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 48
111 #define TILE_SIZE (ds->tilesize)
112 #define BORDER (TILE_SIZE / 2)
113 #define GRIDEXTRA max((TILE_SIZE / 32),1)
115 #define FLASH_TIME 0.4F
117 enum { SYMM_NONE, SYMM_ROT2, SYMM_ROT4, SYMM_REF2, SYMM_REF2D, SYMM_REF4,
118 SYMM_REF4D, SYMM_REF8 };
121 DIFF_SIMPLE, DIFF_INTERSECT, DIFF_SET, DIFF_EXTREME, DIFF_RECURSIVE,
122 DIFF_AMBIGUOUS, DIFF_IMPOSSIBLE };
124 enum { DIFF_KSINGLE, DIFF_KMINMAX, DIFF_KSUMS, DIFF_KINTERSECT };
140 * To determine all possible ways to reach a given sum by adding two or
141 * three numbers from 1..9, each of which occurs exactly once in the sum,
142 * these arrays contain a list of bitmasks for each sum value, where if
143 * bit N is set, it means that N occurs in the sum. Each list is
144 * terminated by a zero if it is shorter than the size of the array.
149 unsigned long sum_bits2[18][MAX_2SUMS];
150 unsigned long sum_bits3[25][MAX_3SUMS];
151 unsigned long sum_bits4[31][MAX_4SUMS];
153 static int find_sum_bits(unsigned long *array, int idx, int value_left,
154 int addends_left, int min_addend,
155 unsigned long bitmask_so_far)
158 assert(addends_left >= 2);
160 for (i = min_addend; i < value_left; i++) {
161 unsigned long new_bitmask = bitmask_so_far | (1L << i);
162 assert(bitmask_so_far != new_bitmask);
164 if (addends_left == 2) {
165 int j = value_left - i;
170 array[idx++] = new_bitmask | (1L << j);
172 idx = find_sum_bits(array, idx, value_left - i,
173 addends_left - 1, i + 1,
179 static void precompute_sum_bits(void)
182 for (i = 3; i < 31; i++) {
185 j = find_sum_bits(sum_bits2[i], 0, i, 2, 1, 0);
186 assert (j <= MAX_2SUMS);
191 j = find_sum_bits(sum_bits3[i], 0, i, 3, 1, 0);
192 assert (j <= MAX_3SUMS);
196 j = find_sum_bits(sum_bits4[i], 0, i, 4, 1, 0);
197 assert (j <= MAX_4SUMS);
205 * For a square puzzle, `c' and `r' indicate the puzzle
206 * parameters as described above.
208 * A jigsaw-style puzzle is indicated by r==1, in which case c
209 * can be whatever it likes (there is no constraint on
210 * compositeness - a 7x7 jigsaw sudoku makes perfect sense).
212 int c, r, symm, diff, kdiff;
213 int xtype; /* require all digits in X-diagonals */
217 struct block_structure {
221 * For text formatting, we do need c and r here.
226 * For any square index, whichblock[i] gives its block index.
228 * For 0 <= b,i < cr, blocks[b][i] gives the index of the ith
229 * square in block b. nr_squares[b] gives the number of squares
230 * in block b (also the number of valid elements in blocks[b]).
232 * blocks_data holds the data pointed to by blocks.
234 * nr_squares may be NULL for block structures where all blocks are
237 int *whichblock, **blocks, *nr_squares, *blocks_data;
238 int nr_blocks, max_nr_squares;
240 #ifdef STANDALONE_SOLVER
242 * Textual descriptions of each block. For normal Sudoku these
243 * are of the form "(1,3)"; for jigsaw they are "starting at
244 * (5,7)". So the sensible usage in both cases is to say
245 * "elimination within block %s" with one of these strings.
247 * Only blocknames itself needs individually freeing; it's all
256 * For historical reasons, I use `cr' to denote the overall
257 * width/height of the puzzle. It was a natural notation when
258 * all puzzles were divided into blocks in a grid, but doesn't
259 * really make much sense given jigsaw puzzles. However, the
260 * obvious `n' is heavily used in the solver to describe the
261 * index of a number being placed, so `cr' will have to stay.
264 struct block_structure *blocks;
265 struct block_structure *kblocks; /* Blocks for killer puzzles. */
268 unsigned char *pencil; /* c*r*c*r elements */
269 unsigned char *immutable; /* marks which digits are clues */
270 int completed, cheated;
273 static game_params *default_params(void)
275 game_params *ret = snew(game_params);
280 ret->symm = SYMM_ROT2; /* a plausible default */
281 ret->diff = DIFF_BLOCK; /* so is this */
282 ret->kdiff = DIFF_KINTERSECT; /* so is this */
287 static void free_params(game_params *params)
292 static game_params *dup_params(game_params *params)
294 game_params *ret = snew(game_params);
295 *ret = *params; /* structure copy */
299 static int game_fetch_preset(int i, char **name, game_params **params)
305 { "2x2 Trivial", { 2, 2, SYMM_ROT2, DIFF_BLOCK, DIFF_KMINMAX, FALSE, FALSE } },
306 { "2x3 Basic", { 2, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
307 { "3x3 Trivial", { 3, 3, SYMM_ROT2, DIFF_BLOCK, DIFF_KMINMAX, FALSE, FALSE } },
308 { "3x3 Basic", { 3, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
309 { "3x3 Basic X", { 3, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, TRUE } },
310 { "3x3 Intermediate", { 3, 3, SYMM_ROT2, DIFF_INTERSECT, DIFF_KMINMAX, FALSE, FALSE } },
311 { "3x3 Advanced", { 3, 3, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, FALSE, FALSE } },
312 { "3x3 Advanced X", { 3, 3, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, TRUE } },
313 { "3x3 Extreme", { 3, 3, SYMM_ROT2, DIFF_EXTREME, DIFF_KMINMAX, FALSE, FALSE } },
314 { "3x3 Unreasonable", { 3, 3, SYMM_ROT2, DIFF_RECURSIVE, DIFF_KMINMAX, FALSE, FALSE } },
315 { "3x3 Killer", { 3, 3, SYMM_NONE, DIFF_BLOCK, DIFF_KINTERSECT, FALSE, TRUE } },
316 { "9 Jigsaw Basic", { 9, 1, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
317 { "9 Jigsaw Basic X", { 9, 1, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, TRUE } },
318 { "9 Jigsaw Advanced", { 9, 1, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, FALSE, FALSE } },
320 { "3x4 Basic", { 3, 4, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
321 { "4x4 Basic", { 4, 4, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
325 if (i < 0 || i >= lenof(presets))
328 *name = dupstr(presets[i].title);
329 *params = dup_params(&presets[i].params);
334 static void decode_params(game_params *ret, char const *string)
338 ret->c = ret->r = atoi(string);
341 while (*string && isdigit((unsigned char)*string)) string++;
342 if (*string == 'x') {
344 ret->r = atoi(string);
346 while (*string && isdigit((unsigned char)*string)) string++;
349 if (*string == 'j') {
354 } else if (*string == 'x') {
357 } else if (*string == 'k') {
360 } else if (*string == 'r' || *string == 'm' || *string == 'a') {
363 if (sc == 'm' && *string == 'd') {
370 while (*string && isdigit((unsigned char)*string)) string++;
371 if (sc == 'm' && sn == 8)
372 ret->symm = SYMM_REF8;
373 if (sc == 'm' && sn == 4)
374 ret->symm = sd ? SYMM_REF4D : SYMM_REF4;
375 if (sc == 'm' && sn == 2)
376 ret->symm = sd ? SYMM_REF2D : SYMM_REF2;
377 if (sc == 'r' && sn == 4)
378 ret->symm = SYMM_ROT4;
379 if (sc == 'r' && sn == 2)
380 ret->symm = SYMM_ROT2;
382 ret->symm = SYMM_NONE;
383 } else if (*string == 'd') {
385 if (*string == 't') /* trivial */
386 string++, ret->diff = DIFF_BLOCK;
387 else if (*string == 'b') /* basic */
388 string++, ret->diff = DIFF_SIMPLE;
389 else if (*string == 'i') /* intermediate */
390 string++, ret->diff = DIFF_INTERSECT;
391 else if (*string == 'a') /* advanced */
392 string++, ret->diff = DIFF_SET;
393 else if (*string == 'e') /* extreme */
394 string++, ret->diff = DIFF_EXTREME;
395 else if (*string == 'u') /* unreasonable */
396 string++, ret->diff = DIFF_RECURSIVE;
398 string++; /* eat unknown character */
402 static char *encode_params(game_params *params, int full)
407 sprintf(str, "%dx%d", params->c, params->r);
409 sprintf(str, "%dj", params->c);
416 switch (params->symm) {
417 case SYMM_REF8: strcat(str, "m8"); break;
418 case SYMM_REF4: strcat(str, "m4"); break;
419 case SYMM_REF4D: strcat(str, "md4"); break;
420 case SYMM_REF2: strcat(str, "m2"); break;
421 case SYMM_REF2D: strcat(str, "md2"); break;
422 case SYMM_ROT4: strcat(str, "r4"); break;
423 /* case SYMM_ROT2: strcat(str, "r2"); break; [default] */
424 case SYMM_NONE: strcat(str, "a"); break;
426 switch (params->diff) {
427 /* case DIFF_BLOCK: strcat(str, "dt"); break; [default] */
428 case DIFF_SIMPLE: strcat(str, "db"); break;
429 case DIFF_INTERSECT: strcat(str, "di"); break;
430 case DIFF_SET: strcat(str, "da"); break;
431 case DIFF_EXTREME: strcat(str, "de"); break;
432 case DIFF_RECURSIVE: strcat(str, "du"); break;
438 static config_item *game_configure(game_params *params)
443 ret = snewn(8, config_item);
445 ret[0].name = "Columns of sub-blocks";
446 ret[0].type = C_STRING;
447 sprintf(buf, "%d", params->c);
448 ret[0].sval = dupstr(buf);
451 ret[1].name = "Rows of sub-blocks";
452 ret[1].type = C_STRING;
453 sprintf(buf, "%d", params->r);
454 ret[1].sval = dupstr(buf);
457 ret[2].name = "\"X\" (require every number in each main diagonal)";
458 ret[2].type = C_BOOLEAN;
460 ret[2].ival = params->xtype;
462 ret[3].name = "Jigsaw (irregularly shaped sub-blocks)";
463 ret[3].type = C_BOOLEAN;
465 ret[3].ival = (params->r == 1);
467 ret[4].name = "Killer (digit sums)";
468 ret[4].type = C_BOOLEAN;
470 ret[4].ival = params->killer;
472 ret[5].name = "Symmetry";
473 ret[5].type = C_CHOICES;
474 ret[5].sval = ":None:2-way rotation:4-way rotation:2-way mirror:"
475 "2-way diagonal mirror:4-way mirror:4-way diagonal mirror:"
477 ret[5].ival = params->symm;
479 ret[6].name = "Difficulty";
480 ret[6].type = C_CHOICES;
481 ret[6].sval = ":Trivial:Basic:Intermediate:Advanced:Extreme:Unreasonable";
482 ret[6].ival = params->diff;
492 static game_params *custom_params(config_item *cfg)
494 game_params *ret = snew(game_params);
496 ret->c = atoi(cfg[0].sval);
497 ret->r = atoi(cfg[1].sval);
498 ret->xtype = cfg[2].ival;
503 ret->killer = cfg[4].ival;
504 ret->symm = cfg[5].ival;
505 ret->diff = cfg[6].ival;
506 ret->kdiff = DIFF_KINTERSECT;
511 static char *validate_params(game_params *params, int full)
514 return "Both dimensions must be at least 2";
515 if (params->c > ORDER_MAX || params->r > ORDER_MAX)
516 return "Dimensions greater than "STR(ORDER_MAX)" are not supported";
517 if ((params->c * params->r) > 31)
518 return "Unable to support more than 31 distinct symbols in a puzzle";
519 if (params->killer && params->c * params->r > 9)
520 return "Killer puzzle dimensions must be smaller than 10.";
525 * ----------------------------------------------------------------------
526 * Block structure functions.
529 static struct block_structure *alloc_block_structure(int c, int r, int area,
534 struct block_structure *b = snew(struct block_structure);
537 b->nr_blocks = nr_blocks;
538 b->max_nr_squares = max_nr_squares;
539 b->c = c; b->r = r; b->area = area;
540 b->whichblock = snewn(area, int);
541 b->blocks_data = snewn(nr_blocks * max_nr_squares, int);
542 b->blocks = snewn(nr_blocks, int *);
543 b->nr_squares = snewn(nr_blocks, int);
545 for (i = 0; i < nr_blocks; i++)
546 b->blocks[i] = b->blocks_data + i*max_nr_squares;
548 #ifdef STANDALONE_SOLVER
549 b->blocknames = (char **)smalloc(c*r*(sizeof(char *)+80));
550 for (i = 0; i < c * r; i++)
551 b->blocknames[i] = NULL;
556 static void free_block_structure(struct block_structure *b)
558 if (--b->refcount == 0) {
559 sfree(b->whichblock);
561 sfree(b->blocks_data);
562 #ifdef STANDALONE_SOLVER
563 sfree(b->blocknames);
565 sfree(b->nr_squares);
570 static struct block_structure *dup_block_structure(struct block_structure *b)
572 struct block_structure *nb;
575 nb = alloc_block_structure(b->c, b->r, b->area, b->max_nr_squares,
577 memcpy(nb->nr_squares, b->nr_squares, b->nr_blocks * sizeof *b->nr_squares);
578 memcpy(nb->whichblock, b->whichblock, b->area * sizeof *b->whichblock);
579 memcpy(nb->blocks_data, b->blocks_data,
580 b->nr_blocks * b->max_nr_squares * sizeof *b->blocks_data);
581 for (i = 0; i < b->nr_blocks; i++)
582 nb->blocks[i] = nb->blocks_data + i*nb->max_nr_squares;
584 #ifdef STANDALONE_SOLVER
585 memcpy(nb->blocknames, b->blocknames, b->c * b->r *(sizeof(char *)+80));
588 for (i = 0; i < b->c * b->r; i++)
589 if (b->blocknames[i] == NULL)
590 nb->blocknames[i] = NULL;
592 nb->blocknames[i] = ((char *)nb->blocknames) + (b->blocknames[i] - (char *)b->blocknames);
598 static void split_block(struct block_structure *b, int *squares, int nr_squares)
601 int previous_block = b->whichblock[squares[0]];
602 int newblock = b->nr_blocks;
604 assert(b->max_nr_squares >= nr_squares);
605 assert(b->nr_squares[previous_block] > nr_squares);
608 b->blocks_data = sresize(b->blocks_data,
609 b->nr_blocks * b->max_nr_squares, int);
610 b->nr_squares = sresize(b->nr_squares, b->nr_blocks, int);
612 b->blocks = snewn(b->nr_blocks, int *);
613 for (i = 0; i < b->nr_blocks; i++)
614 b->blocks[i] = b->blocks_data + i*b->max_nr_squares;
615 for (i = 0; i < nr_squares; i++) {
616 assert(b->whichblock[squares[i]] == previous_block);
617 b->whichblock[squares[i]] = newblock;
618 b->blocks[newblock][i] = squares[i];
620 for (i = j = 0; i < b->nr_squares[previous_block]; i++) {
622 int sq = b->blocks[previous_block][i];
623 for (k = 0; k < nr_squares; k++)
624 if (squares[k] == sq)
627 b->blocks[previous_block][j++] = sq;
629 b->nr_squares[previous_block] -= nr_squares;
630 b->nr_squares[newblock] = nr_squares;
633 static void remove_from_block(struct block_structure *blocks, int b, int n)
636 blocks->whichblock[n] = -1;
637 for (i = j = 0; i < blocks->nr_squares[b]; i++)
638 if (blocks->blocks[b][i] != n)
639 blocks->blocks[b][j++] = blocks->blocks[b][i];
641 blocks->nr_squares[b]--;
644 /* ----------------------------------------------------------------------
647 * This solver is used for two purposes:
648 * + to check solubility of a grid as we gradually remove numbers
650 * + to solve an externally generated puzzle when the user selects
653 * It supports a variety of specific modes of reasoning. By
654 * enabling or disabling subsets of these modes we can arrange a
655 * range of difficulty levels.
659 * Modes of reasoning currently supported:
661 * - Positional elimination: a number must go in a particular
662 * square because all the other empty squares in a given
663 * row/col/blk are ruled out.
665 * - Killer minmax elimination: for killer-type puzzles, a number
666 * is impossible if choosing it would cause the sum in a killer
667 * region to be guaranteed to be too large or too small.
669 * - Numeric elimination: a square must have a particular number
670 * in because all the other numbers that could go in it are
673 * - Intersectional analysis: given two domains which overlap
674 * (hence one must be a block, and the other can be a row or
675 * col), if the possible locations for a particular number in
676 * one of the domains can be narrowed down to the overlap, then
677 * that number can be ruled out everywhere but the overlap in
678 * the other domain too.
680 * - Set elimination: if there is a subset of the empty squares
681 * within a domain such that the union of the possible numbers
682 * in that subset has the same size as the subset itself, then
683 * those numbers can be ruled out everywhere else in the domain.
684 * (For example, if there are five empty squares and the
685 * possible numbers in each are 12, 23, 13, 134 and 1345, then
686 * the first three empty squares form such a subset: the numbers
687 * 1, 2 and 3 _must_ be in those three squares in some
688 * permutation, and hence we can deduce none of them can be in
689 * the fourth or fifth squares.)
690 * + You can also see this the other way round, concentrating
691 * on numbers rather than squares: if there is a subset of
692 * the unplaced numbers within a domain such that the union
693 * of all their possible positions has the same size as the
694 * subset itself, then all other numbers can be ruled out for
695 * those positions. However, it turns out that this is
696 * exactly equivalent to the first formulation at all times:
697 * there is a 1-1 correspondence between suitable subsets of
698 * the unplaced numbers and suitable subsets of the unfilled
699 * places, found by taking the _complement_ of the union of
700 * the numbers' possible positions (or the spaces' possible
703 * - Forcing chains (see comment for solver_forcing().)
705 * - Recursion. If all else fails, we pick one of the currently
706 * most constrained empty squares and take a random guess at its
707 * contents, then continue solving on that basis and see if we
711 struct solver_usage {
713 struct block_structure *blocks, *kblocks, *extra_cages;
715 * We set up a cubic array, indexed by x, y and digit; each
716 * element of this array is TRUE or FALSE according to whether
717 * or not that digit _could_ in principle go in that position.
719 * The way to index this array is cube[(y*cr+x)*cr+n-1]; there
720 * are macros below to help with this.
724 * This is the grid in which we write down our final
725 * deductions. y-coordinates in here are _not_ transformed.
729 * For killer-type puzzles, kclues holds the secondary clue for
730 * each cage. For derived cages, the clue is in extra_clues.
732 digit *kclues, *extra_clues;
734 * Now we keep track, at a slightly higher level, of what we
735 * have yet to work out, to prevent doing the same deduction
738 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
740 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
742 /* blk[i*cr+n-1] TRUE if digit n has been placed in block i */
744 /* diag[i*cr+n-1] TRUE if digit n has been placed in diagonal i */
745 unsigned char *diag; /* diag 0 is \, 1 is / */
751 #define cubepos2(xy,n) ((xy)*usage->cr+(n)-1)
752 #define cubepos(x,y,n) cubepos2((y)*usage->cr+(x),n)
753 #define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
754 #define cube2(xy,n) (usage->cube[cubepos2(xy,n)])
756 #define ondiag0(xy) ((xy) % (cr+1) == 0)
757 #define ondiag1(xy) ((xy) % (cr-1) == 0 && (xy) > 0 && (xy) < cr*cr-1)
758 #define diag0(i) ((i) * (cr+1))
759 #define diag1(i) ((i+1) * (cr-1))
762 * Function called when we are certain that a particular square has
763 * a particular number in it. The y-coordinate passed in here is
766 static void solver_place(struct solver_usage *usage, int x, int y, int n)
769 int sqindex = y*cr+x;
775 * Rule out all other numbers in this square.
777 for (i = 1; i <= cr; i++)
782 * Rule out this number in all other positions in the row.
784 for (i = 0; i < cr; i++)
789 * Rule out this number in all other positions in the column.
791 for (i = 0; i < cr; i++)
796 * Rule out this number in all other positions in the block.
798 bi = usage->blocks->whichblock[sqindex];
799 for (i = 0; i < cr; i++) {
800 int bp = usage->blocks->blocks[bi][i];
806 * Enter the number in the result grid.
808 usage->grid[sqindex] = n;
811 * Cross out this number from the list of numbers left to place
812 * in its row, its column and its block.
814 usage->row[y*cr+n-1] = usage->col[x*cr+n-1] =
815 usage->blk[bi*cr+n-1] = TRUE;
818 if (ondiag0(sqindex)) {
819 for (i = 0; i < cr; i++)
820 if (diag0(i) != sqindex)
821 cube2(diag0(i),n) = FALSE;
822 usage->diag[n-1] = TRUE;
824 if (ondiag1(sqindex)) {
825 for (i = 0; i < cr; i++)
826 if (diag1(i) != sqindex)
827 cube2(diag1(i),n) = FALSE;
828 usage->diag[cr+n-1] = TRUE;
833 #if defined STANDALONE_SOLVER && defined __GNUC__
835 * Forward-declare the functions taking printf-like format arguments
836 * with __attribute__((format)) so as to ensure the argument syntax
839 struct solver_scratch;
840 static int solver_elim(struct solver_usage *usage, int *indices,
841 char *fmt, ...) __attribute__((format(printf,3,4)));
842 static int solver_intersect(struct solver_usage *usage,
843 int *indices1, int *indices2, char *fmt, ...)
844 __attribute__((format(printf,4,5)));
845 static int solver_set(struct solver_usage *usage,
846 struct solver_scratch *scratch,
847 int *indices, char *fmt, ...)
848 __attribute__((format(printf,4,5)));
851 static int solver_elim(struct solver_usage *usage, int *indices
852 #ifdef STANDALONE_SOLVER
861 * Count the number of set bits within this section of the
866 for (i = 0; i < cr; i++)
867 if (usage->cube[indices[i]]) {
881 if (!usage->grid[y*cr+x]) {
882 #ifdef STANDALONE_SOLVER
883 if (solver_show_working) {
885 printf("%*s", solver_recurse_depth*4, "");
889 printf(":\n%*s placing %d at (%d,%d)\n",
890 solver_recurse_depth*4, "", n, 1+x, 1+y);
893 solver_place(usage, x, y, n);
897 #ifdef STANDALONE_SOLVER
898 if (solver_show_working) {
900 printf("%*s", solver_recurse_depth*4, "");
904 printf(":\n%*s no possibilities available\n",
905 solver_recurse_depth*4, "");
914 static int solver_intersect(struct solver_usage *usage,
915 int *indices1, int *indices2
916 #ifdef STANDALONE_SOLVER
925 * Loop over the first domain and see if there's any set bit
926 * not also in the second.
928 for (i = j = 0; i < cr; i++) {
930 while (j < cr && indices2[j] < p)
932 if (usage->cube[p]) {
933 if (j < cr && indices2[j] == p)
934 continue; /* both domains contain this index */
936 return 0; /* there is, so we can't deduce */
941 * We have determined that all set bits in the first domain are
942 * within its overlap with the second. So loop over the second
943 * domain and remove all set bits that aren't also in that
944 * overlap; return +1 iff we actually _did_ anything.
947 for (i = j = 0; i < cr; i++) {
949 while (j < cr && indices1[j] < p)
951 if (usage->cube[p] && (j >= cr || indices1[j] != p)) {
952 #ifdef STANDALONE_SOLVER
953 if (solver_show_working) {
958 printf("%*s", solver_recurse_depth*4, "");
970 printf("%*s ruling out %d at (%d,%d)\n",
971 solver_recurse_depth*4, "", pn, 1+px, 1+py);
974 ret = +1; /* we did something */
982 struct solver_scratch {
983 unsigned char *grid, *rowidx, *colidx, *set;
984 int *neighbours, *bfsqueue;
985 int *indexlist, *indexlist2;
986 #ifdef STANDALONE_SOLVER
991 static int solver_set(struct solver_usage *usage,
992 struct solver_scratch *scratch,
994 #ifdef STANDALONE_SOLVER
1001 unsigned char *grid = scratch->grid;
1002 unsigned char *rowidx = scratch->rowidx;
1003 unsigned char *colidx = scratch->colidx;
1004 unsigned char *set = scratch->set;
1007 * We are passed a cr-by-cr matrix of booleans. Our first job
1008 * is to winnow it by finding any definite placements - i.e.
1009 * any row with a solitary 1 - and discarding that row and the
1010 * column containing the 1.
1012 memset(rowidx, TRUE, cr);
1013 memset(colidx, TRUE, cr);
1014 for (i = 0; i < cr; i++) {
1015 int count = 0, first = -1;
1016 for (j = 0; j < cr; j++)
1017 if (usage->cube[indices[i*cr+j]])
1021 * If count == 0, then there's a row with no 1s at all and
1022 * the puzzle is internally inconsistent. However, we ought
1023 * to have caught this already during the simpler reasoning
1024 * methods, so we can safely fail an assertion if we reach
1029 rowidx[i] = colidx[first] = FALSE;
1033 * Convert each of rowidx/colidx from a list of 0s and 1s to a
1034 * list of the indices of the 1s.
1036 for (i = j = 0; i < cr; i++)
1040 for (i = j = 0; i < cr; i++)
1046 * And create the smaller matrix.
1048 for (i = 0; i < n; i++)
1049 for (j = 0; j < n; j++)
1050 grid[i*cr+j] = usage->cube[indices[rowidx[i]*cr+colidx[j]]];
1053 * Having done that, we now have a matrix in which every row
1054 * has at least two 1s in. Now we search to see if we can find
1055 * a rectangle of zeroes (in the set-theoretic sense of
1056 * `rectangle', i.e. a subset of rows crossed with a subset of
1057 * columns) whose width and height add up to n.
1064 * We have a candidate set. If its size is <=1 or >=n-1
1065 * then we move on immediately.
1067 if (count > 1 && count < n-1) {
1069 * The number of rows we need is n-count. See if we can
1070 * find that many rows which each have a zero in all
1071 * the positions listed in `set'.
1074 for (i = 0; i < n; i++) {
1076 for (j = 0; j < n; j++)
1077 if (set[j] && grid[i*cr+j]) {
1086 * We expect never to be able to get _more_ than
1087 * n-count suitable rows: this would imply that (for
1088 * example) there are four numbers which between them
1089 * have at most three possible positions, and hence it
1090 * indicates a faulty deduction before this point or
1091 * even a bogus clue.
1093 if (rows > n - count) {
1094 #ifdef STANDALONE_SOLVER
1095 if (solver_show_working) {
1097 printf("%*s", solver_recurse_depth*4,
1102 printf(":\n%*s contradiction reached\n",
1103 solver_recurse_depth*4, "");
1109 if (rows >= n - count) {
1110 int progress = FALSE;
1113 * We've got one! Now, for each row which _doesn't_
1114 * satisfy the criterion, eliminate all its set
1115 * bits in the positions _not_ listed in `set'.
1116 * Return +1 (meaning progress has been made) if we
1117 * successfully eliminated anything at all.
1119 * This involves referring back through
1120 * rowidx/colidx in order to work out which actual
1121 * positions in the cube to meddle with.
1123 for (i = 0; i < n; i++) {
1125 for (j = 0; j < n; j++)
1126 if (set[j] && grid[i*cr+j]) {
1131 for (j = 0; j < n; j++)
1132 if (!set[j] && grid[i*cr+j]) {
1133 int fpos = indices[rowidx[i]*cr+colidx[j]];
1134 #ifdef STANDALONE_SOLVER
1135 if (solver_show_working) {
1140 printf("%*s", solver_recurse_depth*4,
1153 printf("%*s ruling out %d at (%d,%d)\n",
1154 solver_recurse_depth*4, "",
1159 usage->cube[fpos] = FALSE;
1171 * Binary increment: change the rightmost 0 to a 1, and
1172 * change all 1s to the right of it to 0s.
1175 while (i > 0 && set[i-1])
1176 set[--i] = 0, count--;
1178 set[--i] = 1, count++;
1187 * Look for forcing chains. A forcing chain is a path of
1188 * pairwise-exclusive squares (i.e. each pair of adjacent squares
1189 * in the path are in the same row, column or block) with the
1190 * following properties:
1192 * (a) Each square on the path has precisely two possible numbers.
1194 * (b) Each pair of squares which are adjacent on the path share
1195 * at least one possible number in common.
1197 * (c) Each square in the middle of the path shares _both_ of its
1198 * numbers with at least one of its neighbours (not the same
1199 * one with both neighbours).
1201 * These together imply that at least one of the possible number
1202 * choices at one end of the path forces _all_ the rest of the
1203 * numbers along the path. In order to make real use of this, we
1204 * need further properties:
1206 * (c) Ruling out some number N from the square at one end of the
1207 * path forces the square at the other end to take the same
1210 * (d) The two end squares are both in line with some third
1213 * (e) That third square currently has N as a possibility.
1215 * If we can find all of that lot, we can deduce that at least one
1216 * of the two ends of the forcing chain has number N, and that
1217 * therefore the mutually adjacent third square does not.
1219 * To find forcing chains, we're going to start a bfs at each
1220 * suitable square, once for each of its two possible numbers.
1222 static int solver_forcing(struct solver_usage *usage,
1223 struct solver_scratch *scratch)
1226 int *bfsqueue = scratch->bfsqueue;
1227 #ifdef STANDALONE_SOLVER
1228 int *bfsprev = scratch->bfsprev;
1230 unsigned char *number = scratch->grid;
1231 int *neighbours = scratch->neighbours;
1234 for (y = 0; y < cr; y++)
1235 for (x = 0; x < cr; x++) {
1239 * If this square doesn't have exactly two candidate
1240 * numbers, don't try it.
1242 * In this loop we also sum the candidate numbers,
1243 * which is a nasty hack to allow us to quickly find
1244 * `the other one' (since we will shortly know there
1247 for (count = t = 0, n = 1; n <= cr; n++)
1254 * Now attempt a bfs for each candidate.
1256 for (n = 1; n <= cr; n++)
1257 if (cube(x, y, n)) {
1258 int orign, currn, head, tail;
1265 memset(number, cr+1, cr*cr);
1267 bfsqueue[tail++] = y*cr+x;
1268 #ifdef STANDALONE_SOLVER
1269 bfsprev[y*cr+x] = -1;
1271 number[y*cr+x] = t - n;
1273 while (head < tail) {
1274 int xx, yy, nneighbours, xt, yt, i;
1276 xx = bfsqueue[head++];
1280 currn = number[yy*cr+xx];
1283 * Find neighbours of yy,xx.
1286 for (yt = 0; yt < cr; yt++)
1287 neighbours[nneighbours++] = yt*cr+xx;
1288 for (xt = 0; xt < cr; xt++)
1289 neighbours[nneighbours++] = yy*cr+xt;
1290 xt = usage->blocks->whichblock[yy*cr+xx];
1291 for (yt = 0; yt < cr; yt++)
1292 neighbours[nneighbours++] = usage->blocks->blocks[xt][yt];
1294 int sqindex = yy*cr+xx;
1295 if (ondiag0(sqindex)) {
1296 for (i = 0; i < cr; i++)
1297 neighbours[nneighbours++] = diag0(i);
1299 if (ondiag1(sqindex)) {
1300 for (i = 0; i < cr; i++)
1301 neighbours[nneighbours++] = diag1(i);
1306 * Try visiting each of those neighbours.
1308 for (i = 0; i < nneighbours; i++) {
1311 xt = neighbours[i] % cr;
1312 yt = neighbours[i] / cr;
1315 * We need this square to not be
1316 * already visited, and to include
1317 * currn as a possible number.
1319 if (number[yt*cr+xt] <= cr)
1321 if (!cube(xt, yt, currn))
1325 * Don't visit _this_ square a second
1328 if (xt == xx && yt == yy)
1332 * To continue with the bfs, we need
1333 * this square to have exactly two
1336 for (cc = tt = 0, nn = 1; nn <= cr; nn++)
1337 if (cube(xt, yt, nn))
1340 bfsqueue[tail++] = yt*cr+xt;
1341 #ifdef STANDALONE_SOLVER
1342 bfsprev[yt*cr+xt] = yy*cr+xx;
1344 number[yt*cr+xt] = tt - currn;
1348 * One other possibility is that this
1349 * might be the square in which we can
1350 * make a real deduction: if it's
1351 * adjacent to x,y, and currn is equal
1352 * to the original number we ruled out.
1354 if (currn == orign &&
1355 (xt == x || yt == y ||
1356 (usage->blocks->whichblock[yt*cr+xt] == usage->blocks->whichblock[y*cr+x]) ||
1357 (usage->diag && ((ondiag0(yt*cr+xt) && ondiag0(y*cr+x)) ||
1358 (ondiag1(yt*cr+xt) && ondiag1(y*cr+x)))))) {
1359 #ifdef STANDALONE_SOLVER
1360 if (solver_show_working) {
1363 printf("%*sforcing chain, %d at ends of ",
1364 solver_recurse_depth*4, "", orign);
1368 printf("%s(%d,%d)", sep, 1+xl,
1370 xl = bfsprev[yl*cr+xl];
1377 printf("\n%*s ruling out %d at (%d,%d)\n",
1378 solver_recurse_depth*4, "",
1382 cube(xt, yt, orign) = FALSE;
1393 static int solver_killer_minmax(struct solver_usage *usage,
1394 struct block_structure *cages, digit *clues,
1396 #ifdef STANDALONE_SOLVER
1404 int nsquares = cages->nr_squares[b];
1409 for (i = 0; i < nsquares; i++) {
1410 int n, x = cages->blocks[b][i];
1412 for (n = 1; n <= cr; n++)
1414 int maxval = 0, minval = 0;
1416 for (j = 0; j < nsquares; j++) {
1418 int y = cages->blocks[b][j];
1421 for (m = 1; m <= cr; m++)
1426 for (m = cr; m > 0; m--)
1432 if (maxval + n < clues[b]) {
1433 cube2(x, n) = FALSE;
1435 #ifdef STANDALONE_SOLVER
1436 if (solver_show_working)
1437 printf("%*s ruling out %d at (%d,%d) as too low %s\n",
1438 solver_recurse_depth*4, "killer minmax analysis",
1439 n, 1 + x%cr, 1 + x/cr, extra);
1442 if (minval + n > clues[b]) {
1443 cube2(x, n) = FALSE;
1445 #ifdef STANDALONE_SOLVER
1446 if (solver_show_working)
1447 printf("%*s ruling out %d at (%d,%d) as too high %s\n",
1448 solver_recurse_depth*4, "killer minmax analysis",
1449 n, 1 + x%cr, 1 + x/cr, extra);
1457 static int solver_killer_sums(struct solver_usage *usage, int b,
1458 struct block_structure *cages, int clue,
1460 #ifdef STANDALONE_SOLVER
1461 , const char *cage_type
1466 int i, ret, max_sums;
1467 int nsquares = cages->nr_squares[b];
1468 unsigned long *sumbits, possible_addends;
1471 assert(nsquares == 0);
1474 assert(nsquares > 0);
1476 if (nsquares < 2 || nsquares > 4)
1479 if (!cage_is_region) {
1480 int known_row = -1, known_col = -1, known_block = -1;
1482 * Verify that the cage lies entirely within one region,
1483 * so that using the precomputed sums is valid.
1485 for (i = 0; i < nsquares; i++) {
1486 int x = cages->blocks[b][i];
1488 assert(usage->grid[x] == 0);
1493 known_block = usage->blocks->whichblock[x];
1495 if (known_row != x/cr)
1497 if (known_col != x%cr)
1499 if (known_block != usage->blocks->whichblock[x])
1503 if (known_block == -1 && known_col == -1 && known_row == -1)
1506 if (nsquares == 2) {
1507 if (clue < 3 || clue > 17)
1510 sumbits = sum_bits2[clue];
1511 max_sums = MAX_2SUMS;
1512 } else if (nsquares == 3) {
1513 if (clue < 6 || clue > 24)
1516 sumbits = sum_bits3[clue];
1517 max_sums = MAX_3SUMS;
1519 if (clue < 10 || clue > 30)
1522 sumbits = sum_bits4[clue];
1523 max_sums = MAX_4SUMS;
1526 * For every possible way to get the sum, see if there is
1527 * one square in the cage that disallows all the required
1528 * addends. If we find one such square, this way to compute
1529 * the sum is impossible.
1531 possible_addends = 0;
1532 for (i = 0; i < max_sums; i++) {
1534 unsigned long bits = sumbits[i];
1539 for (j = 0; j < nsquares; j++) {
1541 unsigned long square_bits = bits;
1542 int x = cages->blocks[b][j];
1543 for (n = 1; n <= cr; n++)
1545 square_bits &= ~(1L << n);
1546 if (square_bits == 0) {
1551 possible_addends |= bits;
1554 * Now we know which addends can possibly be used to
1555 * compute the sum. Remove all other digits from the
1556 * set of possibilities.
1558 if (possible_addends == 0)
1562 for (i = 0; i < nsquares; i++) {
1564 int x = cages->blocks[b][i];
1565 for (n = 1; n <= cr; n++) {
1568 if ((possible_addends & (1 << n)) == 0) {
1569 cube2(x, n) = FALSE;
1571 #ifdef STANDALONE_SOLVER
1572 if (solver_show_working) {
1573 printf("%*s using %s\n",
1574 solver_recurse_depth*4, "killer sums analysis",
1576 printf("%*s ruling out %d at (%d,%d) due to impossible %d-sum\n",
1577 solver_recurse_depth*4, "",
1578 n, 1 + x%cr, 1 + x/cr, nsquares);
1587 static int filter_whole_cages(struct solver_usage *usage, int *squares, int n,
1593 /* First, filter squares with a clue. */
1594 for (i = j = 0; i < n; i++)
1595 if (usage->grid[squares[i]])
1596 *filtered_sum += usage->grid[squares[i]];
1598 squares[j++] = squares[i];
1602 * Filter all cages that are covered entirely by the list of
1606 for (b = 0; b < usage->kblocks->nr_blocks && off < n; b++) {
1607 int b_squares = usage->kblocks->nr_squares[b];
1614 * Find all squares of block b that lie in our list,
1615 * and make them contiguous at off, which is the current position
1616 * in the output list.
1618 for (i = 0; i < b_squares; i++) {
1619 for (j = off; j < n; j++)
1620 if (squares[j] == usage->kblocks->blocks[b][i]) {
1621 int t = squares[off + matched];
1622 squares[off + matched] = squares[j];
1628 /* If so, filter out all squares of b from the list. */
1629 if (matched != usage->kblocks->nr_squares[b]) {
1633 memmove(squares + off, squares + off + matched,
1634 (n - off - matched) * sizeof *squares);
1637 *filtered_sum += usage->kclues[b];
1643 static struct solver_scratch *solver_new_scratch(struct solver_usage *usage)
1645 struct solver_scratch *scratch = snew(struct solver_scratch);
1647 scratch->grid = snewn(cr*cr, unsigned char);
1648 scratch->rowidx = snewn(cr, unsigned char);
1649 scratch->colidx = snewn(cr, unsigned char);
1650 scratch->set = snewn(cr, unsigned char);
1651 scratch->neighbours = snewn(5*cr, int);
1652 scratch->bfsqueue = snewn(cr*cr, int);
1653 #ifdef STANDALONE_SOLVER
1654 scratch->bfsprev = snewn(cr*cr, int);
1656 scratch->indexlist = snewn(cr*cr, int); /* used for set elimination */
1657 scratch->indexlist2 = snewn(cr, int); /* only used for intersect() */
1661 static void solver_free_scratch(struct solver_scratch *scratch)
1663 #ifdef STANDALONE_SOLVER
1664 sfree(scratch->bfsprev);
1666 sfree(scratch->bfsqueue);
1667 sfree(scratch->neighbours);
1668 sfree(scratch->set);
1669 sfree(scratch->colidx);
1670 sfree(scratch->rowidx);
1671 sfree(scratch->grid);
1672 sfree(scratch->indexlist);
1673 sfree(scratch->indexlist2);
1678 * Used for passing information about difficulty levels between the solver
1682 /* Maximum levels allowed. */
1683 int maxdiff, maxkdiff;
1684 /* Levels reached by the solver. */
1688 static void solver(int cr, struct block_structure *blocks,
1689 struct block_structure *kblocks, int xtype,
1690 digit *grid, digit *kgrid, struct difficulty *dlev)
1692 struct solver_usage *usage;
1693 struct solver_scratch *scratch;
1694 int x, y, b, i, n, ret;
1695 int diff = DIFF_BLOCK;
1696 int kdiff = DIFF_KSINGLE;
1699 * Set up a usage structure as a clean slate (everything
1702 usage = snew(struct solver_usage);
1704 usage->blocks = blocks;
1706 usage->kblocks = dup_block_structure(kblocks);
1707 usage->extra_cages = alloc_block_structure (kblocks->c, kblocks->r,
1708 cr * cr, cr, cr * cr);
1709 usage->extra_clues = snewn(cr*cr, digit);
1711 usage->kblocks = usage->extra_cages = NULL;
1712 usage->extra_clues = NULL;
1714 usage->cube = snewn(cr*cr*cr, unsigned char);
1715 usage->grid = grid; /* write straight back to the input */
1720 nclues = kblocks->nr_blocks;
1722 * Allow for expansion of the killer regions, the absolute
1723 * limit is obviously one region per square.
1725 usage->kclues = snewn(cr*cr, digit);
1726 for (i = 0; i < nclues; i++) {
1727 for (n = 0; n < kblocks->nr_squares[i]; n++)
1728 if (kgrid[kblocks->blocks[i][n]] != 0)
1729 usage->kclues[i] = kgrid[kblocks->blocks[i][n]];
1730 assert(usage->kclues[i] > 0);
1732 memset(usage->kclues + nclues, 0, cr*cr - nclues);
1734 usage->kclues = NULL;
1737 memset(usage->cube, TRUE, cr*cr*cr);
1739 usage->row = snewn(cr * cr, unsigned char);
1740 usage->col = snewn(cr * cr, unsigned char);
1741 usage->blk = snewn(cr * cr, unsigned char);
1742 memset(usage->row, FALSE, cr * cr);
1743 memset(usage->col, FALSE, cr * cr);
1744 memset(usage->blk, FALSE, cr * cr);
1747 usage->diag = snewn(cr * 2, unsigned char);
1748 memset(usage->diag, FALSE, cr * 2);
1752 usage->nr_regions = cr * 3 + (xtype ? 2 : 0);
1753 usage->regions = snewn(cr * usage->nr_regions, int);
1754 usage->sq2region = snewn(cr * cr * 3, int *);
1756 for (n = 0; n < cr; n++) {
1757 for (i = 0; i < cr; i++) {
1760 b = usage->blocks->blocks[n][i];
1761 usage->regions[cr*n*3 + i] = x;
1762 usage->regions[cr*n*3 + cr + i] = y;
1763 usage->regions[cr*n*3 + 2*cr + i] = b;
1764 usage->sq2region[x*3] = usage->regions + cr*n*3;
1765 usage->sq2region[y*3 + 1] = usage->regions + cr*n*3 + cr;
1766 usage->sq2region[b*3 + 2] = usage->regions + cr*n*3 + 2*cr;
1770 scratch = solver_new_scratch(usage);
1773 * Place all the clue numbers we are given.
1775 for (x = 0; x < cr; x++)
1776 for (y = 0; y < cr; y++)
1778 solver_place(usage, x, y, grid[y*cr+x]);
1781 * Now loop over the grid repeatedly trying all permitted modes
1782 * of reasoning. The loop terminates if we complete an
1783 * iteration without making any progress; we then return
1784 * failure or success depending on whether the grid is full or
1789 * I'd like to write `continue;' inside each of the
1790 * following loops, so that the solver returns here after
1791 * making some progress. However, I can't specify that I
1792 * want to continue an outer loop rather than the innermost
1793 * one, so I'm apologetically resorting to a goto.
1798 * Blockwise positional elimination.
1800 for (b = 0; b < cr; b++)
1801 for (n = 1; n <= cr; n++)
1802 if (!usage->blk[b*cr+n-1]) {
1803 for (i = 0; i < cr; i++)
1804 scratch->indexlist[i] = cubepos2(usage->blocks->blocks[b][i],n);
1805 ret = solver_elim(usage, scratch->indexlist
1806 #ifdef STANDALONE_SOLVER
1807 , "positional elimination,"
1808 " %d in block %s", n,
1809 usage->blocks->blocknames[b]
1813 diff = DIFF_IMPOSSIBLE;
1815 } else if (ret > 0) {
1816 diff = max(diff, DIFF_BLOCK);
1821 if (usage->kclues != NULL) {
1822 int changed = FALSE;
1825 * First, bring the kblocks into a more useful form: remove
1826 * all filled-in squares, and reduce the sum by their values.
1827 * Walk in reverse order, since otherwise remove_from_block
1828 * can move element past our loop counter.
1830 for (b = 0; b < usage->kblocks->nr_blocks; b++)
1831 for (i = usage->kblocks->nr_squares[b] -1; i >= 0; i--) {
1832 int x = usage->kblocks->blocks[b][i];
1833 int t = usage->grid[x];
1837 remove_from_block(usage->kblocks, b, x);
1838 if (t > usage->kclues[b]) {
1839 diff = DIFF_IMPOSSIBLE;
1842 usage->kclues[b] -= t;
1844 * Since cages are regions, this tells us something
1845 * about the other squares in the cage.
1847 for (n = 0; n < usage->kblocks->nr_squares[b]; n++) {
1848 cube2(usage->kblocks->blocks[b][n], t) = FALSE;
1853 * The most trivial kind of solver for killer puzzles: fill
1854 * single-square cages.
1856 for (b = 0; b < usage->kblocks->nr_blocks; b++) {
1857 int squares = usage->kblocks->nr_squares[b];
1859 int v = usage->kclues[b];
1860 if (v < 1 || v > cr) {
1861 diff = DIFF_IMPOSSIBLE;
1864 x = usage->kblocks->blocks[b][0] % cr;
1865 y = usage->kblocks->blocks[b][0] / cr;
1866 if (!cube(x, y, v)) {
1867 diff = DIFF_IMPOSSIBLE;
1870 solver_place(usage, x, y, v);
1872 #ifdef STANDALONE_SOLVER
1873 if (solver_show_working) {
1874 printf("%*s placing %d at (%d,%d)\n",
1875 solver_recurse_depth*4, "killer single-square cage",
1876 v, 1 + x%cr, 1 + x/cr);
1884 kdiff = max(kdiff, DIFF_KSINGLE);
1888 if (dlev->maxkdiff >= DIFF_KINTERSECT && usage->kclues != NULL) {
1889 int changed = FALSE;
1891 * Now, create the extra_cages information. Every full region
1892 * (row, column, or block) has the same sum total (45 for 3x3
1893 * puzzles. After we try to cover these regions with cages that
1894 * lie entirely within them, any squares that remain must bring
1895 * the total to this known value, and so they form additional
1896 * cages which aren't immediately evident in the displayed form
1899 usage->extra_cages->nr_blocks = 0;
1900 for (i = 0; i < 3; i++) {
1901 for (n = 0; n < cr; n++) {
1902 int *region = usage->regions + cr*n*3 + i*cr;
1903 int sum = cr * (cr + 1) / 2;
1906 int n_extra = usage->extra_cages->nr_blocks;
1907 int *extra_list = usage->extra_cages->blocks[n_extra];
1908 memcpy(extra_list, region, cr * sizeof *extra_list);
1910 nsquares = filter_whole_cages(usage, extra_list, nsquares, &filtered);
1912 if (nsquares == cr || nsquares == 0)
1914 if (dlev->maxdiff >= DIFF_RECURSIVE) {
1916 dlev->diff = DIFF_IMPOSSIBLE;
1922 if (nsquares == 1) {
1924 diff = DIFF_IMPOSSIBLE;
1927 x = extra_list[0] % cr;
1928 y = extra_list[0] / cr;
1929 if (!cube(x, y, sum)) {
1930 diff = DIFF_IMPOSSIBLE;
1933 solver_place(usage, x, y, sum);
1935 #ifdef STANDALONE_SOLVER
1936 if (solver_show_working) {
1937 printf("%*s placing %d at (%d,%d)\n",
1938 solver_recurse_depth*4, "killer single-square deduced cage",
1944 b = usage->kblocks->whichblock[extra_list[0]];
1945 for (x = 1; x < nsquares; x++)
1946 if (usage->kblocks->whichblock[extra_list[x]] != b)
1948 if (x == nsquares) {
1949 assert(usage->kblocks->nr_squares[b] > nsquares);
1950 split_block(usage->kblocks, extra_list, nsquares);
1951 assert(usage->kblocks->nr_squares[usage->kblocks->nr_blocks - 1] == nsquares);
1952 usage->kclues[usage->kblocks->nr_blocks - 1] = sum;
1953 usage->kclues[b] -= sum;
1955 usage->extra_cages->nr_squares[n_extra] = nsquares;
1956 usage->extra_cages->nr_blocks++;
1957 usage->extra_clues[n_extra] = sum;
1962 kdiff = max(kdiff, DIFF_KINTERSECT);
1968 * Another simple killer-type elimination. For every square in a
1969 * cage, find the minimum and maximum possible sums of all the
1970 * other squares in the same cage, and rule out possibilities
1971 * for the given square based on whether they are guaranteed to
1972 * cause the sum to be either too high or too low.
1973 * This is a special case of trying all possible sums across a
1974 * region, which is a recursive algorithm. We should probably
1975 * implement it for a higher difficulty level.
1977 if (dlev->maxkdiff >= DIFF_KMINMAX && usage->kclues != NULL) {
1978 int changed = FALSE;
1979 for (b = 0; b < usage->kblocks->nr_blocks; b++) {
1980 int ret = solver_killer_minmax(usage, usage->kblocks,
1982 #ifdef STANDALONE_SOLVER
1987 diff = DIFF_IMPOSSIBLE;
1992 for (b = 0; b < usage->extra_cages->nr_blocks; b++) {
1993 int ret = solver_killer_minmax(usage, usage->extra_cages,
1994 usage->extra_clues, b
1995 #ifdef STANDALONE_SOLVER
1996 , "using deduced cages"
2000 diff = DIFF_IMPOSSIBLE;
2006 kdiff = max(kdiff, DIFF_KMINMAX);
2012 * Try to use knowledge of which numbers can be used to generate
2014 * This can only be used if a cage lies entirely within a region.
2016 if (dlev->maxkdiff >= DIFF_KSUMS && usage->kclues != NULL) {
2017 int changed = FALSE;
2019 for (b = 0; b < usage->kblocks->nr_blocks; b++) {
2020 int ret = solver_killer_sums(usage, b, usage->kblocks,
2021 usage->kclues[b], TRUE
2022 #ifdef STANDALONE_SOLVER
2028 kdiff = max(kdiff, DIFF_KSUMS);
2029 } else if (ret < 0) {
2030 diff = DIFF_IMPOSSIBLE;
2035 for (b = 0; b < usage->extra_cages->nr_blocks; b++) {
2036 int ret = solver_killer_sums(usage, b, usage->extra_cages,
2037 usage->extra_clues[b], FALSE
2038 #ifdef STANDALONE_SOLVER
2044 kdiff = max(kdiff, DIFF_KSUMS);
2045 } else if (ret < 0) {
2046 diff = DIFF_IMPOSSIBLE;
2055 if (dlev->maxdiff <= DIFF_BLOCK)
2059 * Row-wise positional elimination.
2061 for (y = 0; y < cr; y++)
2062 for (n = 1; n <= cr; n++)
2063 if (!usage->row[y*cr+n-1]) {
2064 for (x = 0; x < cr; x++)
2065 scratch->indexlist[x] = cubepos(x, y, n);
2066 ret = solver_elim(usage, scratch->indexlist
2067 #ifdef STANDALONE_SOLVER
2068 , "positional elimination,"
2069 " %d in row %d", n, 1+y
2073 diff = DIFF_IMPOSSIBLE;
2075 } else if (ret > 0) {
2076 diff = max(diff, DIFF_SIMPLE);
2081 * Column-wise positional elimination.
2083 for (x = 0; x < cr; x++)
2084 for (n = 1; n <= cr; n++)
2085 if (!usage->col[x*cr+n-1]) {
2086 for (y = 0; y < cr; y++)
2087 scratch->indexlist[y] = cubepos(x, y, n);
2088 ret = solver_elim(usage, scratch->indexlist
2089 #ifdef STANDALONE_SOLVER
2090 , "positional elimination,"
2091 " %d in column %d", n, 1+x
2095 diff = DIFF_IMPOSSIBLE;
2097 } else if (ret > 0) {
2098 diff = max(diff, DIFF_SIMPLE);
2104 * X-diagonal positional elimination.
2107 for (n = 1; n <= cr; n++)
2108 if (!usage->diag[n-1]) {
2109 for (i = 0; i < cr; i++)
2110 scratch->indexlist[i] = cubepos2(diag0(i), n);
2111 ret = solver_elim(usage, scratch->indexlist
2112 #ifdef STANDALONE_SOLVER
2113 , "positional elimination,"
2114 " %d in \\-diagonal", n
2118 diff = DIFF_IMPOSSIBLE;
2120 } else if (ret > 0) {
2121 diff = max(diff, DIFF_SIMPLE);
2125 for (n = 1; n <= cr; n++)
2126 if (!usage->diag[cr+n-1]) {
2127 for (i = 0; i < cr; i++)
2128 scratch->indexlist[i] = cubepos2(diag1(i), n);
2129 ret = solver_elim(usage, scratch->indexlist
2130 #ifdef STANDALONE_SOLVER
2131 , "positional elimination,"
2132 " %d in /-diagonal", n
2136 diff = DIFF_IMPOSSIBLE;
2138 } else if (ret > 0) {
2139 diff = max(diff, DIFF_SIMPLE);
2146 * Numeric elimination.
2148 for (x = 0; x < cr; x++)
2149 for (y = 0; y < cr; y++)
2150 if (!usage->grid[y*cr+x]) {
2151 for (n = 1; n <= cr; n++)
2152 scratch->indexlist[n-1] = cubepos(x, y, n);
2153 ret = solver_elim(usage, scratch->indexlist
2154 #ifdef STANDALONE_SOLVER
2155 , "numeric elimination at (%d,%d)",
2160 diff = DIFF_IMPOSSIBLE;
2162 } else if (ret > 0) {
2163 diff = max(diff, DIFF_SIMPLE);
2168 if (dlev->maxdiff <= DIFF_SIMPLE)
2172 * Intersectional analysis, rows vs blocks.
2174 for (y = 0; y < cr; y++)
2175 for (b = 0; b < cr; b++)
2176 for (n = 1; n <= cr; n++) {
2177 if (usage->row[y*cr+n-1] ||
2178 usage->blk[b*cr+n-1])
2180 for (i = 0; i < cr; i++) {
2181 scratch->indexlist[i] = cubepos(i, y, n);
2182 scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
2185 * solver_intersect() never returns -1.
2187 if (solver_intersect(usage, scratch->indexlist,
2189 #ifdef STANDALONE_SOLVER
2190 , "intersectional analysis,"
2191 " %d in row %d vs block %s",
2192 n, 1+y, usage->blocks->blocknames[b]
2195 solver_intersect(usage, scratch->indexlist2,
2197 #ifdef STANDALONE_SOLVER
2198 , "intersectional analysis,"
2199 " %d in block %s vs row %d",
2200 n, usage->blocks->blocknames[b], 1+y
2203 diff = max(diff, DIFF_INTERSECT);
2209 * Intersectional analysis, columns vs blocks.
2211 for (x = 0; x < cr; x++)
2212 for (b = 0; b < cr; b++)
2213 for (n = 1; n <= cr; n++) {
2214 if (usage->col[x*cr+n-1] ||
2215 usage->blk[b*cr+n-1])
2217 for (i = 0; i < cr; i++) {
2218 scratch->indexlist[i] = cubepos(x, i, n);
2219 scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
2221 if (solver_intersect(usage, scratch->indexlist,
2223 #ifdef STANDALONE_SOLVER
2224 , "intersectional analysis,"
2225 " %d in column %d vs block %s",
2226 n, 1+x, usage->blocks->blocknames[b]
2229 solver_intersect(usage, scratch->indexlist2,
2231 #ifdef STANDALONE_SOLVER
2232 , "intersectional analysis,"
2233 " %d in block %s vs column %d",
2234 n, usage->blocks->blocknames[b], 1+x
2237 diff = max(diff, DIFF_INTERSECT);
2244 * Intersectional analysis, \-diagonal vs blocks.
2246 for (b = 0; b < cr; b++)
2247 for (n = 1; n <= cr; n++) {
2248 if (usage->diag[n-1] ||
2249 usage->blk[b*cr+n-1])
2251 for (i = 0; i < cr; i++) {
2252 scratch->indexlist[i] = cubepos2(diag0(i), n);
2253 scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
2255 if (solver_intersect(usage, scratch->indexlist,
2257 #ifdef STANDALONE_SOLVER
2258 , "intersectional analysis,"
2259 " %d in \\-diagonal vs block %s",
2260 n, usage->blocks->blocknames[b]
2263 solver_intersect(usage, scratch->indexlist2,
2265 #ifdef STANDALONE_SOLVER
2266 , "intersectional analysis,"
2267 " %d in block %s vs \\-diagonal",
2268 n, usage->blocks->blocknames[b]
2271 diff = max(diff, DIFF_INTERSECT);
2277 * Intersectional analysis, /-diagonal vs blocks.
2279 for (b = 0; b < cr; b++)
2280 for (n = 1; n <= cr; n++) {
2281 if (usage->diag[cr+n-1] ||
2282 usage->blk[b*cr+n-1])
2284 for (i = 0; i < cr; i++) {
2285 scratch->indexlist[i] = cubepos2(diag1(i), n);
2286 scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
2288 if (solver_intersect(usage, scratch->indexlist,
2290 #ifdef STANDALONE_SOLVER
2291 , "intersectional analysis,"
2292 " %d in /-diagonal vs block %s",
2293 n, usage->blocks->blocknames[b]
2296 solver_intersect(usage, scratch->indexlist2,
2298 #ifdef STANDALONE_SOLVER
2299 , "intersectional analysis,"
2300 " %d in block %s vs /-diagonal",
2301 n, usage->blocks->blocknames[b]
2304 diff = max(diff, DIFF_INTERSECT);
2310 if (dlev->maxdiff <= DIFF_INTERSECT)
2314 * Blockwise set elimination.
2316 for (b = 0; b < cr; b++) {
2317 for (i = 0; i < cr; i++)
2318 for (n = 1; n <= cr; n++)
2319 scratch->indexlist[i*cr+n-1] = cubepos2(usage->blocks->blocks[b][i], n);
2320 ret = solver_set(usage, scratch, scratch->indexlist
2321 #ifdef STANDALONE_SOLVER
2322 , "set elimination, block %s",
2323 usage->blocks->blocknames[b]
2327 diff = DIFF_IMPOSSIBLE;
2329 } else if (ret > 0) {
2330 diff = max(diff, DIFF_SET);
2336 * Row-wise set elimination.
2338 for (y = 0; y < cr; y++) {
2339 for (x = 0; x < cr; x++)
2340 for (n = 1; n <= cr; n++)
2341 scratch->indexlist[x*cr+n-1] = cubepos(x, y, n);
2342 ret = solver_set(usage, scratch, scratch->indexlist
2343 #ifdef STANDALONE_SOLVER
2344 , "set elimination, row %d", 1+y
2348 diff = DIFF_IMPOSSIBLE;
2350 } else if (ret > 0) {
2351 diff = max(diff, DIFF_SET);
2357 * Column-wise set elimination.
2359 for (x = 0; x < cr; x++) {
2360 for (y = 0; y < cr; y++)
2361 for (n = 1; n <= cr; n++)
2362 scratch->indexlist[y*cr+n-1] = cubepos(x, y, n);
2363 ret = solver_set(usage, scratch, scratch->indexlist
2364 #ifdef STANDALONE_SOLVER
2365 , "set elimination, column %d", 1+x
2369 diff = DIFF_IMPOSSIBLE;
2371 } else if (ret > 0) {
2372 diff = max(diff, DIFF_SET);
2379 * \-diagonal set elimination.
2381 for (i = 0; i < cr; i++)
2382 for (n = 1; n <= cr; n++)
2383 scratch->indexlist[i*cr+n-1] = cubepos2(diag0(i), n);
2384 ret = solver_set(usage, scratch, scratch->indexlist
2385 #ifdef STANDALONE_SOLVER
2386 , "set elimination, \\-diagonal"
2390 diff = DIFF_IMPOSSIBLE;
2392 } else if (ret > 0) {
2393 diff = max(diff, DIFF_SET);
2398 * /-diagonal set elimination.
2400 for (i = 0; i < cr; i++)
2401 for (n = 1; n <= cr; n++)
2402 scratch->indexlist[i*cr+n-1] = cubepos2(diag1(i), n);
2403 ret = solver_set(usage, scratch, scratch->indexlist
2404 #ifdef STANDALONE_SOLVER
2405 , "set elimination, /-diagonal"
2409 diff = DIFF_IMPOSSIBLE;
2411 } else if (ret > 0) {
2412 diff = max(diff, DIFF_SET);
2417 if (dlev->maxdiff <= DIFF_SET)
2421 * Row-vs-column set elimination on a single number.
2423 for (n = 1; n <= cr; n++) {
2424 for (y = 0; y < cr; y++)
2425 for (x = 0; x < cr; x++)
2426 scratch->indexlist[y*cr+x] = cubepos(x, y, n);
2427 ret = solver_set(usage, scratch, scratch->indexlist
2428 #ifdef STANDALONE_SOLVER
2429 , "positional set elimination, number %d", n
2433 diff = DIFF_IMPOSSIBLE;
2435 } else if (ret > 0) {
2436 diff = max(diff, DIFF_EXTREME);
2444 if (solver_forcing(usage, scratch)) {
2445 diff = max(diff, DIFF_EXTREME);
2450 * If we reach here, we have made no deductions in this
2451 * iteration, so the algorithm terminates.
2457 * Last chance: if we haven't fully solved the puzzle yet, try
2458 * recursing based on guesses for a particular square. We pick
2459 * one of the most constrained empty squares we can find, which
2460 * has the effect of pruning the search tree as much as
2463 if (dlev->maxdiff >= DIFF_RECURSIVE) {
2464 int best, bestcount;
2469 for (y = 0; y < cr; y++)
2470 for (x = 0; x < cr; x++)
2471 if (!grid[y*cr+x]) {
2475 * An unfilled square. Count the number of
2476 * possible digits in it.
2479 for (n = 1; n <= cr; n++)
2484 * We should have found any impossibilities
2485 * already, so this can safely be an assert.
2489 if (count < bestcount) {
2497 digit *list, *ingrid, *outgrid;
2499 diff = DIFF_IMPOSSIBLE; /* no solution found yet */
2502 * Attempt recursion.
2507 list = snewn(cr, digit);
2508 ingrid = snewn(cr * cr, digit);
2509 outgrid = snewn(cr * cr, digit);
2510 memcpy(ingrid, grid, cr * cr);
2512 /* Make a list of the possible digits. */
2513 for (j = 0, n = 1; n <= cr; n++)
2517 #ifdef STANDALONE_SOLVER
2518 if (solver_show_working) {
2520 printf("%*srecursing on (%d,%d) [",
2521 solver_recurse_depth*4, "", x + 1, y + 1);
2522 for (i = 0; i < j; i++) {
2523 printf("%s%d", sep, list[i]);
2531 * And step along the list, recursing back into the
2532 * main solver at every stage.
2534 for (i = 0; i < j; i++) {
2535 memcpy(outgrid, ingrid, cr * cr);
2536 outgrid[y*cr+x] = list[i];
2538 #ifdef STANDALONE_SOLVER
2539 if (solver_show_working)
2540 printf("%*sguessing %d at (%d,%d)\n",
2541 solver_recurse_depth*4, "", list[i], x + 1, y + 1);
2542 solver_recurse_depth++;
2545 solver(cr, blocks, kblocks, xtype, outgrid, kgrid, dlev);
2547 #ifdef STANDALONE_SOLVER
2548 solver_recurse_depth--;
2549 if (solver_show_working) {
2550 printf("%*sretracting %d at (%d,%d)\n",
2551 solver_recurse_depth*4, "", list[i], x + 1, y + 1);
2556 * If we have our first solution, copy it into the
2557 * grid we will return.
2559 if (diff == DIFF_IMPOSSIBLE && dlev->diff != DIFF_IMPOSSIBLE)
2560 memcpy(grid, outgrid, cr*cr);
2562 if (dlev->diff == DIFF_AMBIGUOUS)
2563 diff = DIFF_AMBIGUOUS;
2564 else if (dlev->diff == DIFF_IMPOSSIBLE)
2565 /* do not change our return value */;
2567 /* the recursion turned up exactly one solution */
2568 if (diff == DIFF_IMPOSSIBLE)
2569 diff = DIFF_RECURSIVE;
2571 diff = DIFF_AMBIGUOUS;
2575 * As soon as we've found more than one solution,
2576 * give up immediately.
2578 if (diff == DIFF_AMBIGUOUS)
2589 * We're forbidden to use recursion, so we just see whether
2590 * our grid is fully solved, and return DIFF_IMPOSSIBLE
2593 for (y = 0; y < cr; y++)
2594 for (x = 0; x < cr; x++)
2596 diff = DIFF_IMPOSSIBLE;
2601 dlev->kdiff = kdiff;
2603 #ifdef STANDALONE_SOLVER
2604 if (solver_show_working)
2605 printf("%*s%s found\n",
2606 solver_recurse_depth*4, "",
2607 diff == DIFF_IMPOSSIBLE ? "no solution" :
2608 diff == DIFF_AMBIGUOUS ? "multiple solutions" :
2612 sfree(usage->sq2region);
2613 sfree(usage->regions);
2618 if (usage->kblocks) {
2619 free_block_structure(usage->kblocks);
2620 free_block_structure(usage->extra_cages);
2621 sfree(usage->extra_clues);
2623 if (usage->kclues) sfree(usage->kclues);
2626 solver_free_scratch(scratch);
2629 /* ----------------------------------------------------------------------
2630 * End of solver code.
2633 /* ----------------------------------------------------------------------
2634 * Killer set generator.
2637 /* ----------------------------------------------------------------------
2638 * Solo filled-grid generator.
2640 * This grid generator works by essentially trying to solve a grid
2641 * starting from no clues, and not worrying that there's more than
2642 * one possible solution. Unfortunately, it isn't computationally
2643 * feasible to do this by calling the above solver with an empty
2644 * grid, because that one needs to allocate a lot of scratch space
2645 * at every recursion level. Instead, I have a much simpler
2646 * algorithm which I shamelessly copied from a Python solver
2647 * written by Andrew Wilkinson (which is GPLed, but I've reused
2648 * only ideas and no code). It mostly just does the obvious
2649 * recursive thing: pick an empty square, put one of the possible
2650 * digits in it, recurse until all squares are filled, backtrack
2651 * and change some choices if necessary.
2653 * The clever bit is that every time it chooses which square to
2654 * fill in next, it does so by counting the number of _possible_
2655 * numbers that can go in each square, and it prioritises so that
2656 * it picks a square with the _lowest_ number of possibilities. The
2657 * idea is that filling in lots of the obvious bits (particularly
2658 * any squares with only one possibility) will cut down on the list
2659 * of possibilities for other squares and hence reduce the enormous
2660 * search space as much as possible as early as possible.
2662 * The use of bit sets implies that we support puzzles up to a size of
2663 * 32x32 (less if anyone finds a 16-bit machine to compile this on).
2667 * Internal data structure used in gridgen to keep track of
2670 struct gridgen_coord { int x, y, r; };
2671 struct gridgen_usage {
2673 struct block_structure *blocks, *kblocks;
2674 /* grid is a copy of the input grid, modified as we go along */
2677 * Bitsets. In each of them, bit n is set if digit n has been placed
2678 * in the corresponding region. row, col and blk are used for all
2679 * puzzles. cge is used only for killer puzzles, and diag is used
2680 * only for x-type puzzles.
2681 * All of these have cr entries, except diag which only has 2,
2682 * and cge, which has as many entries as kblocks.
2684 unsigned int *row, *col, *blk, *cge, *diag;
2685 /* This lists all the empty spaces remaining in the grid. */
2686 struct gridgen_coord *spaces;
2688 /* If we need randomisation in the solve, this is our random state. */
2692 static void gridgen_place(struct gridgen_usage *usage, int x, int y, digit n)
2694 unsigned int bit = 1 << n;
2696 usage->row[y] |= bit;
2697 usage->col[x] |= bit;
2698 usage->blk[usage->blocks->whichblock[y*cr+x]] |= bit;
2700 usage->cge[usage->kblocks->whichblock[y*cr+x]] |= bit;
2702 if (ondiag0(y*cr+x))
2703 usage->diag[0] |= bit;
2704 if (ondiag1(y*cr+x))
2705 usage->diag[1] |= bit;
2707 usage->grid[y*cr+x] = n;
2710 static void gridgen_remove(struct gridgen_usage *usage, int x, int y, digit n)
2712 unsigned int mask = ~(1 << n);
2714 usage->row[y] &= mask;
2715 usage->col[x] &= mask;
2716 usage->blk[usage->blocks->whichblock[y*cr+x]] &= mask;
2718 usage->cge[usage->kblocks->whichblock[y*cr+x]] &= mask;
2720 if (ondiag0(y*cr+x))
2721 usage->diag[0] &= mask;
2722 if (ondiag1(y*cr+x))
2723 usage->diag[1] &= mask;
2725 usage->grid[y*cr+x] = 0;
2731 * The real recursive step in the generating function.
2733 * Return values: 1 means solution found, 0 means no solution
2734 * found on this branch.
2736 static int gridgen_real(struct gridgen_usage *usage, digit *grid, int *steps)
2739 int i, j, n, sx, sy, bestm, bestr, ret;
2744 * Firstly, check for completion! If there are no spaces left
2745 * in the grid, we have a solution.
2747 if (usage->nspaces == 0)
2751 * Next, abandon generation if we went over our steps limit.
2758 * Otherwise, there must be at least one space. Find the most
2759 * constrained space, using the `r' field as a tie-breaker.
2761 bestm = cr+1; /* so that any space will beat it */
2765 for (j = 0; j < usage->nspaces; j++) {
2766 int x = usage->spaces[j].x, y = usage->spaces[j].y;
2767 unsigned int used_xy;
2770 m = usage->blocks->whichblock[y*cr+x];
2771 used_xy = usage->row[y] | usage->col[x] | usage->blk[m];
2772 if (usage->cge != NULL)
2773 used_xy |= usage->cge[usage->kblocks->whichblock[y*cr+x]];
2774 if (usage->cge != NULL)
2775 used_xy |= usage->cge[usage->kblocks->whichblock[y*cr+x]];
2776 if (usage->diag != NULL) {
2777 if (ondiag0(y*cr+x))
2778 used_xy |= usage->diag[0];
2779 if (ondiag1(y*cr+x))
2780 used_xy |= usage->diag[1];
2784 * Find the number of digits that could go in this space.
2787 for (n = 1; n <= cr; n++) {
2788 unsigned int bit = 1 << n;
2789 if ((used_xy & bit) == 0)
2792 if (m < bestm || (m == bestm && usage->spaces[j].r < bestr)) {
2794 bestr = usage->spaces[j].r;
2803 * Swap that square into the final place in the spaces array,
2804 * so that decrementing nspaces will remove it from the list.
2806 if (i != usage->nspaces-1) {
2807 struct gridgen_coord t;
2808 t = usage->spaces[usage->nspaces-1];
2809 usage->spaces[usage->nspaces-1] = usage->spaces[i];
2810 usage->spaces[i] = t;
2814 * Now we've decided which square to start our recursion at,
2815 * simply go through all possible values, shuffling them
2816 * randomly first if necessary.
2818 digits = snewn(bestm, int);
2821 for (n = 1; n <= cr; n++) {
2822 unsigned int bit = 1 << n;
2824 if ((used & bit) == 0)
2829 shuffle(digits, j, sizeof(*digits), usage->rs);
2831 /* And finally, go through the digit list and actually recurse. */
2833 for (i = 0; i < j; i++) {
2836 /* Update the usage structure to reflect the placing of this digit. */
2837 gridgen_place(usage, sx, sy, n);
2840 /* Call the solver recursively. Stop when we find a solution. */
2841 if (gridgen_real(usage, grid, steps)) {
2846 /* Revert the usage structure. */
2847 gridgen_remove(usage, sx, sy, n);
2856 * Entry point to generator. You give it parameters and a starting
2857 * grid, which is simply an array of cr*cr digits.
2859 static int gridgen(int cr, struct block_structure *blocks,
2860 struct block_structure *kblocks, int xtype,
2861 digit *grid, random_state *rs, int maxsteps)
2863 struct gridgen_usage *usage;
2867 * Clear the grid to start with.
2869 memset(grid, 0, cr*cr);
2872 * Create a gridgen_usage structure.
2874 usage = snew(struct gridgen_usage);
2877 usage->blocks = blocks;
2881 usage->row = snewn(cr, unsigned int);
2882 usage->col = snewn(cr, unsigned int);
2883 usage->blk = snewn(cr, unsigned int);
2884 if (kblocks != NULL) {
2885 usage->kblocks = kblocks;
2886 usage->cge = snewn(usage->kblocks->nr_blocks, unsigned int);
2887 memset(usage->cge, FALSE, kblocks->nr_blocks * sizeof *usage->cge);
2892 memset(usage->row, 0, cr * sizeof *usage->row);
2893 memset(usage->col, 0, cr * sizeof *usage->col);
2894 memset(usage->blk, 0, cr * sizeof *usage->blk);
2897 usage->diag = snewn(2, unsigned int);
2898 memset(usage->diag, 0, 2 * sizeof *usage->diag);
2904 * Begin by filling in the whole top row with randomly chosen
2905 * numbers. This cannot introduce any bias or restriction on
2906 * the available grids, since we already know those numbers
2907 * are all distinct so all we're doing is choosing their
2910 for (x = 0; x < cr; x++)
2912 shuffle(grid, cr, sizeof(*grid), rs);
2913 for (x = 0; x < cr; x++)
2914 gridgen_place(usage, x, 0, grid[x]);
2916 usage->spaces = snewn(cr * cr, struct gridgen_coord);
2922 * Initialise the list of grid spaces, taking care to leave
2923 * out the row I've already filled in above.
2925 for (y = 1; y < cr; y++) {
2926 for (x = 0; x < cr; x++) {
2927 usage->spaces[usage->nspaces].x = x;
2928 usage->spaces[usage->nspaces].y = y;
2929 usage->spaces[usage->nspaces].r = random_bits(rs, 31);
2935 * Run the real generator function.
2937 ret = gridgen_real(usage, grid, &maxsteps);
2940 * Clean up the usage structure now we have our answer.
2942 sfree(usage->spaces);
2952 /* ----------------------------------------------------------------------
2953 * End of grid generator code.
2957 * Check whether a grid contains a valid complete puzzle.
2959 static int check_valid(int cr, struct block_structure *blocks,
2960 struct block_structure *kblocks, int xtype, digit *grid)
2962 unsigned char *used;
2965 used = snewn(cr, unsigned char);
2968 * Check that each row contains precisely one of everything.
2970 for (y = 0; y < cr; y++) {
2971 memset(used, FALSE, cr);
2972 for (x = 0; x < cr; x++)
2973 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
2974 used[grid[y*cr+x]-1] = TRUE;
2975 for (n = 0; n < cr; n++)
2983 * Check that each column contains precisely one of everything.
2985 for (x = 0; x < cr; x++) {
2986 memset(used, FALSE, cr);
2987 for (y = 0; y < cr; y++)
2988 if (grid[y*cr+x] > 0 && grid[y*cr+x] <= cr)
2989 used[grid[y*cr+x]-1] = TRUE;
2990 for (n = 0; n < cr; n++)
2998 * Check that each block contains precisely one of everything.
3000 for (i = 0; i < cr; i++) {
3001 memset(used, FALSE, cr);
3002 for (j = 0; j < cr; j++)
3003 if (grid[blocks->blocks[i][j]] > 0 &&
3004 grid[blocks->blocks[i][j]] <= cr)
3005 used[grid[blocks->blocks[i][j]]-1] = TRUE;
3006 for (n = 0; n < cr; n++)
3014 * Check that each Killer cage, if any, contains at most one of
3018 for (i = 0; i < kblocks->nr_blocks; i++) {
3019 memset(used, FALSE, cr);
3020 for (j = 0; j < kblocks->nr_squares[i]; j++)
3021 if (grid[kblocks->blocks[i][j]] > 0 &&
3022 grid[kblocks->blocks[i][j]] <= cr) {
3023 if (used[grid[kblocks->blocks[i][j]]-1]) {
3027 used[grid[kblocks->blocks[i][j]]-1] = TRUE;
3033 * Check that each diagonal contains precisely one of everything.
3036 memset(used, FALSE, cr);
3037 for (i = 0; i < cr; i++)
3038 if (grid[diag0(i)] > 0 && grid[diag0(i)] <= cr)
3039 used[grid[diag0(i)]-1] = TRUE;
3040 for (n = 0; n < cr; n++)
3045 for (i = 0; i < cr; i++)
3046 if (grid[diag1(i)] > 0 && grid[diag1(i)] <= cr)
3047 used[grid[diag1(i)]-1] = TRUE;
3048 for (n = 0; n < cr; n++)
3059 static int symmetries(game_params *params, int x, int y, int *output, int s)
3061 int c = params->c, r = params->r, cr = c*r;
3064 #define ADD(x,y) (*output++ = (x), *output++ = (y), i++)
3070 break; /* just x,y is all we need */
3072 ADD(cr - 1 - x, cr - 1 - y);
3077 ADD(cr - 1 - x, cr - 1 - y);
3088 ADD(cr - 1 - x, cr - 1 - y);
3092 ADD(cr - 1 - x, cr - 1 - y);
3093 ADD(cr - 1 - y, cr - 1 - x);
3098 ADD(cr - 1 - x, cr - 1 - y);
3102 ADD(cr - 1 - y, cr - 1 - x);
3111 static char *encode_solve_move(int cr, digit *grid)
3114 char *ret, *p, *sep;
3117 * It's surprisingly easy to work out _exactly_ how long this
3118 * string needs to be. To decimal-encode all the numbers from 1
3121 * - every number has a units digit; total is n.
3122 * - all numbers above 9 have a tens digit; total is max(n-9,0).
3123 * - all numbers above 99 have a hundreds digit; total is max(n-99,0).
3127 for (i = 1; i <= cr; i *= 10)
3128 len += max(cr - i + 1, 0);
3129 len += cr; /* don't forget the commas */
3130 len *= cr; /* there are cr rows of these */
3133 * Now len is one bigger than the total size of the
3134 * comma-separated numbers (because we counted an
3135 * additional leading comma). We need to have a leading S
3136 * and a trailing NUL, so we're off by one in total.
3140 ret = snewn(len, char);
3144 for (i = 0; i < cr*cr; i++) {
3145 p += sprintf(p, "%s%d", sep, grid[i]);
3149 assert(p - ret == len);
3154 static void dsf_to_blocks(int *dsf, struct block_structure *blocks,
3155 int min_expected, int max_expected)
3157 int cr = blocks->c * blocks->r, area = cr * cr;
3160 for (i = 0; i < area; i++)
3161 blocks->whichblock[i] = -1;
3162 for (i = 0; i < area; i++) {
3163 int j = dsf_canonify(dsf, i);
3164 if (blocks->whichblock[j] < 0)
3165 blocks->whichblock[j] = nb++;
3166 blocks->whichblock[i] = blocks->whichblock[j];
3168 assert(nb >= min_expected && nb <= max_expected);
3169 blocks->nr_blocks = nb;
3172 static void make_blocks_from_whichblock(struct block_structure *blocks)
3176 for (i = 0; i < blocks->nr_blocks; i++) {
3177 blocks->blocks[i][blocks->max_nr_squares-1] = 0;
3178 blocks->nr_squares[i] = 0;
3180 for (i = 0; i < blocks->area; i++) {
3181 int b = blocks->whichblock[i];
3182 int j = blocks->blocks[b][blocks->max_nr_squares-1]++;
3183 assert(j < blocks->max_nr_squares);
3184 blocks->blocks[b][j] = i;
3185 blocks->nr_squares[b]++;
3189 static char *encode_block_structure_desc(char *p, struct block_structure *blocks)
3192 int c = blocks->c, r = blocks->r, cr = c * r;
3195 * Encode the block structure. We do this by encoding
3196 * the pattern of dividing lines: first we iterate
3197 * over the cr*(cr-1) internal vertical grid lines in
3198 * ordinary reading order, then over the cr*(cr-1)
3199 * internal horizontal ones in transposed reading
3202 * We encode the number of non-lines between the
3203 * lines; _ means zero (two adjacent divisions), a
3204 * means 1, ..., y means 25, and z means 25 non-lines
3205 * _and no following line_ (so that za means 26, zb 27
3208 for (i = 0; i <= 2*cr*(cr-1); i++) {
3209 int x, y, p0, p1, edge;
3211 if (i == 2*cr*(cr-1)) {
3212 edge = TRUE; /* terminating virtual edge */
3214 if (i < cr*(cr-1)) {
3225 edge = (blocks->whichblock[p0] != blocks->whichblock[p1]);
3229 while (currrun > 25)
3230 *p++ = 'z', currrun -= 25;
3232 *p++ = 'a'-1 + currrun;
3242 static char *encode_grid(char *desc, digit *grid, int area)
3248 for (i = 0; i <= area; i++) {
3249 int n = (i < area ? grid[i] : -1);
3256 int c = 'a' - 1 + run;
3260 run -= c - ('a' - 1);
3264 * If there's a number in the very top left or
3265 * bottom right, there's no point putting an
3266 * unnecessary _ before or after it.
3268 if (p > desc && n > 0)
3272 p += sprintf(p, "%d", n);
3280 * Conservatively stimate the number of characters required for
3281 * encoding a grid of a certain area.
3283 static int grid_encode_space (int area)
3286 for (count = 1, t = area; t > 26; t -= 26)
3288 return count * area;
3292 * Conservatively stimate the number of characters required for
3293 * encoding a given blocks structure.
3295 static int blocks_encode_space(struct block_structure *blocks)
3297 int cr = blocks->c * blocks->r, area = cr * cr;
3298 return grid_encode_space(area);
3301 static char *encode_puzzle_desc(game_params *params, digit *grid,
3302 struct block_structure *blocks,
3304 struct block_structure *kblocks)
3306 int c = params->c, r = params->r, cr = c*r;
3311 space = grid_encode_space(area) + 1;
3313 space += blocks_encode_space(blocks) + 1;
3314 if (params->killer) {
3315 space += blocks_encode_space(kblocks) + 1;
3316 space += grid_encode_space(area) + 1;
3318 desc = snewn(space, char);
3319 p = encode_grid(desc, grid, area);
3323 p = encode_block_structure_desc(p, blocks);
3325 if (params->killer) {
3327 p = encode_block_structure_desc(p, kblocks);
3329 p = encode_grid(p, kgrid, area);
3331 assert(p - desc < space);
3333 desc = sresize(desc, p - desc, char);
3338 static void merge_blocks(struct block_structure *b, int n1, int n2)
3341 /* Move data towards the lower block number. */
3348 /* Merge n2 into n1, and move the last block into n2's position. */
3349 for (i = 0; i < b->nr_squares[n2]; i++)
3350 b->whichblock[b->blocks[n2][i]] = n1;
3351 memcpy(b->blocks[n1] + b->nr_squares[n1], b->blocks[n2],
3352 b->nr_squares[n2] * sizeof **b->blocks);
3353 b->nr_squares[n1] += b->nr_squares[n2];
3355 n1 = b->nr_blocks - 1;
3357 memcpy(b->blocks[n2], b->blocks[n1],
3358 b->nr_squares[n1] * sizeof **b->blocks);
3359 for (i = 0; i < b->nr_squares[n1]; i++)
3360 b->whichblock[b->blocks[n1][i]] = n2;
3361 b->nr_squares[n2] = b->nr_squares[n1];
3366 static int merge_some_cages(struct block_structure *b, int cr, int area,
3367 digit *grid, random_state *rs)
3370 * Make a list of all the pairs of adjacent blocks.
3378 pairs = snewn(b->nr_blocks * b->nr_blocks, struct pair);
3381 for (i = 0; i < b->nr_blocks; i++) {
3382 for (j = i+1; j < b->nr_blocks; j++) {
3385 * Rule the merger out of consideration if it's
3386 * obviously not viable.
3388 if (b->nr_squares[i] + b->nr_squares[j] > b->max_nr_squares)
3389 continue; /* we couldn't merge these anyway */
3392 * See if these two blocks have a pair of squares
3393 * adjacent to each other.
3395 for (k = 0; k < b->nr_squares[i]; k++) {
3396 int xy = b->blocks[i][k];
3397 int y = xy / cr, x = xy % cr;
3398 if ((y > 0 && b->whichblock[xy - cr] == j) ||
3399 (y+1 < cr && b->whichblock[xy + cr] == j) ||
3400 (x > 0 && b->whichblock[xy - 1] == j) ||
3401 (x+1 < cr && b->whichblock[xy + 1] == j)) {
3403 * Yes! Add this pair to our list.
3405 pairs[npairs].b1 = i;
3406 pairs[npairs].b2 = j;
3414 * Now go through that list in random order until we find a pair
3415 * of blocks we can merge.
3417 while (npairs > 0) {
3419 unsigned int digits_found;
3422 * Pick a random pair, and remove it from the list.
3424 i = random_upto(rs, npairs);
3428 pairs[i] = pairs[npairs-1];
3431 /* Guarantee that the merged cage would still be a region. */
3433 for (i = 0; i < b->nr_squares[n1]; i++)
3434 digits_found |= 1 << grid[b->blocks[n1][i]];
3435 for (i = 0; i < b->nr_squares[n2]; i++)
3436 if (digits_found & (1 << grid[b->blocks[n2][i]]))
3438 if (i != b->nr_squares[n2])
3442 * Got one! Do the merge.
3444 merge_blocks(b, n1, n2);
3453 static void compute_kclues(struct block_structure *cages, digit *kclues,
3454 digit *grid, int area)
3457 memset(kclues, 0, area * sizeof *kclues);
3458 for (i = 0; i < cages->nr_blocks; i++) {
3460 for (j = 0; j < area; j++)
3461 if (cages->whichblock[j] == i)
3463 for (j = 0; j < area; j++)
3464 if (cages->whichblock[j] == i)
3471 static struct block_structure *gen_killer_cages(int cr, random_state *rs,
3472 int remove_singletons)
3475 int x, y, area = cr * cr;
3476 int n_singletons = 0;
3477 struct block_structure *b = alloc_block_structure (1, cr, area, cr, area);
3479 for (x = 0; x < area; x++)
3480 b->whichblock[x] = -1;
3482 for (y = 0; y < cr; y++)
3483 for (x = 0; x < cr; x++) {
3486 if (b->whichblock[xy] != -1)
3488 b->whichblock[xy] = nr;
3490 rnd = random_bits(rs, 4);
3491 if (xy + 1 < area && (rnd >= 4 || (!remove_singletons && rnd >= 1))) {
3493 if (x + 1 == cr || b->whichblock[xy2] != -1 ||
3494 (xy + cr < area && random_bits(rs, 1) == 0))
3499 b->whichblock[xy2] = nr;
3506 make_blocks_from_whichblock(b);
3508 for (x = y = 0; x < b->nr_blocks; x++)
3509 if (b->nr_squares[x] == 1)
3511 assert(y == n_singletons);
3513 if (n_singletons > 0 && remove_singletons) {
3515 for (n = 0; n < b->nr_blocks;) {
3516 int xy, x, y, xy2, other;
3517 if (b->nr_squares[n] > 1) {
3521 xy = b->blocks[n][0];
3526 else if (x + 1 < cr && (y + 1 == cr || random_bits(rs, 1) == 0))
3530 other = b->whichblock[xy2];
3532 if (b->nr_squares[other] == 1)
3535 merge_blocks(b, n, other);
3539 assert(n_singletons == 0);
3544 static char *new_game_desc(game_params *params, random_state *rs,
3545 char **aux, int interactive)
3547 int c = params->c, r = params->r, cr = c*r;
3549 struct block_structure *blocks, *kblocks;
3550 digit *grid, *grid2, *kgrid;
3551 struct xy { int x, y; } *locs;
3554 int coords[16], ncoords;
3556 struct difficulty dlev;
3558 precompute_sum_bits();
3561 * Adjust the maximum difficulty level to be consistent with
3562 * the puzzle size: all 2x2 puzzles appear to be Trivial
3563 * (DIFF_BLOCK) so we cannot hold out for even a Basic
3564 * (DIFF_SIMPLE) one.
3566 dlev.maxdiff = params->diff;
3567 dlev.maxkdiff = params->kdiff;
3568 if (c == 2 && r == 2)
3569 dlev.maxdiff = DIFF_BLOCK;
3571 grid = snewn(area, digit);
3572 locs = snewn(area, struct xy);
3573 grid2 = snewn(area, digit);
3575 blocks = alloc_block_structure (c, r, area, cr, cr);
3578 kgrid = (params->killer) ? snewn(area, digit) : NULL;
3580 #ifdef STANDALONE_SOLVER
3581 assert(!"This should never happen, so we don't need to create blocknames");
3585 * Loop until we get a grid of the required difficulty. This is
3586 * nasty, but it seems to be unpleasantly hard to generate
3587 * difficult grids otherwise.
3591 * Generate a random solved state, starting by
3592 * constructing the block structure.
3594 if (r == 1) { /* jigsaw mode */
3595 int *dsf = divvy_rectangle(cr, cr, cr, rs);
3597 dsf_to_blocks (dsf, blocks, cr, cr);
3600 } else { /* basic Sudoku mode */
3601 for (y = 0; y < cr; y++)
3602 for (x = 0; x < cr; x++)
3603 blocks->whichblock[y*cr+x] = (y/c) * c + (x/r);
3605 make_blocks_from_whichblock(blocks);
3607 if (params->killer) {
3608 if (kblocks) free_block_structure(kblocks);
3609 kblocks = gen_killer_cages(cr, rs, params->kdiff > DIFF_KSINGLE);
3612 if (!gridgen(cr, blocks, kblocks, params->xtype, grid, rs, area*area))
3614 assert(check_valid(cr, blocks, kblocks, params->xtype, grid));
3617 * Save the solved grid in aux.
3621 * We might already have written *aux the last time we
3622 * went round this loop, in which case we should free
3623 * the old aux before overwriting it with the new one.
3629 *aux = encode_solve_move(cr, grid);
3633 * Now we have a solved grid. For normal puzzles, we start removing
3634 * things from it while preserving solubility. Killer puzzles are
3635 * different: we just pass the empty grid to the solver, and use
3636 * the puzzle if it comes back solved.
3639 if (params->killer) {
3640 struct block_structure *good_cages = NULL;
3641 struct block_structure *last_cages = NULL;
3644 memcpy(grid2, grid, area);
3647 compute_kclues(kblocks, kgrid, grid2, area);
3649 memset(grid, 0, area * sizeof *grid);
3650 solver(cr, blocks, kblocks, params->xtype, grid, kgrid, &dlev);
3651 if (dlev.diff == dlev.maxdiff && dlev.kdiff == dlev.maxkdiff) {
3653 * We have one that matches our difficulty. Store it for
3654 * later, but keep going.
3657 free_block_structure(good_cages);
3659 good_cages = dup_block_structure(kblocks);
3660 if (!merge_some_cages(kblocks, cr, area, grid2, rs))
3662 } else if (dlev.diff > dlev.maxdiff || dlev.kdiff > dlev.maxkdiff) {
3664 * Give up after too many tries and either use the good one we
3665 * found, or generate a new grid.
3670 * The difficulty level got too high. If we have a good
3671 * one, use it, otherwise go back to the last one that
3672 * was at a lower difficulty and restart the process from
3675 if (good_cages != NULL) {
3676 free_block_structure(kblocks);
3677 kblocks = dup_block_structure(good_cages);
3678 if (!merge_some_cages(kblocks, cr, area, grid2, rs))
3681 if (last_cages == NULL)
3683 free_block_structure(kblocks);
3684 kblocks = last_cages;
3689 free_block_structure(last_cages);
3690 last_cages = dup_block_structure(kblocks);
3691 if (!merge_some_cages(kblocks, cr, area, grid2, rs))
3696 free_block_structure(last_cages);
3697 if (good_cages != NULL) {
3698 free_block_structure(kblocks);
3699 kblocks = good_cages;
3700 compute_kclues(kblocks, kgrid, grid2, area);
3701 memset(grid, 0, area * sizeof *grid);
3708 * Find the set of equivalence classes of squares permitted
3709 * by the selected symmetry. We do this by enumerating all
3710 * the grid squares which have no symmetric companion
3711 * sorting lower than themselves.
3714 for (y = 0; y < cr; y++)
3715 for (x = 0; x < cr; x++) {
3719 ncoords = symmetries(params, x, y, coords, params->symm);
3720 for (j = 0; j < ncoords; j++)
3721 if (coords[2*j+1]*cr+coords[2*j] < i)
3731 * Now shuffle that list.
3733 shuffle(locs, nlocs, sizeof(*locs), rs);
3736 * Now loop over the shuffled list and, for each element,
3737 * see whether removing that element (and its reflections)
3738 * from the grid will still leave the grid soluble.
3740 for (i = 0; i < nlocs; i++) {
3744 memcpy(grid2, grid, area);
3745 ncoords = symmetries(params, x, y, coords, params->symm);
3746 for (j = 0; j < ncoords; j++)
3747 grid2[coords[2*j+1]*cr+coords[2*j]] = 0;
3749 solver(cr, blocks, kblocks, params->xtype, grid2, kgrid, &dlev);
3750 if (dlev.diff <= dlev.maxdiff &&
3751 (!params->killer || dlev.kdiff <= dlev.maxkdiff)) {
3752 for (j = 0; j < ncoords; j++)
3753 grid[coords[2*j+1]*cr+coords[2*j]] = 0;
3757 memcpy(grid2, grid, area);
3759 solver(cr, blocks, kblocks, params->xtype, grid2, kgrid, &dlev);
3760 if (dlev.diff == dlev.maxdiff &&
3761 (!params->killer || dlev.kdiff == dlev.maxkdiff))
3762 break; /* found one! */
3769 * Now we have the grid as it will be presented to the user.
3770 * Encode it in a game desc.
3772 desc = encode_puzzle_desc(params, grid, blocks, kgrid, kblocks);
3775 free_block_structure(blocks);
3776 if (params->killer) {
3777 free_block_structure(kblocks);
3784 static char *spec_to_grid(char *desc, digit *grid, int area)
3787 while (*desc && *desc != ',') {
3789 if (n >= 'a' && n <= 'z') {
3790 int run = n - 'a' + 1;
3791 assert(i + run <= area);
3794 } else if (n == '_') {
3796 } else if (n > '0' && n <= '9') {
3798 grid[i++] = atoi(desc-1);
3799 while (*desc >= '0' && *desc <= '9')
3802 assert(!"We can't get here");
3810 * Create a DSF from a spec found in *pdesc. Update this to point past the
3811 * end of the block spec, and return an error string or NULL if everything
3812 * is OK. The DSF is stored in *PDSF.
3814 static char *spec_to_dsf(char **pdesc, int **pdsf, int cr, int area)
3816 char *desc = *pdesc;
3820 *pdsf = dsf = snew_dsf(area);
3822 while (*desc && *desc != ',') {
3827 else if (*desc >= 'a' && *desc <= 'z')
3828 c = *desc - 'a' + 1;
3831 return "Invalid character in game description";
3835 adv = (c != 25); /* 'z' is a special case */
3841 * Non-edge; merge the two dsf classes on either
3844 assert(pos < 2*cr*(cr-1));
3845 if (pos < cr*(cr-1)) {
3851 int x = pos/(cr-1) - cr;
3856 dsf_merge(dsf, p0, p1);
3866 * When desc is exhausted, we expect to have gone exactly
3867 * one space _past_ the end of the grid, due to the dummy
3870 if (pos != 2*cr*(cr-1)+1) {
3872 return "Not enough data in block structure specification";
3878 static char *validate_grid_desc(char **pdesc, int range, int area)
3880 char *desc = *pdesc;
3882 while (*desc && *desc != ',') {
3884 if (n >= 'a' && n <= 'z') {
3885 squares += n - 'a' + 1;
3886 } else if (n == '_') {
3888 } else if (n > '0' && n <= '9') {
3889 int val = atoi(desc-1);
3890 if (val < 1 || val > range)
3891 return "Out-of-range number in game description";
3893 while (*desc >= '0' && *desc <= '9')
3896 return "Invalid character in game description";
3900 return "Not enough data to fill grid";
3903 return "Too much data to fit in grid";
3908 static char *validate_block_desc(char **pdesc, int cr, int area,
3909 int min_nr_blocks, int max_nr_blocks,
3910 int min_nr_squares, int max_nr_squares)
3915 err = spec_to_dsf(pdesc, &dsf, cr, area);
3920 if (min_nr_squares == max_nr_squares) {
3921 assert(min_nr_blocks == max_nr_blocks);
3922 assert(min_nr_blocks * min_nr_squares == area);
3925 * Now we've got our dsf. Verify that it matches
3929 int *canons, *counts;
3930 int i, j, c, ncanons = 0;
3932 canons = snewn(max_nr_blocks, int);
3933 counts = snewn(max_nr_blocks, int);
3935 for (i = 0; i < area; i++) {
3936 j = dsf_canonify(dsf, i);
3938 for (c = 0; c < ncanons; c++)
3939 if (canons[c] == j) {
3941 if (counts[c] > max_nr_squares) {
3945 return "A jigsaw block is too big";
3951 if (ncanons >= max_nr_blocks) {
3955 return "Too many distinct jigsaw blocks";
3957 canons[ncanons] = j;
3958 counts[ncanons] = 1;
3963 if (ncanons < min_nr_blocks) {
3967 return "Not enough distinct jigsaw blocks";
3969 for (c = 0; c < ncanons; c++) {
3970 if (counts[c] < min_nr_squares) {
3974 return "A jigsaw block is too small";
3985 static char *validate_desc(game_params *params, char *desc)
3987 int cr = params->c * params->r, area = cr*cr;
3990 err = validate_grid_desc(&desc, cr, area);
3994 if (params->r == 1) {
3996 * Now we expect a suffix giving the jigsaw block
3997 * structure. Parse it and validate that it divides the
3998 * grid into the right number of regions which are the
4002 return "Expected jigsaw block structure in game description";
4004 err = validate_block_desc(&desc, cr, area, cr, cr, cr, cr);
4009 if (params->killer) {
4011 return "Expected killer block structure in game description";
4013 err = validate_block_desc(&desc, cr, area, cr, area, 2, cr);
4017 return "Expected killer clue grid in game description";
4019 err = validate_grid_desc(&desc, cr * area, area);
4024 return "Unexpected data at end of game description";
4029 static game_state *new_game(midend *me, game_params *params, char *desc)
4031 game_state *state = snew(game_state);
4032 int c = params->c, r = params->r, cr = c*r, area = cr * cr;
4035 precompute_sum_bits();
4038 state->xtype = params->xtype;
4039 state->killer = params->killer;
4041 state->grid = snewn(area, digit);
4042 state->pencil = snewn(area * cr, unsigned char);
4043 memset(state->pencil, 0, area * cr);
4044 state->immutable = snewn(area, unsigned char);
4045 memset(state->immutable, FALSE, area);
4047 state->blocks = alloc_block_structure (c, r, area, cr, cr);
4049 if (params->killer) {
4050 state->kblocks = alloc_block_structure (c, r, area, cr, area);
4051 state->kgrid = snewn(area, digit);
4053 state->kblocks = NULL;
4054 state->kgrid = NULL;
4056 state->completed = state->cheated = FALSE;
4058 desc = spec_to_grid(desc, state->grid, area);
4059 for (i = 0; i < area; i++)
4060 if (state->grid[i] != 0)
4061 state->immutable[i] = TRUE;
4066 assert(*desc == ',');
4068 err = spec_to_dsf(&desc, &dsf, cr, area);
4069 assert(err == NULL);
4070 dsf_to_blocks(dsf, state->blocks, cr, cr);
4075 for (y = 0; y < cr; y++)
4076 for (x = 0; x < cr; x++)
4077 state->blocks->whichblock[y*cr+x] = (y/c) * c + (x/r);
4079 make_blocks_from_whichblock(state->blocks);
4081 if (params->killer) {
4084 assert(*desc == ',');
4086 err = spec_to_dsf(&desc, &dsf, cr, area);
4087 assert(err == NULL);
4088 dsf_to_blocks(dsf, state->kblocks, cr, area);
4090 make_blocks_from_whichblock(state->kblocks);
4092 assert(*desc == ',');
4094 desc = spec_to_grid(desc, state->kgrid, area);
4098 #ifdef STANDALONE_SOLVER
4100 * Set up the block names for solver diagnostic output.
4103 char *p = (char *)(state->blocks->blocknames + cr);
4106 for (i = 0; i < area; i++) {
4107 int j = state->blocks->whichblock[i];
4108 if (!state->blocks->blocknames[j]) {
4109 state->blocks->blocknames[j] = p;
4110 p += 1 + sprintf(p, "starting at (%d,%d)",
4111 1 + i%cr, 1 + i/cr);
4116 for (by = 0; by < r; by++)
4117 for (bx = 0; bx < c; bx++) {
4118 state->blocks->blocknames[by*c+bx] = p;
4119 p += 1 + sprintf(p, "(%d,%d)", bx+1, by+1);
4122 assert(p - (char *)state->blocks->blocknames < (int)(cr*(sizeof(char *)+80)));
4123 for (i = 0; i < cr; i++)
4124 assert(state->blocks->blocknames[i]);
4131 static game_state *dup_game(game_state *state)
4133 game_state *ret = snew(game_state);
4134 int cr = state->cr, area = cr * cr;
4136 ret->cr = state->cr;
4137 ret->xtype = state->xtype;
4138 ret->killer = state->killer;
4140 ret->blocks = state->blocks;
4141 ret->blocks->refcount++;
4143 ret->kblocks = state->kblocks;
4145 ret->kblocks->refcount++;
4147 ret->grid = snewn(area, digit);
4148 memcpy(ret->grid, state->grid, area);
4150 if (state->killer) {
4151 ret->kgrid = snewn(area, digit);
4152 memcpy(ret->kgrid, state->kgrid, area);
4156 ret->pencil = snewn(area * cr, unsigned char);
4157 memcpy(ret->pencil, state->pencil, area * cr);
4159 ret->immutable = snewn(area, unsigned char);
4160 memcpy(ret->immutable, state->immutable, area);
4162 ret->completed = state->completed;
4163 ret->cheated = state->cheated;
4168 static void free_game(game_state *state)
4170 free_block_structure(state->blocks);
4172 free_block_structure(state->kblocks);
4174 sfree(state->immutable);
4175 sfree(state->pencil);
4177 if (state->kgrid) sfree(state->kgrid);
4181 static char *solve_game(game_state *state, game_state *currstate,
4182 char *ai, char **error)
4187 struct difficulty dlev;
4190 * If we already have the solution in ai, save ourselves some
4196 grid = snewn(cr*cr, digit);
4197 memcpy(grid, state->grid, cr*cr);
4198 dlev.maxdiff = DIFF_RECURSIVE;
4199 dlev.maxkdiff = DIFF_KINTERSECT;
4200 solver(cr, state->blocks, state->kblocks, state->xtype, grid,
4201 state->kgrid, &dlev);
4205 if (dlev.diff == DIFF_IMPOSSIBLE)
4206 *error = "No solution exists for this puzzle";
4207 else if (dlev.diff == DIFF_AMBIGUOUS)
4208 *error = "Multiple solutions exist for this puzzle";
4215 ret = encode_solve_move(cr, grid);
4222 static char *grid_text_format(int cr, struct block_structure *blocks,
4223 int xtype, digit *grid)
4227 int totallen, linelen, nlines;
4231 * For non-jigsaw Sudoku, we format in the way we always have,
4232 * by having the digits unevenly spaced so that the dividing
4241 * For jigsaw puzzles, however, we must leave space between
4242 * _all_ pairs of digits for an optional dividing line, so we
4243 * have to move to the rather ugly
4253 * We deal with both cases using the same formatting code; we
4254 * simply invent a vmod value such that there's a vertical
4255 * dividing line before column i iff i is divisible by vmod
4256 * (so it's r in the first case and 1 in the second), and hmod
4257 * likewise for horizontal dividing lines.
4260 if (blocks->r != 1) {
4268 * Line length: we have cr digits, each with a space after it,
4269 * and (cr-1)/vmod dividing lines, each with a space after it.
4270 * The final space is replaced by a newline, but that doesn't
4271 * affect the length.
4273 linelen = 2*(cr + (cr-1)/vmod);
4276 * Number of lines: we have cr rows of digits, and (cr-1)/hmod
4279 nlines = cr + (cr-1)/hmod;
4282 * Allocate the space.
4284 totallen = linelen * nlines;
4285 ret = snewn(totallen+1, char); /* leave room for terminating NUL */
4291 for (y = 0; y < cr; y++) {
4295 for (x = 0; x < cr; x++) {
4299 digit d = grid[y*cr+x];
4303 * Empty space: we usually write a dot, but we'll
4304 * highlight spaces on the X-diagonals (in X mode)
4305 * by using underscores instead.
4307 if (xtype && (ondiag0(y*cr+x) || ondiag1(y*cr+x)))
4311 } else if (d <= 9) {
4328 * Optional dividing line.
4330 if (blocks->whichblock[y*cr+x] != blocks->whichblock[y*cr+x+1])
4337 if (y == cr-1 || (y+1) % hmod)
4343 for (x = 0; x < cr; x++) {
4348 * Division between two squares. This varies
4349 * complicatedly in length.
4351 dwid = 2; /* digit and its following space */
4353 dwid--; /* no following space at end of line */
4354 if (x > 0 && x % vmod == 0)
4355 dwid++; /* preceding space after a divider */
4357 if (blocks->whichblock[y*cr+x] != blocks->whichblock[(y+1)*cr+x])
4374 * Corner square. This is:
4375 * - a space if all four surrounding squares are in
4377 * - a vertical line if the two left ones are in one
4378 * block and the two right in another
4379 * - a horizontal line if the two top ones are in one
4380 * block and the two bottom in another
4381 * - a plus sign in all other cases. (If we had a
4382 * richer character set available we could break
4383 * this case up further by doing fun things with
4384 * line-drawing T-pieces.)
4386 tl = blocks->whichblock[y*cr+x];
4387 tr = blocks->whichblock[y*cr+x+1];
4388 bl = blocks->whichblock[(y+1)*cr+x];
4389 br = blocks->whichblock[(y+1)*cr+x+1];
4391 if (tl == tr && tr == bl && bl == br)
4393 else if (tl == bl && tr == br)
4395 else if (tl == tr && bl == br)
4404 assert(p - ret == totallen);
4409 static int game_can_format_as_text_now(game_params *params)
4412 * Formatting Killer puzzles as text is currently unsupported. I
4413 * can't think of any sensible way of doing it which doesn't
4414 * involve expanding the puzzle to such a large scale as to make
4422 static char *game_text_format(game_state *state)
4424 assert(!state->kblocks);
4425 return grid_text_format(state->cr, state->blocks, state->xtype,
4431 * These are the coordinates of the currently highlighted
4432 * square on the grid, if hshow = 1.
4436 * This indicates whether the current highlight is a
4437 * pencil-mark one or a real one.
4441 * This indicates whether or not we're showing the highlight
4442 * (used to be hx = hy = -1); important so that when we're
4443 * using the cursor keys it doesn't keep coming back at a
4444 * fixed position. When hshow = 1, pressing a valid number
4445 * or letter key or Space will enter that number or letter in the grid.
4449 * This indicates whether we're using the highlight as a cursor;
4450 * it means that it doesn't vanish on a keypress, and that it is
4451 * allowed on immutable squares.
4456 static game_ui *new_ui(game_state *state)
4458 game_ui *ui = snew(game_ui);
4460 ui->hx = ui->hy = 0;
4461 ui->hpencil = ui->hshow = ui->hcursor = 0;
4466 static void free_ui(game_ui *ui)
4471 static char *encode_ui(game_ui *ui)
4476 static void decode_ui(game_ui *ui, char *encoding)
4480 static void game_changed_state(game_ui *ui, game_state *oldstate,
4481 game_state *newstate)
4483 int cr = newstate->cr;
4485 * We prevent pencil-mode highlighting of a filled square, unless
4486 * we're using the cursor keys. So if the user has just filled in
4487 * a square which we had a pencil-mode highlight in (by Undo, or
4488 * by Redo, or by Solve), then we cancel the highlight.
4490 if (ui->hshow && ui->hpencil && !ui->hcursor &&
4491 newstate->grid[ui->hy * cr + ui->hx] != 0) {
4496 struct game_drawstate {
4501 unsigned char *pencil;
4503 /* This is scratch space used within a single call to game_redraw. */
4504 int nregions, *entered_items;
4507 static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
4508 int x, int y, int button)
4514 button &= ~MOD_MASK;
4516 tx = (x + TILE_SIZE - BORDER) / TILE_SIZE - 1;
4517 ty = (y + TILE_SIZE - BORDER) / TILE_SIZE - 1;
4519 if (tx >= 0 && tx < cr && ty >= 0 && ty < cr) {
4520 if (button == LEFT_BUTTON) {
4521 if (state->immutable[ty*cr+tx]) {
4523 } else if (tx == ui->hx && ty == ui->hy &&
4524 ui->hshow && ui->hpencil == 0) {
4533 return ""; /* UI activity occurred */
4535 if (button == RIGHT_BUTTON) {
4537 * Pencil-mode highlighting for non filled squares.
4539 if (state->grid[ty*cr+tx] == 0) {
4540 if (tx == ui->hx && ty == ui->hy &&
4541 ui->hshow && ui->hpencil) {
4553 return ""; /* UI activity occurred */
4556 if (IS_CURSOR_MOVE(button)) {
4557 move_cursor(button, &ui->hx, &ui->hy, cr, cr, 0);
4558 ui->hshow = ui->hcursor = 1;
4562 (button == CURSOR_SELECT)) {
4563 ui->hpencil = 1 - ui->hpencil;
4569 ((button >= '0' && button <= '9' && button - '0' <= cr) ||
4570 (button >= 'a' && button <= 'z' && button - 'a' + 10 <= cr) ||
4571 (button >= 'A' && button <= 'Z' && button - 'A' + 10 <= cr) ||
4572 button == CURSOR_SELECT2 || button == '\b')) {
4573 int n = button - '0';
4574 if (button >= 'A' && button <= 'Z')
4575 n = button - 'A' + 10;
4576 if (button >= 'a' && button <= 'z')
4577 n = button - 'a' + 10;
4578 if (button == CURSOR_SELECT2 || button == '\b')
4582 * Can't overwrite this square. This can only happen here
4583 * if we're using the cursor keys.
4585 if (state->immutable[ui->hy*cr+ui->hx])
4589 * Can't make pencil marks in a filled square. Again, this
4590 * can only become highlighted if we're using cursor keys.
4592 if (ui->hpencil && state->grid[ui->hy*cr+ui->hx])
4595 sprintf(buf, "%c%d,%d,%d",
4596 (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n);
4598 if (!ui->hcursor) ui->hshow = 0;
4606 static game_state *execute_move(game_state *from, char *move)
4612 if (move[0] == 'S') {
4615 ret = dup_game(from);
4616 ret->completed = ret->cheated = TRUE;
4619 for (n = 0; n < cr*cr; n++) {
4620 ret->grid[n] = atoi(p);
4622 if (!*p || ret->grid[n] < 1 || ret->grid[n] > cr) {
4627 while (*p && isdigit((unsigned char)*p)) p++;
4632 } else if ((move[0] == 'P' || move[0] == 'R') &&
4633 sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
4634 x >= 0 && x < cr && y >= 0 && y < cr && n >= 0 && n <= cr) {
4636 ret = dup_game(from);
4637 if (move[0] == 'P' && n > 0) {
4638 int index = (y*cr+x) * cr + (n-1);
4639 ret->pencil[index] = !ret->pencil[index];
4641 ret->grid[y*cr+x] = n;
4642 memset(ret->pencil + (y*cr+x)*cr, 0, cr);
4645 * We've made a real change to the grid. Check to see
4646 * if the game has been completed.
4648 if (!ret->completed && check_valid(cr, ret->blocks, ret->kblocks,
4649 ret->xtype, ret->grid)) {
4650 ret->completed = TRUE;
4655 return NULL; /* couldn't parse move string */
4658 /* ----------------------------------------------------------------------
4662 #define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
4663 #define GETTILESIZE(cr, w) ( (double)(w-1) / (double)(cr+1) )
4665 static void game_compute_size(game_params *params, int tilesize,
4668 /* Ick: fake up `ds->tilesize' for macro expansion purposes */
4669 struct { int tilesize; } ads, *ds = &ads;
4670 ads.tilesize = tilesize;
4672 *x = SIZE(params->c * params->r);
4673 *y = SIZE(params->c * params->r);
4676 static void game_set_size(drawing *dr, game_drawstate *ds,
4677 game_params *params, int tilesize)
4679 ds->tilesize = tilesize;
4682 static float *game_colours(frontend *fe, int *ncolours)
4684 float *ret = snewn(3 * NCOLOURS, float);
4686 frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
4688 ret[COL_XDIAGONALS * 3 + 0] = 0.9F * ret[COL_BACKGROUND * 3 + 0];
4689 ret[COL_XDIAGONALS * 3 + 1] = 0.9F * ret[COL_BACKGROUND * 3 + 1];
4690 ret[COL_XDIAGONALS * 3 + 2] = 0.9F * ret[COL_BACKGROUND * 3 + 2];
4692 ret[COL_GRID * 3 + 0] = 0.0F;
4693 ret[COL_GRID * 3 + 1] = 0.0F;
4694 ret[COL_GRID * 3 + 2] = 0.0F;
4696 ret[COL_CLUE * 3 + 0] = 0.0F;
4697 ret[COL_CLUE * 3 + 1] = 0.0F;
4698 ret[COL_CLUE * 3 + 2] = 0.0F;
4700 ret[COL_USER * 3 + 0] = 0.0F;
4701 ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
4702 ret[COL_USER * 3 + 2] = 0.0F;
4704 ret[COL_HIGHLIGHT * 3 + 0] = 0.78F * ret[COL_BACKGROUND * 3 + 0];
4705 ret[COL_HIGHLIGHT * 3 + 1] = 0.78F * ret[COL_BACKGROUND * 3 + 1];
4706 ret[COL_HIGHLIGHT * 3 + 2] = 0.78F * ret[COL_BACKGROUND * 3 + 2];
4708 ret[COL_ERROR * 3 + 0] = 1.0F;
4709 ret[COL_ERROR * 3 + 1] = 0.0F;
4710 ret[COL_ERROR * 3 + 2] = 0.0F;
4712 ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
4713 ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
4714 ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
4716 ret[COL_KILLER * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
4717 ret[COL_KILLER * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
4718 ret[COL_KILLER * 3 + 2] = 0.1F * ret[COL_BACKGROUND * 3 + 2];
4720 *ncolours = NCOLOURS;
4724 static game_drawstate *game_new_drawstate(drawing *dr, game_state *state)
4726 struct game_drawstate *ds = snew(struct game_drawstate);
4729 ds->started = FALSE;
4731 ds->xtype = state->xtype;
4732 ds->grid = snewn(cr*cr, digit);
4733 memset(ds->grid, cr+2, cr*cr);
4734 ds->pencil = snewn(cr*cr*cr, digit);
4735 memset(ds->pencil, 0, cr*cr*cr);
4736 ds->hl = snewn(cr*cr, unsigned char);
4737 memset(ds->hl, 0, cr*cr);
4739 * ds->entered_items needs one row of cr entries per entity in
4740 * which digits may not be duplicated. That's one for each row,
4741 * each column, each block, each diagonal, and each Killer cage.
4743 ds->nregions = cr*3 + 2;
4745 ds->nregions += state->kblocks->nr_blocks;
4746 ds->entered_items = snewn(cr * ds->nregions, int);
4747 ds->tilesize = 0; /* not decided yet */
4751 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
4756 sfree(ds->entered_items);
4760 static void draw_number(drawing *dr, game_drawstate *ds, game_state *state,
4761 int x, int y, int hl)
4766 int col_killer = (hl & 32 ? COL_ERROR : COL_KILLER);
4769 if (ds->grid[y*cr+x] == state->grid[y*cr+x] &&
4770 ds->hl[y*cr+x] == hl &&
4771 !memcmp(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr))
4772 return; /* no change required */
4774 tx = BORDER + x * TILE_SIZE + 1 + GRIDEXTRA;
4775 ty = BORDER + y * TILE_SIZE + 1 + GRIDEXTRA;
4779 cw = tw = TILE_SIZE-1-2*GRIDEXTRA;
4780 ch = th = TILE_SIZE-1-2*GRIDEXTRA;
4782 if (x > 0 && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[y*cr+x-1])
4783 cx -= GRIDEXTRA, cw += GRIDEXTRA;
4784 if (x+1 < cr && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[y*cr+x+1])
4786 if (y > 0 && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[(y-1)*cr+x])
4787 cy -= GRIDEXTRA, ch += GRIDEXTRA;
4788 if (y+1 < cr && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[(y+1)*cr+x])
4791 clip(dr, cx, cy, cw, ch);
4793 /* background needs erasing */
4794 draw_rect(dr, cx, cy, cw, ch,
4795 ((hl & 15) == 1 ? COL_HIGHLIGHT :
4796 (ds->xtype && (ondiag0(y*cr+x) || ondiag1(y*cr+x))) ? COL_XDIAGONALS :
4800 * Draw the corners of thick lines in corner-adjacent squares,
4801 * which jut into this square by one pixel.
4803 if (x > 0 && y > 0 && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y-1)*cr+x-1])
4804 draw_rect(dr, tx-GRIDEXTRA, ty-GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
4805 if (x+1 < cr && y > 0 && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y-1)*cr+x+1])
4806 draw_rect(dr, tx+TILE_SIZE-1-2*GRIDEXTRA, ty-GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
4807 if (x > 0 && y+1 < cr && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y+1)*cr+x-1])
4808 draw_rect(dr, tx-GRIDEXTRA, ty+TILE_SIZE-1-2*GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
4809 if (x+1 < cr && y+1 < cr && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y+1)*cr+x+1])
4810 draw_rect(dr, tx+TILE_SIZE-1-2*GRIDEXTRA, ty+TILE_SIZE-1-2*GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
4812 /* pencil-mode highlight */
4813 if ((hl & 15) == 2) {
4817 coords[2] = cx+cw/2;
4820 coords[5] = cy+ch/2;
4821 draw_polygon(dr, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
4824 if (state->kblocks) {
4825 int t = GRIDEXTRA * 3;
4826 int kcx, kcy, kcw, kch;
4828 int has_left = 0, has_right = 0, has_top = 0, has_bottom = 0;
4831 * In non-jigsaw mode, the Killer cages are placed at a
4832 * fixed offset from the outer edge of the cell dividing
4833 * lines, so that they look right whether those lines are
4834 * thick or thin. In jigsaw mode, however, doing this will
4835 * sometimes cause the cage outlines in adjacent squares to
4836 * fail to match up with each other, so we must offset a
4837 * fixed amount from the _centre_ of the cell dividing
4840 if (state->blocks->r == 1) {
4857 * First, draw the lines dividing this area from neighbouring
4860 if (x == 0 || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[y*cr+x-1])
4861 has_left = 1, kl += t;
4862 if (x+1 >= cr || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[y*cr+x+1])
4863 has_right = 1, kr -= t;
4864 if (y == 0 || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x])
4865 has_top = 1, kt += t;
4866 if (y+1 >= cr || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x])
4867 has_bottom = 1, kb -= t;
4869 draw_line(dr, kl, kt, kr, kt, col_killer);
4871 draw_line(dr, kl, kb, kr, kb, col_killer);
4873 draw_line(dr, kl, kt, kl, kb, col_killer);
4875 draw_line(dr, kr, kt, kr, kb, col_killer);
4877 * Now, take care of the corners (just as for the normal borders).
4878 * We only need a corner if there wasn't a full edge.
4880 if (x > 0 && y > 0 && !has_left && !has_top
4881 && state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x-1])
4883 draw_line(dr, kl, kt + t, kl + t, kt + t, col_killer);
4884 draw_line(dr, kl + t, kt, kl + t, kt + t, col_killer);
4886 if (x+1 < cr && y > 0 && !has_right && !has_top
4887 && state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x+1])
4889 draw_line(dr, kcx + kcw - t, kt + t, kcx + kcw, kt + t, col_killer);
4890 draw_line(dr, kcx + kcw - t, kt, kcx + kcw - t, kt + t, col_killer);
4892 if (x > 0 && y+1 < cr && !has_left && !has_bottom
4893 && state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x-1])
4895 draw_line(dr, kl, kcy + kch - t, kl + t, kcy + kch - t, col_killer);
4896 draw_line(dr, kl + t, kcy + kch - t, kl + t, kcy + kch, col_killer);
4898 if (x+1 < cr && y+1 < cr && !has_right && !has_bottom
4899 && state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x+1])
4901 draw_line(dr, kcx + kcw - t, kcy + kch - t, kcx + kcw - t, kcy + kch, col_killer);
4902 draw_line(dr, kcx + kcw - t, kcy + kch - t, kcx + kcw, kcy + kch - t, col_killer);
4907 if (state->killer && state->kgrid[y*cr+x]) {
4908 sprintf (str, "%d", state->kgrid[y*cr+x]);
4909 draw_text(dr, tx + GRIDEXTRA * 4, ty + GRIDEXTRA * 4 + TILE_SIZE/4,
4910 FONT_VARIABLE, TILE_SIZE/4, ALIGN_VNORMAL | ALIGN_HLEFT,
4914 /* new number needs drawing? */
4915 if (state->grid[y*cr+x]) {
4917 str[0] = state->grid[y*cr+x] + '0';
4919 str[0] += 'a' - ('9'+1);
4920 draw_text(dr, tx + TILE_SIZE/2, ty + TILE_SIZE/2,
4921 FONT_VARIABLE, TILE_SIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
4922 state->immutable[y*cr+x] ? COL_CLUE : (hl & 16) ? COL_ERROR : COL_USER, str);
4927 int pw, ph, minph, pbest, fontsize;
4929 /* Count the pencil marks required. */
4930 for (i = npencil = 0; i < cr; i++)
4931 if (state->pencil[(y*cr+x)*cr+i])
4938 * Determine the bounding rectangle within which we're going
4939 * to put the pencil marks.
4941 /* Start with the whole square */
4942 pl = tx + GRIDEXTRA;
4943 pr = pl + TILE_SIZE - GRIDEXTRA;
4944 pt = ty + GRIDEXTRA;
4945 pb = pt + TILE_SIZE - GRIDEXTRA;
4946 if (state->killer) {
4948 * Make space for the Killer cages. We do this
4949 * unconditionally, for uniformity between squares,
4950 * rather than making it depend on whether a Killer
4951 * cage edge is actually present on any given side.
4953 pl += GRIDEXTRA * 3;
4954 pr -= GRIDEXTRA * 3;
4955 pt += GRIDEXTRA * 3;
4956 pb -= GRIDEXTRA * 3;
4957 if (state->kgrid[y*cr+x] != 0) {
4958 /* Make further space for the Killer number. */
4965 * We arrange our pencil marks in a grid layout, with
4966 * the number of rows and columns adjusted to allow the
4967 * maximum font size.
4969 * So now we work out what the grid size ought to be.
4974 for (pw = 3; pw < max(npencil,4); pw++) {
4977 ph = (npencil + pw - 1) / pw;
4978 ph = max(ph, minph);
4979 fw = (pr - pl) / (float)pw;
4980 fh = (pb - pt) / (float)ph;
4982 if (fs > bestsize) {
4989 ph = (npencil + pw - 1) / pw;
4990 ph = max(ph, minph);
4993 * Now we've got our grid dimensions, work out the pixel
4994 * size of a grid element, and round it to the nearest
4995 * pixel. (We don't want rounding errors to make the
4996 * grid look uneven at low pixel sizes.)
4998 fontsize = min((pr - pl) / pw, (pb - pt) / ph);
5001 * Centre the resulting figure in the square.
5003 pl = tx + (TILE_SIZE - fontsize * pw) / 2;
5004 pt = ty + (TILE_SIZE - fontsize * ph) / 2;
5007 * And move it down a bit if it's collided with the
5008 * Killer cage number.
5010 if (state->killer && state->kgrid[y*cr+x] != 0) {
5011 pt = max(pt, ty + GRIDEXTRA * 3 + TILE_SIZE/4);
5015 * Now actually draw the pencil marks.
5017 for (i = j = 0; i < cr; i++)
5018 if (state->pencil[(y*cr+x)*cr+i]) {
5019 int dx = j % pw, dy = j / pw;
5024 str[0] += 'a' - ('9'+1);
5025 draw_text(dr, pl + fontsize * (2*dx+1) / 2,
5026 pt + fontsize * (2*dy+1) / 2,
5027 FONT_VARIABLE, fontsize,
5028 ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
5036 draw_update(dr, cx, cy, cw, ch);
5038 ds->grid[y*cr+x] = state->grid[y*cr+x];
5039 memcpy(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr);
5040 ds->hl[y*cr+x] = hl;
5043 static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
5044 game_state *state, int dir, game_ui *ui,
5045 float animtime, float flashtime)
5052 * The initial contents of the window are not guaranteed
5053 * and can vary with front ends. To be on the safe side,
5054 * all games should start by drawing a big
5055 * background-colour rectangle covering the whole window.
5057 draw_rect(dr, 0, 0, SIZE(cr), SIZE(cr), COL_BACKGROUND);
5060 * Draw the grid. We draw it as a big thick rectangle of
5061 * COL_GRID initially; individual calls to draw_number()
5062 * will poke the right-shaped holes in it.
5064 draw_rect(dr, BORDER-GRIDEXTRA, BORDER-GRIDEXTRA,
5065 cr*TILE_SIZE+1+2*GRIDEXTRA, cr*TILE_SIZE+1+2*GRIDEXTRA,
5070 * This array is used to keep track of rows, columns and boxes
5071 * which contain a number more than once.
5073 for (x = 0; x < cr * ds->nregions; x++)
5074 ds->entered_items[x] = 0;
5075 for (x = 0; x < cr; x++)
5076 for (y = 0; y < cr; y++) {
5077 digit d = state->grid[y*cr+x];
5082 ds->entered_items[x*cr+d-1]++;
5085 ds->entered_items[(y+cr)*cr+d-1]++;
5088 box = state->blocks->whichblock[y*cr+x];
5089 ds->entered_items[(box+2*cr)*cr+d-1]++;
5093 if (ondiag0(y*cr+x))
5094 ds->entered_items[(3*cr)*cr+d-1]++;
5095 if (ondiag1(y*cr+x))
5096 ds->entered_items[(3*cr+1)*cr+d-1]++;
5100 if (state->kblocks) {
5101 kbox = state->kblocks->whichblock[y*cr+x];
5102 ds->entered_items[(kbox+3*cr+2)*cr+d-1]++;
5108 * Draw any numbers which need redrawing.
5110 for (x = 0; x < cr; x++) {
5111 for (y = 0; y < cr; y++) {
5113 digit d = state->grid[y*cr+x];
5115 if (flashtime > 0 &&
5116 (flashtime <= FLASH_TIME/3 ||
5117 flashtime >= FLASH_TIME*2/3))
5120 /* Highlight active input areas. */
5121 if (x == ui->hx && y == ui->hy && ui->hshow)
5122 highlight = ui->hpencil ? 2 : 1;
5124 /* Mark obvious errors (ie, numbers which occur more than once
5125 * in a single row, column, or box). */
5126 if (d && (ds->entered_items[x*cr+d-1] > 1 ||
5127 ds->entered_items[(y+cr)*cr+d-1] > 1 ||
5128 ds->entered_items[(state->blocks->whichblock[y*cr+x]
5129 +2*cr)*cr+d-1] > 1 ||
5130 (ds->xtype && ((ondiag0(y*cr+x) &&
5131 ds->entered_items[(3*cr)*cr+d-1] > 1) ||
5133 ds->entered_items[(3*cr+1)*cr+d-1]>1)))||
5135 ds->entered_items[(state->kblocks->whichblock[y*cr+x]
5136 +3*cr+2)*cr+d-1] > 1)))
5139 if (d && state->kblocks) {
5140 int i, b = state->kblocks->whichblock[y*cr+x];
5141 int n_squares = state->kblocks->nr_squares[b];
5142 int sum = 0, clue = 0;
5143 for (i = 0; i < n_squares; i++) {
5144 int xy = state->kblocks->blocks[b][i];
5145 if (state->grid[xy] == 0)
5148 sum += state->grid[xy];
5149 if (state->kgrid[xy]) {
5151 clue = state->kgrid[xy];
5155 if (i == n_squares) {
5162 draw_number(dr, ds, state, x, y, highlight);
5167 * Update the _entire_ grid if necessary.
5170 draw_update(dr, 0, 0, SIZE(cr), SIZE(cr));
5175 static float game_anim_length(game_state *oldstate, game_state *newstate,
5176 int dir, game_ui *ui)
5181 static float game_flash_length(game_state *oldstate, game_state *newstate,
5182 int dir, game_ui *ui)
5184 if (!oldstate->completed && newstate->completed &&
5185 !oldstate->cheated && !newstate->cheated)
5190 static int game_status(game_state *state)
5192 return state->completed ? +1 : 0;
5195 static int game_timing_state(game_state *state, game_ui *ui)
5197 if (state->completed)
5202 static void game_print_size(game_params *params, float *x, float *y)
5207 * I'll use 9mm squares by default. They should be quite big
5208 * for this game, because players will want to jot down no end
5209 * of pencil marks in the squares.
5211 game_compute_size(params, 900, &pw, &ph);
5217 * Subfunction to draw the thick lines between cells. In order to do
5218 * this using the line-drawing rather than rectangle-drawing API (so
5219 * as to get line thicknesses to scale correctly) and yet have
5220 * correctly mitred joins between lines, we must do this by tracing
5221 * the boundary of each sub-block and drawing it in one go as a
5224 * This subfunction is also reused with thinner dotted lines to
5225 * outline the Killer cages, this time offsetting the outline toward
5226 * the interior of the affected squares.
5228 static void outline_block_structure(drawing *dr, game_drawstate *ds,
5230 struct block_structure *blocks,
5236 int x, y, dx, dy, sx, sy, sdx, sdy;
5239 * Maximum perimeter of a k-omino is 2k+2. (Proof: start
5240 * with k unconnected squares, with total perimeter 4k.
5241 * Now repeatedly join two disconnected components
5242 * together into a larger one; every time you do so you
5243 * remove at least two unit edges, and you require k-1 of
5244 * these operations to create a single connected piece, so
5245 * you must have at most 4k-2(k-1) = 2k+2 unit edges left
5248 coords = snewn(4*cr+4, int); /* 2k+2 points, 2 coords per point */
5251 * Iterate over all the blocks.
5253 for (bi = 0; bi < blocks->nr_blocks; bi++) {
5254 if (blocks->nr_squares[bi] == 0)
5258 * For each block, find a starting square within it
5259 * which has a boundary at the left.
5261 for (i = 0; i < cr; i++) {
5262 int j = blocks->blocks[bi][i];
5263 if (j % cr == 0 || blocks->whichblock[j-1] != bi)
5266 assert(i < cr); /* every block must have _some_ leftmost square */
5267 x = blocks->blocks[bi][i] % cr;
5268 y = blocks->blocks[bi][i] / cr;
5273 * Now begin tracing round the perimeter. At all
5274 * times, (x,y) describes some square within the
5275 * block, and (x+dx,y+dy) is some adjacent square
5276 * outside it; so the edge between those two squares
5277 * is always an edge of the block.
5279 sx = x, sy = y, sdx = dx, sdy = dy; /* save starting position */
5282 int cx, cy, tx, ty, nin;
5285 * Advance to the next edge, by looking at the two
5286 * squares beyond it. If they're both outside the block,
5287 * we turn right (by leaving x,y the same and rotating
5288 * dx,dy clockwise); if they're both inside, we turn
5289 * left (by rotating dx,dy anticlockwise and contriving
5290 * to leave x+dx,y+dy unchanged); if one of each, we go
5291 * straight on (and may enforce by assertion that
5292 * they're one of each the _right_ way round).
5297 nin += (tx >= 0 && tx < cr && ty >= 0 && ty < cr &&
5298 blocks->whichblock[ty*cr+tx] == bi);
5301 nin += (tx >= 0 && tx < cr && ty >= 0 && ty < cr &&
5302 blocks->whichblock[ty*cr+tx] == bi);
5311 } else if (nin == 2) {
5335 * Now enforce by assertion that we ended up
5336 * somewhere sensible.
5338 assert(x >= 0 && x < cr && y >= 0 && y < cr &&
5339 blocks->whichblock[y*cr+x] == bi);
5340 assert(x+dx < 0 || x+dx >= cr || y+dy < 0 || y+dy >= cr ||
5341 blocks->whichblock[(y+dy)*cr+(x+dx)] != bi);
5344 * Record the point we just went past at one end of the
5345 * edge. To do this, we translate (x,y) down and right
5346 * by half a unit (so they're describing a point in the
5347 * _centre_ of the square) and then translate back again
5348 * in a manner rotated by dy and dx.
5351 cx = ((2*x+1) + dy + dx) / 2;
5352 cy = ((2*y+1) - dx + dy) / 2;
5353 coords[2*n+0] = BORDER + cx * TILE_SIZE;
5354 coords[2*n+1] = BORDER + cy * TILE_SIZE;
5355 coords[2*n+0] -= dx * inset;
5356 coords[2*n+1] -= dy * inset;
5359 * We turned right, so inset this corner back along
5360 * the edge towards the centre of the square.
5362 coords[2*n+0] -= dy * inset;
5363 coords[2*n+1] += dx * inset;
5364 } else if (nin == 2) {
5366 * We turned left, so inset this corner further
5367 * _out_ along the edge into the next square.
5369 coords[2*n+0] += dy * inset;
5370 coords[2*n+1] -= dx * inset;
5374 } while (x != sx || y != sy || dx != sdx || dy != sdy);
5377 * That's our polygon; now draw it.
5379 draw_polygon(dr, coords, n, -1, ink);
5385 static void game_print(drawing *dr, game_state *state, int tilesize)
5388 int ink = print_mono_colour(dr, 0);
5391 /* Ick: fake up `ds->tilesize' for macro expansion purposes */
5392 game_drawstate ads, *ds = &ads;
5393 game_set_size(dr, ds, NULL, tilesize);
5398 print_line_width(dr, 3 * TILE_SIZE / 40);
5399 draw_rect_outline(dr, BORDER, BORDER, cr*TILE_SIZE, cr*TILE_SIZE, ink);
5402 * Highlight X-diagonal squares.
5406 int xhighlight = print_grey_colour(dr, 0.90F);
5408 for (i = 0; i < cr; i++)
5409 draw_rect(dr, BORDER + i*TILE_SIZE, BORDER + i*TILE_SIZE,
5410 TILE_SIZE, TILE_SIZE, xhighlight);
5411 for (i = 0; i < cr; i++)
5412 if (i*2 != cr-1) /* avoid redoing centre square, just for fun */
5413 draw_rect(dr, BORDER + i*TILE_SIZE,
5414 BORDER + (cr-1-i)*TILE_SIZE,
5415 TILE_SIZE, TILE_SIZE, xhighlight);
5421 for (x = 1; x < cr; x++) {
5422 print_line_width(dr, TILE_SIZE / 40);
5423 draw_line(dr, BORDER+x*TILE_SIZE, BORDER,
5424 BORDER+x*TILE_SIZE, BORDER+cr*TILE_SIZE, ink);
5426 for (y = 1; y < cr; y++) {
5427 print_line_width(dr, TILE_SIZE / 40);
5428 draw_line(dr, BORDER, BORDER+y*TILE_SIZE,
5429 BORDER+cr*TILE_SIZE, BORDER+y*TILE_SIZE, ink);
5433 * Thick lines between cells.
5435 print_line_width(dr, 3 * TILE_SIZE / 40);
5436 outline_block_structure(dr, ds, state, state->blocks, ink, 0);
5439 * Killer cages and their totals.
5441 if (state->kblocks) {
5442 print_line_width(dr, TILE_SIZE / 40);
5443 print_line_dotted(dr, TRUE);
5444 outline_block_structure(dr, ds, state, state->kblocks, ink,
5445 5 * TILE_SIZE / 40);
5446 print_line_dotted(dr, FALSE);
5447 for (y = 0; y < cr; y++)
5448 for (x = 0; x < cr; x++)
5449 if (state->kgrid[y*cr+x]) {
5451 sprintf(str, "%d", state->kgrid[y*cr+x]);
5453 BORDER+x*TILE_SIZE + 7*TILE_SIZE/40,
5454 BORDER+y*TILE_SIZE + 16*TILE_SIZE/40,
5455 FONT_VARIABLE, TILE_SIZE/4,
5456 ALIGN_VNORMAL | ALIGN_HLEFT,
5462 * Standard (non-Killer) clue numbers.
5464 for (y = 0; y < cr; y++)
5465 for (x = 0; x < cr; x++)
5466 if (state->grid[y*cr+x]) {
5469 str[0] = state->grid[y*cr+x] + '0';
5471 str[0] += 'a' - ('9'+1);
5472 draw_text(dr, BORDER + x*TILE_SIZE + TILE_SIZE/2,
5473 BORDER + y*TILE_SIZE + TILE_SIZE/2,
5474 FONT_VARIABLE, TILE_SIZE/2,
5475 ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
5480 #define thegame solo
5483 const struct game thegame = {
5484 "Solo", "games.solo", "solo",
5491 TRUE, game_configure, custom_params,
5499 TRUE, game_can_format_as_text_now, game_text_format,
5507 PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
5510 game_free_drawstate,
5515 TRUE, FALSE, game_print_size, game_print,
5516 FALSE, /* wants_statusbar */
5517 FALSE, game_timing_state,
5518 REQUIRE_RBUTTON | REQUIRE_NUMPAD, /* flags */
5521 #ifdef STANDALONE_SOLVER
5523 int main(int argc, char **argv)
5527 char *id = NULL, *desc, *err;
5529 struct difficulty dlev;
5531 while (--argc > 0) {
5533 if (!strcmp(p, "-v")) {
5534 solver_show_working = TRUE;
5535 } else if (!strcmp(p, "-g")) {
5537 } else if (*p == '-') {
5538 fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
5546 fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
5550 desc = strchr(id, ':');
5552 fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
5557 p = default_params();
5558 decode_params(p, id);
5559 err = validate_desc(p, desc);
5561 fprintf(stderr, "%s: %s\n", argv[0], err);
5564 s = new_game(NULL, p, desc);
5566 dlev.maxdiff = DIFF_RECURSIVE;
5567 dlev.maxkdiff = DIFF_KINTERSECT;
5568 solver(s->cr, s->blocks, s->kblocks, s->xtype, s->grid, s->kgrid, &dlev);
5570 printf("Difficulty rating: %s\n",
5571 dlev.diff==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)":
5572 dlev.diff==DIFF_SIMPLE ? "Basic (row/column/number elimination required)":
5573 dlev.diff==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)":
5574 dlev.diff==DIFF_SET ? "Advanced (set elimination required)":
5575 dlev.diff==DIFF_EXTREME ? "Extreme (complex non-recursive techniques required)":
5576 dlev.diff==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)":
5577 dlev.diff==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)":
5578 dlev.diff==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)":
5579 "INTERNAL ERROR: unrecognised difficulty code");
5581 printf("Killer difficulty: %s\n",
5582 dlev.kdiff==DIFF_KSINGLE ? "Trivial (single square cages only)":
5583 dlev.kdiff==DIFF_KMINMAX ? "Simple (maximum sum analysis required)":
5584 dlev.kdiff==DIFF_KSUMS ? "Intermediate (sum possibilities)":
5585 dlev.kdiff==DIFF_KINTERSECT ? "Advanced (sum region intersections)":
5586 "INTERNAL ERROR: unrecognised difficulty code");
5588 printf("%s\n", grid_text_format(s->cr, s->blocks, s->xtype, s->grid));
5596 /* vim: set shiftwidth=4 tabstop=8: */