if (nsolve_set(usage, scratch, cubepos(0,y,1), cr*cr, 1
1242 #ifdef STANDALONE_SOLVER
1243 , "set elimination, row %d", 1+YUNTRANS(y)
1246 diff = max(diff, DIFF_SET);
1251 * Column-wise set elimination.
1253 for (x = 0; x < cr; x++)
1254 if (nsolve_set(usage, scratch, cubepos(x,0,1), cr, 1
1255 #ifdef STANDALONE_SOLVER
1256 , "set elimination, column %d", 1+x
1259 diff = max(diff, DIFF_SET);
1264 * If we reach here, we have made no deductions in this
1265 * iteration, so the algorithm terminates.
1270 nsolve_free_scratch(scratch);
1278 for (x = 0; x < cr; x++)
1279 for (y = 0; y < cr; y++)
1281 return DIFF_IMPOSSIBLE;
1285 /* ----------------------------------------------------------------------
1286 * End of non-recursive solver code.
1290 * Check whether a grid contains a valid complete puzzle.
1292 static int check_valid(int c, int r, digit *grid)
1295 unsigned char *used;
1298 used = snewn(cr, unsigned char);
1301 * Check that each row contains precisely one of everything.
1303 for (y = 0; y < cr; y++) {
1304 memset(used, FALSE, cr);
1305 for (x = 0; x < cr; x++)
1306 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
1307 used[grid[y*cr+x]-1] = TRUE;
1308 for (n = 0; n < cr; n++)
1316 * Check that each column contains precisely one of everything.
1318 for (x = 0; x < cr; x++) {
1319 memset(used, FALSE, cr);
1320 for (y = 0; y < cr; y++)
1321 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
1322 used[grid[y*cr+x]-1] = TRUE;
1323 for (n = 0; n < cr; n++)
1331 * Check that each block contains precisely one of everything.
1333 for (x = 0; x < cr; x += r) {
1334 for (y = 0; y < cr; y += c) {
1336 memset(used, FALSE, cr);
1337 for (xx = x; xx < x+r; xx++)
1338 for (yy = 0; yy < y+c; yy++)
1339 if (grid[yy*cr+xx] > 0 && grid[yy*cr+xx] <= cr)
1340 used[grid[yy*cr+xx]-1] = TRUE;
1341 for (n = 0; n < cr; n++)
1353 static void symmetry_limit(game_params *params, int *xlim, int *ylim, int s)
1355 int c = params->c, r = params->r, cr = c*r;
1367 *xlim = *ylim = (cr+1) / 2;
1372 static int symmetries(game_params *params, int x, int y, int *output, int s)
1374 int c = params->c, r = params->r, cr = c*r;
1383 break; /* just x,y is all we need */
1388 *output++ = cr - 1 - x;
1393 *output++ = cr - 1 - y;
1397 *output++ = cr - 1 - y;
1402 *output++ = cr - 1 - x;
1408 *output++ = cr - 1 - x;
1409 *output++ = cr - 1 - y;
1417 struct game_aux_info {
1422 static char *new_game_desc(game_params *params, random_state *rs,
1423 game_aux_info **aux, int interactive)
1425 int c = params->c, r = params->r, cr = c*r;
1427 digit *grid, *grid2;
1428 struct xy { int x, y; } *locs;
1432 int coords[16], ncoords;
1434 int maxdiff, recursing;
1437 * Adjust the maximum difficulty level to be consistent with
1438 * the puzzle size: all 2x2 puzzles appear to be Trivial
1439 * (DIFF_BLOCK) so we cannot hold out for even a Basic
1440 * (DIFF_SIMPLE) one.
1442 maxdiff = params->diff;
1443 if (c == 2 && r == 2)
1444 maxdiff = DIFF_BLOCK;
1446 grid = snewn(area, digit);
1447 locs = snewn(area, struct xy);
1448 grid2 = snewn(area, digit);
1451 * Loop until we get a grid of the required difficulty. This is
1452 * nasty, but it seems to be unpleasantly hard to generate
1453 * difficult grids otherwise.
1457 * Start the recursive solver with an empty grid to generate a
1458 * random solved state.
1460 memset(grid, 0, area);
1461 ret = rsolve(c, r, grid, rs, 1);
1463 assert(check_valid(c, r, grid));
1466 * Save the solved grid in the aux_info.
1469 game_aux_info *ai = snew(game_aux_info);
1472 ai->grid = snewn(cr * cr, digit);
1473 memcpy(ai->grid, grid, cr * cr * sizeof(digit));
1475 * We might already have written *aux the last time we
1476 * went round this loop, in which case we should free
1477 * the old aux_info before overwriting it with the new
1481 sfree((*aux)->grid);
1488 * Now we have a solved grid, start removing things from it
1489 * while preserving solubility.
1491 symmetry_limit(params, &xlim, &ylim, params->symm);
1497 * Iterate over the grid and enumerate all the filled
1498 * squares we could empty.
1502 for (x = 0; x < xlim; x++)
1503 for (y = 0; y < ylim; y++)
1511 * Now shuffle that list.
1513 for (i = nlocs; i > 1; i--) {
1514 int p = random_upto(rs, i);
1516 struct xy t = locs[p];
1517 locs[p] = locs[i-1];
1523 * Now loop over the shuffled list and, for each element,
1524 * see whether removing that element (and its reflections)
1525 * from the grid will still leave the grid soluble by
1528 for (i = 0; i < nlocs; i++) {
1534 memcpy(grid2, grid, area);
1535 ncoords = symmetries(params, x, y, coords, params->symm);
1536 for (j = 0; j < ncoords; j++)
1537 grid2[coords[2*j+1]*cr+coords[2*j]] = 0;
1540 ret = (rsolve(c, r, grid2, NULL, 2) == 1);
1542 ret = (nsolve(c, r, grid2) <= maxdiff);
1545 for (j = 0; j < ncoords; j++)
1546 grid[coords[2*j+1]*cr+coords[2*j]] = 0;
1553 * There was nothing we could remove without
1554 * destroying solvability. If we're trying to
1555 * generate a recursion-only grid and haven't
1556 * switched over to rsolve yet, we now do;
1557 * otherwise we give up.
1559 if (maxdiff == DIFF_RECURSIVE && !recursing) {
1567 memcpy(grid2, grid, area);
1568 } while (nsolve(c, r, grid2) < maxdiff);
1574 * Now we have the grid as it will be presented to the user.
1575 * Encode it in a game desc.
1581 desc = snewn(5 * area, char);
1584 for (i = 0; i <= area; i++) {
1585 int n = (i < area ? grid[i] : -1);
1592 int c = 'a' - 1 + run;
1596 run -= c - ('a' - 1);
1600 * If there's a number in the very top left or
1601 * bottom right, there's no point putting an
1602 * unnecessary _ before or after it.
1604 if (p > desc && n > 0)
1608 p += sprintf(p, "%d", n);
1612 assert(p - desc < 5 * area);
1614 desc = sresize(desc, p - desc, char);
1622 static void game_free_aux_info(game_aux_info *aux)
1628 static char *validate_desc(game_params *params, char *desc)
1630 int area = params->r * params->r * params->c * params->c;
1635 if (n >= 'a' && n <= 'z') {
1636 squares += n - 'a' + 1;
1637 } else if (n == '_') {
1639 } else if (n > '0' && n <= '9') {
1641 while (*desc >= '0' && *desc <= '9')
1644 return "Invalid character in game description";
1648 return "Not enough data to fill grid";
1651 return "Too much data to fit in grid";
1656 static game_state *new_game(midend_data *me, game_params *params, char *desc)
1658 game_state *state = snew(game_state);
1659 int c = params->c, r = params->r, cr = c*r, area = cr * cr;
1662 state->c = params->c;
1663 state->r = params->r;
1665 state->grid = snewn(area, digit);
1666 state->pencil = snewn(area * cr, unsigned char);
1667 memset(state->pencil, 0, area * cr);
1668 state->immutable = snewn(area, unsigned char);
1669 memset(state->immutable, FALSE, area);
1671 state->completed = state->cheated = FALSE;
1676 if (n >= 'a' && n <= 'z') {
1677 int run = n - 'a' + 1;
1678 assert(i + run <= area);
1680 state->grid[i++] = 0;
1681 } else if (n == '_') {
1683 } else if (n > '0' && n <= '9') {
1685 state->immutable[i] = TRUE;
1686 state->grid[i++] = atoi(desc-1);
1687 while (*desc >= '0' && *desc <= '9')
1690 assert(!"We can't get here");
1698 static game_state *dup_game(game_state *state)
1700 game_state *ret = snew(game_state);
1701 int c = state->c, r = state->r, cr = c*r, area = cr * cr;
1706 ret->grid = snewn(area, digit);
1707 memcpy(ret->grid, state->grid, area);
1709 ret->pencil = snewn(area * cr, unsigned char);
1710 memcpy(ret->pencil, state->pencil, area * cr);
1712 ret->immutable = snewn(area, unsigned char);
1713 memcpy(ret->immutable, state->immutable, area);
1715 ret->completed = state->completed;
1716 ret->cheated = state->cheated;
1721 static void free_game(game_state *state)
1723 sfree(state->immutable);
1724 sfree(state->pencil);
1729 static game_state *solve_game(game_state *state, game_aux_info *ai,
1733 int c = state->c, r = state->r, cr = c*r;
1736 ret = dup_game(state);
1737 ret->completed = ret->cheated = TRUE;
1740 * If we already have the solution in the aux_info, save
1741 * ourselves some time.
1747 memcpy(ret->grid, ai->grid, cr * cr * sizeof(digit));
1750 rsolve_ret = rsolve(c, r, ret->grid, NULL, 2);
1752 if (rsolve_ret != 1) {
1754 if (rsolve_ret == 0)
1755 *error = "No solution exists for this puzzle";
1757 *error = "Multiple solutions exist for this puzzle";
1765 static char *grid_text_format(int c, int r, digit *grid)
1773 * There are cr lines of digits, plus r-1 lines of block
1774 * separators. Each line contains cr digits, cr-1 separating
1775 * spaces, and c-1 two-character block separators. Thus, the
1776 * total length of a line is 2*cr+2*c-3 (not counting the
1777 * newline), and there are cr+r-1 of them.
1779 maxlen = (cr+r-1) * (2*cr+2*c-2);
1780 ret = snewn(maxlen+1, char);
1783 for (y = 0; y < cr; y++) {
1784 for (x = 0; x < cr; x++) {
1785 int ch = grid[y * cr + x];
1795 if ((x+1) % r == 0) {
1802 if (y+1 < cr && (y+1) % c == 0) {
1803 for (x = 0; x < cr; x++) {
1807 if ((x+1) % r == 0) {
1817 assert(p - ret == maxlen);
1822 static char *game_text_format(game_state *state)
1824 return grid_text_format(state->c, state->r, state->grid);
1829 * These are the coordinates of the currently highlighted
1830 * square on the grid, or -1,-1 if there isn't one. When there
1831 * is, pressing a valid number or letter key or Space will
1832 * enter that number or letter in the grid.
1836 * This indicates whether the current highlight is a
1837 * pencil-mark one or a real one.
1842 static game_ui *new_ui(game_state *state)
1844 game_ui *ui = snew(game_ui);
1846 ui->hx = ui->hy = -1;
1852 static void free_ui(game_ui *ui)
1857 static void game_changed_state(game_ui *ui, game_state *oldstate,
1858 game_state *newstate)
1860 int c = newstate->c, r = newstate->r, cr = c*r;
1862 * We prevent pencil-mode highlighting of a filled square. So
1863 * if the user has just filled in a square which we had a
1864 * pencil-mode highlight in (by Undo, or by Redo, or by Solve),
1865 * then we cancel the highlight.
1867 if (ui->hx >= 0 && ui->hy >= 0 && ui->hpencil &&
1868 newstate->grid[ui->hy * cr + ui->hx] != 0) {
1869 ui->hx = ui->hy = -1;
1873 struct game_drawstate {
1878 unsigned char *pencil;
1880 /* This is scratch space used within a single call to game_redraw. */
1884 static game_state *make_move(game_state *from, game_ui *ui, game_drawstate *ds,
1885 int x, int y, int button)
1887 int c = from->c, r = from->r, cr = c*r;
1891 button &= ~MOD_MASK;
1893 tx = (x + TILE_SIZE - BORDER) / TILE_SIZE - 1;
1894 ty = (y + TILE_SIZE - BORDER) / TILE_SIZE - 1;
1896 if (tx >= 0 && tx < cr && ty >= 0 && ty < cr) {
1897 if (button == LEFT_BUTTON) {
1898 if (from->immutable[ty*cr+tx]) {
1899 ui->hx = ui->hy = -1;
1900 } else if (tx == ui->hx && ty == ui->hy && ui->hpencil == 0) {
1901 ui->hx = ui->hy = -1;
1907 return from; /* UI activity occurred */
1909 if (button == RIGHT_BUTTON) {
1911 * Pencil-mode highlighting for non filled squares.
1913 if (from->grid[ty*cr+tx] == 0) {
1914 if (tx == ui->hx && ty == ui->hy && ui->hpencil) {
1915 ui->hx = ui->hy = -1;
1922 ui->hx = ui->hy = -1;
1924 return from; /* UI activity occurred */
1928 if (ui->hx != -1 && ui->hy != -1 &&
1929 ((button >= '1' && button <= '9' && button - '0' <= cr) ||
1930 (button >= 'a' && button <= 'z' && button - 'a' + 10 <= cr) ||
1931 (button >= 'A' && button <= 'Z' && button - 'A' + 10 <= cr) ||
1933 int n = button - '0';
1934 if (button >= 'A' && button <= 'Z')
1935 n = button - 'A' + 10;
1936 if (button >= 'a' && button <= 'z')
1937 n = button - 'a' + 10;
1942 * Can't overwrite this square. In principle this shouldn't
1943 * happen anyway because we should never have even been
1944 * able to highlight the square, but it never hurts to be
1947 if (from->immutable[ui->hy*cr+ui->hx])
1951 * Can't make pencil marks in a filled square. In principle
1952 * this shouldn't happen anyway because we should never
1953 * have even been able to pencil-highlight the square, but
1954 * it never hurts to be careful.
1956 if (ui->hpencil && from->grid[ui->hy*cr+ui->hx])
1959 ret = dup_game(from);
1960 if (ui->hpencil && n > 0) {
1961 int index = (ui->hy*cr+ui->hx) * cr + (n-1);
1962 ret->pencil[index] = !ret->pencil[index];
1964 ret->grid[ui->hy*cr+ui->hx] = n;
1965 memset(ret->pencil + (ui->hy*cr+ui->hx)*cr, 0, cr);
1968 * We've made a real change to the grid. Check to see
1969 * if the game has been completed.
1971 if (!ret->completed && check_valid(c, r, ret->grid)) {
1972 ret->completed = TRUE;
1975 ui->hx = ui->hy = -1;
1977 return ret; /* made a valid move */
1983 /* ----------------------------------------------------------------------
1987 #define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
1988 #define GETTILESIZE(cr, w) ( (w-1) / (cr+1) )
1990 static void game_size(game_params *params, game_drawstate *ds,
1991 int *x, int *y, int expand)
1993 int c = params->c, r = params->r, cr = c*r;
1996 ts = min(GETTILESIZE(cr, *x), GETTILESIZE(cr, *y));
2000 ds->tilesize = min(ts, PREFERRED_TILE_SIZE);
2006 static float *game_colours(frontend *fe, game_state *state, int *ncolours)
2008 float *ret = snewn(3 * NCOLOURS, float);
2010 frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
2012 ret[COL_GRID * 3 + 0] = 0.0F;
2013 ret[COL_GRID * 3 + 1] = 0.0F;
2014 ret[COL_GRID * 3 + 2] = 0.0F;
2016 ret[COL_CLUE * 3 + 0] = 0.0F;
2017 ret[COL_CLUE * 3 + 1] = 0.0F;
2018 ret[COL_CLUE * 3 + 2] = 0.0F;
2020 ret[COL_USER * 3 + 0] = 0.0F;
2021 ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
2022 ret[COL_USER * 3 + 2] = 0.0F;
2024 ret[COL_HIGHLIGHT * 3 + 0] = 0.85F * ret[COL_BACKGROUND * 3 + 0];
2025 ret[COL_HIGHLIGHT * 3 + 1] = 0.85F * ret[COL_BACKGROUND * 3 + 1];
2026 ret[COL_HIGHLIGHT * 3 + 2] = 0.85F * ret[COL_BACKGROUND * 3 + 2];
2028 ret[COL_ERROR * 3 + 0] = 1.0F;
2029 ret[COL_ERROR * 3 + 1] = 0.0F;
2030 ret[COL_ERROR * 3 + 2] = 0.0F;
2032 ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
2033 ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
2034 ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
2036 *ncolours = NCOLOURS;
2040 static game_drawstate *game_new_drawstate(game_state *state)
2042 struct game_drawstate *ds = snew(struct game_drawstate);
2043 int c = state->c, r = state->r, cr = c*r;
2045 ds->started = FALSE;
2049 ds->grid = snewn(cr*cr, digit);
2050 memset(ds->grid, 0, cr*cr);
2051 ds->pencil = snewn(cr*cr*cr, digit);
2052 memset(ds->pencil, 0, cr*cr*cr);
2053 ds->hl = snewn(cr*cr, unsigned char);
2054 memset(ds->hl, 0, cr*cr);
2055 ds->entered_items = snewn(cr*cr, int);
2056 ds->tilesize = 0; /* not decided yet */
2060 static void game_free_drawstate(game_drawstate *ds)
2065 sfree(ds->entered_items);
2069 static void draw_number(frontend *fe, game_drawstate *ds, game_state *state,
2070 int x, int y, int hl)
2072 int c = state->c, r = state->r, cr = c*r;
2077 if (ds->grid[y*cr+x] == state->grid[y*cr+x] &&
2078 ds->hl[y*cr+x] == hl &&
2079 !memcmp(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr))
2080 return; /* no change required */
2082 tx = BORDER + x * TILE_SIZE + 2;
2083 ty = BORDER + y * TILE_SIZE + 2;
2099 clip(fe, cx, cy, cw, ch);
2101 /* background needs erasing */
2102 draw_rect(fe, cx, cy, cw, ch, (hl & 15) == 1 ? COL_HIGHLIGHT : COL_BACKGROUND);
2104 /* pencil-mode highlight */
2105 if ((hl & 15) == 2) {
2109 coords[2] = cx+cw/2;
2112 coords[5] = cy+ch/2;
2113 draw_polygon(fe, coords, 3, TRUE, COL_HIGHLIGHT);
2116 /* new number needs drawing? */
2117 if (state->grid[y*cr+x]) {
2119 str[0] = state->grid[y*cr+x] + '0';
2121 str[0] += 'a' - ('9'+1);
2122 draw_text(fe, tx + TILE_SIZE/2, ty + TILE_SIZE/2,
2123 FONT_VARIABLE, TILE_SIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
2124 state->immutable[y*cr+x] ? COL_CLUE : (hl & 16) ? COL_ERROR : COL_USER, str);
2127 int pw, ph, pmax, fontsize;
2129 /* count the pencil marks required */
2130 for (i = npencil = 0; i < cr; i++)
2131 if (state->pencil[(y*cr+x)*cr+i])
2135 * It's not sensible to arrange pencil marks in the same
2136 * layout as the squares within a block, because this leads
2137 * to the font being too small. Instead, we arrange pencil
2138 * marks in the nearest thing we can to a square layout,
2139 * and we adjust the square layout depending on the number
2140 * of pencil marks in the square.
2142 for (pw = 1; pw * pw < npencil; pw++);
2143 if (pw < 3) pw = 3; /* otherwise it just looks _silly_ */
2144 ph = (npencil + pw - 1) / pw;
2145 if (ph < 2) ph = 2; /* likewise */
2147 fontsize = TILE_SIZE/(pmax*(11-pmax)/8);
2149 for (i = j = 0; i < cr; i++)
2150 if (state->pencil[(y*cr+x)*cr+i]) {
2151 int dx = j % pw, dy = j / pw;
2156 str[0] += 'a' - ('9'+1);
2157 draw_text(fe, tx + (4*dx+3) * TILE_SIZE / (4*pw+2),
2158 ty + (4*dy+3) * TILE_SIZE / (4*ph+2),
2159 FONT_VARIABLE, fontsize,
2160 ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
2167 draw_update(fe, cx, cy, cw, ch);
2169 ds->grid[y*cr+x] = state->grid[y*cr+x];
2170 memcpy(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr);
2171 ds->hl[y*cr+x] = hl;
2174 static void game_redraw(frontend *fe, game_drawstate *ds, game_state *oldstate,
2175 game_state *state, int dir, game_ui *ui,
2176 float animtime, float flashtime)
2178 int c = state->c, r = state->r, cr = c*r;
2183 * The initial contents of the window are not guaranteed
2184 * and can vary with front ends. To be on the safe side,
2185 * all games should start by drawing a big
2186 * background-colour rectangle covering the whole window.
2188 draw_rect(fe, 0, 0, SIZE(cr), SIZE(cr), COL_BACKGROUND);
2193 for (x = 0; x <= cr; x++) {
2194 int thick = (x % r ? 0 : 1);
2195 draw_rect(fe, BORDER + x*TILE_SIZE - thick, BORDER-1,
2196 1+2*thick, cr*TILE_SIZE+3, COL_GRID);
2198 for (y = 0; y <= cr; y++) {
2199 int thick = (y % c ? 0 : 1);
2200 draw_rect(fe, BORDER-1, BORDER + y*TILE_SIZE - thick,
2201 cr*TILE_SIZE+3, 1+2*thick, COL_GRID);
2206 * This array is used to keep track of rows, columns and boxes
2207 * which contain a number more than once.
2209 for (x = 0; x < cr * cr; x++)
2210 ds->entered_items[x] = 0;
2211 for (x = 0; x < cr; x++)
2212 for (y = 0; y < cr; y++) {
2213 digit d = state->grid[y*cr+x];
2215 int box = (x/r)+(y/c)*c;
2216 ds->entered_items[x*cr+d-1] |= ((ds->entered_items[x*cr+d-1] & 1) << 1) | 1;
2217 ds->entered_items[y*cr+d-1] |= ((ds->entered_items[y*cr+d-1] & 4) << 1) | 4;
2218 ds->entered_items[box*cr+d-1] |= ((ds->entered_items[box*cr+d-1] & 16) << 1) | 16;
2223 * Draw any numbers which need redrawing.
2225 for (x = 0; x < cr; x++) {
2226 for (y = 0; y < cr; y++) {
2228 digit d = state->grid[y*cr+x];
2230 if (flashtime > 0 &&
2231 (flashtime <= FLASH_TIME/3 ||
2232 flashtime >= FLASH_TIME*2/3))
2235 /* Highlight active input areas. */
2236 if (x == ui->hx && y == ui->hy)
2237 highlight = ui->hpencil ? 2 : 1;
2239 /* Mark obvious errors (ie, numbers which occur more than once
2240 * in a single row, column, or box). */
2241 if (d && ((ds->entered_items[x*cr+d-1] & 2) ||
2242 (ds->entered_items[y*cr+d-1] & 8) ||
2243 (ds->entered_items[((x/r)+(y/c)*c)*cr+d-1] & 32)))
2246 draw_number(fe, ds, state, x, y, highlight);
2251 * Update the _entire_ grid if necessary.
2254 draw_update(fe, 0, 0, SIZE(cr), SIZE(cr));
2259 static float game_anim_length(game_state *oldstate, game_state *newstate,
2260 int dir, game_ui *ui)
2265 static float game_flash_length(game_state *oldstate, game_state *newstate,
2266 int dir, game_ui *ui)
2268 if (!oldstate->completed && newstate->completed &&
2269 !oldstate->cheated && !newstate->cheated)
2274 static int game_wants_statusbar(void)
2279 static int game_timing_state(game_state *state)
2285 #define thegame solo
2288 const struct game thegame = {
2289 "Solo", "games.solo",
2296 TRUE, game_configure, custom_params,
2305 TRUE, game_text_format,
2313 game_free_drawstate,
2317 game_wants_statusbar,
2318 FALSE, game_timing_state,
2319 0, /* mouse_priorities */
2322 #ifdef STANDALONE_SOLVER
2325 * gcc -DSTANDALONE_SOLVER -o solosolver solo.c malloc.c
2328 void frontend_default_colour(frontend *fe, float *output) {}
2329 void draw_text(frontend *fe, int x, int y, int fonttype, int fontsize,
2330 int align, int colour, char *text) {}
2331 void draw_rect(frontend *fe, int x, int y, int w, int h, int colour) {}
2332 void draw_line(frontend *fe, int x1, int y1, int x2, int y2, int colour) {}
2333 void draw_polygon(frontend *fe, int *coords, int npoints,
2334 int fill, int colour) {}
2335 void clip(frontend *fe, int x, int y, int w, int h) {}
2336 void unclip(frontend *fe) {}
2337 void start_draw(frontend *fe) {}
2338 void draw_update(frontend *fe, int x, int y, int w, int h) {}
2339 void end_draw(frontend *fe) {}
2340 unsigned long random_bits(random_state *state, int bits)
2341 { assert(!"Shouldn't get randomness"); return 0; }
2342 unsigned long random_upto(random_state *state, unsigned long limit)
2343 { assert(!"Shouldn't get randomness"); return 0; }
2345 void fatal(char *fmt, ...)
2349 fprintf(stderr, "fatal error: ");
2352 vfprintf(stderr, fmt, ap);
2355 fprintf(stderr, "\n");
2359 int main(int argc, char **argv)
2364 char *id = NULL, *desc, *err;
2368 while (--argc > 0) {
2370 if (!strcmp(p, "-r")) {
2372 } else if (!strcmp(p, "-n")) {
2374 } else if (!strcmp(p, "-v")) {
2375 solver_show_working = TRUE;
2377 } else if (!strcmp(p, "-g")) {
2380 } else if (*p == '-') {
2381 fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0]);
2389 fprintf(stderr, "usage: %s [-n | -r | -g | -v] <game_id>\n", argv[0]);
2393 desc = strchr(id, ':');
2395 fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
2400 p = default_params();
2401 decode_params(p, id);
2402 err = validate_desc(p, desc);
2404 fprintf(stderr, "%s: %s\n", argv[0], err);
2407 s = new_game(NULL, p, desc);
2410 int ret = rsolve(p->c, p->r, s->grid, NULL, 2);
2412 fprintf(stderr, "%s: rsolve: multiple solutions detected\n",
2416 int ret = nsolve(p->c, p->r, s->grid);
2418 if (ret == DIFF_IMPOSSIBLE) {
2420 * Now resort to rsolve to determine whether it's
2423 ret = rsolve(p->c, p->r, s->grid, NULL, 2);
2425 ret = DIFF_IMPOSSIBLE;
2427 ret = DIFF_RECURSIVE;
2429 ret = DIFF_AMBIGUOUS;
2431 printf("Difficulty rating: %s\n",
2432 ret==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)":
2433 ret==DIFF_SIMPLE ? "Basic (row/column/number elimination required)":
2434 ret==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)":
2435 ret==DIFF_SET ? "Advanced (set elimination required)":
2436 ret==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)":
2437 ret==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)":
2438 ret==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)":
2439 "INTERNAL ERROR: unrecognised difficulty code");
2443 printf("%s\n", grid_text_format(p->c, p->r, s->grid));