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";
333 /* ----------------------------------------------------------------------
336 * This solver is used for several purposes:
337 * + to generate filled grids as the basis for new puzzles (by
338 * supplying no clue squares at all)
339 * + to check solubility of a grid as we gradually remove numbers
341 * + to solve an externally generated puzzle when the user selects
344 * It supports a variety of specific modes of reasoning. By
345 * enabling or disabling subsets of these modes we can arrange a
346 * range of difficulty levels.
350 * Modes of reasoning currently supported:
352 * - Positional elimination: a number must go in a particular
353 * square because all the other empty squares in a given
354 * row/col/blk are ruled out.
356 * - Numeric elimination: a square must have a particular number
357 * in because all the other numbers that could go in it are
360 * - Intersectional analysis: given two domains which overlap
361 * (hence one must be a block, and the other can be a row or
362 * col), if the possible locations for a particular number in
363 * one of the domains can be narrowed down to the overlap, then
364 * that number can be ruled out everywhere but the overlap in
365 * the other domain too.
367 * - Set elimination: if there is a subset of the empty squares
368 * within a domain such that the union of the possible numbers
369 * in that subset has the same size as the subset itself, then
370 * those numbers can be ruled out everywhere else in the domain.
371 * (For example, if there are five empty squares and the
372 * possible numbers in each are 12, 23, 13, 134 and 1345, then
373 * the first three empty squares form such a subset: the numbers
374 * 1, 2 and 3 _must_ be in those three squares in some
375 * permutation, and hence we can deduce none of them can be in
376 * the fourth or fifth squares.)
377 * + You can also see this the other way round, concentrating
378 * on numbers rather than squares: if there is a subset of
379 * the unplaced numbers within a domain such that the union
380 * of all their possible positions has the same size as the
381 * subset itself, then all other numbers can be ruled out for
382 * those positions. However, it turns out that this is
383 * exactly equivalent to the first formulation at all times:
384 * there is a 1-1 correspondence between suitable subsets of
385 * the unplaced numbers and suitable subsets of the unfilled
386 * places, found by taking the _complement_ of the union of
387 * the numbers' possible positions (or the spaces' possible
390 * - Recursion. If all else fails, we pick one of the currently
391 * most constrained empty squares and take a random guess at its
392 * contents, then continue solving on that basis and see if we
397 * Within this solver, I'm going to transform all y-coordinates by
398 * inverting the significance of the block number and the position
399 * within the block. That is, we will start with the top row of
400 * each block in order, then the second row of each block in order,
403 * This transformation has the enormous advantage that it means
404 * every row, column _and_ block is described by an arithmetic
405 * progression of coordinates within the cubic array, so that I can
406 * use the same very simple function to do blockwise, row-wise and
407 * column-wise elimination.
409 #define YTRANS(y) (((y)%c)*r+(y)/c)
410 #define YUNTRANS(y) (((y)%r)*c+(y)/r)
412 struct solver_usage {
415 * We set up a cubic array, indexed by x, y and digit; each
416 * element of this array is TRUE or FALSE according to whether
417 * or not that digit _could_ in principle go in that position.
419 * The way to index this array is cube[(x*cr+y)*cr+n-1].
420 * y-coordinates in here are transformed.
424 * This is the grid in which we write down our final
425 * deductions. y-coordinates in here are _not_ transformed.
429 * Now we keep track, at a slightly higher level, of what we
430 * have yet to work out, to prevent doing the same deduction
433 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
435 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
437 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
440 #define cubepos(x,y,n) (((x)*usage->cr+(y))*usage->cr+(n)-1)
441 #define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
444 * Function called when we are certain that a particular square has
445 * a particular number in it. The y-coordinate passed in here is
448 static void solver_place(struct solver_usage *usage, int x, int y, int n)
450 int c = usage->c, r = usage->r, cr = usage->cr;
456 * Rule out all other numbers in this square.
458 for (i = 1; i <= cr; i++)
463 * Rule out this number in all other positions in the row.
465 for (i = 0; i < cr; i++)
470 * Rule out this number in all other positions in the column.
472 for (i = 0; i < cr; i++)
477 * Rule out this number in all other positions in the block.
481 for (i = 0; i < r; i++)
482 for (j = 0; j < c; j++)
483 if (bx+i != x || by+j*r != y)
484 cube(bx+i,by+j*r,n) = FALSE;
487 * Enter the number in the result grid.
489 usage->grid[YUNTRANS(y)*cr+x] = n;
492 * Cross out this number from the list of numbers left to place
493 * in its row, its column and its block.
495 usage->row[y*cr+n-1] = usage->col[x*cr+n-1] =
496 usage->blk[((y%r)*c+(x/r))*cr+n-1] = TRUE;
499 static int solver_elim(struct solver_usage *usage, int start, int step
500 #ifdef STANDALONE_SOLVER
505 int c = usage->c, r = usage->r, cr = c*r;
509 * Count the number of set bits within this section of the
514 for (i = 0; i < cr; i++)
515 if (usage->cube[start+i*step]) {
529 if (!usage->grid[YUNTRANS(y)*cr+x]) {
530 #ifdef STANDALONE_SOLVER
531 if (solver_show_working) {
533 printf("%*s", solver_recurse_depth*4, "");
537 printf(":\n%*s placing %d at (%d,%d)\n",
538 solver_recurse_depth*4, "", n, 1+x, 1+YUNTRANS(y));
541 solver_place(usage, x, y, n);
545 #ifdef STANDALONE_SOLVER
546 if (solver_show_working) {
548 printf("%*s", solver_recurse_depth*4, "");
552 printf(":\n%*s no possibilities available\n",
553 solver_recurse_depth*4, "");
562 static int solver_intersect(struct solver_usage *usage,
563 int start1, int step1, int start2, int step2
564 #ifdef STANDALONE_SOLVER
569 int c = usage->c, r = usage->r, cr = c*r;
573 * Loop over the first domain and see if there's any set bit
574 * not also in the second.
576 for (i = 0; i < cr; i++) {
577 int p = start1+i*step1;
578 if (usage->cube[p] &&
579 !(p >= start2 && p < start2+cr*step2 &&
580 (p - start2) % step2 == 0))
581 return 0; /* there is, so we can't deduce */
585 * We have determined that all set bits in the first domain are
586 * within its overlap with the second. So loop over the second
587 * domain and remove all set bits that aren't also in that
588 * overlap; return +1 iff we actually _did_ anything.
591 for (i = 0; i < cr; i++) {
592 int p = start2+i*step2;
593 if (usage->cube[p] &&
594 !(p >= start1 && p < start1+cr*step1 && (p - start1) % step1 == 0))
596 #ifdef STANDALONE_SOLVER
597 if (solver_show_working) {
602 printf("%*s", solver_recurse_depth*4, "");
614 printf("%*s ruling out %d at (%d,%d)\n",
615 solver_recurse_depth*4, "", pn, 1+px, 1+YUNTRANS(py));
618 ret = +1; /* we did something */
626 struct solver_scratch {
627 unsigned char *grid, *rowidx, *colidx, *set;
630 static int solver_set(struct solver_usage *usage,
631 struct solver_scratch *scratch,
632 int start, int step1, int step2
633 #ifdef STANDALONE_SOLVER
638 int c = usage->c, r = usage->r, cr = c*r;
640 unsigned char *grid = scratch->grid;
641 unsigned char *rowidx = scratch->rowidx;
642 unsigned char *colidx = scratch->colidx;
643 unsigned char *set = scratch->set;
646 * We are passed a cr-by-cr matrix of booleans. Our first job
647 * is to winnow it by finding any definite placements - i.e.
648 * any row with a solitary 1 - and discarding that row and the
649 * column containing the 1.
651 memset(rowidx, TRUE, cr);
652 memset(colidx, TRUE, cr);
653 for (i = 0; i < cr; i++) {
654 int count = 0, first = -1;
655 for (j = 0; j < cr; j++)
656 if (usage->cube[start+i*step1+j*step2])
660 * If count == 0, then there's a row with no 1s at all and
661 * the puzzle is internally inconsistent. However, we ought
662 * to have caught this already during the simpler reasoning
663 * methods, so we can safely fail an assertion if we reach
668 rowidx[i] = colidx[first] = FALSE;
672 * Convert each of rowidx/colidx from a list of 0s and 1s to a
673 * list of the indices of the 1s.
675 for (i = j = 0; i < cr; i++)
679 for (i = j = 0; i < cr; i++)
685 * And create the smaller matrix.
687 for (i = 0; i < n; i++)
688 for (j = 0; j < n; j++)
689 grid[i*cr+j] = usage->cube[start+rowidx[i]*step1+colidx[j]*step2];
692 * Having done that, we now have a matrix in which every row
693 * has at least two 1s in. Now we search to see if we can find
694 * a rectangle of zeroes (in the set-theoretic sense of
695 * `rectangle', i.e. a subset of rows crossed with a subset of
696 * columns) whose width and height add up to n.
703 * We have a candidate set. If its size is <=1 or >=n-1
704 * then we move on immediately.
706 if (count > 1 && count < n-1) {
708 * The number of rows we need is n-count. See if we can
709 * find that many rows which each have a zero in all
710 * the positions listed in `set'.
713 for (i = 0; i < n; i++) {
715 for (j = 0; j < n; j++)
716 if (set[j] && grid[i*cr+j]) {
725 * We expect never to be able to get _more_ than
726 * n-count suitable rows: this would imply that (for
727 * example) there are four numbers which between them
728 * have at most three possible positions, and hence it
729 * indicates a faulty deduction before this point or
732 if (rows > n - count) {
733 #ifdef STANDALONE_SOLVER
734 if (solver_show_working) {
736 printf("%*s", solver_recurse_depth*4,
741 printf(":\n%*s contradiction reached\n",
742 solver_recurse_depth*4, "");
748 if (rows >= n - count) {
749 int progress = FALSE;
752 * We've got one! Now, for each row which _doesn't_
753 * satisfy the criterion, eliminate all its set
754 * bits in the positions _not_ listed in `set'.
755 * Return +1 (meaning progress has been made) if we
756 * successfully eliminated anything at all.
758 * This involves referring back through
759 * rowidx/colidx in order to work out which actual
760 * positions in the cube to meddle with.
762 for (i = 0; i < n; i++) {
764 for (j = 0; j < n; j++)
765 if (set[j] && grid[i*cr+j]) {
770 for (j = 0; j < n; j++)
771 if (!set[j] && grid[i*cr+j]) {
772 int fpos = (start+rowidx[i]*step1+
774 #ifdef STANDALONE_SOLVER
775 if (solver_show_working) {
780 printf("%*s", solver_recurse_depth*4,
793 printf("%*s ruling out %d at (%d,%d)\n",
794 solver_recurse_depth*4, "",
795 pn, 1+px, 1+YUNTRANS(py));
799 usage->cube[fpos] = FALSE;
811 * Binary increment: change the rightmost 0 to a 1, and
812 * change all 1s to the right of it to 0s.
815 while (i > 0 && set[i-1])
816 set[--i] = 0, count--;
818 set[--i] = 1, count++;
826 static struct solver_scratch *solver_new_scratch(struct solver_usage *usage)
828 struct solver_scratch *scratch = snew(struct solver_scratch);
830 scratch->grid = snewn(cr*cr, unsigned char);
831 scratch->rowidx = snewn(cr, unsigned char);
832 scratch->colidx = snewn(cr, unsigned char);
833 scratch->set = snewn(cr, unsigned char);
837 static void solver_free_scratch(struct solver_scratch *scratch)
840 sfree(scratch->colidx);
841 sfree(scratch->rowidx);
842 sfree(scratch->grid);
846 static int solver(int c, int r, digit *grid, random_state *rs, int maxdiff)
848 struct solver_usage *usage;
849 struct solver_scratch *scratch;
852 int diff = DIFF_BLOCK;
855 * Set up a usage structure as a clean slate (everything
858 usage = snew(struct solver_usage);
862 usage->cube = snewn(cr*cr*cr, unsigned char);
863 usage->grid = grid; /* write straight back to the input */
864 memset(usage->cube, TRUE, cr*cr*cr);
866 usage->row = snewn(cr * cr, unsigned char);
867 usage->col = snewn(cr * cr, unsigned char);
868 usage->blk = snewn(cr * cr, unsigned char);
869 memset(usage->row, FALSE, cr * cr);
870 memset(usage->col, FALSE, cr * cr);
871 memset(usage->blk, FALSE, cr * cr);
873 scratch = solver_new_scratch(usage);
876 * Place all the clue numbers we are given.
878 for (x = 0; x < cr; x++)
879 for (y = 0; y < cr; y++)
881 solver_place(usage, x, YTRANS(y), grid[y*cr+x]);
884 * Now loop over the grid repeatedly trying all permitted modes
885 * of reasoning. The loop terminates if we complete an
886 * iteration without making any progress; we then return
887 * failure or success depending on whether the grid is full or
892 * I'd like to write `continue;' inside each of the
893 * following loops, so that the solver returns here after
894 * making some progress. However, I can't specify that I
895 * want to continue an outer loop rather than the innermost
896 * one, so I'm apologetically resorting to a goto.
901 * Blockwise positional elimination.
903 for (x = 0; x < cr; x += r)
904 for (y = 0; y < r; y++)
905 for (n = 1; n <= cr; n++)
906 if (!usage->blk[(y*c+(x/r))*cr+n-1]) {
907 ret = solver_elim(usage, cubepos(x,y,n), r*cr
908 #ifdef STANDALONE_SOLVER
909 , "positional elimination,"
910 " %d in block (%d,%d)", n, 1+x/r, 1+y
914 diff = DIFF_IMPOSSIBLE;
916 } else if (ret > 0) {
917 diff = max(diff, DIFF_BLOCK);
922 if (maxdiff <= DIFF_BLOCK)
926 * Row-wise positional elimination.
928 for (y = 0; y < cr; y++)
929 for (n = 1; n <= cr; n++)
930 if (!usage->row[y*cr+n-1]) {
931 ret = solver_elim(usage, cubepos(0,y,n), cr*cr
932 #ifdef STANDALONE_SOLVER
933 , "positional elimination,"
934 " %d in row %d", n, 1+YUNTRANS(y)
938 diff = DIFF_IMPOSSIBLE;
940 } else if (ret > 0) {
941 diff = max(diff, DIFF_SIMPLE);
946 * Column-wise positional elimination.
948 for (x = 0; x < cr; x++)
949 for (n = 1; n <= cr; n++)
950 if (!usage->col[x*cr+n-1]) {
951 ret = solver_elim(usage, cubepos(x,0,n), cr
952 #ifdef STANDALONE_SOLVER
953 , "positional elimination,"
954 " %d in column %d", n, 1+x
958 diff = DIFF_IMPOSSIBLE;
960 } else if (ret > 0) {
961 diff = max(diff, DIFF_SIMPLE);
967 * Numeric elimination.
969 for (x = 0; x < cr; x++)
970 for (y = 0; y < cr; y++)
971 if (!usage->grid[YUNTRANS(y)*cr+x]) {
972 ret = solver_elim(usage, cubepos(x,y,1), 1
973 #ifdef STANDALONE_SOLVER
974 , "numeric elimination at (%d,%d)", 1+x,
979 diff = DIFF_IMPOSSIBLE;
981 } else if (ret > 0) {
982 diff = max(diff, DIFF_SIMPLE);
987 if (maxdiff <= DIFF_SIMPLE)
991 * Intersectional analysis, rows vs blocks.
993 for (y = 0; y < cr; y++)
994 for (x = 0; x < cr; x += r)
995 for (n = 1; n <= cr; n++)
997 * solver_intersect() never returns -1.
999 if (!usage->row[y*cr+n-1] &&
1000 !usage->blk[((y%r)*c+(x/r))*cr+n-1] &&
1001 (solver_intersect(usage, cubepos(0,y,n), cr*cr,
1002 cubepos(x,y%r,n), r*cr
1003 #ifdef STANDALONE_SOLVER
1004 , "intersectional analysis,"
1005 " %d in row %d vs block (%d,%d)",
1006 n, 1+YUNTRANS(y), 1+x/r, 1+y%r
1009 solver_intersect(usage, cubepos(x,y%r,n), r*cr,
1010 cubepos(0,y,n), cr*cr
1011 #ifdef STANDALONE_SOLVER
1012 , "intersectional analysis,"
1013 " %d in block (%d,%d) vs row %d",
1014 n, 1+x/r, 1+y%r, 1+YUNTRANS(y)
1017 diff = max(diff, DIFF_INTERSECT);
1022 * Intersectional analysis, columns vs blocks.
1024 for (x = 0; x < cr; x++)
1025 for (y = 0; y < r; y++)
1026 for (n = 1; n <= cr; n++)
1027 if (!usage->col[x*cr+n-1] &&
1028 !usage->blk[(y*c+(x/r))*cr+n-1] &&
1029 (solver_intersect(usage, cubepos(x,0,n), cr,
1030 cubepos((x/r)*r,y,n), r*cr
1031 #ifdef STANDALONE_SOLVER
1032 , "intersectional analysis,"
1033 " %d in column %d vs block (%d,%d)",
1037 solver_intersect(usage, cubepos((x/r)*r,y,n), r*cr,
1039 #ifdef STANDALONE_SOLVER
1040 , "intersectional analysis,"
1041 " %d in block (%d,%d) vs column %d",
1045 diff = max(diff, DIFF_INTERSECT);
1049 if (maxdiff <= DIFF_INTERSECT)
1053 * Blockwise set elimination.
1055 for (x = 0; x < cr; x += r)
1056 for (y = 0; y < r; y++) {
1057 ret = solver_set(usage, scratch, cubepos(x,y,1), r*cr, 1
1058 #ifdef STANDALONE_SOLVER
1059 , "set elimination, block (%d,%d)", 1+x/r, 1+y
1063 diff = DIFF_IMPOSSIBLE;
1065 } else if (ret > 0) {
1066 diff = max(diff, DIFF_SET);
1072 * Row-wise set elimination.
1074 for (y = 0; y < cr; y++) {
1075 ret = solver_set(usage, scratch, cubepos(0,y,1), cr*cr, 1
1076 #ifdef STANDALONE_SOLVER
1077 , "set elimination, row %d", 1+YUNTRANS(y)
1081 diff = DIFF_IMPOSSIBLE;
1083 } else if (ret > 0) {
1084 diff = max(diff, DIFF_SET);
1090 * Column-wise set elimination.
1092 for (x = 0; x < cr; x++) {
1093 ret = solver_set(usage, scratch, cubepos(x,0,1), cr, 1
1094 #ifdef STANDALONE_SOLVER
1095 , "set elimination, column %d", 1+x
1099 diff = DIFF_IMPOSSIBLE;
1101 } else if (ret > 0) {
1102 diff = max(diff, DIFF_SET);
1108 * If we reach here, we have made no deductions in this
1109 * iteration, so the algorithm terminates.
1115 * Last chance: if we haven't fully solved the puzzle yet, try
1116 * recursing based on guesses for a particular square. We pick
1117 * one of the most constrained empty squares we can find, which
1118 * has the effect of pruning the search tree as much as
1121 if (maxdiff >= DIFF_RECURSIVE) {
1122 int best, bestcount, bestnumber;
1128 for (y = 0; y < cr; y++)
1129 for (x = 0; x < cr; x++)
1130 if (!grid[y*cr+x]) {
1134 * An unfilled square. Count the number of
1135 * possible digits in it.
1138 for (n = 1; n <= cr; n++)
1139 if (cube(x,YTRANS(y),n))
1143 * We should have found any impossibilities
1144 * already, so this can safely be an assert.
1148 if (count < bestcount) {
1153 if (count == bestcount) {
1155 if (bestnumber == 1 ||
1156 (rs && random_upto(rs, bestnumber) == 0))
1163 digit *list, *ingrid, *outgrid;
1165 diff = DIFF_IMPOSSIBLE; /* no solution found yet */
1168 * Attempt recursion.
1173 list = snewn(cr, digit);
1174 ingrid = snewn(cr * cr, digit);
1175 outgrid = snewn(cr * cr, digit);
1176 memcpy(ingrid, grid, cr * cr);
1178 /* Make a list of the possible digits. */
1179 for (j = 0, n = 1; n <= cr; n++)
1180 if (cube(x,YTRANS(y),n))
1183 #ifdef STANDALONE_SOLVER
1184 if (solver_show_working) {
1186 printf("%*srecursing on (%d,%d) [",
1187 solver_recurse_depth*4, "", x, y);
1188 for (i = 0; i < j; i++) {
1189 printf("%s%d", sep, list[i]);
1196 /* Now shuffle the list. */
1198 for (i = j; i > 1; i--) {
1199 int p = random_upto(rs, i);
1202 list[p] = list[i-1];
1209 * And step along the list, recursing back into the
1210 * main solver at every stage.
1212 for (i = 0; i < j; i++) {
1215 memcpy(outgrid, ingrid, cr * cr);
1216 outgrid[y*cr+x] = list[i];
1218 #ifdef STANDALONE_SOLVER
1219 if (solver_show_working)
1220 printf("%*sguessing %d at (%d,%d)\n",
1221 solver_recurse_depth*4, "", list[i], x, y);
1222 solver_recurse_depth++;
1225 ret = solver(c, r, outgrid, rs, maxdiff);
1227 #ifdef STANDALONE_SOLVER
1228 solver_recurse_depth--;
1229 if (solver_show_working) {
1230 printf("%*sretracting %d at (%d,%d)\n",
1231 solver_recurse_depth*4, "", list[i], x, y);
1236 * If we have our first solution, copy it into the
1237 * grid we will return.
1239 if (diff == DIFF_IMPOSSIBLE && ret != DIFF_IMPOSSIBLE)
1240 memcpy(grid, outgrid, cr*cr);
1242 if (ret == DIFF_AMBIGUOUS)
1243 diff = DIFF_AMBIGUOUS;
1244 else if (ret == DIFF_IMPOSSIBLE)
1245 /* do not change our return value */;
1247 /* the recursion turned up exactly one solution */
1248 if (diff == DIFF_IMPOSSIBLE)
1249 diff = DIFF_RECURSIVE;
1251 diff = DIFF_AMBIGUOUS;
1255 * As soon as we've found more than one solution,
1256 * give up immediately.
1258 if (diff == DIFF_AMBIGUOUS)
1269 * We're forbidden to use recursion, so we just see whether
1270 * our grid is fully solved, and return DIFF_IMPOSSIBLE
1273 for (y = 0; y < cr; y++)
1274 for (x = 0; x < cr; x++)
1276 diff = DIFF_IMPOSSIBLE;
1281 #ifdef STANDALONE_SOLVER
1282 if (solver_show_working)
1283 printf("%*s%s found\n",
1284 solver_recurse_depth*4, "",
1285 diff == DIFF_IMPOSSIBLE ? "no solution" :
1286 diff == DIFF_AMBIGUOUS ? "multiple solutions" :
1296 solver_free_scratch(scratch);
1301 /* ----------------------------------------------------------------------
1302 * End of solver code.
1305 /* ----------------------------------------------------------------------
1306 * Solo filled-grid generator.
1308 * This grid generator works by essentially trying to solve a grid
1309 * starting from no clues, and not worrying that there's more than
1310 * one possible solution. Unfortunately, it isn't computationally
1311 * feasible to do this by calling the above solver with an empty
1312 * grid, because that one needs to allocate a lot of scratch space
1313 * at every recursion level. Instead, I have a much simpler
1314 * algorithm which I shamelessly copied from a Python solver
1315 * written by Andrew Wilkinson (which is GPLed, but I've reused
1316 * only ideas and no code). It mostly just does the obvious
1317 * recursive thing: pick an empty square, put one of the possible
1318 * digits in it, recurse until all squares are filled, backtrack
1319 * and change some choices if necessary.
1321 * The clever bit is that every time it chooses which square to
1322 * fill in next, it does so by counting the number of _possible_
1323 * numbers that can go in each square, and it prioritises so that
1324 * it picks a square with the _lowest_ number of possibilities. The
1325 * idea is that filling in lots of the obvious bits (particularly
1326 * any squares with only one possibility) will cut down on the list
1327 * of possibilities for other squares and hence reduce the enormous
1328 * search space as much as possible as early as possible.
1332 * Internal data structure used in gridgen to keep track of
1335 struct gridgen_coord { int x, y, r; };
1336 struct gridgen_usage {
1337 int c, r, cr; /* cr == c*r */
1338 /* grid is a copy of the input grid, modified as we go along */
1340 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
1342 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
1344 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
1346 /* This lists all the empty spaces remaining in the grid. */
1347 struct gridgen_coord *spaces;
1349 /* If we need randomisation in the solve, this is our random state. */
1354 * The real recursive step in the generating function.
1356 static int gridgen_real(struct gridgen_usage *usage, digit *grid)
1358 int c = usage->c, r = usage->r, cr = usage->cr;
1359 int i, j, n, sx, sy, bestm, bestr, ret;
1363 * Firstly, check for completion! If there are no spaces left
1364 * in the grid, we have a solution.
1366 if (usage->nspaces == 0) {
1367 memcpy(grid, usage->grid, cr * cr);
1372 * Otherwise, there must be at least one space. Find the most
1373 * constrained space, using the `r' field as a tie-breaker.
1375 bestm = cr+1; /* so that any space will beat it */
1378 for (j = 0; j < usage->nspaces; j++) {
1379 int x = usage->spaces[j].x, y = usage->spaces[j].y;
1383 * Find the number of digits that could go in this space.
1386 for (n = 0; n < cr; n++)
1387 if (!usage->row[y*cr+n] && !usage->col[x*cr+n] &&
1388 !usage->blk[((y/c)*c+(x/r))*cr+n])
1391 if (m < bestm || (m == bestm && usage->spaces[j].r < bestr)) {
1393 bestr = usage->spaces[j].r;
1401 * Swap that square into the final place in the spaces array,
1402 * so that decrementing nspaces will remove it from the list.
1404 if (i != usage->nspaces-1) {
1405 struct gridgen_coord t;
1406 t = usage->spaces[usage->nspaces-1];
1407 usage->spaces[usage->nspaces-1] = usage->spaces[i];
1408 usage->spaces[i] = t;
1412 * Now we've decided which square to start our recursion at,
1413 * simply go through all possible values, shuffling them
1414 * randomly first if necessary.
1416 digits = snewn(bestm, int);
1418 for (n = 0; n < cr; n++)
1419 if (!usage->row[sy*cr+n] && !usage->col[sx*cr+n] &&
1420 !usage->blk[((sy/c)*c+(sx/r))*cr+n]) {
1426 for (i = j; i > 1; i--) {
1427 int p = random_upto(usage->rs, i);
1430 digits[p] = digits[i-1];
1436 /* And finally, go through the digit list and actually recurse. */
1438 for (i = 0; i < j; i++) {
1441 /* Update the usage structure to reflect the placing of this digit. */
1442 usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
1443 usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = TRUE;
1444 usage->grid[sy*cr+sx] = n;
1447 /* Call the solver recursively. Stop when we find a solution. */
1448 if (gridgen_real(usage, grid))
1451 /* Revert the usage structure. */
1452 usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
1453 usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = FALSE;
1454 usage->grid[sy*cr+sx] = 0;
1466 * Entry point to generator. You give it dimensions and a starting
1467 * grid, which is simply an array of cr*cr digits.
1469 static void gridgen(int c, int r, digit *grid, random_state *rs)
1471 struct gridgen_usage *usage;
1475 * Clear the grid to start with.
1477 memset(grid, 0, cr*cr);
1480 * Create a gridgen_usage structure.
1482 usage = snew(struct gridgen_usage);
1488 usage->grid = snewn(cr * cr, digit);
1489 memcpy(usage->grid, grid, cr * cr);
1491 usage->row = snewn(cr * cr, unsigned char);
1492 usage->col = snewn(cr * cr, unsigned char);
1493 usage->blk = snewn(cr * cr, unsigned char);
1494 memset(usage->row, FALSE, cr * cr);
1495 memset(usage->col, FALSE, cr * cr);
1496 memset(usage->blk, FALSE, cr * cr);
1498 usage->spaces = snewn(cr * cr, struct gridgen_coord);
1504 * Initialise the list of grid spaces.
1506 for (y = 0; y < cr; y++) {
1507 for (x = 0; x < cr; x++) {
1508 usage->spaces[usage->nspaces].x = x;
1509 usage->spaces[usage->nspaces].y = y;
1510 usage->spaces[usage->nspaces].r = random_bits(rs, 31);
1516 * Run the real generator function.
1518 gridgen_real(usage, grid);
1521 * Clean up the usage structure now we have our answer.
1523 sfree(usage->spaces);
1531 /* ----------------------------------------------------------------------
1532 * End of grid generator code.
1536 * Check whether a grid contains a valid complete puzzle.
1538 static int check_valid(int c, int r, digit *grid)
1541 unsigned char *used;
1544 used = snewn(cr, unsigned char);
1547 * Check that each row contains precisely one of everything.
1549 for (y = 0; y < cr; y++) {
1550 memset(used, FALSE, cr);
1551 for (x = 0; x < cr; x++)
1552 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
1553 used[grid[y*cr+x]-1] = TRUE;
1554 for (n = 0; n < cr; n++)
1562 * Check that each column contains precisely one of everything.
1564 for (x = 0; x < cr; x++) {
1565 memset(used, FALSE, cr);
1566 for (y = 0; y < cr; y++)
1567 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
1568 used[grid[y*cr+x]-1] = TRUE;
1569 for (n = 0; n < cr; n++)
1577 * Check that each block contains precisely one of everything.
1579 for (x = 0; x < cr; x += r) {
1580 for (y = 0; y < cr; y += c) {
1582 memset(used, FALSE, cr);
1583 for (xx = x; xx < x+r; xx++)
1584 for (yy = 0; yy < y+c; yy++)
1585 if (grid[yy*cr+xx] > 0 && grid[yy*cr+xx] <= cr)
1586 used[grid[yy*cr+xx]-1] = TRUE;
1587 for (n = 0; n < cr; n++)
1599 static int symmetries(game_params *params, int x, int y, int *output, int s)
1601 int c = params->c, r = params->r, cr = c*r;
1604 #define ADD(x,y) (*output++ = (x), *output++ = (y), i++)
1610 break; /* just x,y is all we need */
1612 ADD(cr - 1 - x, cr - 1 - y);
1617 ADD(cr - 1 - x, cr - 1 - y);
1628 ADD(cr - 1 - x, cr - 1 - y);
1632 ADD(cr - 1 - x, cr - 1 - y);
1633 ADD(cr - 1 - y, cr - 1 - x);
1638 ADD(cr - 1 - x, cr - 1 - y);
1642 ADD(cr - 1 - y, cr - 1 - x);
1651 static char *encode_solve_move(int cr, digit *grid)
1654 char *ret, *p, *sep;
1657 * It's surprisingly easy to work out _exactly_ how long this
1658 * string needs to be. To decimal-encode all the numbers from 1
1661 * - every number has a units digit; total is n.
1662 * - all numbers above 9 have a tens digit; total is max(n-9,0).
1663 * - all numbers above 99 have a hundreds digit; total is max(n-99,0).
1667 for (i = 1; i <= cr; i *= 10)
1668 len += max(cr - i + 1, 0);
1669 len += cr; /* don't forget the commas */
1670 len *= cr; /* there are cr rows of these */
1673 * Now len is one bigger than the total size of the
1674 * comma-separated numbers (because we counted an
1675 * additional leading comma). We need to have a leading S
1676 * and a trailing NUL, so we're off by one in total.
1680 ret = snewn(len, char);
1684 for (i = 0; i < cr*cr; i++) {
1685 p += sprintf(p, "%s%d", sep, grid[i]);
1689 assert(p - ret == len);
1694 static char *new_game_desc(game_params *params, random_state *rs,
1695 char **aux, int interactive)
1697 int c = params->c, r = params->r, cr = c*r;
1699 digit *grid, *grid2;
1700 struct xy { int x, y; } *locs;
1703 int coords[16], ncoords;
1704 int *symmclasses, nsymmclasses;
1705 int maxdiff, recursing;
1708 * Adjust the maximum difficulty level to be consistent with
1709 * the puzzle size: all 2x2 puzzles appear to be Trivial
1710 * (DIFF_BLOCK) so we cannot hold out for even a Basic
1711 * (DIFF_SIMPLE) one.
1713 maxdiff = params->diff;
1714 if (c == 2 && r == 2)
1715 maxdiff = DIFF_BLOCK;
1717 grid = snewn(area, digit);
1718 locs = snewn(area, struct xy);
1719 grid2 = snewn(area, digit);
1722 * Find the set of equivalence classes of squares permitted
1723 * by the selected symmetry. We do this by enumerating all
1724 * the grid squares which have no symmetric companion
1725 * sorting lower than themselves.
1728 symmclasses = snewn(cr * cr, int);
1732 for (y = 0; y < cr; y++)
1733 for (x = 0; x < cr; x++) {
1737 ncoords = symmetries(params, x, y, coords, params->symm);
1738 for (j = 0; j < ncoords; j++)
1739 if (coords[2*j+1]*cr+coords[2*j] < i)
1742 symmclasses[nsymmclasses++] = i;
1747 * Loop until we get a grid of the required difficulty. This is
1748 * nasty, but it seems to be unpleasantly hard to generate
1749 * difficult grids otherwise.
1753 * Generate a random solved state.
1755 gridgen(c, r, grid, rs);
1756 assert(check_valid(c, r, grid));
1759 * Save the solved grid in aux.
1763 * We might already have written *aux the last time we
1764 * went round this loop, in which case we should free
1765 * the old aux before overwriting it with the new one.
1771 *aux = encode_solve_move(cr, grid);
1775 * Now we have a solved grid, start removing things from it
1776 * while preserving solubility.
1783 * Iterate over the grid and enumerate all the filled
1784 * squares we could empty.
1788 for (i = 0; i < nsymmclasses; i++) {
1789 x = symmclasses[i] % cr;
1790 y = symmclasses[i] / cr;
1799 * Now shuffle that list.
1801 for (i = nlocs; i > 1; i--) {
1802 int p = random_upto(rs, i);
1804 struct xy t = locs[p];
1805 locs[p] = locs[i-1];
1811 * Now loop over the shuffled list and, for each element,
1812 * see whether removing that element (and its reflections)
1813 * from the grid will still leave the grid soluble by
1816 for (i = 0; i < nlocs; i++) {
1822 memcpy(grid2, grid, area);
1823 ncoords = symmetries(params, x, y, coords, params->symm);
1824 for (j = 0; j < ncoords; j++)
1825 grid2[coords[2*j+1]*cr+coords[2*j]] = 0;
1827 ret = solver(c, r, grid2, NULL, maxdiff);
1828 if (ret != DIFF_IMPOSSIBLE && ret != DIFF_AMBIGUOUS) {
1829 for (j = 0; j < ncoords; j++)
1830 grid[coords[2*j+1]*cr+coords[2*j]] = 0;
1837 * There was nothing we could remove without
1838 * destroying solvability. Give up.
1844 memcpy(grid2, grid, area);
1845 } while (solver(c, r, grid2, NULL, maxdiff) < maxdiff);
1853 * Now we have the grid as it will be presented to the user.
1854 * Encode it in a game desc.
1860 desc = snewn(5 * area, char);
1863 for (i = 0; i <= area; i++) {
1864 int n = (i < area ? grid[i] : -1);
1871 int c = 'a' - 1 + run;
1875 run -= c - ('a' - 1);
1879 * If there's a number in the very top left or
1880 * bottom right, there's no point putting an
1881 * unnecessary _ before or after it.
1883 if (p > desc && n > 0)
1887 p += sprintf(p, "%d", n);
1891 assert(p - desc < 5 * area);
1893 desc = sresize(desc, p - desc, char);
1901 static char *validate_desc(game_params *params, char *desc)
1903 int area = params->r * params->r * params->c * params->c;
1908 if (n >= 'a' && n <= 'z') {
1909 squares += n - 'a' + 1;
1910 } else if (n == '_') {
1912 } else if (n > '0' && n <= '9') {
1914 while (*desc >= '0' && *desc <= '9')
1917 return "Invalid character in game description";
1921 return "Not enough data to fill grid";
1924 return "Too much data to fit in grid";
1929 static game_state *new_game(midend_data *me, game_params *params, char *desc)
1931 game_state *state = snew(game_state);
1932 int c = params->c, r = params->r, cr = c*r, area = cr * cr;
1935 state->c = params->c;
1936 state->r = params->r;
1938 state->grid = snewn(area, digit);
1939 state->pencil = snewn(area * cr, unsigned char);
1940 memset(state->pencil, 0, area * cr);
1941 state->immutable = snewn(area, unsigned char);
1942 memset(state->immutable, FALSE, area);
1944 state->completed = state->cheated = FALSE;
1949 if (n >= 'a' && n <= 'z') {
1950 int run = n - 'a' + 1;
1951 assert(i + run <= area);
1953 state->grid[i++] = 0;
1954 } else if (n == '_') {
1956 } else if (n > '0' && n <= '9') {
1958 state->immutable[i] = TRUE;
1959 state->grid[i++] = atoi(desc-1);
1960 while (*desc >= '0' && *desc <= '9')
1963 assert(!"We can't get here");
1971 static game_state *dup_game(game_state *state)
1973 game_state *ret = snew(game_state);
1974 int c = state->c, r = state->r, cr = c*r, area = cr * cr;
1979 ret->grid = snewn(area, digit);
1980 memcpy(ret->grid, state->grid, area);
1982 ret->pencil = snewn(area * cr, unsigned char);
1983 memcpy(ret->pencil, state->pencil, area * cr);
1985 ret->immutable = snewn(area, unsigned char);
1986 memcpy(ret->immutable, state->immutable, area);
1988 ret->completed = state->completed;
1989 ret->cheated = state->cheated;
1994 static void free_game(game_state *state)
1996 sfree(state->immutable);
1997 sfree(state->pencil);
2002 static char *solve_game(game_state *state, game_state *currstate,
2003 char *ai, char **error)
2005 int c = state->c, r = state->r, cr = c*r;
2011 * If we already have the solution in ai, save ourselves some
2017 grid = snewn(cr*cr, digit);
2018 memcpy(grid, state->grid, cr*cr);
2019 solve_ret = solver(c, r, grid, NULL, DIFF_RECURSIVE);
2023 if (solve_ret == DIFF_IMPOSSIBLE)
2024 *error = "No solution exists for this puzzle";
2025 else if (solve_ret == DIFF_AMBIGUOUS)
2026 *error = "Multiple solutions exist for this puzzle";
2033 ret = encode_solve_move(cr, grid);
2040 static char *grid_text_format(int c, int r, digit *grid)
2048 * There are cr lines of digits, plus r-1 lines of block
2049 * separators. Each line contains cr digits, cr-1 separating
2050 * spaces, and c-1 two-character block separators. Thus, the
2051 * total length of a line is 2*cr+2*c-3 (not counting the
2052 * newline), and there are cr+r-1 of them.
2054 maxlen = (cr+r-1) * (2*cr+2*c-2);
2055 ret = snewn(maxlen+1, char);
2058 for (y = 0; y < cr; y++) {
2059 for (x = 0; x < cr; x++) {
2060 int ch = grid[y * cr + x];
2070 if ((x+1) % r == 0) {
2077 if (y+1 < cr && (y+1) % c == 0) {
2078 for (x = 0; x < cr; x++) {
2082 if ((x+1) % r == 0) {
2092 assert(p - ret == maxlen);
2097 static char *game_text_format(game_state *state)
2099 return grid_text_format(state->c, state->r, state->grid);
2104 * These are the coordinates of the currently highlighted
2105 * square on the grid, or -1,-1 if there isn't one. When there
2106 * is, pressing a valid number or letter key or Space will
2107 * enter that number or letter in the grid.
2111 * This indicates whether the current highlight is a
2112 * pencil-mark one or a real one.
2117 static game_ui *new_ui(game_state *state)
2119 game_ui *ui = snew(game_ui);
2121 ui->hx = ui->hy = -1;
2127 static void free_ui(game_ui *ui)
2132 static char *encode_ui(game_ui *ui)
2137 static void decode_ui(game_ui *ui, char *encoding)
2141 static void game_changed_state(game_ui *ui, game_state *oldstate,
2142 game_state *newstate)
2144 int c = newstate->c, r = newstate->r, cr = c*r;
2146 * We prevent pencil-mode highlighting of a filled square. So
2147 * if the user has just filled in a square which we had a
2148 * pencil-mode highlight in (by Undo, or by Redo, or by Solve),
2149 * then we cancel the highlight.
2151 if (ui->hx >= 0 && ui->hy >= 0 && ui->hpencil &&
2152 newstate->grid[ui->hy * cr + ui->hx] != 0) {
2153 ui->hx = ui->hy = -1;
2157 struct game_drawstate {
2162 unsigned char *pencil;
2164 /* This is scratch space used within a single call to game_redraw. */
2168 static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
2169 int x, int y, int button)
2171 int c = state->c, r = state->r, cr = c*r;
2175 button &= ~MOD_MASK;
2177 tx = (x + TILE_SIZE - BORDER) / TILE_SIZE - 1;
2178 ty = (y + TILE_SIZE - BORDER) / TILE_SIZE - 1;
2180 if (tx >= 0 && tx < cr && ty >= 0 && ty < cr) {
2181 if (button == LEFT_BUTTON) {
2182 if (state->immutable[ty*cr+tx]) {
2183 ui->hx = ui->hy = -1;
2184 } else if (tx == ui->hx && ty == ui->hy && ui->hpencil == 0) {
2185 ui->hx = ui->hy = -1;
2191 return ""; /* UI activity occurred */
2193 if (button == RIGHT_BUTTON) {
2195 * Pencil-mode highlighting for non filled squares.
2197 if (state->grid[ty*cr+tx] == 0) {
2198 if (tx == ui->hx && ty == ui->hy && ui->hpencil) {
2199 ui->hx = ui->hy = -1;
2206 ui->hx = ui->hy = -1;
2208 return ""; /* UI activity occurred */
2212 if (ui->hx != -1 && ui->hy != -1 &&
2213 ((button >= '1' && button <= '9' && button - '0' <= cr) ||
2214 (button >= 'a' && button <= 'z' && button - 'a' + 10 <= cr) ||
2215 (button >= 'A' && button <= 'Z' && button - 'A' + 10 <= cr) ||
2217 int n = button - '0';
2218 if (button >= 'A' && button <= 'Z')
2219 n = button - 'A' + 10;
2220 if (button >= 'a' && button <= 'z')
2221 n = button - 'a' + 10;
2226 * Can't overwrite this square. In principle this shouldn't
2227 * happen anyway because we should never have even been
2228 * able to highlight the square, but it never hurts to be
2231 if (state->immutable[ui->hy*cr+ui->hx])
2235 * Can't make pencil marks in a filled square. In principle
2236 * this shouldn't happen anyway because we should never
2237 * have even been able to pencil-highlight the square, but
2238 * it never hurts to be careful.
2240 if (ui->hpencil && state->grid[ui->hy*cr+ui->hx])
2243 sprintf(buf, "%c%d,%d,%d",
2244 (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n);
2246 ui->hx = ui->hy = -1;
2254 static game_state *execute_move(game_state *from, char *move)
2256 int c = from->c, r = from->r, cr = c*r;
2260 if (move[0] == 'S') {
2263 ret = dup_game(from);
2264 ret->completed = ret->cheated = TRUE;
2267 for (n = 0; n < cr*cr; n++) {
2268 ret->grid[n] = atoi(p);
2270 if (!*p || ret->grid[n] < 1 || ret->grid[n] > cr) {
2275 while (*p && isdigit((unsigned char)*p)) p++;
2280 } else if ((move[0] == 'P' || move[0] == 'R') &&
2281 sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
2282 x >= 0 && x < cr && y >= 0 && y < cr && n >= 0 && n <= cr) {
2284 ret = dup_game(from);
2285 if (move[0] == 'P' && n > 0) {
2286 int index = (y*cr+x) * cr + (n-1);
2287 ret->pencil[index] = !ret->pencil[index];
2289 ret->grid[y*cr+x] = n;
2290 memset(ret->pencil + (y*cr+x)*cr, 0, cr);
2293 * We've made a real change to the grid. Check to see
2294 * if the game has been completed.
2296 if (!ret->completed && check_valid(c, r, ret->grid)) {
2297 ret->completed = TRUE;
2302 return NULL; /* couldn't parse move string */
2305 /* ----------------------------------------------------------------------
2309 #define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
2310 #define GETTILESIZE(cr, w) ( (double)(w-1) / (double)(cr+1) )
2312 static void game_compute_size(game_params *params, int tilesize,
2315 /* Ick: fake up `ds->tilesize' for macro expansion purposes */
2316 struct { int tilesize; } ads, *ds = &ads;
2317 ads.tilesize = tilesize;
2319 *x = SIZE(params->c * params->r);
2320 *y = SIZE(params->c * params->r);
2323 static void game_set_size(game_drawstate *ds, game_params *params,
2326 ds->tilesize = tilesize;
2329 static float *game_colours(frontend *fe, game_state *state, int *ncolours)
2331 float *ret = snewn(3 * NCOLOURS, float);
2333 frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
2335 ret[COL_GRID * 3 + 0] = 0.0F;
2336 ret[COL_GRID * 3 + 1] = 0.0F;
2337 ret[COL_GRID * 3 + 2] = 0.0F;
2339 ret[COL_CLUE * 3 + 0] = 0.0F;
2340 ret[COL_CLUE * 3 + 1] = 0.0F;
2341 ret[COL_CLUE * 3 + 2] = 0.0F;
2343 ret[COL_USER * 3 + 0] = 0.0F;
2344 ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
2345 ret[COL_USER * 3 + 2] = 0.0F;
2347 ret[COL_HIGHLIGHT * 3 + 0] = 0.85F * ret[COL_BACKGROUND * 3 + 0];
2348 ret[COL_HIGHLIGHT * 3 + 1] = 0.85F * ret[COL_BACKGROUND * 3 + 1];
2349 ret[COL_HIGHLIGHT * 3 + 2] = 0.85F * ret[COL_BACKGROUND * 3 + 2];
2351 ret[COL_ERROR * 3 + 0] = 1.0F;
2352 ret[COL_ERROR * 3 + 1] = 0.0F;
2353 ret[COL_ERROR * 3 + 2] = 0.0F;
2355 ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
2356 ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
2357 ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
2359 *ncolours = NCOLOURS;
2363 static game_drawstate *game_new_drawstate(game_state *state)
2365 struct game_drawstate *ds = snew(struct game_drawstate);
2366 int c = state->c, r = state->r, cr = c*r;
2368 ds->started = FALSE;
2372 ds->grid = snewn(cr*cr, digit);
2373 memset(ds->grid, 0, cr*cr);
2374 ds->pencil = snewn(cr*cr*cr, digit);
2375 memset(ds->pencil, 0, cr*cr*cr);
2376 ds->hl = snewn(cr*cr, unsigned char);
2377 memset(ds->hl, 0, cr*cr);
2378 ds->entered_items = snewn(cr*cr, int);
2379 ds->tilesize = 0; /* not decided yet */
2383 static void game_free_drawstate(game_drawstate *ds)
2388 sfree(ds->entered_items);
2392 static void draw_number(frontend *fe, game_drawstate *ds, game_state *state,
2393 int x, int y, int hl)
2395 int c = state->c, r = state->r, cr = c*r;
2400 if (ds->grid[y*cr+x] == state->grid[y*cr+x] &&
2401 ds->hl[y*cr+x] == hl &&
2402 !memcmp(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr))
2403 return; /* no change required */
2405 tx = BORDER + x * TILE_SIZE + 2;
2406 ty = BORDER + y * TILE_SIZE + 2;
2422 clip(fe, cx, cy, cw, ch);
2424 /* background needs erasing */
2425 draw_rect(fe, cx, cy, cw, ch, (hl & 15) == 1 ? COL_HIGHLIGHT : COL_BACKGROUND);
2427 /* pencil-mode highlight */
2428 if ((hl & 15) == 2) {
2432 coords[2] = cx+cw/2;
2435 coords[5] = cy+ch/2;
2436 draw_polygon(fe, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
2439 /* new number needs drawing? */
2440 if (state->grid[y*cr+x]) {
2442 str[0] = state->grid[y*cr+x] + '0';
2444 str[0] += 'a' - ('9'+1);
2445 draw_text(fe, tx + TILE_SIZE/2, ty + TILE_SIZE/2,
2446 FONT_VARIABLE, TILE_SIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
2447 state->immutable[y*cr+x] ? COL_CLUE : (hl & 16) ? COL_ERROR : COL_USER, str);
2450 int pw, ph, pmax, fontsize;
2452 /* count the pencil marks required */
2453 for (i = npencil = 0; i < cr; i++)
2454 if (state->pencil[(y*cr+x)*cr+i])
2458 * It's not sensible to arrange pencil marks in the same
2459 * layout as the squares within a block, because this leads
2460 * to the font being too small. Instead, we arrange pencil
2461 * marks in the nearest thing we can to a square layout,
2462 * and we adjust the square layout depending on the number
2463 * of pencil marks in the square.
2465 for (pw = 1; pw * pw < npencil; pw++);
2466 if (pw < 3) pw = 3; /* otherwise it just looks _silly_ */
2467 ph = (npencil + pw - 1) / pw;
2468 if (ph < 2) ph = 2; /* likewise */
2470 fontsize = TILE_SIZE/(pmax*(11-pmax)/8);
2472 for (i = j = 0; i < cr; i++)
2473 if (state->pencil[(y*cr+x)*cr+i]) {
2474 int dx = j % pw, dy = j / pw;
2479 str[0] += 'a' - ('9'+1);
2480 draw_text(fe, tx + (4*dx+3) * TILE_SIZE / (4*pw+2),
2481 ty + (4*dy+3) * TILE_SIZE / (4*ph+2),
2482 FONT_VARIABLE, fontsize,
2483 ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
2490 draw_update(fe, cx, cy, cw, ch);
2492 ds->grid[y*cr+x] = state->grid[y*cr+x];
2493 memcpy(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr);
2494 ds->hl[y*cr+x] = hl;
2497 static void game_redraw(frontend *fe, game_drawstate *ds, game_state *oldstate,
2498 game_state *state, int dir, game_ui *ui,
2499 float animtime, float flashtime)
2501 int c = state->c, r = state->r, cr = c*r;
2506 * The initial contents of the window are not guaranteed
2507 * and can vary with front ends. To be on the safe side,
2508 * all games should start by drawing a big
2509 * background-colour rectangle covering the whole window.
2511 draw_rect(fe, 0, 0, SIZE(cr), SIZE(cr), COL_BACKGROUND);
2516 for (x = 0; x <= cr; x++) {
2517 int thick = (x % r ? 0 : 1);
2518 draw_rect(fe, BORDER + x*TILE_SIZE - thick, BORDER-1,
2519 1+2*thick, cr*TILE_SIZE+3, COL_GRID);
2521 for (y = 0; y <= cr; y++) {
2522 int thick = (y % c ? 0 : 1);
2523 draw_rect(fe, BORDER-1, BORDER + y*TILE_SIZE - thick,
2524 cr*TILE_SIZE+3, 1+2*thick, COL_GRID);
2529 * This array is used to keep track of rows, columns and boxes
2530 * which contain a number more than once.
2532 for (x = 0; x < cr * cr; x++)
2533 ds->entered_items[x] = 0;
2534 for (x = 0; x < cr; x++)
2535 for (y = 0; y < cr; y++) {
2536 digit d = state->grid[y*cr+x];
2538 int box = (x/r)+(y/c)*c;
2539 ds->entered_items[x*cr+d-1] |= ((ds->entered_items[x*cr+d-1] & 1) << 1) | 1;
2540 ds->entered_items[y*cr+d-1] |= ((ds->entered_items[y*cr+d-1] & 4) << 1) | 4;
2541 ds->entered_items[box*cr+d-1] |= ((ds->entered_items[box*cr+d-1] & 16) << 1) | 16;
2546 * Draw any numbers which need redrawing.
2548 for (x = 0; x < cr; x++) {
2549 for (y = 0; y < cr; y++) {
2551 digit d = state->grid[y*cr+x];
2553 if (flashtime > 0 &&
2554 (flashtime <= FLASH_TIME/3 ||
2555 flashtime >= FLASH_TIME*2/3))
2558 /* Highlight active input areas. */
2559 if (x == ui->hx && y == ui->hy)
2560 highlight = ui->hpencil ? 2 : 1;
2562 /* Mark obvious errors (ie, numbers which occur more than once
2563 * in a single row, column, or box). */
2564 if (d && ((ds->entered_items[x*cr+d-1] & 2) ||
2565 (ds->entered_items[y*cr+d-1] & 8) ||
2566 (ds->entered_items[((x/r)+(y/c)*c)*cr+d-1] & 32)))
2569 draw_number(fe, ds, state, x, y, highlight);
2574 * Update the _entire_ grid if necessary.
2577 draw_update(fe, 0, 0, SIZE(cr), SIZE(cr));
2582 static float game_anim_length(game_state *oldstate, game_state *newstate,
2583 int dir, game_ui *ui)
2588 static float game_flash_length(game_state *oldstate, game_state *newstate,
2589 int dir, game_ui *ui)
2591 if (!oldstate->completed && newstate->completed &&
2592 !oldstate->cheated && !newstate->cheated)
2597 static int game_wants_statusbar(void)
2602 static int game_timing_state(game_state *state, game_ui *ui)
2608 #define thegame solo
2611 const struct game thegame = {
2612 "Solo", "games.solo",
2619 TRUE, game_configure, custom_params,
2627 TRUE, game_text_format,
2635 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
2638 game_free_drawstate,
2642 game_wants_statusbar,
2643 FALSE, game_timing_state,
2644 0, /* mouse_priorities */
2647 #ifdef STANDALONE_SOLVER
2650 * gcc -DSTANDALONE_SOLVER -o solosolver solo.c malloc.c
2653 void frontend_default_colour(frontend *fe, float *output) {}
2654 void draw_text(frontend *fe, int x, int y, int fonttype, int fontsize,
2655 int align, int colour, char *text) {}
2656 void draw_rect(frontend *fe, int x, int y, int w, int h, int colour) {}
2657 void draw_line(frontend *fe, int x1, int y1, int x2, int y2, int colour) {}
2658 void draw_polygon(frontend *fe, int *coords, int npoints,
2659 int fillcolour, int outlinecolour) {}
2660 void clip(frontend *fe, int x, int y, int w, int h) {}
2661 void unclip(frontend *fe) {}
2662 void start_draw(frontend *fe) {}
2663 void draw_update(frontend *fe, int x, int y, int w, int h) {}
2664 void end_draw(frontend *fe) {}
2665 unsigned long random_bits(random_state *state, int bits)
2666 { assert(!"Shouldn't get randomness"); return 0; }
2667 unsigned long random_upto(random_state *state, unsigned long limit)
2668 { assert(!"Shouldn't get randomness"); return 0; }
2670 void fatal(char *fmt, ...)
2674 fprintf(stderr, "fatal error: ");
2677 vfprintf(stderr, fmt, ap);
2680 fprintf(stderr, "\n");
2684 int main(int argc, char **argv)
2688 char *id = NULL, *desc, *err;
2692 while (--argc > 0) {
2694 if (!strcmp(p, "-v")) {
2695 solver_show_working = TRUE;
2696 } else if (!strcmp(p, "-g")) {
2698 } else if (*p == '-') {
2699 fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
2707 fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
2711 desc = strchr(id, ':');
2713 fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
2718 p = default_params();
2719 decode_params(p, id);
2720 err = validate_desc(p, desc);
2722 fprintf(stderr, "%s: %s\n", argv[0], err);
2725 s = new_game(NULL, p, desc);
2727 ret = solver(p->c, p->r, s->grid, NULL, DIFF_RECURSIVE);
2729 printf("Difficulty rating: %s\n",
2730 ret==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)":
2731 ret==DIFF_SIMPLE ? "Basic (row/column/number elimination required)":
2732 ret==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)":
2733 ret==DIFF_SET ? "Advanced (set elimination required)":
2734 ret==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)":
2735 ret==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)":
2736 ret==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)":
2737 "INTERNAL ERROR: unrecognised difficulty code");
2739 printf("%s\n", grid_text_format(p->c, p->r, s->grid));