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, solver_recurse_depth;
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, int full)
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";
330 if ((params->c * params->r) > 36)
331 return "Unable to support more than 36 distinct symbols in a puzzle";
335 /* ----------------------------------------------------------------------
338 * This solver is used for several purposes:
339 * + to generate filled grids as the basis for new puzzles (by
340 * supplying no clue squares at all)
341 * + to check solubility of a grid as we gradually remove numbers
343 * + to solve an externally generated puzzle when the user selects
346 * It supports a variety of specific modes of reasoning. By
347 * enabling or disabling subsets of these modes we can arrange a
348 * range of difficulty levels.
352 * Modes of reasoning currently supported:
354 * - Positional elimination: a number must go in a particular
355 * square because all the other empty squares in a given
356 * row/col/blk are ruled out.
358 * - Numeric elimination: a square must have a particular number
359 * in because all the other numbers that could go in it are
362 * - Intersectional analysis: given two domains which overlap
363 * (hence one must be a block, and the other can be a row or
364 * col), if the possible locations for a particular number in
365 * one of the domains can be narrowed down to the overlap, then
366 * that number can be ruled out everywhere but the overlap in
367 * the other domain too.
369 * - Set elimination: if there is a subset of the empty squares
370 * within a domain such that the union of the possible numbers
371 * in that subset has the same size as the subset itself, then
372 * those numbers can be ruled out everywhere else in the domain.
373 * (For example, if there are five empty squares and the
374 * possible numbers in each are 12, 23, 13, 134 and 1345, then
375 * the first three empty squares form such a subset: the numbers
376 * 1, 2 and 3 _must_ be in those three squares in some
377 * permutation, and hence we can deduce none of them can be in
378 * the fourth or fifth squares.)
379 * + You can also see this the other way round, concentrating
380 * on numbers rather than squares: if there is a subset of
381 * the unplaced numbers within a domain such that the union
382 * of all their possible positions has the same size as the
383 * subset itself, then all other numbers can be ruled out for
384 * those positions. However, it turns out that this is
385 * exactly equivalent to the first formulation at all times:
386 * there is a 1-1 correspondence between suitable subsets of
387 * the unplaced numbers and suitable subsets of the unfilled
388 * places, found by taking the _complement_ of the union of
389 * the numbers' possible positions (or the spaces' possible
392 * - Recursion. If all else fails, we pick one of the currently
393 * most constrained empty squares and take a random guess at its
394 * contents, then continue solving on that basis and see if we
399 * Within this solver, I'm going to transform all y-coordinates by
400 * inverting the significance of the block number and the position
401 * within the block. That is, we will start with the top row of
402 * each block in order, then the second row of each block in order,
405 * This transformation has the enormous advantage that it means
406 * every row, column _and_ block is described by an arithmetic
407 * progression of coordinates within the cubic array, so that I can
408 * use the same very simple function to do blockwise, row-wise and
409 * column-wise elimination.
411 #define YTRANS(y) (((y)%c)*r+(y)/c)
412 #define YUNTRANS(y) (((y)%r)*c+(y)/r)
414 struct solver_usage {
417 * We set up a cubic array, indexed by x, y and digit; each
418 * element of this array is TRUE or FALSE according to whether
419 * or not that digit _could_ in principle go in that position.
421 * The way to index this array is cube[(x*cr+y)*cr+n-1].
422 * y-coordinates in here are transformed.
426 * This is the grid in which we write down our final
427 * deductions. y-coordinates in here are _not_ transformed.
431 * Now we keep track, at a slightly higher level, of what we
432 * have yet to work out, to prevent doing the same deduction
435 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
437 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
439 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
442 #define cubepos(x,y,n) (((x)*usage->cr+(y))*usage->cr+(n)-1)
443 #define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
446 * Function called when we are certain that a particular square has
447 * a particular number in it. The y-coordinate passed in here is
450 static void solver_place(struct solver_usage *usage, int x, int y, int n)
452 int c = usage->c, r = usage->r, cr = usage->cr;
458 * Rule out all other numbers in this square.
460 for (i = 1; i <= cr; i++)
465 * Rule out this number in all other positions in the row.
467 for (i = 0; i < cr; i++)
472 * Rule out this number in all other positions in the column.
474 for (i = 0; i < cr; i++)
479 * Rule out this number in all other positions in the block.
483 for (i = 0; i < r; i++)
484 for (j = 0; j < c; j++)
485 if (bx+i != x || by+j*r != y)
486 cube(bx+i,by+j*r,n) = FALSE;
489 * Enter the number in the result grid.
491 usage->grid[YUNTRANS(y)*cr+x] = n;
494 * Cross out this number from the list of numbers left to place
495 * in its row, its column and its block.
497 usage->row[y*cr+n-1] = usage->col[x*cr+n-1] =
498 usage->blk[((y%r)*c+(x/r))*cr+n-1] = TRUE;
501 static int solver_elim(struct solver_usage *usage, int start, int step
502 #ifdef STANDALONE_SOLVER
507 int c = usage->c, r = usage->r, cr = c*r;
511 * Count the number of set bits within this section of the
516 for (i = 0; i < cr; i++)
517 if (usage->cube[start+i*step]) {
531 if (!usage->grid[YUNTRANS(y)*cr+x]) {
532 #ifdef STANDALONE_SOLVER
533 if (solver_show_working) {
535 printf("%*s", solver_recurse_depth*4, "");
539 printf(":\n%*s placing %d at (%d,%d)\n",
540 solver_recurse_depth*4, "", n, 1+x, 1+YUNTRANS(y));
543 solver_place(usage, x, y, n);
547 #ifdef STANDALONE_SOLVER
548 if (solver_show_working) {
550 printf("%*s", solver_recurse_depth*4, "");
554 printf(":\n%*s no possibilities available\n",
555 solver_recurse_depth*4, "");
564 static int solver_intersect(struct solver_usage *usage,
565 int start1, int step1, int start2, int step2
566 #ifdef STANDALONE_SOLVER
571 int c = usage->c, r = usage->r, cr = c*r;
575 * Loop over the first domain and see if there's any set bit
576 * not also in the second.
578 for (i = 0; i < cr; i++) {
579 int p = start1+i*step1;
580 if (usage->cube[p] &&
581 !(p >= start2 && p < start2+cr*step2 &&
582 (p - start2) % step2 == 0))
583 return 0; /* there is, so we can't deduce */
587 * We have determined that all set bits in the first domain are
588 * within its overlap with the second. So loop over the second
589 * domain and remove all set bits that aren't also in that
590 * overlap; return +1 iff we actually _did_ anything.
593 for (i = 0; i < cr; i++) {
594 int p = start2+i*step2;
595 if (usage->cube[p] &&
596 !(p >= start1 && p < start1+cr*step1 && (p - start1) % step1 == 0))
598 #ifdef STANDALONE_SOLVER
599 if (solver_show_working) {
604 printf("%*s", solver_recurse_depth*4, "");
616 printf("%*s ruling out %d at (%d,%d)\n",
617 solver_recurse_depth*4, "", pn, 1+px, 1+YUNTRANS(py));
620 ret = +1; /* we did something */
628 struct solver_scratch {
629 unsigned char *grid, *rowidx, *colidx, *set;
632 static int solver_set(struct solver_usage *usage,
633 struct solver_scratch *scratch,
634 int start, int step1, int step2
635 #ifdef STANDALONE_SOLVER
640 int c = usage->c, r = usage->r, cr = c*r;
642 unsigned char *grid = scratch->grid;
643 unsigned char *rowidx = scratch->rowidx;
644 unsigned char *colidx = scratch->colidx;
645 unsigned char *set = scratch->set;
648 * We are passed a cr-by-cr matrix of booleans. Our first job
649 * is to winnow it by finding any definite placements - i.e.
650 * any row with a solitary 1 - and discarding that row and the
651 * column containing the 1.
653 memset(rowidx, TRUE, cr);
654 memset(colidx, TRUE, cr);
655 for (i = 0; i < cr; i++) {
656 int count = 0, first = -1;
657 for (j = 0; j < cr; j++)
658 if (usage->cube[start+i*step1+j*step2])
662 * If count == 0, then there's a row with no 1s at all and
663 * the puzzle is internally inconsistent. However, we ought
664 * to have caught this already during the simpler reasoning
665 * methods, so we can safely fail an assertion if we reach
670 rowidx[i] = colidx[first] = FALSE;
674 * Convert each of rowidx/colidx from a list of 0s and 1s to a
675 * list of the indices of the 1s.
677 for (i = j = 0; i < cr; i++)
681 for (i = j = 0; i < cr; i++)
687 * And create the smaller matrix.
689 for (i = 0; i < n; i++)
690 for (j = 0; j < n; j++)
691 grid[i*cr+j] = usage->cube[start+rowidx[i]*step1+colidx[j]*step2];
694 * Having done that, we now have a matrix in which every row
695 * has at least two 1s in. Now we search to see if we can find
696 * a rectangle of zeroes (in the set-theoretic sense of
697 * `rectangle', i.e. a subset of rows crossed with a subset of
698 * columns) whose width and height add up to n.
705 * We have a candidate set. If its size is <=1 or >=n-1
706 * then we move on immediately.
708 if (count > 1 && count < n-1) {
710 * The number of rows we need is n-count. See if we can
711 * find that many rows which each have a zero in all
712 * the positions listed in `set'.
715 for (i = 0; i < n; i++) {
717 for (j = 0; j < n; j++)
718 if (set[j] && grid[i*cr+j]) {
727 * We expect never to be able to get _more_ than
728 * n-count suitable rows: this would imply that (for
729 * example) there are four numbers which between them
730 * have at most three possible positions, and hence it
731 * indicates a faulty deduction before this point or
734 if (rows > n - count) {
735 #ifdef STANDALONE_SOLVER
736 if (solver_show_working) {
738 printf("%*s", solver_recurse_depth*4,
743 printf(":\n%*s contradiction reached\n",
744 solver_recurse_depth*4, "");
750 if (rows >= n - count) {
751 int progress = FALSE;
754 * We've got one! Now, for each row which _doesn't_
755 * satisfy the criterion, eliminate all its set
756 * bits in the positions _not_ listed in `set'.
757 * Return +1 (meaning progress has been made) if we
758 * successfully eliminated anything at all.
760 * This involves referring back through
761 * rowidx/colidx in order to work out which actual
762 * positions in the cube to meddle with.
764 for (i = 0; i < n; i++) {
766 for (j = 0; j < n; j++)
767 if (set[j] && grid[i*cr+j]) {
772 for (j = 0; j < n; j++)
773 if (!set[j] && grid[i*cr+j]) {
774 int fpos = (start+rowidx[i]*step1+
776 #ifdef STANDALONE_SOLVER
777 if (solver_show_working) {
782 printf("%*s", solver_recurse_depth*4,
795 printf("%*s ruling out %d at (%d,%d)\n",
796 solver_recurse_depth*4, "",
797 pn, 1+px, 1+YUNTRANS(py));
801 usage->cube[fpos] = FALSE;
813 * Binary increment: change the rightmost 0 to a 1, and
814 * change all 1s to the right of it to 0s.
817 while (i > 0 && set[i-1])
818 set[--i] = 0, count--;
820 set[--i] = 1, count++;
828 static struct solver_scratch *solver_new_scratch(struct solver_usage *usage)
830 struct solver_scratch *scratch = snew(struct solver_scratch);
832 scratch->grid = snewn(cr*cr, unsigned char);
833 scratch->rowidx = snewn(cr, unsigned char);
834 scratch->colidx = snewn(cr, unsigned char);
835 scratch->set = snewn(cr, unsigned char);
839 static void solver_free_scratch(struct solver_scratch *scratch)
842 sfree(scratch->colidx);
843 sfree(scratch->rowidx);
844 sfree(scratch->grid);
848 static int solver(int c, int r, digit *grid, int maxdiff)
850 struct solver_usage *usage;
851 struct solver_scratch *scratch;
854 int diff = DIFF_BLOCK;
857 * Set up a usage structure as a clean slate (everything
860 usage = snew(struct solver_usage);
864 usage->cube = snewn(cr*cr*cr, unsigned char);
865 usage->grid = grid; /* write straight back to the input */
866 memset(usage->cube, TRUE, cr*cr*cr);
868 usage->row = snewn(cr * cr, unsigned char);
869 usage->col = snewn(cr * cr, unsigned char);
870 usage->blk = snewn(cr * cr, unsigned char);
871 memset(usage->row, FALSE, cr * cr);
872 memset(usage->col, FALSE, cr * cr);
873 memset(usage->blk, FALSE, cr * cr);
875 scratch = solver_new_scratch(usage);
878 * Place all the clue numbers we are given.
880 for (x = 0; x < cr; x++)
881 for (y = 0; y < cr; y++)
883 solver_place(usage, x, YTRANS(y), grid[y*cr+x]);
886 * Now loop over the grid repeatedly trying all permitted modes
887 * of reasoning. The loop terminates if we complete an
888 * iteration without making any progress; we then return
889 * failure or success depending on whether the grid is full or
894 * I'd like to write `continue;' inside each of the
895 * following loops, so that the solver returns here after
896 * making some progress. However, I can't specify that I
897 * want to continue an outer loop rather than the innermost
898 * one, so I'm apologetically resorting to a goto.
903 * Blockwise positional elimination.
905 for (x = 0; x < cr; x += r)
906 for (y = 0; y < r; y++)
907 for (n = 1; n <= cr; n++)
908 if (!usage->blk[(y*c+(x/r))*cr+n-1]) {
909 ret = solver_elim(usage, cubepos(x,y,n), r*cr
910 #ifdef STANDALONE_SOLVER
911 , "positional elimination,"
912 " %d in block (%d,%d)", n, 1+x/r, 1+y
916 diff = DIFF_IMPOSSIBLE;
918 } else if (ret > 0) {
919 diff = max(diff, DIFF_BLOCK);
924 if (maxdiff <= DIFF_BLOCK)
928 * Row-wise positional elimination.
930 for (y = 0; y < cr; y++)
931 for (n = 1; n <= cr; n++)
932 if (!usage->row[y*cr+n-1]) {
933 ret = solver_elim(usage, cubepos(0,y,n), cr*cr
934 #ifdef STANDALONE_SOLVER
935 , "positional elimination,"
936 " %d in row %d", n, 1+YUNTRANS(y)
940 diff = DIFF_IMPOSSIBLE;
942 } else if (ret > 0) {
943 diff = max(diff, DIFF_SIMPLE);
948 * Column-wise positional elimination.
950 for (x = 0; x < cr; x++)
951 for (n = 1; n <= cr; n++)
952 if (!usage->col[x*cr+n-1]) {
953 ret = solver_elim(usage, cubepos(x,0,n), cr
954 #ifdef STANDALONE_SOLVER
955 , "positional elimination,"
956 " %d in column %d", n, 1+x
960 diff = DIFF_IMPOSSIBLE;
962 } else if (ret > 0) {
963 diff = max(diff, DIFF_SIMPLE);
969 * Numeric elimination.
971 for (x = 0; x < cr; x++)
972 for (y = 0; y < cr; y++)
973 if (!usage->grid[YUNTRANS(y)*cr+x]) {
974 ret = solver_elim(usage, cubepos(x,y,1), 1
975 #ifdef STANDALONE_SOLVER
976 , "numeric elimination at (%d,%d)", 1+x,
981 diff = DIFF_IMPOSSIBLE;
983 } else if (ret > 0) {
984 diff = max(diff, DIFF_SIMPLE);
989 if (maxdiff <= DIFF_SIMPLE)
993 * Intersectional analysis, rows vs blocks.
995 for (y = 0; y < cr; y++)
996 for (x = 0; x < cr; x += r)
997 for (n = 1; n <= cr; n++)
999 * solver_intersect() never returns -1.
1001 if (!usage->row[y*cr+n-1] &&
1002 !usage->blk[((y%r)*c+(x/r))*cr+n-1] &&
1003 (solver_intersect(usage, cubepos(0,y,n), cr*cr,
1004 cubepos(x,y%r,n), r*cr
1005 #ifdef STANDALONE_SOLVER
1006 , "intersectional analysis,"
1007 " %d in row %d vs block (%d,%d)",
1008 n, 1+YUNTRANS(y), 1+x/r, 1+y%r
1011 solver_intersect(usage, cubepos(x,y%r,n), r*cr,
1012 cubepos(0,y,n), cr*cr
1013 #ifdef STANDALONE_SOLVER
1014 , "intersectional analysis,"
1015 " %d in block (%d,%d) vs row %d",
1016 n, 1+x/r, 1+y%r, 1+YUNTRANS(y)
1019 diff = max(diff, DIFF_INTERSECT);
1024 * Intersectional analysis, columns vs blocks.
1026 for (x = 0; x < cr; x++)
1027 for (y = 0; y < r; y++)
1028 for (n = 1; n <= cr; n++)
1029 if (!usage->col[x*cr+n-1] &&
1030 !usage->blk[(y*c+(x/r))*cr+n-1] &&
1031 (solver_intersect(usage, cubepos(x,0,n), cr,
1032 cubepos((x/r)*r,y,n), r*cr
1033 #ifdef STANDALONE_SOLVER
1034 , "intersectional analysis,"
1035 " %d in column %d vs block (%d,%d)",
1039 solver_intersect(usage, cubepos((x/r)*r,y,n), r*cr,
1041 #ifdef STANDALONE_SOLVER
1042 , "intersectional analysis,"
1043 " %d in block (%d,%d) vs column %d",
1047 diff = max(diff, DIFF_INTERSECT);
1051 if (maxdiff <= DIFF_INTERSECT)
1055 * Blockwise set elimination.
1057 for (x = 0; x < cr; x += r)
1058 for (y = 0; y < r; y++) {
1059 ret = solver_set(usage, scratch, cubepos(x,y,1), r*cr, 1
1060 #ifdef STANDALONE_SOLVER
1061 , "set elimination, block (%d,%d)", 1+x/r, 1+y
1065 diff = DIFF_IMPOSSIBLE;
1067 } else if (ret > 0) {
1068 diff = max(diff, DIFF_SET);
1074 * Row-wise set elimination.
1076 for (y = 0; y < cr; y++) {
1077 ret = solver_set(usage, scratch, cubepos(0,y,1), cr*cr, 1
1078 #ifdef STANDALONE_SOLVER
1079 , "set elimination, row %d", 1+YUNTRANS(y)
1083 diff = DIFF_IMPOSSIBLE;
1085 } else if (ret > 0) {
1086 diff = max(diff, DIFF_SET);
1092 * Column-wise set elimination.
1094 for (x = 0; x < cr; x++) {
1095 ret = solver_set(usage, scratch, cubepos(x,0,1), cr, 1
1096 #ifdef STANDALONE_SOLVER
1097 , "set elimination, column %d", 1+x
1101 diff = DIFF_IMPOSSIBLE;
1103 } else if (ret > 0) {
1104 diff = max(diff, DIFF_SET);
1110 * If we reach here, we have made no deductions in this
1111 * iteration, so the algorithm terminates.
1117 * Last chance: if we haven't fully solved the puzzle yet, try
1118 * recursing based on guesses for a particular square. We pick
1119 * one of the most constrained empty squares we can find, which
1120 * has the effect of pruning the search tree as much as
1123 if (maxdiff >= DIFF_RECURSIVE) {
1124 int best, bestcount;
1129 for (y = 0; y < cr; y++)
1130 for (x = 0; x < cr; x++)
1131 if (!grid[y*cr+x]) {
1135 * An unfilled square. Count the number of
1136 * possible digits in it.
1139 for (n = 1; n <= cr; n++)
1140 if (cube(x,YTRANS(y),n))
1144 * We should have found any impossibilities
1145 * already, so this can safely be an assert.
1149 if (count < bestcount) {
1157 digit *list, *ingrid, *outgrid;
1159 diff = DIFF_IMPOSSIBLE; /* no solution found yet */
1162 * Attempt recursion.
1167 list = snewn(cr, digit);
1168 ingrid = snewn(cr * cr, digit);
1169 outgrid = snewn(cr * cr, digit);
1170 memcpy(ingrid, grid, cr * cr);
1172 /* Make a list of the possible digits. */
1173 for (j = 0, n = 1; n <= cr; n++)
1174 if (cube(x,YTRANS(y),n))
1177 #ifdef STANDALONE_SOLVER
1178 if (solver_show_working) {
1180 printf("%*srecursing on (%d,%d) [",
1181 solver_recurse_depth*4, "", x, y);
1182 for (i = 0; i < j; i++) {
1183 printf("%s%d", sep, list[i]);
1191 * And step along the list, recursing back into the
1192 * main solver at every stage.
1194 for (i = 0; i < j; i++) {
1197 memcpy(outgrid, ingrid, cr * cr);
1198 outgrid[y*cr+x] = list[i];
1200 #ifdef STANDALONE_SOLVER
1201 if (solver_show_working)
1202 printf("%*sguessing %d at (%d,%d)\n",
1203 solver_recurse_depth*4, "", list[i], x, y);
1204 solver_recurse_depth++;
1207 ret = solver(c, r, outgrid, maxdiff);
1209 #ifdef STANDALONE_SOLVER
1210 solver_recurse_depth--;
1211 if (solver_show_working) {
1212 printf("%*sretracting %d at (%d,%d)\n",
1213 solver_recurse_depth*4, "", list[i], x, y);
1218 * If we have our first solution, copy it into the
1219 * grid we will return.
1221 if (diff == DIFF_IMPOSSIBLE && ret != DIFF_IMPOSSIBLE)
1222 memcpy(grid, outgrid, cr*cr);
1224 if (ret == DIFF_AMBIGUOUS)
1225 diff = DIFF_AMBIGUOUS;
1226 else if (ret == DIFF_IMPOSSIBLE)
1227 /* do not change our return value */;
1229 /* the recursion turned up exactly one solution */
1230 if (diff == DIFF_IMPOSSIBLE)
1231 diff = DIFF_RECURSIVE;
1233 diff = DIFF_AMBIGUOUS;
1237 * As soon as we've found more than one solution,
1238 * give up immediately.
1240 if (diff == DIFF_AMBIGUOUS)
1251 * We're forbidden to use recursion, so we just see whether
1252 * our grid is fully solved, and return DIFF_IMPOSSIBLE
1255 for (y = 0; y < cr; y++)
1256 for (x = 0; x < cr; x++)
1258 diff = DIFF_IMPOSSIBLE;
1263 #ifdef STANDALONE_SOLVER
1264 if (solver_show_working)
1265 printf("%*s%s found\n",
1266 solver_recurse_depth*4, "",
1267 diff == DIFF_IMPOSSIBLE ? "no solution" :
1268 diff == DIFF_AMBIGUOUS ? "multiple solutions" :
1278 solver_free_scratch(scratch);
1283 /* ----------------------------------------------------------------------
1284 * End of solver code.
1287 /* ----------------------------------------------------------------------
1288 * Solo filled-grid generator.
1290 * This grid generator works by essentially trying to solve a grid
1291 * starting from no clues, and not worrying that there's more than
1292 * one possible solution. Unfortunately, it isn't computationally
1293 * feasible to do this by calling the above solver with an empty
1294 * grid, because that one needs to allocate a lot of scratch space
1295 * at every recursion level. Instead, I have a much simpler
1296 * algorithm which I shamelessly copied from a Python solver
1297 * written by Andrew Wilkinson (which is GPLed, but I've reused
1298 * only ideas and no code). It mostly just does the obvious
1299 * recursive thing: pick an empty square, put one of the possible
1300 * digits in it, recurse until all squares are filled, backtrack
1301 * and change some choices if necessary.
1303 * The clever bit is that every time it chooses which square to
1304 * fill in next, it does so by counting the number of _possible_
1305 * numbers that can go in each square, and it prioritises so that
1306 * it picks a square with the _lowest_ number of possibilities. The
1307 * idea is that filling in lots of the obvious bits (particularly
1308 * any squares with only one possibility) will cut down on the list
1309 * of possibilities for other squares and hence reduce the enormous
1310 * search space as much as possible as early as possible.
1314 * Internal data structure used in gridgen to keep track of
1317 struct gridgen_coord { int x, y, r; };
1318 struct gridgen_usage {
1319 int c, r, cr; /* cr == c*r */
1320 /* grid is a copy of the input grid, modified as we go along */
1322 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
1324 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
1326 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
1328 /* This lists all the empty spaces remaining in the grid. */
1329 struct gridgen_coord *spaces;
1331 /* If we need randomisation in the solve, this is our random state. */
1336 * The real recursive step in the generating function.
1338 static int gridgen_real(struct gridgen_usage *usage, digit *grid)
1340 int c = usage->c, r = usage->r, cr = usage->cr;
1341 int i, j, n, sx, sy, bestm, bestr, ret;
1345 * Firstly, check for completion! If there are no spaces left
1346 * in the grid, we have a solution.
1348 if (usage->nspaces == 0) {
1349 memcpy(grid, usage->grid, cr * cr);
1354 * Otherwise, there must be at least one space. Find the most
1355 * constrained space, using the `r' field as a tie-breaker.
1357 bestm = cr+1; /* so that any space will beat it */
1360 for (j = 0; j < usage->nspaces; j++) {
1361 int x = usage->spaces[j].x, y = usage->spaces[j].y;
1365 * Find the number of digits that could go in this space.
1368 for (n = 0; n < cr; n++)
1369 if (!usage->row[y*cr+n] && !usage->col[x*cr+n] &&
1370 !usage->blk[((y/c)*c+(x/r))*cr+n])
1373 if (m < bestm || (m == bestm && usage->spaces[j].r < bestr)) {
1375 bestr = usage->spaces[j].r;
1383 * Swap that square into the final place in the spaces array,
1384 * so that decrementing nspaces will remove it from the list.
1386 if (i != usage->nspaces-1) {
1387 struct gridgen_coord t;
1388 t = usage->spaces[usage->nspaces-1];
1389 usage->spaces[usage->nspaces-1] = usage->spaces[i];
1390 usage->spaces[i] = t;
1394 * Now we've decided which square to start our recursion at,
1395 * simply go through all possible values, shuffling them
1396 * randomly first if necessary.
1398 digits = snewn(bestm, int);
1400 for (n = 0; n < cr; n++)
1401 if (!usage->row[sy*cr+n] && !usage->col[sx*cr+n] &&
1402 !usage->blk[((sy/c)*c+(sx/r))*cr+n]) {
1407 shuffle(digits, j, sizeof(*digits), usage->rs);
1409 /* And finally, go through the digit list and actually recurse. */
1411 for (i = 0; i < j; i++) {
1414 /* Update the usage structure to reflect the placing of this digit. */
1415 usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
1416 usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = TRUE;
1417 usage->grid[sy*cr+sx] = n;
1420 /* Call the solver recursively. Stop when we find a solution. */
1421 if (gridgen_real(usage, grid))
1424 /* Revert the usage structure. */
1425 usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
1426 usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = FALSE;
1427 usage->grid[sy*cr+sx] = 0;
1439 * Entry point to generator. You give it dimensions and a starting
1440 * grid, which is simply an array of cr*cr digits.
1442 static void gridgen(int c, int r, digit *grid, random_state *rs)
1444 struct gridgen_usage *usage;
1448 * Clear the grid to start with.
1450 memset(grid, 0, cr*cr);
1453 * Create a gridgen_usage structure.
1455 usage = snew(struct gridgen_usage);
1461 usage->grid = snewn(cr * cr, digit);
1462 memcpy(usage->grid, grid, cr * cr);
1464 usage->row = snewn(cr * cr, unsigned char);
1465 usage->col = snewn(cr * cr, unsigned char);
1466 usage->blk = snewn(cr * cr, unsigned char);
1467 memset(usage->row, FALSE, cr * cr);
1468 memset(usage->col, FALSE, cr * cr);
1469 memset(usage->blk, FALSE, cr * cr);
1471 usage->spaces = snewn(cr * cr, struct gridgen_coord);
1477 * Initialise the list of grid spaces.
1479 for (y = 0; y < cr; y++) {
1480 for (x = 0; x < cr; x++) {
1481 usage->spaces[usage->nspaces].x = x;
1482 usage->spaces[usage->nspaces].y = y;
1483 usage->spaces[usage->nspaces].r = random_bits(rs, 31);
1489 * Run the real generator function.
1491 gridgen_real(usage, grid);
1494 * Clean up the usage structure now we have our answer.
1496 sfree(usage->spaces);
1504 /* ----------------------------------------------------------------------
1505 * End of grid generator code.
1509 * Check whether a grid contains a valid complete puzzle.
1511 static int check_valid(int c, int r, digit *grid)
1514 unsigned char *used;
1517 used = snewn(cr, unsigned char);
1520 * Check that each row contains precisely one of everything.
1522 for (y = 0; y < cr; y++) {
1523 memset(used, FALSE, cr);
1524 for (x = 0; x < cr; x++)
1525 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
1526 used[grid[y*cr+x]-1] = TRUE;
1527 for (n = 0; n < cr; n++)
1535 * Check that each column contains precisely one of everything.
1537 for (x = 0; x < cr; x++) {
1538 memset(used, FALSE, cr);
1539 for (y = 0; y < cr; y++)
1540 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
1541 used[grid[y*cr+x]-1] = TRUE;
1542 for (n = 0; n < cr; n++)
1550 * Check that each block contains precisely one of everything.
1552 for (x = 0; x < cr; x += r) {
1553 for (y = 0; y < cr; y += c) {
1555 memset(used, FALSE, cr);
1556 for (xx = x; xx < x+r; xx++)
1557 for (yy = 0; yy < y+c; yy++)
1558 if (grid[yy*cr+xx] > 0 && grid[yy*cr+xx] <= cr)
1559 used[grid[yy*cr+xx]-1] = TRUE;
1560 for (n = 0; n < cr; n++)
1572 static int symmetries(game_params *params, int x, int y, int *output, int s)
1574 int c = params->c, r = params->r, cr = c*r;
1577 #define ADD(x,y) (*output++ = (x), *output++ = (y), i++)
1583 break; /* just x,y is all we need */
1585 ADD(cr - 1 - x, cr - 1 - y);
1590 ADD(cr - 1 - x, cr - 1 - y);
1601 ADD(cr - 1 - x, cr - 1 - y);
1605 ADD(cr - 1 - x, cr - 1 - y);
1606 ADD(cr - 1 - y, cr - 1 - x);
1611 ADD(cr - 1 - x, cr - 1 - y);
1615 ADD(cr - 1 - y, cr - 1 - x);
1624 static char *encode_solve_move(int cr, digit *grid)
1627 char *ret, *p, *sep;
1630 * It's surprisingly easy to work out _exactly_ how long this
1631 * string needs to be. To decimal-encode all the numbers from 1
1634 * - every number has a units digit; total is n.
1635 * - all numbers above 9 have a tens digit; total is max(n-9,0).
1636 * - all numbers above 99 have a hundreds digit; total is max(n-99,0).
1640 for (i = 1; i <= cr; i *= 10)
1641 len += max(cr - i + 1, 0);
1642 len += cr; /* don't forget the commas */
1643 len *= cr; /* there are cr rows of these */
1646 * Now len is one bigger than the total size of the
1647 * comma-separated numbers (because we counted an
1648 * additional leading comma). We need to have a leading S
1649 * and a trailing NUL, so we're off by one in total.
1653 ret = snewn(len, char);
1657 for (i = 0; i < cr*cr; i++) {
1658 p += sprintf(p, "%s%d", sep, grid[i]);
1662 assert(p - ret == len);
1667 static char *new_game_desc(game_params *params, random_state *rs,
1668 char **aux, int interactive)
1670 int c = params->c, r = params->r, cr = c*r;
1672 digit *grid, *grid2;
1673 struct xy { int x, y; } *locs;
1676 int coords[16], ncoords;
1681 * Adjust the maximum difficulty level to be consistent with
1682 * the puzzle size: all 2x2 puzzles appear to be Trivial
1683 * (DIFF_BLOCK) so we cannot hold out for even a Basic
1684 * (DIFF_SIMPLE) one.
1686 maxdiff = params->diff;
1687 if (c == 2 && r == 2)
1688 maxdiff = DIFF_BLOCK;
1690 grid = snewn(area, digit);
1691 locs = snewn(area, struct xy);
1692 grid2 = snewn(area, digit);
1695 * Loop until we get a grid of the required difficulty. This is
1696 * nasty, but it seems to be unpleasantly hard to generate
1697 * difficult grids otherwise.
1701 * Generate a random solved state.
1703 gridgen(c, r, grid, rs);
1704 assert(check_valid(c, r, grid));
1707 * Save the solved grid in aux.
1711 * We might already have written *aux the last time we
1712 * went round this loop, in which case we should free
1713 * the old aux before overwriting it with the new one.
1719 *aux = encode_solve_move(cr, grid);
1723 * Now we have a solved grid, start removing things from it
1724 * while preserving solubility.
1728 * Find the set of equivalence classes of squares permitted
1729 * by the selected symmetry. We do this by enumerating all
1730 * the grid squares which have no symmetric companion
1731 * sorting lower than themselves.
1734 for (y = 0; y < cr; y++)
1735 for (x = 0; x < cr; x++) {
1739 ncoords = symmetries(params, x, y, coords, params->symm);
1740 for (j = 0; j < ncoords; j++)
1741 if (coords[2*j+1]*cr+coords[2*j] < i)
1751 * Now shuffle that list.
1753 shuffle(locs, nlocs, sizeof(*locs), rs);
1756 * Now loop over the shuffled list and, for each element,
1757 * see whether removing that element (and its reflections)
1758 * from the grid will still leave the grid soluble.
1760 for (i = 0; i < nlocs; i++) {
1766 memcpy(grid2, grid, area);
1767 ncoords = symmetries(params, x, y, coords, params->symm);
1768 for (j = 0; j < ncoords; j++)
1769 grid2[coords[2*j+1]*cr+coords[2*j]] = 0;
1771 ret = solver(c, r, grid2, maxdiff);
1772 if (ret != DIFF_IMPOSSIBLE && ret != DIFF_AMBIGUOUS) {
1773 for (j = 0; j < ncoords; j++)
1774 grid[coords[2*j+1]*cr+coords[2*j]] = 0;
1778 memcpy(grid2, grid, area);
1779 } while (solver(c, r, grid2, maxdiff) < maxdiff);
1785 * Now we have the grid as it will be presented to the user.
1786 * Encode it in a game desc.
1792 desc = snewn(5 * area, char);
1795 for (i = 0; i <= area; i++) {
1796 int n = (i < area ? grid[i] : -1);
1803 int c = 'a' - 1 + run;
1807 run -= c - ('a' - 1);
1811 * If there's a number in the very top left or
1812 * bottom right, there's no point putting an
1813 * unnecessary _ before or after it.
1815 if (p > desc && n > 0)
1819 p += sprintf(p, "%d", n);
1823 assert(p - desc < 5 * area);
1825 desc = sresize(desc, p - desc, char);
1833 static char *validate_desc(game_params *params, char *desc)
1835 int area = params->r * params->r * params->c * params->c;
1840 if (n >= 'a' && n <= 'z') {
1841 squares += n - 'a' + 1;
1842 } else if (n == '_') {
1844 } else if (n > '0' && n <= '9') {
1846 while (*desc >= '0' && *desc <= '9')
1849 return "Invalid character in game description";
1853 return "Not enough data to fill grid";
1856 return "Too much data to fit in grid";
1861 static game_state *new_game(midend_data *me, game_params *params, char *desc)
1863 game_state *state = snew(game_state);
1864 int c = params->c, r = params->r, cr = c*r, area = cr * cr;
1867 state->c = params->c;
1868 state->r = params->r;
1870 state->grid = snewn(area, digit);
1871 state->pencil = snewn(area * cr, unsigned char);
1872 memset(state->pencil, 0, area * cr);
1873 state->immutable = snewn(area, unsigned char);
1874 memset(state->immutable, FALSE, area);
1876 state->completed = state->cheated = FALSE;
1881 if (n >= 'a' && n <= 'z') {
1882 int run = n - 'a' + 1;
1883 assert(i + run <= area);
1885 state->grid[i++] = 0;
1886 } else if (n == '_') {
1888 } else if (n > '0' && n <= '9') {
1890 state->immutable[i] = TRUE;
1891 state->grid[i++] = atoi(desc-1);
1892 while (*desc >= '0' && *desc <= '9')
1895 assert(!"We can't get here");
1903 static game_state *dup_game(game_state *state)
1905 game_state *ret = snew(game_state);
1906 int c = state->c, r = state->r, cr = c*r, area = cr * cr;
1911 ret->grid = snewn(area, digit);
1912 memcpy(ret->grid, state->grid, area);
1914 ret->pencil = snewn(area * cr, unsigned char);
1915 memcpy(ret->pencil, state->pencil, area * cr);
1917 ret->immutable = snewn(area, unsigned char);
1918 memcpy(ret->immutable, state->immutable, area);
1920 ret->completed = state->completed;
1921 ret->cheated = state->cheated;
1926 static void free_game(game_state *state)
1928 sfree(state->immutable);
1929 sfree(state->pencil);
1934 static char *solve_game(game_state *state, game_state *currstate,
1935 char *ai, char **error)
1937 int c = state->c, r = state->r, cr = c*r;
1943 * If we already have the solution in ai, save ourselves some
1949 grid = snewn(cr*cr, digit);
1950 memcpy(grid, state->grid, cr*cr);
1951 solve_ret = solver(c, r, grid, DIFF_RECURSIVE);
1955 if (solve_ret == DIFF_IMPOSSIBLE)
1956 *error = "No solution exists for this puzzle";
1957 else if (solve_ret == DIFF_AMBIGUOUS)
1958 *error = "Multiple solutions exist for this puzzle";
1965 ret = encode_solve_move(cr, grid);
1972 static char *grid_text_format(int c, int r, digit *grid)
1980 * There are cr lines of digits, plus r-1 lines of block
1981 * separators. Each line contains cr digits, cr-1 separating
1982 * spaces, and c-1 two-character block separators. Thus, the
1983 * total length of a line is 2*cr+2*c-3 (not counting the
1984 * newline), and there are cr+r-1 of them.
1986 maxlen = (cr+r-1) * (2*cr+2*c-2);
1987 ret = snewn(maxlen+1, char);
1990 for (y = 0; y < cr; y++) {
1991 for (x = 0; x < cr; x++) {
1992 int ch = grid[y * cr + x];
2002 if ((x+1) % r == 0) {
2009 if (y+1 < cr && (y+1) % c == 0) {
2010 for (x = 0; x < cr; x++) {
2014 if ((x+1) % r == 0) {
2024 assert(p - ret == maxlen);
2029 static char *game_text_format(game_state *state)
2031 return grid_text_format(state->c, state->r, state->grid);
2036 * These are the coordinates of the currently highlighted
2037 * square on the grid, or -1,-1 if there isn't one. When there
2038 * is, pressing a valid number or letter key or Space will
2039 * enter that number or letter in the grid.
2043 * This indicates whether the current highlight is a
2044 * pencil-mark one or a real one.
2049 static game_ui *new_ui(game_state *state)
2051 game_ui *ui = snew(game_ui);
2053 ui->hx = ui->hy = -1;
2059 static void free_ui(game_ui *ui)
2064 static char *encode_ui(game_ui *ui)
2069 static void decode_ui(game_ui *ui, char *encoding)
2073 static void game_changed_state(game_ui *ui, game_state *oldstate,
2074 game_state *newstate)
2076 int c = newstate->c, r = newstate->r, cr = c*r;
2078 * We prevent pencil-mode highlighting of a filled square. So
2079 * if the user has just filled in a square which we had a
2080 * pencil-mode highlight in (by Undo, or by Redo, or by Solve),
2081 * then we cancel the highlight.
2083 if (ui->hx >= 0 && ui->hy >= 0 && ui->hpencil &&
2084 newstate->grid[ui->hy * cr + ui->hx] != 0) {
2085 ui->hx = ui->hy = -1;
2089 struct game_drawstate {
2094 unsigned char *pencil;
2096 /* This is scratch space used within a single call to game_redraw. */
2100 static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
2101 int x, int y, int button)
2103 int c = state->c, r = state->r, cr = c*r;
2107 button &= ~MOD_MASK;
2109 tx = (x + TILE_SIZE - BORDER) / TILE_SIZE - 1;
2110 ty = (y + TILE_SIZE - BORDER) / TILE_SIZE - 1;
2112 if (tx >= 0 && tx < cr && ty >= 0 && ty < cr) {
2113 if (button == LEFT_BUTTON) {
2114 if (state->immutable[ty*cr+tx]) {
2115 ui->hx = ui->hy = -1;
2116 } else if (tx == ui->hx && ty == ui->hy && ui->hpencil == 0) {
2117 ui->hx = ui->hy = -1;
2123 return ""; /* UI activity occurred */
2125 if (button == RIGHT_BUTTON) {
2127 * Pencil-mode highlighting for non filled squares.
2129 if (state->grid[ty*cr+tx] == 0) {
2130 if (tx == ui->hx && ty == ui->hy && ui->hpencil) {
2131 ui->hx = ui->hy = -1;
2138 ui->hx = ui->hy = -1;
2140 return ""; /* UI activity occurred */
2144 if (ui->hx != -1 && ui->hy != -1 &&
2145 ((button >= '1' && button <= '9' && button - '0' <= cr) ||
2146 (button >= 'a' && button <= 'z' && button - 'a' + 10 <= cr) ||
2147 (button >= 'A' && button <= 'Z' && button - 'A' + 10 <= cr) ||
2149 int n = button - '0';
2150 if (button >= 'A' && button <= 'Z')
2151 n = button - 'A' + 10;
2152 if (button >= 'a' && button <= 'z')
2153 n = button - 'a' + 10;
2158 * Can't overwrite this square. In principle this shouldn't
2159 * happen anyway because we should never have even been
2160 * able to highlight the square, but it never hurts to be
2163 if (state->immutable[ui->hy*cr+ui->hx])
2167 * Can't make pencil marks in a filled square. In principle
2168 * this shouldn't happen anyway because we should never
2169 * have even been able to pencil-highlight the square, but
2170 * it never hurts to be careful.
2172 if (ui->hpencil && state->grid[ui->hy*cr+ui->hx])
2175 sprintf(buf, "%c%d,%d,%d",
2176 (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n);
2178 ui->hx = ui->hy = -1;
2186 static game_state *execute_move(game_state *from, char *move)
2188 int c = from->c, r = from->r, cr = c*r;
2192 if (move[0] == 'S') {
2195 ret = dup_game(from);
2196 ret->completed = ret->cheated = TRUE;
2199 for (n = 0; n < cr*cr; n++) {
2200 ret->grid[n] = atoi(p);
2202 if (!*p || ret->grid[n] < 1 || ret->grid[n] > cr) {
2207 while (*p && isdigit((unsigned char)*p)) p++;
2212 } else if ((move[0] == 'P' || move[0] == 'R') &&
2213 sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
2214 x >= 0 && x < cr && y >= 0 && y < cr && n >= 0 && n <= cr) {
2216 ret = dup_game(from);
2217 if (move[0] == 'P' && n > 0) {
2218 int index = (y*cr+x) * cr + (n-1);
2219 ret->pencil[index] = !ret->pencil[index];
2221 ret->grid[y*cr+x] = n;
2222 memset(ret->pencil + (y*cr+x)*cr, 0, cr);
2225 * We've made a real change to the grid. Check to see
2226 * if the game has been completed.
2228 if (!ret->completed && check_valid(c, r, ret->grid)) {
2229 ret->completed = TRUE;
2234 return NULL; /* couldn't parse move string */
2237 /* ----------------------------------------------------------------------
2241 #define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
2242 #define GETTILESIZE(cr, w) ( (double)(w-1) / (double)(cr+1) )
2244 static void game_compute_size(game_params *params, int tilesize,
2247 /* Ick: fake up `ds->tilesize' for macro expansion purposes */
2248 struct { int tilesize; } ads, *ds = &ads;
2249 ads.tilesize = tilesize;
2251 *x = SIZE(params->c * params->r);
2252 *y = SIZE(params->c * params->r);
2255 static void game_set_size(game_drawstate *ds, game_params *params,
2258 ds->tilesize = tilesize;
2261 static float *game_colours(frontend *fe, game_state *state, int *ncolours)
2263 float *ret = snewn(3 * NCOLOURS, float);
2265 frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
2267 ret[COL_GRID * 3 + 0] = 0.0F;
2268 ret[COL_GRID * 3 + 1] = 0.0F;
2269 ret[COL_GRID * 3 + 2] = 0.0F;
2271 ret[COL_CLUE * 3 + 0] = 0.0F;
2272 ret[COL_CLUE * 3 + 1] = 0.0F;
2273 ret[COL_CLUE * 3 + 2] = 0.0F;
2275 ret[COL_USER * 3 + 0] = 0.0F;
2276 ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
2277 ret[COL_USER * 3 + 2] = 0.0F;
2279 ret[COL_HIGHLIGHT * 3 + 0] = 0.85F * ret[COL_BACKGROUND * 3 + 0];
2280 ret[COL_HIGHLIGHT * 3 + 1] = 0.85F * ret[COL_BACKGROUND * 3 + 1];
2281 ret[COL_HIGHLIGHT * 3 + 2] = 0.85F * ret[COL_BACKGROUND * 3 + 2];
2283 ret[COL_ERROR * 3 + 0] = 1.0F;
2284 ret[COL_ERROR * 3 + 1] = 0.0F;
2285 ret[COL_ERROR * 3 + 2] = 0.0F;
2287 ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
2288 ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
2289 ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
2291 *ncolours = NCOLOURS;
2295 static game_drawstate *game_new_drawstate(game_state *state)
2297 struct game_drawstate *ds = snew(struct game_drawstate);
2298 int c = state->c, r = state->r, cr = c*r;
2300 ds->started = FALSE;
2304 ds->grid = snewn(cr*cr, digit);
2305 memset(ds->grid, 0, cr*cr);
2306 ds->pencil = snewn(cr*cr*cr, digit);
2307 memset(ds->pencil, 0, cr*cr*cr);
2308 ds->hl = snewn(cr*cr, unsigned char);
2309 memset(ds->hl, 0, cr*cr);
2310 ds->entered_items = snewn(cr*cr, int);
2311 ds->tilesize = 0; /* not decided yet */
2315 static void game_free_drawstate(game_drawstate *ds)
2320 sfree(ds->entered_items);
2324 static void draw_number(frontend *fe, game_drawstate *ds, game_state *state,
2325 int x, int y, int hl)
2327 int c = state->c, r = state->r, cr = c*r;
2332 if (ds->grid[y*cr+x] == state->grid[y*cr+x] &&
2333 ds->hl[y*cr+x] == hl &&
2334 !memcmp(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr))
2335 return; /* no change required */
2337 tx = BORDER + x * TILE_SIZE + 2;
2338 ty = BORDER + y * TILE_SIZE + 2;
2354 clip(fe, cx, cy, cw, ch);
2356 /* background needs erasing */
2357 draw_rect(fe, cx, cy, cw, ch, (hl & 15) == 1 ? COL_HIGHLIGHT : COL_BACKGROUND);
2359 /* pencil-mode highlight */
2360 if ((hl & 15) == 2) {
2364 coords[2] = cx+cw/2;
2367 coords[5] = cy+ch/2;
2368 draw_polygon(fe, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
2371 /* new number needs drawing? */
2372 if (state->grid[y*cr+x]) {
2374 str[0] = state->grid[y*cr+x] + '0';
2376 str[0] += 'a' - ('9'+1);
2377 draw_text(fe, tx + TILE_SIZE/2, ty + TILE_SIZE/2,
2378 FONT_VARIABLE, TILE_SIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
2379 state->immutable[y*cr+x] ? COL_CLUE : (hl & 16) ? COL_ERROR : COL_USER, str);
2382 int pw, ph, pmax, fontsize;
2384 /* count the pencil marks required */
2385 for (i = npencil = 0; i < cr; i++)
2386 if (state->pencil[(y*cr+x)*cr+i])
2390 * It's not sensible to arrange pencil marks in the same
2391 * layout as the squares within a block, because this leads
2392 * to the font being too small. Instead, we arrange pencil
2393 * marks in the nearest thing we can to a square layout,
2394 * and we adjust the square layout depending on the number
2395 * of pencil marks in the square.
2397 for (pw = 1; pw * pw < npencil; pw++);
2398 if (pw < 3) pw = 3; /* otherwise it just looks _silly_ */
2399 ph = (npencil + pw - 1) / pw;
2400 if (ph < 2) ph = 2; /* likewise */
2402 fontsize = TILE_SIZE/(pmax*(11-pmax)/8);
2404 for (i = j = 0; i < cr; i++)
2405 if (state->pencil[(y*cr+x)*cr+i]) {
2406 int dx = j % pw, dy = j / pw;
2411 str[0] += 'a' - ('9'+1);
2412 draw_text(fe, tx + (4*dx+3) * TILE_SIZE / (4*pw+2),
2413 ty + (4*dy+3) * TILE_SIZE / (4*ph+2),
2414 FONT_VARIABLE, fontsize,
2415 ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
2422 draw_update(fe, cx, cy, cw, ch);
2424 ds->grid[y*cr+x] = state->grid[y*cr+x];
2425 memcpy(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr);
2426 ds->hl[y*cr+x] = hl;
2429 static void game_redraw(frontend *fe, game_drawstate *ds, game_state *oldstate,
2430 game_state *state, int dir, game_ui *ui,
2431 float animtime, float flashtime)
2433 int c = state->c, r = state->r, cr = c*r;
2438 * The initial contents of the window are not guaranteed
2439 * and can vary with front ends. To be on the safe side,
2440 * all games should start by drawing a big
2441 * background-colour rectangle covering the whole window.
2443 draw_rect(fe, 0, 0, SIZE(cr), SIZE(cr), COL_BACKGROUND);
2448 for (x = 0; x <= cr; x++) {
2449 int thick = (x % r ? 0 : 1);
2450 draw_rect(fe, BORDER + x*TILE_SIZE - thick, BORDER-1,
2451 1+2*thick, cr*TILE_SIZE+3, COL_GRID);
2453 for (y = 0; y <= cr; y++) {
2454 int thick = (y % c ? 0 : 1);
2455 draw_rect(fe, BORDER-1, BORDER + y*TILE_SIZE - thick,
2456 cr*TILE_SIZE+3, 1+2*thick, COL_GRID);
2461 * This array is used to keep track of rows, columns and boxes
2462 * which contain a number more than once.
2464 for (x = 0; x < cr * cr; x++)
2465 ds->entered_items[x] = 0;
2466 for (x = 0; x < cr; x++)
2467 for (y = 0; y < cr; y++) {
2468 digit d = state->grid[y*cr+x];
2470 int box = (x/r)+(y/c)*c;
2471 ds->entered_items[x*cr+d-1] |= ((ds->entered_items[x*cr+d-1] & 1) << 1) | 1;
2472 ds->entered_items[y*cr+d-1] |= ((ds->entered_items[y*cr+d-1] & 4) << 1) | 4;
2473 ds->entered_items[box*cr+d-1] |= ((ds->entered_items[box*cr+d-1] & 16) << 1) | 16;
2478 * Draw any numbers which need redrawing.
2480 for (x = 0; x < cr; x++) {
2481 for (y = 0; y < cr; y++) {
2483 digit d = state->grid[y*cr+x];
2485 if (flashtime > 0 &&
2486 (flashtime <= FLASH_TIME/3 ||
2487 flashtime >= FLASH_TIME*2/3))
2490 /* Highlight active input areas. */
2491 if (x == ui->hx && y == ui->hy)
2492 highlight = ui->hpencil ? 2 : 1;
2494 /* Mark obvious errors (ie, numbers which occur more than once
2495 * in a single row, column, or box). */
2496 if (d && ((ds->entered_items[x*cr+d-1] & 2) ||
2497 (ds->entered_items[y*cr+d-1] & 8) ||
2498 (ds->entered_items[((x/r)+(y/c)*c)*cr+d-1] & 32)))
2501 draw_number(fe, ds, state, x, y, highlight);
2506 * Update the _entire_ grid if necessary.
2509 draw_update(fe, 0, 0, SIZE(cr), SIZE(cr));
2514 static float game_anim_length(game_state *oldstate, game_state *newstate,
2515 int dir, game_ui *ui)
2520 static float game_flash_length(game_state *oldstate, game_state *newstate,
2521 int dir, game_ui *ui)
2523 if (!oldstate->completed && newstate->completed &&
2524 !oldstate->cheated && !newstate->cheated)
2529 static int game_wants_statusbar(void)
2534 static int game_timing_state(game_state *state, game_ui *ui)
2540 #define thegame solo
2543 const struct game thegame = {
2544 "Solo", "games.solo",
2551 TRUE, game_configure, custom_params,
2559 TRUE, game_text_format,
2567 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
2570 game_free_drawstate,
2574 game_wants_statusbar,
2575 FALSE, game_timing_state,
2576 0, /* mouse_priorities */
2579 #ifdef STANDALONE_SOLVER
2582 * gcc -DSTANDALONE_SOLVER -o solosolver solo.c malloc.c
2585 void frontend_default_colour(frontend *fe, float *output) {}
2586 void draw_text(frontend *fe, int x, int y, int fonttype, int fontsize,
2587 int align, int colour, char *text) {}
2588 void draw_rect(frontend *fe, int x, int y, int w, int h, int colour) {}
2589 void draw_line(frontend *fe, int x1, int y1, int x2, int y2, int colour) {}
2590 void draw_polygon(frontend *fe, int *coords, int npoints,
2591 int fillcolour, int outlinecolour) {}
2592 void clip(frontend *fe, int x, int y, int w, int h) {}
2593 void unclip(frontend *fe) {}
2594 void start_draw(frontend *fe) {}
2595 void draw_update(frontend *fe, int x, int y, int w, int h) {}
2596 void end_draw(frontend *fe) {}
2597 unsigned long random_bits(random_state *state, int bits)
2598 { assert(!"Shouldn't get randomness"); return 0; }
2599 unsigned long random_upto(random_state *state, unsigned long limit)
2600 { assert(!"Shouldn't get randomness"); return 0; }
2601 void shuffle(void *array, int nelts, int eltsize, random_state *rs)
2602 { assert(!"Shouldn't get randomness"); }
2604 void fatal(char *fmt, ...)
2608 fprintf(stderr, "fatal error: ");
2611 vfprintf(stderr, fmt, ap);
2614 fprintf(stderr, "\n");
2618 int main(int argc, char **argv)
2622 char *id = NULL, *desc, *err;
2626 while (--argc > 0) {
2628 if (!strcmp(p, "-v")) {
2629 solver_show_working = TRUE;
2630 } else if (!strcmp(p, "-g")) {
2632 } else if (*p == '-') {
2633 fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
2641 fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
2645 desc = strchr(id, ':');
2647 fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
2652 p = default_params();
2653 decode_params(p, id);
2654 err = validate_desc(p, desc);
2656 fprintf(stderr, "%s: %s\n", argv[0], err);
2659 s = new_game(NULL, p, desc);
2661 ret = solver(p->c, p->r, s->grid, DIFF_RECURSIVE);
2663 printf("Difficulty rating: %s\n",
2664 ret==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)":
2665 ret==DIFF_SIMPLE ? "Basic (row/column/number elimination required)":
2666 ret==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)":
2667 ret==DIFF_SET ? "Advanced (set elimination required)":
2668 ret==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)":
2669 ret==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)":
2670 ret==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)":
2671 "INTERNAL ERROR: unrecognised difficulty code");
2673 printf("%s\n", grid_text_format(p->c, p->r, s->grid));