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 nb
->blocknames
= (char **)smalloc(b
->c
* b
->r
*(sizeof(char *)+80));
586 memcpy(nb
->blocknames
, b
->blocknames
, b
->c
* b
->r
*(sizeof(char *)+80));
589 for (i
= 0; i
< b
->c
* b
->r
; i
++)
590 if (b
->blocknames
[i
] == NULL
)
591 nb
->blocknames
[i
] = NULL
;
593 nb
->blocknames
[i
] = ((char *)nb
->blocknames
) + (b
->blocknames
[i
] - (char *)b
->blocknames
);
599 static void split_block(struct block_structure
*b
, int *squares
, int nr_squares
)
602 int previous_block
= b
->whichblock
[squares
[0]];
603 int newblock
= b
->nr_blocks
;
605 assert(b
->max_nr_squares
>= nr_squares
);
606 assert(b
->nr_squares
[previous_block
] > nr_squares
);
609 b
->blocks_data
= sresize(b
->blocks_data
,
610 b
->nr_blocks
* b
->max_nr_squares
, int);
611 b
->nr_squares
= sresize(b
->nr_squares
, b
->nr_blocks
, int);
613 b
->blocks
= snewn(b
->nr_blocks
, int *);
614 for (i
= 0; i
< b
->nr_blocks
; i
++)
615 b
->blocks
[i
] = b
->blocks_data
+ i
*b
->max_nr_squares
;
616 for (i
= 0; i
< nr_squares
; i
++) {
617 assert(b
->whichblock
[squares
[i
]] == previous_block
);
618 b
->whichblock
[squares
[i
]] = newblock
;
619 b
->blocks
[newblock
][i
] = squares
[i
];
621 for (i
= j
= 0; i
< b
->nr_squares
[previous_block
]; i
++) {
623 int sq
= b
->blocks
[previous_block
][i
];
624 for (k
= 0; k
< nr_squares
; k
++)
625 if (squares
[k
] == sq
)
628 b
->blocks
[previous_block
][j
++] = sq
;
630 b
->nr_squares
[previous_block
] -= nr_squares
;
631 b
->nr_squares
[newblock
] = nr_squares
;
634 static void remove_from_block(struct block_structure
*blocks
, int b
, int n
)
637 blocks
->whichblock
[n
] = -1;
638 for (i
= j
= 0; i
< blocks
->nr_squares
[b
]; i
++)
639 if (blocks
->blocks
[b
][i
] != n
)
640 blocks
->blocks
[b
][j
++] = blocks
->blocks
[b
][i
];
642 blocks
->nr_squares
[b
]--;
645 /* ----------------------------------------------------------------------
648 * This solver is used for two purposes:
649 * + to check solubility of a grid as we gradually remove numbers
651 * + to solve an externally generated puzzle when the user selects
654 * It supports a variety of specific modes of reasoning. By
655 * enabling or disabling subsets of these modes we can arrange a
656 * range of difficulty levels.
660 * Modes of reasoning currently supported:
662 * - Positional elimination: a number must go in a particular
663 * square because all the other empty squares in a given
664 * row/col/blk are ruled out.
666 * - Killer minmax elimination: for killer-type puzzles, a number
667 * is impossible if choosing it would cause the sum in a killer
668 * region to be guaranteed to be too large or too small.
670 * - Numeric elimination: a square must have a particular number
671 * in because all the other numbers that could go in it are
674 * - Intersectional analysis: given two domains which overlap
675 * (hence one must be a block, and the other can be a row or
676 * col), if the possible locations for a particular number in
677 * one of the domains can be narrowed down to the overlap, then
678 * that number can be ruled out everywhere but the overlap in
679 * the other domain too.
681 * - Set elimination: if there is a subset of the empty squares
682 * within a domain such that the union of the possible numbers
683 * in that subset has the same size as the subset itself, then
684 * those numbers can be ruled out everywhere else in the domain.
685 * (For example, if there are five empty squares and the
686 * possible numbers in each are 12, 23, 13, 134 and 1345, then
687 * the first three empty squares form such a subset: the numbers
688 * 1, 2 and 3 _must_ be in those three squares in some
689 * permutation, and hence we can deduce none of them can be in
690 * the fourth or fifth squares.)
691 * + You can also see this the other way round, concentrating
692 * on numbers rather than squares: if there is a subset of
693 * the unplaced numbers within a domain such that the union
694 * of all their possible positions has the same size as the
695 * subset itself, then all other numbers can be ruled out for
696 * those positions. However, it turns out that this is
697 * exactly equivalent to the first formulation at all times:
698 * there is a 1-1 correspondence between suitable subsets of
699 * the unplaced numbers and suitable subsets of the unfilled
700 * places, found by taking the _complement_ of the union of
701 * the numbers' possible positions (or the spaces' possible
704 * - Forcing chains (see comment for solver_forcing().)
706 * - Recursion. If all else fails, we pick one of the currently
707 * most constrained empty squares and take a random guess at its
708 * contents, then continue solving on that basis and see if we
712 struct solver_usage
{
714 struct block_structure
*blocks
, *kblocks
, *extra_cages
;
716 * We set up a cubic array, indexed by x, y and digit; each
717 * element of this array is TRUE or FALSE according to whether
718 * or not that digit _could_ in principle go in that position.
720 * The way to index this array is cube[(y*cr+x)*cr+n-1]; there
721 * are macros below to help with this.
725 * This is the grid in which we write down our final
726 * deductions. y-coordinates in here are _not_ transformed.
730 * For killer-type puzzles, kclues holds the secondary clue for
731 * each cage. For derived cages, the clue is in extra_clues.
733 digit
*kclues
, *extra_clues
;
735 * Now we keep track, at a slightly higher level, of what we
736 * have yet to work out, to prevent doing the same deduction
739 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
741 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
743 /* blk[i*cr+n-1] TRUE if digit n has been placed in block i */
745 /* diag[i*cr+n-1] TRUE if digit n has been placed in diagonal i */
746 unsigned char *diag
; /* diag 0 is \, 1 is / */
752 #define cubepos2(xy,n) ((xy)*usage->cr+(n)-1)
753 #define cubepos(x,y,n) cubepos2((y)*usage->cr+(x),n)
754 #define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
755 #define cube2(xy,n) (usage->cube[cubepos2(xy,n)])
757 #define ondiag0(xy) ((xy) % (cr+1) == 0)
758 #define ondiag1(xy) ((xy) % (cr-1) == 0 && (xy) > 0 && (xy) < cr*cr-1)
759 #define diag0(i) ((i) * (cr+1))
760 #define diag1(i) ((i+1) * (cr-1))
763 * Function called when we are certain that a particular square has
764 * a particular number in it. The y-coordinate passed in here is
767 static void solver_place(struct solver_usage
*usage
, int x
, int y
, int n
)
770 int sqindex
= y
*cr
+x
;
776 * Rule out all other numbers in this square.
778 for (i
= 1; i
<= cr
; i
++)
783 * Rule out this number in all other positions in the row.
785 for (i
= 0; i
< cr
; i
++)
790 * Rule out this number in all other positions in the column.
792 for (i
= 0; i
< cr
; i
++)
797 * Rule out this number in all other positions in the block.
799 bi
= usage
->blocks
->whichblock
[sqindex
];
800 for (i
= 0; i
< cr
; i
++) {
801 int bp
= usage
->blocks
->blocks
[bi
][i
];
807 * Enter the number in the result grid.
809 usage
->grid
[sqindex
] = n
;
812 * Cross out this number from the list of numbers left to place
813 * in its row, its column and its block.
815 usage
->row
[y
*cr
+n
-1] = usage
->col
[x
*cr
+n
-1] =
816 usage
->blk
[bi
*cr
+n
-1] = TRUE
;
819 if (ondiag0(sqindex
)) {
820 for (i
= 0; i
< cr
; i
++)
821 if (diag0(i
) != sqindex
)
822 cube2(diag0(i
),n
) = FALSE
;
823 usage
->diag
[n
-1] = TRUE
;
825 if (ondiag1(sqindex
)) {
826 for (i
= 0; i
< cr
; i
++)
827 if (diag1(i
) != sqindex
)
828 cube2(diag1(i
),n
) = FALSE
;
829 usage
->diag
[cr
+n
-1] = TRUE
;
834 static int solver_elim(struct solver_usage
*usage
, int *indices
835 #ifdef STANDALONE_SOLVER
844 * Count the number of set bits within this section of the
849 for (i
= 0; i
< cr
; i
++)
850 if (usage
->cube
[indices
[i
]]) {
864 if (!usage
->grid
[y
*cr
+x
]) {
865 #ifdef STANDALONE_SOLVER
866 if (solver_show_working
) {
868 printf("%*s", solver_recurse_depth
*4, "");
872 printf(":\n%*s placing %d at (%d,%d)\n",
873 solver_recurse_depth
*4, "", n
, 1+x
, 1+y
);
876 solver_place(usage
, x
, y
, n
);
880 #ifdef STANDALONE_SOLVER
881 if (solver_show_working
) {
883 printf("%*s", solver_recurse_depth
*4, "");
887 printf(":\n%*s no possibilities available\n",
888 solver_recurse_depth
*4, "");
897 static int solver_intersect(struct solver_usage
*usage
,
898 int *indices1
, int *indices2
899 #ifdef STANDALONE_SOLVER
908 * Loop over the first domain and see if there's any set bit
909 * not also in the second.
911 for (i
= j
= 0; i
< cr
; i
++) {
913 while (j
< cr
&& indices2
[j
] < p
)
915 if (usage
->cube
[p
]) {
916 if (j
< cr
&& indices2
[j
] == p
)
917 continue; /* both domains contain this index */
919 return 0; /* there is, so we can't deduce */
924 * We have determined that all set bits in the first domain are
925 * within its overlap with the second. So loop over the second
926 * domain and remove all set bits that aren't also in that
927 * overlap; return +1 iff we actually _did_ anything.
930 for (i
= j
= 0; i
< cr
; i
++) {
932 while (j
< cr
&& indices1
[j
] < p
)
934 if (usage
->cube
[p
] && (j
>= cr
|| indices1
[j
] != p
)) {
935 #ifdef STANDALONE_SOLVER
936 if (solver_show_working
) {
941 printf("%*s", solver_recurse_depth
*4, "");
953 printf("%*s ruling out %d at (%d,%d)\n",
954 solver_recurse_depth
*4, "", pn
, 1+px
, 1+py
);
957 ret
= +1; /* we did something */
965 struct solver_scratch
{
966 unsigned char *grid
, *rowidx
, *colidx
, *set
;
967 int *neighbours
, *bfsqueue
;
968 int *indexlist
, *indexlist2
;
969 #ifdef STANDALONE_SOLVER
974 static int solver_set(struct solver_usage
*usage
,
975 struct solver_scratch
*scratch
,
977 #ifdef STANDALONE_SOLVER
984 unsigned char *grid
= scratch
->grid
;
985 unsigned char *rowidx
= scratch
->rowidx
;
986 unsigned char *colidx
= scratch
->colidx
;
987 unsigned char *set
= scratch
->set
;
990 * We are passed a cr-by-cr matrix of booleans. Our first job
991 * is to winnow it by finding any definite placements - i.e.
992 * any row with a solitary 1 - and discarding that row and the
993 * column containing the 1.
995 memset(rowidx
, TRUE
, cr
);
996 memset(colidx
, TRUE
, cr
);
997 for (i
= 0; i
< cr
; i
++) {
998 int count
= 0, first
= -1;
999 for (j
= 0; j
< cr
; j
++)
1000 if (usage
->cube
[indices
[i
*cr
+j
]])
1004 * If count == 0, then there's a row with no 1s at all and
1005 * the puzzle is internally inconsistent. However, we ought
1006 * to have caught this already during the simpler reasoning
1007 * methods, so we can safely fail an assertion if we reach
1012 rowidx
[i
] = colidx
[first
] = FALSE
;
1016 * Convert each of rowidx/colidx from a list of 0s and 1s to a
1017 * list of the indices of the 1s.
1019 for (i
= j
= 0; i
< cr
; i
++)
1023 for (i
= j
= 0; i
< cr
; i
++)
1029 * And create the smaller matrix.
1031 for (i
= 0; i
< n
; i
++)
1032 for (j
= 0; j
< n
; j
++)
1033 grid
[i
*cr
+j
] = usage
->cube
[indices
[rowidx
[i
]*cr
+colidx
[j
]]];
1036 * Having done that, we now have a matrix in which every row
1037 * has at least two 1s in. Now we search to see if we can find
1038 * a rectangle of zeroes (in the set-theoretic sense of
1039 * `rectangle', i.e. a subset of rows crossed with a subset of
1040 * columns) whose width and height add up to n.
1047 * We have a candidate set. If its size is <=1 or >=n-1
1048 * then we move on immediately.
1050 if (count
> 1 && count
< n
-1) {
1052 * The number of rows we need is n-count. See if we can
1053 * find that many rows which each have a zero in all
1054 * the positions listed in `set'.
1057 for (i
= 0; i
< n
; i
++) {
1059 for (j
= 0; j
< n
; j
++)
1060 if (set
[j
] && grid
[i
*cr
+j
]) {
1069 * We expect never to be able to get _more_ than
1070 * n-count suitable rows: this would imply that (for
1071 * example) there are four numbers which between them
1072 * have at most three possible positions, and hence it
1073 * indicates a faulty deduction before this point or
1074 * even a bogus clue.
1076 if (rows
> n
- count
) {
1077 #ifdef STANDALONE_SOLVER
1078 if (solver_show_working
) {
1080 printf("%*s", solver_recurse_depth
*4,
1085 printf(":\n%*s contradiction reached\n",
1086 solver_recurse_depth
*4, "");
1092 if (rows
>= n
- count
) {
1093 int progress
= FALSE
;
1096 * We've got one! Now, for each row which _doesn't_
1097 * satisfy the criterion, eliminate all its set
1098 * bits in the positions _not_ listed in `set'.
1099 * Return +1 (meaning progress has been made) if we
1100 * successfully eliminated anything at all.
1102 * This involves referring back through
1103 * rowidx/colidx in order to work out which actual
1104 * positions in the cube to meddle with.
1106 for (i
= 0; i
< n
; i
++) {
1108 for (j
= 0; j
< n
; j
++)
1109 if (set
[j
] && grid
[i
*cr
+j
]) {
1114 for (j
= 0; j
< n
; j
++)
1115 if (!set
[j
] && grid
[i
*cr
+j
]) {
1116 int fpos
= indices
[rowidx
[i
]*cr
+colidx
[j
]];
1117 #ifdef STANDALONE_SOLVER
1118 if (solver_show_working
) {
1123 printf("%*s", solver_recurse_depth
*4,
1136 printf("%*s ruling out %d at (%d,%d)\n",
1137 solver_recurse_depth
*4, "",
1142 usage
->cube
[fpos
] = FALSE
;
1154 * Binary increment: change the rightmost 0 to a 1, and
1155 * change all 1s to the right of it to 0s.
1158 while (i
> 0 && set
[i
-1])
1159 set
[--i
] = 0, count
--;
1161 set
[--i
] = 1, count
++;
1170 * Look for forcing chains. A forcing chain is a path of
1171 * pairwise-exclusive squares (i.e. each pair of adjacent squares
1172 * in the path are in the same row, column or block) with the
1173 * following properties:
1175 * (a) Each square on the path has precisely two possible numbers.
1177 * (b) Each pair of squares which are adjacent on the path share
1178 * at least one possible number in common.
1180 * (c) Each square in the middle of the path shares _both_ of its
1181 * numbers with at least one of its neighbours (not the same
1182 * one with both neighbours).
1184 * These together imply that at least one of the possible number
1185 * choices at one end of the path forces _all_ the rest of the
1186 * numbers along the path. In order to make real use of this, we
1187 * need further properties:
1189 * (c) Ruling out some number N from the square at one end of the
1190 * path forces the square at the other end to take the same
1193 * (d) The two end squares are both in line with some third
1196 * (e) That third square currently has N as a possibility.
1198 * If we can find all of that lot, we can deduce that at least one
1199 * of the two ends of the forcing chain has number N, and that
1200 * therefore the mutually adjacent third square does not.
1202 * To find forcing chains, we're going to start a bfs at each
1203 * suitable square, once for each of its two possible numbers.
1205 static int solver_forcing(struct solver_usage
*usage
,
1206 struct solver_scratch
*scratch
)
1209 int *bfsqueue
= scratch
->bfsqueue
;
1210 #ifdef STANDALONE_SOLVER
1211 int *bfsprev
= scratch
->bfsprev
;
1213 unsigned char *number
= scratch
->grid
;
1214 int *neighbours
= scratch
->neighbours
;
1217 for (y
= 0; y
< cr
; y
++)
1218 for (x
= 0; x
< cr
; x
++) {
1222 * If this square doesn't have exactly two candidate
1223 * numbers, don't try it.
1225 * In this loop we also sum the candidate numbers,
1226 * which is a nasty hack to allow us to quickly find
1227 * `the other one' (since we will shortly know there
1230 for (count
= t
= 0, n
= 1; n
<= cr
; n
++)
1237 * Now attempt a bfs for each candidate.
1239 for (n
= 1; n
<= cr
; n
++)
1240 if (cube(x
, y
, n
)) {
1241 int orign
, currn
, head
, tail
;
1248 memset(number
, cr
+1, cr
*cr
);
1250 bfsqueue
[tail
++] = y
*cr
+x
;
1251 #ifdef STANDALONE_SOLVER
1252 bfsprev
[y
*cr
+x
] = -1;
1254 number
[y
*cr
+x
] = t
- n
;
1256 while (head
< tail
) {
1257 int xx
, yy
, nneighbours
, xt
, yt
, i
;
1259 xx
= bfsqueue
[head
++];
1263 currn
= number
[yy
*cr
+xx
];
1266 * Find neighbours of yy,xx.
1269 for (yt
= 0; yt
< cr
; yt
++)
1270 neighbours
[nneighbours
++] = yt
*cr
+xx
;
1271 for (xt
= 0; xt
< cr
; xt
++)
1272 neighbours
[nneighbours
++] = yy
*cr
+xt
;
1273 xt
= usage
->blocks
->whichblock
[yy
*cr
+xx
];
1274 for (yt
= 0; yt
< cr
; yt
++)
1275 neighbours
[nneighbours
++] = usage
->blocks
->blocks
[xt
][yt
];
1277 int sqindex
= yy
*cr
+xx
;
1278 if (ondiag0(sqindex
)) {
1279 for (i
= 0; i
< cr
; i
++)
1280 neighbours
[nneighbours
++] = diag0(i
);
1282 if (ondiag1(sqindex
)) {
1283 for (i
= 0; i
< cr
; i
++)
1284 neighbours
[nneighbours
++] = diag1(i
);
1289 * Try visiting each of those neighbours.
1291 for (i
= 0; i
< nneighbours
; i
++) {
1294 xt
= neighbours
[i
] % cr
;
1295 yt
= neighbours
[i
] / cr
;
1298 * We need this square to not be
1299 * already visited, and to include
1300 * currn as a possible number.
1302 if (number
[yt
*cr
+xt
] <= cr
)
1304 if (!cube(xt
, yt
, currn
))
1308 * Don't visit _this_ square a second
1311 if (xt
== xx
&& yt
== yy
)
1315 * To continue with the bfs, we need
1316 * this square to have exactly two
1319 for (cc
= tt
= 0, nn
= 1; nn
<= cr
; nn
++)
1320 if (cube(xt
, yt
, nn
))
1323 bfsqueue
[tail
++] = yt
*cr
+xt
;
1324 #ifdef STANDALONE_SOLVER
1325 bfsprev
[yt
*cr
+xt
] = yy
*cr
+xx
;
1327 number
[yt
*cr
+xt
] = tt
- currn
;
1331 * One other possibility is that this
1332 * might be the square in which we can
1333 * make a real deduction: if it's
1334 * adjacent to x,y, and currn is equal
1335 * to the original number we ruled out.
1337 if (currn
== orign
&&
1338 (xt
== x
|| yt
== y
||
1339 (usage
->blocks
->whichblock
[yt
*cr
+xt
] == usage
->blocks
->whichblock
[y
*cr
+x
]) ||
1340 (usage
->diag
&& ((ondiag0(yt
*cr
+xt
) && ondiag0(y
*cr
+x
)) ||
1341 (ondiag1(yt
*cr
+xt
) && ondiag1(y
*cr
+x
)))))) {
1342 #ifdef STANDALONE_SOLVER
1343 if (solver_show_working
) {
1346 printf("%*sforcing chain, %d at ends of ",
1347 solver_recurse_depth
*4, "", orign
);
1351 printf("%s(%d,%d)", sep
, 1+xl
,
1353 xl
= bfsprev
[yl
*cr
+xl
];
1360 printf("\n%*s ruling out %d at (%d,%d)\n",
1361 solver_recurse_depth
*4, "",
1365 cube(xt
, yt
, orign
) = FALSE
;
1376 static int solver_killer_minmax(struct solver_usage
*usage
,
1377 struct block_structure
*cages
, digit
*clues
,
1379 #ifdef STANDALONE_SOLVER
1387 int nsquares
= cages
->nr_squares
[b
];
1392 for (i
= 0; i
< nsquares
; i
++) {
1393 int n
, x
= cages
->blocks
[b
][i
];
1395 for (n
= 1; n
<= cr
; n
++)
1397 int maxval
= 0, minval
= 0;
1399 for (j
= 0; j
< nsquares
; j
++) {
1401 int y
= cages
->blocks
[b
][j
];
1404 for (m
= 1; m
<= cr
; m
++)
1409 for (m
= cr
; m
> 0; m
--)
1415 if (maxval
+ n
< clues
[b
]) {
1416 cube2(x
, n
) = FALSE
;
1418 #ifdef STANDALONE_SOLVER
1419 if (solver_show_working
)
1420 printf("%*s ruling out %d at (%d,%d) as too low %s\n",
1421 solver_recurse_depth
*4, "killer minmax analysis",
1422 n
, 1 + x
%cr
, 1 + x
/cr
, extra
);
1425 if (minval
+ n
> clues
[b
]) {
1426 cube2(x
, n
) = FALSE
;
1428 #ifdef STANDALONE_SOLVER
1429 if (solver_show_working
)
1430 printf("%*s ruling out %d at (%d,%d) as too high %s\n",
1431 solver_recurse_depth
*4, "killer minmax analysis",
1432 n
, 1 + x
%cr
, 1 + x
/cr
, extra
);
1440 static int solver_killer_sums(struct solver_usage
*usage
, int b
,
1441 struct block_structure
*cages
, int clue
,
1443 #ifdef STANDALONE_SOLVER
1444 , const char *cage_type
1449 int i
, ret
, max_sums
;
1450 int nsquares
= cages
->nr_squares
[b
];
1451 unsigned long *sumbits
, possible_addends
;
1454 assert(nsquares
== 0);
1457 assert(nsquares
> 0);
1462 if (!cage_is_region
) {
1463 int known_row
= -1, known_col
= -1, known_block
= -1;
1465 * Verify that the cage lies entirely within one region,
1466 * so that using the precomputed sums is valid.
1468 for (i
= 0; i
< nsquares
; i
++) {
1469 int x
= cages
->blocks
[b
][i
];
1471 assert(usage
->grid
[x
] == 0);
1476 known_block
= usage
->blocks
->whichblock
[x
];
1478 if (known_row
!= x
/cr
)
1480 if (known_col
!= x
%cr
)
1482 if (known_block
!= usage
->blocks
->whichblock
[x
])
1486 if (known_block
== -1 && known_col
== -1 && known_row
== -1)
1489 if (nsquares
== 2) {
1490 if (clue
< 3 || clue
> 17)
1493 sumbits
= sum_bits2
[clue
];
1494 max_sums
= MAX_2SUMS
;
1495 } else if (nsquares
== 3) {
1496 if (clue
< 6 || clue
> 24)
1499 sumbits
= sum_bits3
[clue
];
1500 max_sums
= MAX_3SUMS
;
1502 if (clue
< 10 || clue
> 30)
1505 sumbits
= sum_bits4
[clue
];
1506 max_sums
= MAX_4SUMS
;
1509 * For every possible way to get the sum, see if there is
1510 * one square in the cage that disallows all the required
1511 * addends. If we find one such square, this way to compute
1512 * the sum is impossible.
1514 possible_addends
= 0;
1515 for (i
= 0; i
< max_sums
; i
++) {
1517 unsigned long bits
= sumbits
[i
];
1522 for (j
= 0; j
< nsquares
; j
++) {
1524 unsigned long square_bits
= bits
;
1525 int x
= cages
->blocks
[b
][j
];
1526 for (n
= 1; n
<= cr
; n
++)
1528 square_bits
&= ~(1L << n
);
1529 if (square_bits
== 0) {
1534 possible_addends
|= bits
;
1537 * Now we know which addends can possibly be used to
1538 * compute the sum. Remove all other digits from the
1539 * set of possibilities.
1541 if (possible_addends
== 0)
1545 for (i
= 0; i
< nsquares
; i
++) {
1547 int x
= cages
->blocks
[b
][i
];
1548 for (n
= 1; n
<= cr
; n
++) {
1551 if ((possible_addends
& (1 << n
)) == 0) {
1552 cube2(x
, n
) = FALSE
;
1554 #ifdef STANDALONE_SOLVER
1555 if (solver_show_working
) {
1556 printf("%*s using %s\n",
1557 solver_recurse_depth
*4, "killer sums analysis",
1559 printf("%*s ruling out %d at (%d,%d) due to impossible %d-sum\n",
1560 solver_recurse_depth
*4, "",
1561 n
, 1 + x
%cr
, 1 + x
/cr
, nsquares
);
1570 static int filter_whole_cages(struct solver_usage
*usage
, int *squares
, int n
,
1576 /* First, filter squares with a clue. */
1577 for (i
= j
= 0; i
< n
; i
++)
1578 if (usage
->grid
[squares
[i
]])
1579 *filtered_sum
+= usage
->grid
[squares
[i
]];
1581 squares
[j
++] = squares
[i
];
1585 * Filter all cages that are covered entirely by the list of
1589 for (b
= 0; b
< usage
->kblocks
->nr_blocks
&& off
< n
; b
++) {
1590 int b_squares
= usage
->kblocks
->nr_squares
[b
];
1597 * Find all squares of block b that lie in our list,
1598 * and make them contiguous at off, which is the current position
1599 * in the output list.
1601 for (i
= 0; i
< b_squares
; i
++) {
1602 for (j
= off
; j
< n
; j
++)
1603 if (squares
[j
] == usage
->kblocks
->blocks
[b
][i
]) {
1604 int t
= squares
[off
+ matched
];
1605 squares
[off
+ matched
] = squares
[j
];
1611 /* If so, filter out all squares of b from the list. */
1612 if (matched
!= usage
->kblocks
->nr_squares
[b
]) {
1616 memmove(squares
+ off
, squares
+ off
+ matched
,
1617 (n
- off
- matched
) * sizeof *squares
);
1620 *filtered_sum
+= usage
->kclues
[b
];
1626 static struct solver_scratch
*solver_new_scratch(struct solver_usage
*usage
)
1628 struct solver_scratch
*scratch
= snew(struct solver_scratch
);
1630 scratch
->grid
= snewn(cr
*cr
, unsigned char);
1631 scratch
->rowidx
= snewn(cr
, unsigned char);
1632 scratch
->colidx
= snewn(cr
, unsigned char);
1633 scratch
->set
= snewn(cr
, unsigned char);
1634 scratch
->neighbours
= snewn(5*cr
, int);
1635 scratch
->bfsqueue
= snewn(cr
*cr
, int);
1636 #ifdef STANDALONE_SOLVER
1637 scratch
->bfsprev
= snewn(cr
*cr
, int);
1639 scratch
->indexlist
= snewn(cr
*cr
, int); /* used for set elimination */
1640 scratch
->indexlist2
= snewn(cr
, int); /* only used for intersect() */
1644 static void solver_free_scratch(struct solver_scratch
*scratch
)
1646 #ifdef STANDALONE_SOLVER
1647 sfree(scratch
->bfsprev
);
1649 sfree(scratch
->bfsqueue
);
1650 sfree(scratch
->neighbours
);
1651 sfree(scratch
->set
);
1652 sfree(scratch
->colidx
);
1653 sfree(scratch
->rowidx
);
1654 sfree(scratch
->grid
);
1655 sfree(scratch
->indexlist
);
1656 sfree(scratch
->indexlist2
);
1661 * Used for passing information about difficulty levels between the solver
1665 /* Maximum levels allowed. */
1666 int maxdiff
, maxkdiff
;
1667 /* Levels reached by the solver. */
1671 static void solver(int cr
, struct block_structure
*blocks
,
1672 struct block_structure
*kblocks
, int xtype
,
1673 digit
*grid
, digit
*kgrid
, struct difficulty
*dlev
)
1675 struct solver_usage
*usage
;
1676 struct solver_scratch
*scratch
;
1677 int x
, y
, b
, i
, n
, ret
;
1678 int diff
= DIFF_BLOCK
;
1679 int kdiff
= DIFF_KSINGLE
;
1682 * Set up a usage structure as a clean slate (everything
1685 usage
= snew(struct solver_usage
);
1687 usage
->blocks
= blocks
;
1689 usage
->kblocks
= dup_block_structure(kblocks
);
1690 usage
->extra_cages
= alloc_block_structure (kblocks
->c
, kblocks
->r
,
1691 cr
* cr
, cr
, cr
* cr
);
1692 usage
->extra_clues
= snewn(cr
*cr
, digit
);
1694 usage
->kblocks
= usage
->extra_cages
= NULL
;
1695 usage
->extra_clues
= NULL
;
1697 usage
->cube
= snewn(cr
*cr
*cr
, unsigned char);
1698 usage
->grid
= grid
; /* write straight back to the input */
1700 int nclues
= kblocks
->nr_blocks
;
1702 * Allow for expansion of the killer regions, the absolute
1703 * limit is obviously one region per square.
1705 usage
->kclues
= snewn(cr
*cr
, digit
);
1706 for (i
= 0; i
< nclues
; i
++) {
1707 for (n
= 0; n
< kblocks
->nr_squares
[i
]; n
++)
1708 if (kgrid
[kblocks
->blocks
[i
][n
]] != 0)
1709 usage
->kclues
[i
] = kgrid
[kblocks
->blocks
[i
][n
]];
1710 assert(usage
->kclues
[i
] > 0);
1712 memset(usage
->kclues
+ nclues
, 0, cr
*cr
- nclues
);
1714 usage
->kclues
= NULL
;
1717 memset(usage
->cube
, TRUE
, cr
*cr
*cr
);
1719 usage
->row
= snewn(cr
* cr
, unsigned char);
1720 usage
->col
= snewn(cr
* cr
, unsigned char);
1721 usage
->blk
= snewn(cr
* cr
, unsigned char);
1722 memset(usage
->row
, FALSE
, cr
* cr
);
1723 memset(usage
->col
, FALSE
, cr
* cr
);
1724 memset(usage
->blk
, FALSE
, cr
* cr
);
1727 usage
->diag
= snewn(cr
* 2, unsigned char);
1728 memset(usage
->diag
, FALSE
, cr
* 2);
1732 usage
->nr_regions
= cr
* 3 + (xtype ?
2 : 0);
1733 usage
->regions
= snewn(cr
* usage
->nr_regions
, int);
1734 usage
->sq2region
= snewn(cr
* cr
* 3, int *);
1736 for (n
= 0; n
< cr
; n
++) {
1737 for (i
= 0; i
< cr
; i
++) {
1740 b
= usage
->blocks
->blocks
[n
][i
];
1741 usage
->regions
[cr
*n
*3 + i
] = x
;
1742 usage
->regions
[cr
*n
*3 + cr
+ i
] = y
;
1743 usage
->regions
[cr
*n
*3 + 2*cr
+ i
] = b
;
1744 usage
->sq2region
[x
*3] = usage
->regions
+ cr
*n
*3;
1745 usage
->sq2region
[y
*3 + 1] = usage
->regions
+ cr
*n
*3 + cr
;
1746 usage
->sq2region
[b
*3 + 2] = usage
->regions
+ cr
*n
*3 + 2*cr
;
1750 scratch
= solver_new_scratch(usage
);
1753 * Place all the clue numbers we are given.
1755 for (x
= 0; x
< cr
; x
++)
1756 for (y
= 0; y
< cr
; y
++)
1758 solver_place(usage
, x
, y
, grid
[y
*cr
+x
]);
1761 * Now loop over the grid repeatedly trying all permitted modes
1762 * of reasoning. The loop terminates if we complete an
1763 * iteration without making any progress; we then return
1764 * failure or success depending on whether the grid is full or
1769 * I'd like to write `continue;' inside each of the
1770 * following loops, so that the solver returns here after
1771 * making some progress. However, I can't specify that I
1772 * want to continue an outer loop rather than the innermost
1773 * one, so I'm apologetically resorting to a goto.
1778 * Blockwise positional elimination.
1780 for (b
= 0; b
< cr
; b
++)
1781 for (n
= 1; n
<= cr
; n
++)
1782 if (!usage
->blk
[b
*cr
+n
-1]) {
1783 for (i
= 0; i
< cr
; i
++)
1784 scratch
->indexlist
[i
] = cubepos2(usage
->blocks
->blocks
[b
][i
],n
);
1785 ret
= solver_elim(usage
, scratch
->indexlist
1786 #ifdef STANDALONE_SOLVER
1787 , "positional elimination,"
1788 " %d in block %s", n
,
1789 usage
->blocks
->blocknames
[b
]
1793 diff
= DIFF_IMPOSSIBLE
;
1795 } else if (ret
> 0) {
1796 diff
= max(diff
, DIFF_BLOCK
);
1801 if (usage
->kclues
!= NULL
) {
1802 int changed
= FALSE
;
1805 * First, bring the kblocks into a more useful form: remove
1806 * all filled-in squares, and reduce the sum by their values.
1807 * Walk in reverse order, since otherwise remove_from_block
1808 * can move element past our loop counter.
1810 for (b
= 0; b
< usage
->kblocks
->nr_blocks
; b
++)
1811 for (i
= usage
->kblocks
->nr_squares
[b
] -1; i
>= 0; i
--) {
1812 int x
= usage
->kblocks
->blocks
[b
][i
];
1813 int t
= usage
->grid
[x
];
1817 remove_from_block(usage
->kblocks
, b
, x
);
1818 if (t
> usage
->kclues
[b
]) {
1819 diff
= DIFF_IMPOSSIBLE
;
1822 usage
->kclues
[b
] -= t
;
1824 * Since cages are regions, this tells us something
1825 * about the other squares in the cage.
1827 for (n
= 0; n
< usage
->kblocks
->nr_squares
[b
]; n
++) {
1828 cube2(usage
->kblocks
->blocks
[b
][n
], t
) = FALSE
;
1833 * The most trivial kind of solver for killer puzzles: fill
1834 * single-square cages.
1836 for (b
= 0; b
< usage
->kblocks
->nr_blocks
; b
++) {
1837 int squares
= usage
->kblocks
->nr_squares
[b
];
1839 int v
= usage
->kclues
[b
];
1840 if (v
< 1 || v
> cr
) {
1841 diff
= DIFF_IMPOSSIBLE
;
1844 x
= usage
->kblocks
->blocks
[b
][0] % cr
;
1845 y
= usage
->kblocks
->blocks
[b
][0] / cr
;
1846 if (!cube(x
, y
, v
)) {
1847 diff
= DIFF_IMPOSSIBLE
;
1850 solver_place(usage
, x
, y
, v
);
1852 #ifdef STANDALONE_SOLVER
1853 if (solver_show_working
) {
1854 printf("%*s placing %d at (%d,%d)\n",
1855 solver_recurse_depth
*4, "killer single-square cage",
1856 v
, 1 + x
%cr
, 1 + x
/cr
);
1864 kdiff
= max(kdiff
, DIFF_KSINGLE
);
1868 if (dlev
->maxkdiff
>= DIFF_KINTERSECT
&& usage
->kclues
!= NULL
) {
1869 int changed
= FALSE
;
1871 * Now, create the extra_cages information. Every full region
1872 * (row, column, or block) has the same sum total (45 for 3x3
1873 * puzzles. After we try to cover these regions with cages that
1874 * lie entirely within them, any squares that remain must bring
1875 * the total to this known value, and so they form additional
1876 * cages which aren't immediately evident in the displayed form
1879 usage
->extra_cages
->nr_blocks
= 0;
1880 for (i
= 0; i
< 3; i
++) {
1881 for (n
= 0; n
< cr
; n
++) {
1882 int *region
= usage
->regions
+ cr
*n
*3 + i
*cr
;
1883 int sum
= cr
* (cr
+ 1) / 2;
1886 int n_extra
= usage
->extra_cages
->nr_blocks
;
1887 int *extra_list
= usage
->extra_cages
->blocks
[n_extra
];
1888 memcpy(extra_list
, region
, cr
* sizeof *extra_list
);
1890 nsquares
= filter_whole_cages(usage
, extra_list
, nsquares
, &filtered
);
1892 if (nsquares
== cr
|| nsquares
== 0)
1894 if (dlev
->maxdiff
>= DIFF_RECURSIVE
) {
1896 dlev
->diff
= DIFF_IMPOSSIBLE
;
1902 if (nsquares
== 1) {
1904 diff
= DIFF_IMPOSSIBLE
;
1907 x
= extra_list
[0] % cr
;
1908 y
= extra_list
[0] / cr
;
1909 if (!cube(x
, y
, sum
)) {
1910 diff
= DIFF_IMPOSSIBLE
;
1913 solver_place(usage
, x
, y
, sum
);
1915 #ifdef STANDALONE_SOLVER
1916 if (solver_show_working
) {
1917 printf("%*s placing %d at (%d,%d)\n",
1918 solver_recurse_depth
*4, "killer single-square deduced cage",
1924 b
= usage
->kblocks
->whichblock
[extra_list
[0]];
1925 for (x
= 1; x
< nsquares
; x
++)
1926 if (usage
->kblocks
->whichblock
[extra_list
[x
]] != b
)
1928 if (x
== nsquares
) {
1929 assert(usage
->kblocks
->nr_squares
[b
] > nsquares
);
1930 split_block(usage
->kblocks
, extra_list
, nsquares
);
1931 assert(usage
->kblocks
->nr_squares
[usage
->kblocks
->nr_blocks
- 1] == nsquares
);
1932 usage
->kclues
[usage
->kblocks
->nr_blocks
- 1] = sum
;
1933 usage
->kclues
[b
] -= sum
;
1935 usage
->extra_cages
->nr_squares
[n_extra
] = nsquares
;
1936 usage
->extra_cages
->nr_blocks
++;
1937 usage
->extra_clues
[n_extra
] = sum
;
1942 kdiff
= max(kdiff
, DIFF_KINTERSECT
);
1948 * Another simple killer-type elimination. For every square in a
1949 * cage, find the minimum and maximum possible sums of all the
1950 * other squares in the same cage, and rule out possibilities
1951 * for the given square based on whether they are guaranteed to
1952 * cause the sum to be either too high or too low.
1953 * This is a special case of trying all possible sums across a
1954 * region, which is a recursive algorithm. We should probably
1955 * implement it for a higher difficulty level.
1957 if (dlev
->maxkdiff
>= DIFF_KMINMAX
&& usage
->kclues
!= NULL
) {
1958 int changed
= FALSE
;
1959 for (b
= 0; b
< usage
->kblocks
->nr_blocks
; b
++) {
1960 int ret
= solver_killer_minmax(usage
, usage
->kblocks
,
1962 #ifdef STANDALONE_SOLVER
1967 diff
= DIFF_IMPOSSIBLE
;
1972 for (b
= 0; b
< usage
->extra_cages
->nr_blocks
; b
++) {
1973 int ret
= solver_killer_minmax(usage
, usage
->extra_cages
,
1974 usage
->extra_clues
, b
1975 #ifdef STANDALONE_SOLVER
1976 , "using deduced cages"
1980 diff
= DIFF_IMPOSSIBLE
;
1986 kdiff
= max(kdiff
, DIFF_KMINMAX
);
1992 * Try to use knowledge of which numbers can be used to generate
1994 * This can only be used if a cage lies entirely within a region.
1996 if (dlev
->maxkdiff
>= DIFF_KSUMS
&& usage
->kclues
!= NULL
) {
1997 int changed
= FALSE
;
1999 for (b
= 0; b
< usage
->kblocks
->nr_blocks
; b
++) {
2000 int ret
= solver_killer_sums(usage
, b
, usage
->kblocks
,
2001 usage
->kclues
[b
], TRUE
2002 #ifdef STANDALONE_SOLVER
2008 kdiff
= max(kdiff
, DIFF_KSUMS
);
2009 } else if (ret
< 0) {
2010 diff
= DIFF_IMPOSSIBLE
;
2015 for (b
= 0; b
< usage
->extra_cages
->nr_blocks
; b
++) {
2016 int ret
= solver_killer_sums(usage
, b
, usage
->extra_cages
,
2017 usage
->extra_clues
[b
], FALSE
2018 #ifdef STANDALONE_SOLVER
2024 kdiff
= max(kdiff
, DIFF_KINTERSECT
);
2025 } else if (ret
< 0) {
2026 diff
= DIFF_IMPOSSIBLE
;
2035 if (dlev
->maxdiff
<= DIFF_BLOCK
)
2039 * Row-wise positional elimination.
2041 for (y
= 0; y
< cr
; y
++)
2042 for (n
= 1; n
<= cr
; n
++)
2043 if (!usage
->row
[y
*cr
+n
-1]) {
2044 for (x
= 0; x
< cr
; x
++)
2045 scratch
->indexlist
[x
] = cubepos(x
, y
, n
);
2046 ret
= solver_elim(usage
, scratch
->indexlist
2047 #ifdef STANDALONE_SOLVER
2048 , "positional elimination,"
2049 " %d in row %d", n
, 1+y
2053 diff
= DIFF_IMPOSSIBLE
;
2055 } else if (ret
> 0) {
2056 diff
= max(diff
, DIFF_SIMPLE
);
2061 * Column-wise positional elimination.
2063 for (x
= 0; x
< cr
; x
++)
2064 for (n
= 1; n
<= cr
; n
++)
2065 if (!usage
->col
[x
*cr
+n
-1]) {
2066 for (y
= 0; y
< cr
; y
++)
2067 scratch
->indexlist
[y
] = cubepos(x
, y
, n
);
2068 ret
= solver_elim(usage
, scratch
->indexlist
2069 #ifdef STANDALONE_SOLVER
2070 , "positional elimination,"
2071 " %d in column %d", n
, 1+x
2075 diff
= DIFF_IMPOSSIBLE
;
2077 } else if (ret
> 0) {
2078 diff
= max(diff
, DIFF_SIMPLE
);
2084 * X-diagonal positional elimination.
2087 for (n
= 1; n
<= cr
; n
++)
2088 if (!usage
->diag
[n
-1]) {
2089 for (i
= 0; i
< cr
; i
++)
2090 scratch
->indexlist
[i
] = cubepos2(diag0(i
), n
);
2091 ret
= solver_elim(usage
, scratch
->indexlist
2092 #ifdef STANDALONE_SOLVER
2093 , "positional elimination,"
2094 " %d in \\-diagonal", n
2098 diff
= DIFF_IMPOSSIBLE
;
2100 } else if (ret
> 0) {
2101 diff
= max(diff
, DIFF_SIMPLE
);
2105 for (n
= 1; n
<= cr
; n
++)
2106 if (!usage
->diag
[cr
+n
-1]) {
2107 for (i
= 0; i
< cr
; i
++)
2108 scratch
->indexlist
[i
] = cubepos2(diag1(i
), n
);
2109 ret
= solver_elim(usage
, scratch
->indexlist
2110 #ifdef STANDALONE_SOLVER
2111 , "positional elimination,"
2112 " %d in /-diagonal", n
2116 diff
= DIFF_IMPOSSIBLE
;
2118 } else if (ret
> 0) {
2119 diff
= max(diff
, DIFF_SIMPLE
);
2126 * Numeric elimination.
2128 for (x
= 0; x
< cr
; x
++)
2129 for (y
= 0; y
< cr
; y
++)
2130 if (!usage
->grid
[y
*cr
+x
]) {
2131 for (n
= 1; n
<= cr
; n
++)
2132 scratch
->indexlist
[n
-1] = cubepos(x
, y
, n
);
2133 ret
= solver_elim(usage
, scratch
->indexlist
2134 #ifdef STANDALONE_SOLVER
2135 , "numeric elimination at (%d,%d)",
2140 diff
= DIFF_IMPOSSIBLE
;
2142 } else if (ret
> 0) {
2143 diff
= max(diff
, DIFF_SIMPLE
);
2148 if (dlev
->maxdiff
<= DIFF_SIMPLE
)
2152 * Intersectional analysis, rows vs blocks.
2154 for (y
= 0; y
< cr
; y
++)
2155 for (b
= 0; b
< cr
; b
++)
2156 for (n
= 1; n
<= cr
; n
++) {
2157 if (usage
->row
[y
*cr
+n
-1] ||
2158 usage
->blk
[b
*cr
+n
-1])
2160 for (i
= 0; i
< cr
; i
++) {
2161 scratch
->indexlist
[i
] = cubepos(i
, y
, n
);
2162 scratch
->indexlist2
[i
] = cubepos2(usage
->blocks
->blocks
[b
][i
], n
);
2165 * solver_intersect() never returns -1.
2167 if (solver_intersect(usage
, scratch
->indexlist
,
2169 #ifdef STANDALONE_SOLVER
2170 , "intersectional analysis,"
2171 " %d in row %d vs block %s",
2172 n
, 1+y
, usage
->blocks
->blocknames
[b
]
2175 solver_intersect(usage
, scratch
->indexlist2
,
2177 #ifdef STANDALONE_SOLVER
2178 , "intersectional analysis,"
2179 " %d in block %s vs row %d",
2180 n
, usage
->blocks
->blocknames
[b
], 1+y
2183 diff
= max(diff
, DIFF_INTERSECT
);
2189 * Intersectional analysis, columns vs blocks.
2191 for (x
= 0; x
< cr
; x
++)
2192 for (b
= 0; b
< cr
; b
++)
2193 for (n
= 1; n
<= cr
; n
++) {
2194 if (usage
->col
[x
*cr
+n
-1] ||
2195 usage
->blk
[b
*cr
+n
-1])
2197 for (i
= 0; i
< cr
; i
++) {
2198 scratch
->indexlist
[i
] = cubepos(x
, i
, n
);
2199 scratch
->indexlist2
[i
] = cubepos2(usage
->blocks
->blocks
[b
][i
], n
);
2201 if (solver_intersect(usage
, scratch
->indexlist
,
2203 #ifdef STANDALONE_SOLVER
2204 , "intersectional analysis,"
2205 " %d in column %d vs block %s",
2206 n
, 1+x
, usage
->blocks
->blocknames
[b
]
2209 solver_intersect(usage
, scratch
->indexlist2
,
2211 #ifdef STANDALONE_SOLVER
2212 , "intersectional analysis,"
2213 " %d in block %s vs column %d",
2214 n
, usage
->blocks
->blocknames
[b
], 1+x
2217 diff
= max(diff
, DIFF_INTERSECT
);
2224 * Intersectional analysis, \-diagonal vs blocks.
2226 for (b
= 0; b
< cr
; b
++)
2227 for (n
= 1; n
<= cr
; n
++) {
2228 if (usage
->diag
[n
-1] ||
2229 usage
->blk
[b
*cr
+n
-1])
2231 for (i
= 0; i
< cr
; i
++) {
2232 scratch
->indexlist
[i
] = cubepos2(diag0(i
), n
);
2233 scratch
->indexlist2
[i
] = cubepos2(usage
->blocks
->blocks
[b
][i
], n
);
2235 if (solver_intersect(usage
, scratch
->indexlist
,
2237 #ifdef STANDALONE_SOLVER
2238 , "intersectional analysis,"
2239 " %d in \\-diagonal vs block %s",
2240 n
, 1+x
, usage
->blocks
->blocknames
[b
]
2243 solver_intersect(usage
, scratch
->indexlist2
,
2245 #ifdef STANDALONE_SOLVER
2246 , "intersectional analysis,"
2247 " %d in block %s vs \\-diagonal",
2248 n
, usage
->blocks
->blocknames
[b
], 1+x
2251 diff
= max(diff
, DIFF_INTERSECT
);
2257 * Intersectional analysis, /-diagonal vs blocks.
2259 for (b
= 0; b
< cr
; b
++)
2260 for (n
= 1; n
<= cr
; n
++) {
2261 if (usage
->diag
[cr
+n
-1] ||
2262 usage
->blk
[b
*cr
+n
-1])
2264 for (i
= 0; i
< cr
; i
++) {
2265 scratch
->indexlist
[i
] = cubepos2(diag1(i
), n
);
2266 scratch
->indexlist2
[i
] = cubepos2(usage
->blocks
->blocks
[b
][i
], n
);
2268 if (solver_intersect(usage
, scratch
->indexlist
,
2270 #ifdef STANDALONE_SOLVER
2271 , "intersectional analysis,"
2272 " %d in /-diagonal vs block %s",
2273 n
, 1+x
, usage
->blocks
->blocknames
[b
]
2276 solver_intersect(usage
, scratch
->indexlist2
,
2278 #ifdef STANDALONE_SOLVER
2279 , "intersectional analysis,"
2280 " %d in block %s vs /-diagonal",
2281 n
, usage
->blocks
->blocknames
[b
], 1+x
2284 diff
= max(diff
, DIFF_INTERSECT
);
2290 if (dlev
->maxdiff
<= DIFF_INTERSECT
)
2294 * Blockwise set elimination.
2296 for (b
= 0; b
< cr
; b
++) {
2297 for (i
= 0; i
< cr
; i
++)
2298 for (n
= 1; n
<= cr
; n
++)
2299 scratch
->indexlist
[i
*cr
+n
-1] = cubepos2(usage
->blocks
->blocks
[b
][i
], n
);
2300 ret
= solver_set(usage
, scratch
, scratch
->indexlist
2301 #ifdef STANDALONE_SOLVER
2302 , "set elimination, block %s",
2303 usage
->blocks
->blocknames
[b
]
2307 diff
= DIFF_IMPOSSIBLE
;
2309 } else if (ret
> 0) {
2310 diff
= max(diff
, DIFF_SET
);
2316 * Row-wise set elimination.
2318 for (y
= 0; y
< cr
; y
++) {
2319 for (x
= 0; x
< cr
; x
++)
2320 for (n
= 1; n
<= cr
; n
++)
2321 scratch
->indexlist
[x
*cr
+n
-1] = cubepos(x
, y
, n
);
2322 ret
= solver_set(usage
, scratch
, scratch
->indexlist
2323 #ifdef STANDALONE_SOLVER
2324 , "set elimination, row %d", 1+y
2328 diff
= DIFF_IMPOSSIBLE
;
2330 } else if (ret
> 0) {
2331 diff
= max(diff
, DIFF_SET
);
2337 * Column-wise set elimination.
2339 for (x
= 0; x
< cr
; x
++) {
2340 for (y
= 0; y
< cr
; y
++)
2341 for (n
= 1; n
<= cr
; n
++)
2342 scratch
->indexlist
[y
*cr
+n
-1] = cubepos(x
, y
, n
);
2343 ret
= solver_set(usage
, scratch
, scratch
->indexlist
2344 #ifdef STANDALONE_SOLVER
2345 , "set elimination, column %d", 1+x
2349 diff
= DIFF_IMPOSSIBLE
;
2351 } else if (ret
> 0) {
2352 diff
= max(diff
, DIFF_SET
);
2359 * \-diagonal set elimination.
2361 for (i
= 0; i
< cr
; i
++)
2362 for (n
= 1; n
<= cr
; n
++)
2363 scratch
->indexlist
[i
*cr
+n
-1] = cubepos2(diag0(i
), n
);
2364 ret
= solver_set(usage
, scratch
, scratch
->indexlist
2365 #ifdef STANDALONE_SOLVER
2366 , "set elimination, \\-diagonal"
2370 diff
= DIFF_IMPOSSIBLE
;
2372 } else if (ret
> 0) {
2373 diff
= max(diff
, DIFF_SET
);
2378 * /-diagonal set elimination.
2380 for (i
= 0; i
< cr
; i
++)
2381 for (n
= 1; n
<= cr
; n
++)
2382 scratch
->indexlist
[i
*cr
+n
-1] = cubepos2(diag1(i
), n
);
2383 ret
= solver_set(usage
, scratch
, scratch
->indexlist
2384 #ifdef STANDALONE_SOLVER
2385 , "set elimination, \\-diagonal"
2389 diff
= DIFF_IMPOSSIBLE
;
2391 } else if (ret
> 0) {
2392 diff
= max(diff
, DIFF_SET
);
2397 if (dlev
->maxdiff
<= DIFF_SET
)
2401 * Row-vs-column set elimination on a single number.
2403 for (n
= 1; n
<= cr
; n
++) {
2404 for (y
= 0; y
< cr
; y
++)
2405 for (x
= 0; x
< cr
; x
++)
2406 scratch
->indexlist
[y
*cr
+x
] = cubepos(x
, y
, n
);
2407 ret
= solver_set(usage
, scratch
, scratch
->indexlist
2408 #ifdef STANDALONE_SOLVER
2409 , "positional set elimination, number %d", n
2413 diff
= DIFF_IMPOSSIBLE
;
2415 } else if (ret
> 0) {
2416 diff
= max(diff
, DIFF_EXTREME
);
2424 if (solver_forcing(usage
, scratch
)) {
2425 diff
= max(diff
, DIFF_EXTREME
);
2430 * If we reach here, we have made no deductions in this
2431 * iteration, so the algorithm terminates.
2437 * Last chance: if we haven't fully solved the puzzle yet, try
2438 * recursing based on guesses for a particular square. We pick
2439 * one of the most constrained empty squares we can find, which
2440 * has the effect of pruning the search tree as much as
2443 if (dlev
->maxdiff
>= DIFF_RECURSIVE
) {
2444 int best
, bestcount
;
2449 for (y
= 0; y
< cr
; y
++)
2450 for (x
= 0; x
< cr
; x
++)
2451 if (!grid
[y
*cr
+x
]) {
2455 * An unfilled square. Count the number of
2456 * possible digits in it.
2459 for (n
= 1; n
<= cr
; n
++)
2464 * We should have found any impossibilities
2465 * already, so this can safely be an assert.
2469 if (count
< bestcount
) {
2477 digit
*list
, *ingrid
, *outgrid
;
2479 diff
= DIFF_IMPOSSIBLE
; /* no solution found yet */
2482 * Attempt recursion.
2487 list
= snewn(cr
, digit
);
2488 ingrid
= snewn(cr
* cr
, digit
);
2489 outgrid
= snewn(cr
* cr
, digit
);
2490 memcpy(ingrid
, grid
, cr
* cr
);
2492 /* Make a list of the possible digits. */
2493 for (j
= 0, n
= 1; n
<= cr
; n
++)
2497 #ifdef STANDALONE_SOLVER
2498 if (solver_show_working
) {
2500 printf("%*srecursing on (%d,%d) [",
2501 solver_recurse_depth
*4, "", x
+ 1, y
+ 1);
2502 for (i
= 0; i
< j
; i
++) {
2503 printf("%s%d", sep
, list
[i
]);
2511 * And step along the list, recursing back into the
2512 * main solver at every stage.
2514 for (i
= 0; i
< j
; i
++) {
2515 memcpy(outgrid
, ingrid
, cr
* cr
);
2516 outgrid
[y
*cr
+x
] = list
[i
];
2518 #ifdef STANDALONE_SOLVER
2519 if (solver_show_working
)
2520 printf("%*sguessing %d at (%d,%d)\n",
2521 solver_recurse_depth
*4, "", list
[i
], x
+ 1, y
+ 1);
2522 solver_recurse_depth
++;
2525 solver(cr
, blocks
, kblocks
, xtype
, outgrid
, kgrid
, dlev
);
2527 #ifdef STANDALONE_SOLVER
2528 solver_recurse_depth
--;
2529 if (solver_show_working
) {
2530 printf("%*sretracting %d at (%d,%d)\n",
2531 solver_recurse_depth
*4, "", list
[i
], x
+ 1, y
+ 1);
2536 * If we have our first solution, copy it into the
2537 * grid we will return.
2539 if (diff
== DIFF_IMPOSSIBLE
&& dlev
->diff
!= DIFF_IMPOSSIBLE
)
2540 memcpy(grid
, outgrid
, cr
*cr
);
2542 if (dlev
->diff
== DIFF_AMBIGUOUS
)
2543 diff
= DIFF_AMBIGUOUS
;
2544 else if (dlev
->diff
== DIFF_IMPOSSIBLE
)
2545 /* do not change our return value */;
2547 /* the recursion turned up exactly one solution */
2548 if (diff
== DIFF_IMPOSSIBLE
)
2549 diff
= DIFF_RECURSIVE
;
2551 diff
= DIFF_AMBIGUOUS
;
2555 * As soon as we've found more than one solution,
2556 * give up immediately.
2558 if (diff
== DIFF_AMBIGUOUS
)
2569 * We're forbidden to use recursion, so we just see whether
2570 * our grid is fully solved, and return DIFF_IMPOSSIBLE
2573 for (y
= 0; y
< cr
; y
++)
2574 for (x
= 0; x
< cr
; x
++)
2576 diff
= DIFF_IMPOSSIBLE
;
2581 dlev
->kdiff
= kdiff
;
2583 #ifdef STANDALONE_SOLVER
2584 if (solver_show_working
)
2585 printf("%*s%s found\n",
2586 solver_recurse_depth
*4, "",
2587 diff
== DIFF_IMPOSSIBLE ?
"no solution" :
2588 diff
== DIFF_AMBIGUOUS ?
"multiple solutions" :
2596 if (usage
->kblocks
) {
2597 free_block_structure(usage
->kblocks
);
2598 free_block_structure(usage
->extra_cages
);
2599 sfree(usage
->extra_clues
);
2603 solver_free_scratch(scratch
);
2606 /* ----------------------------------------------------------------------
2607 * End of solver code.
2610 /* ----------------------------------------------------------------------
2611 * Killer set generator.
2614 /* ----------------------------------------------------------------------
2615 * Solo filled-grid generator.
2617 * This grid generator works by essentially trying to solve a grid
2618 * starting from no clues, and not worrying that there's more than
2619 * one possible solution. Unfortunately, it isn't computationally
2620 * feasible to do this by calling the above solver with an empty
2621 * grid, because that one needs to allocate a lot of scratch space
2622 * at every recursion level. Instead, I have a much simpler
2623 * algorithm which I shamelessly copied from a Python solver
2624 * written by Andrew Wilkinson (which is GPLed, but I've reused
2625 * only ideas and no code). It mostly just does the obvious
2626 * recursive thing: pick an empty square, put one of the possible
2627 * digits in it, recurse until all squares are filled, backtrack
2628 * and change some choices if necessary.
2630 * The clever bit is that every time it chooses which square to
2631 * fill in next, it does so by counting the number of _possible_
2632 * numbers that can go in each square, and it prioritises so that
2633 * it picks a square with the _lowest_ number of possibilities. The
2634 * idea is that filling in lots of the obvious bits (particularly
2635 * any squares with only one possibility) will cut down on the list
2636 * of possibilities for other squares and hence reduce the enormous
2637 * search space as much as possible as early as possible.
2639 * The use of bit sets implies that we support puzzles up to a size of
2640 * 32x32 (less if anyone finds a 16-bit machine to compile this on).
2644 * Internal data structure used in gridgen to keep track of
2647 struct gridgen_coord
{ int x
, y
, r
; };
2648 struct gridgen_usage
{
2650 struct block_structure
*blocks
, *kblocks
;
2651 /* grid is a copy of the input grid, modified as we go along */
2654 * Bitsets. In each of them, bit n is set if digit n has been placed
2655 * in the corresponding region. row, col and blk are used for all
2656 * puzzles. cge is used only for killer puzzles, and diag is used
2657 * only for x-type puzzles.
2658 * All of these have cr entries, except diag which only has 2,
2659 * and cge, which has as many entries as kblocks.
2661 unsigned int *row
, *col
, *blk
, *cge
, *diag
;
2662 /* This lists all the empty spaces remaining in the grid. */
2663 struct gridgen_coord
*spaces
;
2665 /* If we need randomisation in the solve, this is our random state. */
2669 static void gridgen_place(struct gridgen_usage
*usage
, int x
, int y
, digit n
)
2671 unsigned int bit
= 1 << n
;
2673 usage
->row
[y
] |= bit
;
2674 usage
->col
[x
] |= bit
;
2675 usage
->blk
[usage
->blocks
->whichblock
[y
*cr
+x
]] |= bit
;
2677 usage
->cge
[usage
->kblocks
->whichblock
[y
*cr
+x
]] |= bit
;
2679 if (ondiag0(y
*cr
+x
))
2680 usage
->diag
[0] |= bit
;
2681 if (ondiag1(y
*cr
+x
))
2682 usage
->diag
[1] |= bit
;
2684 usage
->grid
[y
*cr
+x
] = n
;
2687 static void gridgen_remove(struct gridgen_usage
*usage
, int x
, int y
, digit n
)
2689 unsigned int mask
= ~(1 << n
);
2691 usage
->row
[y
] &= mask
;
2692 usage
->col
[x
] &= mask
;
2693 usage
->blk
[usage
->blocks
->whichblock
[y
*cr
+x
]] &= mask
;
2695 usage
->cge
[usage
->kblocks
->whichblock
[y
*cr
+x
]] &= mask
;
2697 if (ondiag0(y
*cr
+x
))
2698 usage
->diag
[0] &= mask
;
2699 if (ondiag1(y
*cr
+x
))
2700 usage
->diag
[1] &= mask
;
2702 usage
->grid
[y
*cr
+x
] = 0;
2708 * The real recursive step in the generating function.
2710 * Return values: 1 means solution found, 0 means no solution
2711 * found on this branch.
2713 static int gridgen_real(struct gridgen_usage
*usage
, digit
*grid
, int *steps
)
2716 int i
, j
, n
, sx
, sy
, bestm
, bestr
, ret
;
2721 * Firstly, check for completion! If there are no spaces left
2722 * in the grid, we have a solution.
2724 if (usage
->nspaces
== 0)
2728 * Next, abandon generation if we went over our steps limit.
2735 * Otherwise, there must be at least one space. Find the most
2736 * constrained space, using the `r' field as a tie-breaker.
2738 bestm
= cr
+1; /* so that any space will beat it */
2742 for (j
= 0; j
< usage
->nspaces
; j
++) {
2743 int x
= usage
->spaces
[j
].x
, y
= usage
->spaces
[j
].y
;
2744 unsigned int used_xy
;
2747 m
= usage
->blocks
->whichblock
[y
*cr
+x
];
2748 used_xy
= usage
->row
[y
] | usage
->col
[x
] | usage
->blk
[m
];
2749 if (usage
->cge
!= NULL
)
2750 used_xy
|= usage
->cge
[usage
->kblocks
->whichblock
[y
*cr
+x
]];
2751 if (usage
->cge
!= NULL
)
2752 used_xy
|= usage
->cge
[usage
->kblocks
->whichblock
[y
*cr
+x
]];
2753 if (usage
->diag
!= NULL
) {
2754 if (ondiag0(y
*cr
+x
))
2755 used_xy
|= usage
->diag
[0];
2756 if (ondiag1(y
*cr
+x
))
2757 used_xy
|= usage
->diag
[1];
2761 * Find the number of digits that could go in this space.
2764 for (n
= 1; n
<= cr
; n
++) {
2765 unsigned int bit
= 1 << n
;
2766 if ((used_xy
& bit
) == 0)
2769 if (m
< bestm
|| (m
== bestm
&& usage
->spaces
[j
].r
< bestr
)) {
2771 bestr
= usage
->spaces
[j
].r
;
2780 * Swap that square into the final place in the spaces array,
2781 * so that decrementing nspaces will remove it from the list.
2783 if (i
!= usage
->nspaces
-1) {
2784 struct gridgen_coord t
;
2785 t
= usage
->spaces
[usage
->nspaces
-1];
2786 usage
->spaces
[usage
->nspaces
-1] = usage
->spaces
[i
];
2787 usage
->spaces
[i
] = t
;
2791 * Now we've decided which square to start our recursion at,
2792 * simply go through all possible values, shuffling them
2793 * randomly first if necessary.
2795 digits
= snewn(bestm
, int);
2798 for (n
= 1; n
<= cr
; n
++) {
2799 unsigned int bit
= 1 << n
;
2801 if ((used
& bit
) == 0)
2806 shuffle(digits
, j
, sizeof(*digits
), usage
->rs
);
2808 /* And finally, go through the digit list and actually recurse. */
2810 for (i
= 0; i
< j
; i
++) {
2813 /* Update the usage structure to reflect the placing of this digit. */
2814 gridgen_place(usage
, sx
, sy
, n
);
2817 /* Call the solver recursively. Stop when we find a solution. */
2818 if (gridgen_real(usage
, grid
, steps
)) {
2823 /* Revert the usage structure. */
2824 gridgen_remove(usage
, sx
, sy
, n
);
2833 * Entry point to generator. You give it parameters and a starting
2834 * grid, which is simply an array of cr*cr digits.
2836 static int gridgen(int cr
, struct block_structure
*blocks
,
2837 struct block_structure
*kblocks
, int xtype
,
2838 digit
*grid
, random_state
*rs
, int maxsteps
)
2840 struct gridgen_usage
*usage
;
2844 * Clear the grid to start with.
2846 memset(grid
, 0, cr
*cr
);
2849 * Create a gridgen_usage structure.
2851 usage
= snew(struct gridgen_usage
);
2854 usage
->blocks
= blocks
;
2858 usage
->row
= snewn(cr
, unsigned int);
2859 usage
->col
= snewn(cr
, unsigned int);
2860 usage
->blk
= snewn(cr
, unsigned int);
2861 if (kblocks
!= NULL
) {
2862 usage
->kblocks
= kblocks
;
2863 usage
->cge
= snewn(usage
->kblocks
->nr_blocks
, unsigned int);
2864 memset(usage
->cge
, FALSE
, kblocks
->nr_blocks
* sizeof *usage
->cge
);
2869 memset(usage
->row
, 0, cr
* sizeof *usage
->row
);
2870 memset(usage
->col
, 0, cr
* sizeof *usage
->col
);
2871 memset(usage
->blk
, 0, cr
* sizeof *usage
->blk
);
2874 usage
->diag
= snewn(2, unsigned int);
2875 memset(usage
->diag
, 0, 2 * sizeof *usage
->diag
);
2881 * Begin by filling in the whole top row with randomly chosen
2882 * numbers. This cannot introduce any bias or restriction on
2883 * the available grids, since we already know those numbers
2884 * are all distinct so all we're doing is choosing their
2887 for (x
= 0; x
< cr
; x
++)
2889 shuffle(grid
, cr
, sizeof(*grid
), rs
);
2890 for (x
= 0; x
< cr
; x
++)
2891 gridgen_place(usage
, x
, 0, grid
[x
]);
2893 usage
->spaces
= snewn(cr
* cr
, struct gridgen_coord
);
2899 * Initialise the list of grid spaces, taking care to leave
2900 * out the row I've already filled in above.
2902 for (y
= 1; y
< cr
; y
++) {
2903 for (x
= 0; x
< cr
; x
++) {
2904 usage
->spaces
[usage
->nspaces
].x
= x
;
2905 usage
->spaces
[usage
->nspaces
].y
= y
;
2906 usage
->spaces
[usage
->nspaces
].r
= random_bits(rs
, 31);
2912 * Run the real generator function.
2914 ret
= gridgen_real(usage
, grid
, &maxsteps
);
2917 * Clean up the usage structure now we have our answer.
2919 sfree(usage
->spaces
);
2929 /* ----------------------------------------------------------------------
2930 * End of grid generator code.
2934 * Check whether a grid contains a valid complete puzzle.
2936 static int check_valid(int cr
, struct block_structure
*blocks
,
2937 struct block_structure
*kblocks
, int xtype
, digit
*grid
)
2939 unsigned char *used
;
2942 used
= snewn(cr
, unsigned char);
2945 * Check that each row contains precisely one of everything.
2947 for (y
= 0; y
< cr
; y
++) {
2948 memset(used
, FALSE
, cr
);
2949 for (x
= 0; x
< cr
; x
++)
2950 if (grid
[y
*cr
+x
] > 0 && grid
[y
*cr
+x
] <= cr
)
2951 used
[grid
[y
*cr
+x
]-1] = TRUE
;
2952 for (n
= 0; n
< cr
; n
++)
2960 * Check that each column contains precisely one of everything.
2962 for (x
= 0; x
< cr
; x
++) {
2963 memset(used
, FALSE
, cr
);
2964 for (y
= 0; y
< cr
; y
++)
2965 if (grid
[y
*cr
+x
] > 0 && grid
[y
*cr
+x
] <= cr
)
2966 used
[grid
[y
*cr
+x
]-1] = TRUE
;
2967 for (n
= 0; n
< cr
; n
++)
2975 * Check that each block contains precisely one of everything.
2977 for (i
= 0; i
< cr
; i
++) {
2978 memset(used
, FALSE
, cr
);
2979 for (j
= 0; j
< cr
; j
++)
2980 if (grid
[blocks
->blocks
[i
][j
]] > 0 &&
2981 grid
[blocks
->blocks
[i
][j
]] <= cr
)
2982 used
[grid
[blocks
->blocks
[i
][j
]]-1] = TRUE
;
2983 for (n
= 0; n
< cr
; n
++)
2991 * Check that each Killer cage, if any, contains at most one of
2995 for (i
= 0; i
< kblocks
->nr_blocks
; i
++) {
2996 memset(used
, FALSE
, cr
);
2997 for (j
= 0; j
< kblocks
->nr_squares
[i
]; j
++)
2998 if (grid
[kblocks
->blocks
[i
][j
]] > 0 &&
2999 grid
[kblocks
->blocks
[i
][j
]] <= cr
) {
3000 if (used
[grid
[kblocks
->blocks
[i
][j
]]-1]) {
3004 used
[grid
[kblocks
->blocks
[i
][j
]]-1] = TRUE
;
3010 * Check that each diagonal contains precisely one of everything.
3013 memset(used
, FALSE
, cr
);
3014 for (i
= 0; i
< cr
; i
++)
3015 if (grid
[diag0(i
)] > 0 && grid
[diag0(i
)] <= cr
)
3016 used
[grid
[diag0(i
)]-1] = TRUE
;
3017 for (n
= 0; n
< cr
; n
++)
3022 for (i
= 0; i
< cr
; i
++)
3023 if (grid
[diag1(i
)] > 0 && grid
[diag1(i
)] <= cr
)
3024 used
[grid
[diag1(i
)]-1] = TRUE
;
3025 for (n
= 0; n
< cr
; n
++)
3036 static int symmetries(game_params
*params
, int x
, int y
, int *output
, int s
)
3038 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
3041 #define ADD(x,y) (*output++ = (x), *output++ = (y), i++)
3047 break; /* just x,y is all we need */
3049 ADD(cr
- 1 - x
, cr
- 1 - y
);
3054 ADD(cr
- 1 - x
, cr
- 1 - y
);
3065 ADD(cr
- 1 - x
, cr
- 1 - y
);
3069 ADD(cr
- 1 - x
, cr
- 1 - y
);
3070 ADD(cr
- 1 - y
, cr
- 1 - x
);
3075 ADD(cr
- 1 - x
, cr
- 1 - y
);
3079 ADD(cr
- 1 - y
, cr
- 1 - x
);
3088 static char *encode_solve_move(int cr
, digit
*grid
)
3091 char *ret
, *p
, *sep
;
3094 * It's surprisingly easy to work out _exactly_ how long this
3095 * string needs to be. To decimal-encode all the numbers from 1
3098 * - every number has a units digit; total is n.
3099 * - all numbers above 9 have a tens digit; total is max(n-9,0).
3100 * - all numbers above 99 have a hundreds digit; total is max(n-99,0).
3104 for (i
= 1; i
<= cr
; i
*= 10)
3105 len
+= max(cr
- i
+ 1, 0);
3106 len
+= cr
; /* don't forget the commas */
3107 len
*= cr
; /* there are cr rows of these */
3110 * Now len is one bigger than the total size of the
3111 * comma-separated numbers (because we counted an
3112 * additional leading comma). We need to have a leading S
3113 * and a trailing NUL, so we're off by one in total.
3117 ret
= snewn(len
, char);
3121 for (i
= 0; i
< cr
*cr
; i
++) {
3122 p
+= sprintf(p
, "%s%d", sep
, grid
[i
]);
3126 assert(p
- ret
== len
);
3131 static void dsf_to_blocks(int *dsf
, struct block_structure
*blocks
,
3132 int min_expected
, int max_expected
)
3134 int cr
= blocks
->c
* blocks
->r
, area
= cr
* cr
;
3137 for (i
= 0; i
< area
; i
++)
3138 blocks
->whichblock
[i
] = -1;
3139 for (i
= 0; i
< area
; i
++) {
3140 int j
= dsf_canonify(dsf
, i
);
3141 if (blocks
->whichblock
[j
] < 0)
3142 blocks
->whichblock
[j
] = nb
++;
3143 blocks
->whichblock
[i
] = blocks
->whichblock
[j
];
3145 assert(nb
>= min_expected
&& nb
<= max_expected
);
3146 blocks
->nr_blocks
= nb
;
3149 static void make_blocks_from_whichblock(struct block_structure
*blocks
)
3153 for (i
= 0; i
< blocks
->nr_blocks
; i
++) {
3154 blocks
->blocks
[i
][blocks
->max_nr_squares
-1] = 0;
3155 blocks
->nr_squares
[i
] = 0;
3157 for (i
= 0; i
< blocks
->area
; i
++) {
3158 int b
= blocks
->whichblock
[i
];
3159 int j
= blocks
->blocks
[b
][blocks
->max_nr_squares
-1]++;
3160 assert(j
< blocks
->max_nr_squares
);
3161 blocks
->blocks
[b
][j
] = i
;
3162 blocks
->nr_squares
[b
]++;
3166 static char *encode_block_structure_desc(char *p
, struct block_structure
*blocks
)
3169 int c
= blocks
->c
, r
= blocks
->r
, cr
= c
* r
;
3172 * Encode the block structure. We do this by encoding
3173 * the pattern of dividing lines: first we iterate
3174 * over the cr*(cr-1) internal vertical grid lines in
3175 * ordinary reading order, then over the cr*(cr-1)
3176 * internal horizontal ones in transposed reading
3179 * We encode the number of non-lines between the
3180 * lines; _ means zero (two adjacent divisions), a
3181 * means 1, ..., y means 25, and z means 25 non-lines
3182 * _and no following line_ (so that za means 26, zb 27
3185 for (i
= 0; i
<= 2*cr
*(cr
-1); i
++) {
3186 int x
, y
, p0
, p1
, edge
;
3188 if (i
== 2*cr
*(cr
-1)) {
3189 edge
= TRUE
; /* terminating virtual edge */
3191 if (i
< cr
*(cr
-1)) {
3202 edge
= (blocks
->whichblock
[p0
] != blocks
->whichblock
[p1
]);
3206 while (currrun
> 25)
3207 *p
++ = 'z', currrun
-= 25;
3209 *p
++ = 'a'-1 + currrun
;
3219 static char *encode_grid(char *desc
, digit
*grid
, int area
)
3225 for (i
= 0; i
<= area
; i
++) {
3226 int n
= (i
< area ? grid
[i
] : -1);
3233 int c
= 'a' - 1 + run
;
3237 run
-= c
- ('a' - 1);
3241 * If there's a number in the very top left or
3242 * bottom right, there's no point putting an
3243 * unnecessary _ before or after it.
3245 if (p
> desc
&& n
> 0)
3249 p
+= sprintf(p
, "%d", n
);
3257 * Conservatively stimate the number of characters required for
3258 * encoding a grid of a certain area.
3260 static int grid_encode_space (int area
)
3263 for (count
= 1, t
= area
; t
> 26; t
-= 26)
3265 return count
* area
;
3269 * Conservatively stimate the number of characters required for
3270 * encoding a given blocks structure.
3272 static int blocks_encode_space(struct block_structure
*blocks
)
3274 int cr
= blocks
->c
* blocks
->r
, area
= cr
* cr
;
3275 return grid_encode_space(area
);
3278 static char *encode_puzzle_desc(game_params
*params
, digit
*grid
,
3279 struct block_structure
*blocks
,
3281 struct block_structure
*kblocks
)
3283 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
3288 space
= grid_encode_space(area
) + 1;
3290 space
+= blocks_encode_space(blocks
) + 1;
3291 if (params
->killer
) {
3292 space
+= blocks_encode_space(kblocks
) + 1;
3293 space
+= grid_encode_space(area
) + 1;
3295 desc
= snewn(space
, char);
3296 p
= encode_grid(desc
, grid
, area
);
3300 p
= encode_block_structure_desc(p
, blocks
);
3302 if (params
->killer
) {
3304 p
= encode_block_structure_desc(p
, kblocks
);
3306 p
= encode_grid(p
, kgrid
, area
);
3308 assert(p
- desc
< space
);
3310 desc
= sresize(desc
, p
- desc
, char);
3315 static void merge_blocks(struct block_structure
*b
, int n1
, int n2
)
3318 /* Move data towards the lower block number. */
3325 /* Merge n2 into n1, and move the last block into n2's position. */
3326 for (i
= 0; i
< b
->nr_squares
[n2
]; i
++)
3327 b
->whichblock
[b
->blocks
[n2
][i
]] = n1
;
3328 memcpy(b
->blocks
[n1
] + b
->nr_squares
[n1
], b
->blocks
[n2
],
3329 b
->nr_squares
[n2
] * sizeof **b
->blocks
);
3330 b
->nr_squares
[n1
] += b
->nr_squares
[n2
];
3332 n1
= b
->nr_blocks
- 1;
3334 memcpy(b
->blocks
[n2
], b
->blocks
[n1
],
3335 b
->nr_squares
[n1
] * sizeof **b
->blocks
);
3336 for (i
= 0; i
< b
->nr_squares
[n1
]; i
++)
3337 b
->whichblock
[b
->blocks
[n1
][i
]] = n2
;
3338 b
->nr_squares
[n2
] = b
->nr_squares
[n1
];
3343 static void merge_some_cages(struct block_structure
*b
, int cr
, int area
,
3344 digit
*grid
, random_state
*rs
)
3347 /* Find two candidates for merging. */
3349 int x
= 1 + random_bits(rs
, 20) % (cr
- 2);
3350 int y
= 1 + random_bits(rs
, 20) % (cr
- 2);
3352 int off
= random_bits(rs
, 1) == 0 ?
-1 : 1;
3354 unsigned int digits_found
;
3356 if (random_bits(rs
, 1) == 0)
3359 other
= xy
+ off
* cr
;
3360 n1
= b
->whichblock
[xy
];
3361 n2
= b
->whichblock
[other
];
3365 assert(n1
>= 0 && n2
>= 0 && n1
< b
->nr_blocks
&& n2
< b
->nr_blocks
);
3367 if (b
->nr_squares
[n1
] + b
->nr_squares
[n2
] > b
->max_nr_squares
)
3370 /* Guarantee that the merged cage would still be a region. */
3372 for (i
= 0; i
< b
->nr_squares
[n1
]; i
++)
3373 digits_found
|= 1 << grid
[b
->blocks
[n1
][i
]];
3374 for (i
= 0; i
< b
->nr_squares
[n2
]; i
++)
3375 if (digits_found
& (1 << grid
[b
->blocks
[n2
][i
]]))
3377 if (i
!= b
->nr_squares
[n2
])
3380 merge_blocks(b
, n1
, n2
);
3385 static void compute_kclues(struct block_structure
*cages
, digit
*kclues
,
3386 digit
*grid
, int area
)
3389 memset(kclues
, 0, area
* sizeof *kclues
);
3390 for (i
= 0; i
< cages
->nr_blocks
; i
++) {
3392 for (j
= 0; j
< area
; j
++)
3393 if (cages
->whichblock
[j
] == i
)
3395 for (j
= 0; j
< area
; j
++)
3396 if (cages
->whichblock
[j
] == i
)
3403 static struct block_structure
*gen_killer_cages(int cr
, random_state
*rs
,
3404 int remove_singletons
)
3407 int x
, y
, area
= cr
* cr
;
3408 int n_singletons
= 0;
3409 struct block_structure
*b
= alloc_block_structure (1, cr
, area
, cr
, area
);
3411 for (x
= 0; x
< area
; x
++)
3412 b
->whichblock
[x
] = -1;
3414 for (y
= 0; y
< cr
; y
++)
3415 for (x
= 0; x
< cr
; x
++) {
3418 if (b
->whichblock
[xy
] != -1)
3420 b
->whichblock
[xy
] = nr
;
3422 rnd
= random_bits(rs
, 4);
3423 if (xy
+ 1 < area
&& (rnd
>= 4 || (!remove_singletons
&& rnd
>= 1))) {
3425 if (x
+ 1 == cr
|| b
->whichblock
[xy2
] != -1 ||
3426 (xy
+ cr
< area
&& random_bits(rs
, 1) == 0))
3431 b
->whichblock
[xy2
] = nr
;
3438 make_blocks_from_whichblock(b
);
3440 for (x
= y
= 0; x
< b
->nr_blocks
; x
++)
3441 if (b
->nr_squares
[x
] == 1)
3443 assert(y
== n_singletons
);
3445 if (n_singletons
> 0 && remove_singletons
) {
3447 for (n
= 0; n
< b
->nr_blocks
;) {
3448 int xy
, x
, y
, xy2
, other
;
3449 if (b
->nr_squares
[n
] > 1) {
3453 xy
= b
->blocks
[n
][0];
3458 else if (x
+ 1 < cr
&& (y
+ 1 == cr
|| random_bits(rs
, 1) == 0))
3462 other
= b
->whichblock
[xy2
];
3464 if (b
->nr_squares
[other
] == 1)
3467 merge_blocks(b
, n
, other
);
3471 assert(n_singletons
== 0);
3476 static char *new_game_desc(game_params
*params
, random_state
*rs
,
3477 char **aux
, int interactive
)
3479 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
3481 struct block_structure
*blocks
, *kblocks
;
3482 digit
*grid
, *grid2
, *kgrid
;
3483 struct xy
{ int x
, y
; } *locs
;
3486 int coords
[16], ncoords
;
3488 struct difficulty dlev
;
3490 precompute_sum_bits();
3493 * Adjust the maximum difficulty level to be consistent with
3494 * the puzzle size: all 2x2 puzzles appear to be Trivial
3495 * (DIFF_BLOCK) so we cannot hold out for even a Basic
3496 * (DIFF_SIMPLE) one.
3498 dlev
.maxdiff
= params
->diff
;
3499 dlev
.maxkdiff
= params
->kdiff
;
3500 if (c
== 2 && r
== 2)
3501 dlev
.maxdiff
= DIFF_BLOCK
;
3503 grid
= snewn(area
, digit
);
3504 locs
= snewn(area
, struct xy
);
3505 grid2
= snewn(area
, digit
);
3507 blocks
= alloc_block_structure (c
, r
, area
, cr
, cr
);
3509 if (params
->killer
) {
3510 kblocks
= alloc_block_structure (c
, r
, area
, cr
, area
);
3511 kgrid
= snewn(area
, digit
);
3517 #ifdef STANDALONE_SOLVER
3518 assert(!"This should never happen, so we don't need to create blocknames");
3522 * Loop until we get a grid of the required difficulty. This is
3523 * nasty, but it seems to be unpleasantly hard to generate
3524 * difficult grids otherwise.
3528 * Generate a random solved state, starting by
3529 * constructing the block structure.
3531 if (r
== 1) { /* jigsaw mode */
3532 int *dsf
= divvy_rectangle(cr
, cr
, cr
, rs
);
3534 dsf_to_blocks (dsf
, blocks
, cr
, cr
);
3537 } else { /* basic Sudoku mode */
3538 for (y
= 0; y
< cr
; y
++)
3539 for (x
= 0; x
< cr
; x
++)
3540 blocks
->whichblock
[y
*cr
+x
] = (y
/c
) * c
+ (x
/r
);
3542 make_blocks_from_whichblock(blocks
);
3544 if (params
->killer
) {
3545 kblocks
= gen_killer_cages(cr
, rs
, params
->kdiff
> DIFF_KSINGLE
);
3548 if (!gridgen(cr
, blocks
, kblocks
, params
->xtype
, grid
, rs
, area
*area
))
3550 assert(check_valid(cr
, blocks
, kblocks
, params
->xtype
, grid
));
3553 * Save the solved grid in aux.
3557 * We might already have written *aux the last time we
3558 * went round this loop, in which case we should free
3559 * the old aux before overwriting it with the new one.
3565 *aux
= encode_solve_move(cr
, grid
);
3569 * Now we have a solved grid. For normal puzzles, we start removing
3570 * things from it while preserving solubility. Killer puzzles are
3571 * different: we just pass the empty grid to the solver, and use
3572 * the puzzle if it comes back solved.
3575 if (params
->killer
) {
3576 struct block_structure
*good_cages
= NULL
;
3577 struct block_structure
*last_cages
= NULL
;
3580 memcpy(grid2
, grid
, area
);
3583 compute_kclues(kblocks
, kgrid
, grid2
, area
);
3585 memset(grid
, 0, area
* sizeof *grid
);
3586 solver(cr
, blocks
, kblocks
, params
->xtype
, grid
, kgrid
, &dlev
);
3587 if (dlev
.diff
== dlev
.maxdiff
&& dlev
.kdiff
== dlev
.maxkdiff
) {
3589 * We have one that matches our difficulty. Store it for
3590 * later, but keep going.
3593 free_block_structure(good_cages
);
3595 good_cages
= dup_block_structure(kblocks
);
3596 merge_some_cages(kblocks
, cr
, area
, grid2
, rs
);
3597 } else if (dlev
.diff
> dlev
.maxdiff
|| dlev
.kdiff
> dlev
.maxkdiff
) {
3599 * Give up after too many tries and either use the good one we
3600 * found, or generate a new grid.
3605 * The difficulty level got too high. If we have a good
3606 * one, use it, otherwise go back to the last one that
3607 * was at a lower difficulty and restart the process from
3610 if (good_cages
!= NULL
) {
3611 free_block_structure(kblocks
);
3612 kblocks
= dup_block_structure(good_cages
);
3613 merge_some_cages(kblocks
, cr
, area
, grid2
, rs
);
3615 if (last_cages
== NULL
)
3617 free_block_structure(kblocks
);
3618 kblocks
= last_cages
;
3623 free_block_structure(last_cages
);
3624 last_cages
= dup_block_structure(kblocks
);
3625 merge_some_cages(kblocks
, cr
, area
, grid2
, rs
);
3629 free_block_structure(last_cages
);
3630 if (good_cages
!= NULL
) {
3631 free_block_structure(kblocks
);
3632 kblocks
= good_cages
;
3633 compute_kclues(kblocks
, kgrid
, grid2
, area
);
3634 memset(grid
, 0, area
* sizeof *grid
);
3641 * Find the set of equivalence classes of squares permitted
3642 * by the selected symmetry. We do this by enumerating all
3643 * the grid squares which have no symmetric companion
3644 * sorting lower than themselves.
3647 for (y
= 0; y
< cr
; y
++)
3648 for (x
= 0; x
< cr
; x
++) {
3652 ncoords
= symmetries(params
, x
, y
, coords
, params
->symm
);
3653 for (j
= 0; j
< ncoords
; j
++)
3654 if (coords
[2*j
+1]*cr
+coords
[2*j
] < i
)
3664 * Now shuffle that list.
3666 shuffle(locs
, nlocs
, sizeof(*locs
), rs
);
3669 * Now loop over the shuffled list and, for each element,
3670 * see whether removing that element (and its reflections)
3671 * from the grid will still leave the grid soluble.
3673 for (i
= 0; i
< nlocs
; i
++) {
3677 memcpy(grid2
, grid
, area
);
3678 ncoords
= symmetries(params
, x
, y
, coords
, params
->symm
);
3679 for (j
= 0; j
< ncoords
; j
++)
3680 grid2
[coords
[2*j
+1]*cr
+coords
[2*j
]] = 0;
3682 solver(cr
, blocks
, kblocks
, params
->xtype
, grid2
, kgrid
, &dlev
);
3683 if (dlev
.diff
<= dlev
.maxdiff
&&
3684 (!params
->killer
|| dlev
.kdiff
<= dlev
.maxkdiff
)) {
3685 for (j
= 0; j
< ncoords
; j
++)
3686 grid
[coords
[2*j
+1]*cr
+coords
[2*j
]] = 0;
3690 memcpy(grid2
, grid
, area
);
3692 solver(cr
, blocks
, kblocks
, params
->xtype
, grid2
, kgrid
, &dlev
);
3693 if (dlev
.diff
== dlev
.maxdiff
&&
3694 (!params
->killer
|| dlev
.kdiff
== dlev
.maxkdiff
))
3695 break; /* found one! */
3702 * Now we have the grid as it will be presented to the user.
3703 * Encode it in a game desc.
3705 desc
= encode_puzzle_desc(params
, grid
, blocks
, kgrid
, kblocks
);
3712 static char *spec_to_grid(char *desc
, digit
*grid
, int area
)
3715 while (*desc
&& *desc
!= ',') {
3717 if (n
>= 'a' && n
<= 'z') {
3718 int run
= n
- 'a' + 1;
3719 assert(i
+ run
<= area
);
3722 } else if (n
== '_') {
3724 } else if (n
> '0' && n
<= '9') {
3726 grid
[i
++] = atoi(desc
-1);
3727 while (*desc
>= '0' && *desc
<= '9')
3730 assert(!"We can't get here");
3738 * Create a DSF from a spec found in *pdesc. Update this to point past the
3739 * end of the block spec, and return an error string or NULL if everything
3740 * is OK. The DSF is stored in *PDSF.
3742 static char *spec_to_dsf(char **pdesc
, int **pdsf
, int cr
, int area
)
3744 char *desc
= *pdesc
;
3748 *pdsf
= dsf
= snew_dsf(area
);
3750 while (*desc
&& *desc
!= ',') {
3755 else if (*desc
>= 'a' && *desc
<= 'z')
3756 c
= *desc
- 'a' + 1;
3759 return "Invalid character in game description";
3763 adv
= (c
!= 25); /* 'z' is a special case */
3769 * Non-edge; merge the two dsf classes on either
3772 assert(pos
< 2*cr
*(cr
-1));
3773 if (pos
< cr
*(cr
-1)) {
3779 int x
= pos
/(cr
-1) - cr
;
3784 dsf_merge(dsf
, p0
, p1
);
3794 * When desc is exhausted, we expect to have gone exactly
3795 * one space _past_ the end of the grid, due to the dummy
3798 if (pos
!= 2*cr
*(cr
-1)+1) {
3800 return "Not enough data in block structure specification";
3806 static char *validate_grid_desc(char **pdesc
, int range
, int area
)
3808 char *desc
= *pdesc
;
3810 while (*desc
&& *desc
!= ',') {
3812 if (n
>= 'a' && n
<= 'z') {
3813 squares
+= n
- 'a' + 1;
3814 } else if (n
== '_') {
3816 } else if (n
> '0' && n
<= '9') {
3817 int val
= atoi(desc
-1);
3818 if (val
< 1 || val
> range
)
3819 return "Out-of-range number in game description";
3821 while (*desc
>= '0' && *desc
<= '9')
3824 return "Invalid character in game description";
3828 return "Not enough data to fill grid";
3831 return "Too much data to fit in grid";
3836 static char *validate_block_desc(char **pdesc
, int cr
, int area
,
3837 int min_nr_blocks
, int max_nr_blocks
,
3838 int min_nr_squares
, int max_nr_squares
)
3843 err
= spec_to_dsf(pdesc
, &dsf
, cr
, area
);
3848 if (min_nr_squares
== max_nr_squares
) {
3849 assert(min_nr_blocks
== max_nr_blocks
);
3850 assert(min_nr_blocks
* min_nr_squares
== area
);
3853 * Now we've got our dsf. Verify that it matches
3857 int *canons
, *counts
;
3858 int i
, j
, c
, ncanons
= 0;
3860 canons
= snewn(max_nr_blocks
, int);
3861 counts
= snewn(max_nr_blocks
, int);
3863 for (i
= 0; i
< area
; i
++) {
3864 j
= dsf_canonify(dsf
, i
);
3866 for (c
= 0; c
< ncanons
; c
++)
3867 if (canons
[c
] == j
) {
3869 if (counts
[c
] > max_nr_squares
) {
3873 return "A jigsaw block is too big";
3879 if (ncanons
>= max_nr_blocks
) {
3883 return "Too many distinct jigsaw blocks";
3885 canons
[ncanons
] = j
;
3886 counts
[ncanons
] = 1;
3891 if (ncanons
< min_nr_blocks
) {
3895 return "Not enough distinct jigsaw blocks";
3897 for (c
= 0; c
< ncanons
; c
++) {
3898 if (counts
[c
] < min_nr_squares
) {
3902 return "A jigsaw block is too small";
3913 static char *validate_desc(game_params
*params
, char *desc
)
3915 int cr
= params
->c
* params
->r
, area
= cr
*cr
;
3918 err
= validate_grid_desc(&desc
, cr
, area
);
3922 if (params
->r
== 1) {
3924 * Now we expect a suffix giving the jigsaw block
3925 * structure. Parse it and validate that it divides the
3926 * grid into the right number of regions which are the
3930 return "Expected jigsaw block structure in game description";
3932 err
= validate_block_desc(&desc
, cr
, area
, cr
, cr
, cr
, cr
);
3937 if (params
->killer
) {
3939 return "Expected killer block structure in game description";
3941 err
= validate_block_desc(&desc
, cr
, area
, cr
, area
, 2, cr
);
3945 return "Expected killer clue grid in game description";
3947 err
= validate_grid_desc(&desc
, cr
* area
, area
);
3952 return "Unexpected data at end of game description";
3957 static game_state
*new_game(midend
*me
, game_params
*params
, char *desc
)
3959 game_state
*state
= snew(game_state
);
3960 int c
= params
->c
, r
= params
->r
, cr
= c
*r
, area
= cr
* cr
;
3963 precompute_sum_bits();
3966 state
->xtype
= params
->xtype
;
3967 state
->killer
= params
->killer
;
3969 state
->grid
= snewn(area
, digit
);
3970 state
->pencil
= snewn(area
* cr
, unsigned char);
3971 memset(state
->pencil
, 0, area
* cr
);
3972 state
->immutable
= snewn(area
, unsigned char);
3973 memset(state
->immutable
, FALSE
, area
);
3975 state
->blocks
= alloc_block_structure (c
, r
, area
, cr
, cr
);
3977 if (params
->killer
) {
3978 state
->kblocks
= alloc_block_structure (c
, r
, area
, cr
, area
);
3979 state
->kgrid
= snewn(area
, digit
);
3981 state
->kblocks
= NULL
;
3982 state
->kgrid
= NULL
;
3984 state
->completed
= state
->cheated
= FALSE
;
3986 desc
= spec_to_grid(desc
, state
->grid
, area
);
3987 for (i
= 0; i
< area
; i
++)
3988 if (state
->grid
[i
] != 0)
3989 state
->immutable
[i
] = TRUE
;
3994 assert(*desc
== ',');
3996 err
= spec_to_dsf(&desc
, &dsf
, cr
, area
);
3997 assert(err
== NULL
);
3998 dsf_to_blocks(dsf
, state
->blocks
, cr
, cr
);
4003 for (y
= 0; y
< cr
; y
++)
4004 for (x
= 0; x
< cr
; x
++)
4005 state
->blocks
->whichblock
[y
*cr
+x
] = (y
/c
) * c
+ (x
/r
);
4007 make_blocks_from_whichblock(state
->blocks
);
4009 if (params
->killer
) {
4012 assert(*desc
== ',');
4014 err
= spec_to_dsf(&desc
, &dsf
, cr
, area
);
4015 assert(err
== NULL
);
4016 dsf_to_blocks(dsf
, state
->kblocks
, cr
, area
);
4018 make_blocks_from_whichblock(state
->kblocks
);
4020 assert(*desc
== ',');
4022 desc
= spec_to_grid(desc
, state
->kgrid
, area
);
4026 #ifdef STANDALONE_SOLVER
4028 * Set up the block names for solver diagnostic output.
4031 char *p
= (char *)(state
->blocks
->blocknames
+ cr
);
4034 for (i
= 0; i
< area
; i
++) {
4035 int j
= state
->blocks
->whichblock
[i
];
4036 if (!state
->blocks
->blocknames
[j
]) {
4037 state
->blocks
->blocknames
[j
] = p
;
4038 p
+= 1 + sprintf(p
, "starting at (%d,%d)",
4039 1 + i
%cr
, 1 + i
/cr
);
4044 for (by
= 0; by
< r
; by
++)
4045 for (bx
= 0; bx
< c
; bx
++) {
4046 state
->blocks
->blocknames
[by
*c
+bx
] = p
;
4047 p
+= 1 + sprintf(p
, "(%d,%d)", bx
+1, by
+1);
4050 assert(p
- (char *)state
->blocks
->blocknames
< (int)(cr
*(sizeof(char *)+80)));
4051 for (i
= 0; i
< cr
; i
++)
4052 assert(state
->blocks
->blocknames
[i
]);
4059 static game_state
*dup_game(game_state
*state
)
4061 game_state
*ret
= snew(game_state
);
4062 int cr
= state
->cr
, area
= cr
* cr
;
4064 ret
->cr
= state
->cr
;
4065 ret
->xtype
= state
->xtype
;
4066 ret
->killer
= state
->killer
;
4068 ret
->blocks
= state
->blocks
;
4069 ret
->blocks
->refcount
++;
4071 ret
->kblocks
= state
->kblocks
;
4073 ret
->kblocks
->refcount
++;
4075 ret
->grid
= snewn(area
, digit
);
4076 memcpy(ret
->grid
, state
->grid
, area
);
4078 if (state
->killer
) {
4079 ret
->kgrid
= snewn(area
, digit
);
4080 memcpy(ret
->kgrid
, state
->kgrid
, area
);
4084 ret
->pencil
= snewn(area
* cr
, unsigned char);
4085 memcpy(ret
->pencil
, state
->pencil
, area
* cr
);
4087 ret
->immutable
= snewn(area
, unsigned char);
4088 memcpy(ret
->immutable
, state
->immutable
, area
);
4090 ret
->completed
= state
->completed
;
4091 ret
->cheated
= state
->cheated
;
4096 static void free_game(game_state
*state
)
4098 free_block_structure(state
->blocks
);
4100 free_block_structure(state
->kblocks
);
4102 sfree(state
->immutable
);
4103 sfree(state
->pencil
);
4108 static char *solve_game(game_state
*state
, game_state
*currstate
,
4109 char *ai
, char **error
)
4114 struct difficulty dlev
;
4117 * If we already have the solution in ai, save ourselves some
4123 grid
= snewn(cr
*cr
, digit
);
4124 memcpy(grid
, state
->grid
, cr
*cr
);
4125 dlev
.maxdiff
= DIFF_RECURSIVE
;
4126 dlev
.maxkdiff
= DIFF_KINTERSECT
;
4127 solver(cr
, state
->blocks
, state
->kblocks
, state
->xtype
, grid
,
4128 state
->kgrid
, &dlev
);
4132 if (dlev
.diff
== DIFF_IMPOSSIBLE
)
4133 *error
= "No solution exists for this puzzle";
4134 else if (dlev
.diff
== DIFF_AMBIGUOUS
)
4135 *error
= "Multiple solutions exist for this puzzle";
4142 ret
= encode_solve_move(cr
, grid
);
4149 static char *grid_text_format(int cr
, struct block_structure
*blocks
,
4150 int xtype
, digit
*grid
)
4154 int totallen
, linelen
, nlines
;
4158 * For non-jigsaw Sudoku, we format in the way we always have,
4159 * by having the digits unevenly spaced so that the dividing
4168 * For jigsaw puzzles, however, we must leave space between
4169 * _all_ pairs of digits for an optional dividing line, so we
4170 * have to move to the rather ugly
4180 * We deal with both cases using the same formatting code; we
4181 * simply invent a vmod value such that there's a vertical
4182 * dividing line before column i iff i is divisible by vmod
4183 * (so it's r in the first case and 1 in the second), and hmod
4184 * likewise for horizontal dividing lines.
4187 if (blocks
->r
!= 1) {
4195 * Line length: we have cr digits, each with a space after it,
4196 * and (cr-1)/vmod dividing lines, each with a space after it.
4197 * The final space is replaced by a newline, but that doesn't
4198 * affect the length.
4200 linelen
= 2*(cr
+ (cr
-1)/vmod
);
4203 * Number of lines: we have cr rows of digits, and (cr-1)/hmod
4206 nlines
= cr
+ (cr
-1)/hmod
;
4209 * Allocate the space.
4211 totallen
= linelen
* nlines
;
4212 ret
= snewn(totallen
+1, char); /* leave room for terminating NUL */
4218 for (y
= 0; y
< cr
; y
++) {
4222 for (x
= 0; x
< cr
; x
++) {
4226 digit d
= grid
[y
*cr
+x
];
4230 * Empty space: we usually write a dot, but we'll
4231 * highlight spaces on the X-diagonals (in X mode)
4232 * by using underscores instead.
4234 if (xtype
&& (ondiag0(y
*cr
+x
) || ondiag1(y
*cr
+x
)))
4238 } else if (d
<= 9) {
4255 * Optional dividing line.
4257 if (blocks
->whichblock
[y
*cr
+x
] != blocks
->whichblock
[y
*cr
+x
+1])
4264 if (y
== cr
-1 || (y
+1) % hmod
)
4270 for (x
= 0; x
< cr
; x
++) {
4275 * Division between two squares. This varies
4276 * complicatedly in length.
4278 dwid
= 2; /* digit and its following space */
4280 dwid
--; /* no following space at end of line */
4281 if (x
> 0 && x
% vmod
== 0)
4282 dwid
++; /* preceding space after a divider */
4284 if (blocks
->whichblock
[y
*cr
+x
] != blocks
->whichblock
[(y
+1)*cr
+x
])
4301 * Corner square. This is:
4302 * - a space if all four surrounding squares are in
4304 * - a vertical line if the two left ones are in one
4305 * block and the two right in another
4306 * - a horizontal line if the two top ones are in one
4307 * block and the two bottom in another
4308 * - a plus sign in all other cases. (If we had a
4309 * richer character set available we could break
4310 * this case up further by doing fun things with
4311 * line-drawing T-pieces.)
4313 tl
= blocks
->whichblock
[y
*cr
+x
];
4314 tr
= blocks
->whichblock
[y
*cr
+x
+1];
4315 bl
= blocks
->whichblock
[(y
+1)*cr
+x
];
4316 br
= blocks
->whichblock
[(y
+1)*cr
+x
+1];
4318 if (tl
== tr
&& tr
== bl
&& bl
== br
)
4320 else if (tl
== bl
&& tr
== br
)
4322 else if (tl
== tr
&& bl
== br
)
4331 assert(p
- ret
== totallen
);
4336 static int game_can_format_as_text_now(game_params
*params
)
4339 * Formatting Killer puzzles as text is currently unsupported. I
4340 * can't think of any sensible way of doing it which doesn't
4341 * involve expanding the puzzle to such a large scale as to make
4349 static char *game_text_format(game_state
*state
)
4351 assert(!state
->kblocks
);
4352 return grid_text_format(state
->cr
, state
->blocks
, state
->xtype
,
4358 * These are the coordinates of the currently highlighted
4359 * square on the grid, if hshow = 1.
4363 * This indicates whether the current highlight is a
4364 * pencil-mark one or a real one.
4368 * This indicates whether or not we're showing the highlight
4369 * (used to be hx = hy = -1); important so that when we're
4370 * using the cursor keys it doesn't keep coming back at a
4371 * fixed position. When hshow = 1, pressing a valid number
4372 * or letter key or Space will enter that number or letter in the grid.
4376 * This indicates whether we're using the highlight as a cursor;
4377 * it means that it doesn't vanish on a keypress, and that it is
4378 * allowed on immutable squares.
4383 static game_ui
*new_ui(game_state
*state
)
4385 game_ui
*ui
= snew(game_ui
);
4387 ui
->hx
= ui
->hy
= 0;
4388 ui
->hpencil
= ui
->hshow
= ui
->hcursor
= 0;
4393 static void free_ui(game_ui
*ui
)
4398 static char *encode_ui(game_ui
*ui
)
4403 static void decode_ui(game_ui
*ui
, char *encoding
)
4407 static void game_changed_state(game_ui
*ui
, game_state
*oldstate
,
4408 game_state
*newstate
)
4410 int cr
= newstate
->cr
;
4412 * We prevent pencil-mode highlighting of a filled square, unless
4413 * we're using the cursor keys. So if the user has just filled in
4414 * a square which we had a pencil-mode highlight in (by Undo, or
4415 * by Redo, or by Solve), then we cancel the highlight.
4417 if (ui
->hshow
&& ui
->hpencil
&& !ui
->hcursor
&&
4418 newstate
->grid
[ui
->hy
* cr
+ ui
->hx
] != 0) {
4423 struct game_drawstate
{
4428 unsigned char *pencil
;
4430 /* This is scratch space used within a single call to game_redraw. */
4431 int nregions
, *entered_items
;
4434 static char *interpret_move(game_state
*state
, game_ui
*ui
, game_drawstate
*ds
,
4435 int x
, int y
, int button
)
4441 button
&= ~MOD_MASK
;
4443 tx
= (x
+ TILE_SIZE
- BORDER
) / TILE_SIZE
- 1;
4444 ty
= (y
+ TILE_SIZE
- BORDER
) / TILE_SIZE
- 1;
4446 if (tx
>= 0 && tx
< cr
&& ty
>= 0 && ty
< cr
) {
4447 if (button
== LEFT_BUTTON
) {
4448 if (state
->immutable
[ty
*cr
+tx
]) {
4450 } else if (tx
== ui
->hx
&& ty
== ui
->hy
&&
4451 ui
->hshow
&& ui
->hpencil
== 0) {
4460 return ""; /* UI activity occurred */
4462 if (button
== RIGHT_BUTTON
) {
4464 * Pencil-mode highlighting for non filled squares.
4466 if (state
->grid
[ty
*cr
+tx
] == 0) {
4467 if (tx
== ui
->hx
&& ty
== ui
->hy
&&
4468 ui
->hshow
&& ui
->hpencil
) {
4480 return ""; /* UI activity occurred */
4483 if (IS_CURSOR_MOVE(button
)) {
4484 move_cursor(button
, &ui
->hx
, &ui
->hy
, cr
, cr
, 0);
4485 ui
->hshow
= ui
->hcursor
= 1;
4489 (button
== CURSOR_SELECT
)) {
4490 ui
->hpencil
= 1 - ui
->hpencil
;
4496 ((button
>= '0' && button
<= '9' && button
- '0' <= cr
) ||
4497 (button
>= 'a' && button
<= 'z' && button
- 'a' + 10 <= cr
) ||
4498 (button
>= 'A' && button
<= 'Z' && button
- 'A' + 10 <= cr
) ||
4499 button
== CURSOR_SELECT2
|| button
== '\010' || button
== '\177')) {
4500 int n
= button
- '0';
4501 if (button
>= 'A' && button
<= 'Z')
4502 n
= button
- 'A' + 10;
4503 if (button
>= 'a' && button
<= 'z')
4504 n
= button
- 'a' + 10;
4505 if (button
== CURSOR_SELECT2
|| button
== '\010' || button
== '\177')
4509 * Can't overwrite this square. This can only happen here
4510 * if we're using the cursor keys.
4512 if (state
->immutable
[ui
->hy
*cr
+ui
->hx
])
4516 * Can't make pencil marks in a filled square. Again, this
4517 * can only become highlighted if we're using cursor keys.
4519 if (ui
->hpencil
&& state
->grid
[ui
->hy
*cr
+ui
->hx
])
4522 sprintf(buf
, "%c%d,%d,%d",
4523 (char)(ui
->hpencil
&& n
> 0 ?
'P' : 'R'), ui
->hx
, ui
->hy
, n
);
4525 if (!ui
->hcursor
) ui
->hshow
= 0;
4533 static game_state
*execute_move(game_state
*from
, char *move
)
4539 if (move
[0] == 'S') {
4542 ret
= dup_game(from
);
4543 ret
->completed
= ret
->cheated
= TRUE
;
4546 for (n
= 0; n
< cr
*cr
; n
++) {
4547 ret
->grid
[n
] = atoi(p
);
4549 if (!*p
|| ret
->grid
[n
] < 1 || ret
->grid
[n
] > cr
) {
4554 while (*p
&& isdigit((unsigned char)*p
)) p
++;
4559 } else if ((move
[0] == 'P' || move
[0] == 'R') &&
4560 sscanf(move
+1, "%d,%d,%d", &x
, &y
, &n
) == 3 &&
4561 x
>= 0 && x
< cr
&& y
>= 0 && y
< cr
&& n
>= 0 && n
<= cr
) {
4563 ret
= dup_game(from
);
4564 if (move
[0] == 'P' && n
> 0) {
4565 int index
= (y
*cr
+x
) * cr
+ (n
-1);
4566 ret
->pencil
[index
] = !ret
->pencil
[index
];
4568 ret
->grid
[y
*cr
+x
] = n
;
4569 memset(ret
->pencil
+ (y
*cr
+x
)*cr
, 0, cr
);
4572 * We've made a real change to the grid. Check to see
4573 * if the game has been completed.
4575 if (!ret
->completed
&& check_valid(cr
, ret
->blocks
, ret
->kblocks
,
4576 ret
->xtype
, ret
->grid
)) {
4577 ret
->completed
= TRUE
;
4582 return NULL
; /* couldn't parse move string */
4585 /* ----------------------------------------------------------------------
4589 #define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
4590 #define GETTILESIZE(cr, w) ( (double)(w-1) / (double)(cr+1) )
4592 static void game_compute_size(game_params
*params
, int tilesize
,
4595 /* Ick: fake up `ds->tilesize' for macro expansion purposes */
4596 struct { int tilesize
; } ads
, *ds
= &ads
;
4597 ads
.tilesize
= tilesize
;
4599 *x
= SIZE(params
->c
* params
->r
);
4600 *y
= SIZE(params
->c
* params
->r
);
4603 static void game_set_size(drawing
*dr
, game_drawstate
*ds
,
4604 game_params
*params
, int tilesize
)
4606 ds
->tilesize
= tilesize
;
4609 static float *game_colours(frontend
*fe
, int *ncolours
)
4611 float *ret
= snewn(3 * NCOLOURS
, float);
4613 frontend_default_colour(fe
, &ret
[COL_BACKGROUND
* 3]);
4615 ret
[COL_XDIAGONALS
* 3 + 0] = 0.9F
* ret
[COL_BACKGROUND
* 3 + 0];
4616 ret
[COL_XDIAGONALS
* 3 + 1] = 0.9F
* ret
[COL_BACKGROUND
* 3 + 1];
4617 ret
[COL_XDIAGONALS
* 3 + 2] = 0.9F
* ret
[COL_BACKGROUND
* 3 + 2];
4619 ret
[COL_GRID
* 3 + 0] = 0.0F
;
4620 ret
[COL_GRID
* 3 + 1] = 0.0F
;
4621 ret
[COL_GRID
* 3 + 2] = 0.0F
;
4623 ret
[COL_CLUE
* 3 + 0] = 0.0F
;
4624 ret
[COL_CLUE
* 3 + 1] = 0.0F
;
4625 ret
[COL_CLUE
* 3 + 2] = 0.0F
;
4627 ret
[COL_USER
* 3 + 0] = 0.0F
;
4628 ret
[COL_USER
* 3 + 1] = 0.6F
* ret
[COL_BACKGROUND
* 3 + 1];
4629 ret
[COL_USER
* 3 + 2] = 0.0F
;
4631 ret
[COL_HIGHLIGHT
* 3 + 0] = 0.78F
* ret
[COL_BACKGROUND
* 3 + 0];
4632 ret
[COL_HIGHLIGHT
* 3 + 1] = 0.78F
* ret
[COL_BACKGROUND
* 3 + 1];
4633 ret
[COL_HIGHLIGHT
* 3 + 2] = 0.78F
* ret
[COL_BACKGROUND
* 3 + 2];
4635 ret
[COL_ERROR
* 3 + 0] = 1.0F
;
4636 ret
[COL_ERROR
* 3 + 1] = 0.0F
;
4637 ret
[COL_ERROR
* 3 + 2] = 0.0F
;
4639 ret
[COL_PENCIL
* 3 + 0] = 0.5F
* ret
[COL_BACKGROUND
* 3 + 0];
4640 ret
[COL_PENCIL
* 3 + 1] = 0.5F
* ret
[COL_BACKGROUND
* 3 + 1];
4641 ret
[COL_PENCIL
* 3 + 2] = ret
[COL_BACKGROUND
* 3 + 2];
4643 ret
[COL_KILLER
* 3 + 0] = 0.5F
* ret
[COL_BACKGROUND
* 3 + 0];
4644 ret
[COL_KILLER
* 3 + 1] = 0.5F
* ret
[COL_BACKGROUND
* 3 + 1];
4645 ret
[COL_KILLER
* 3 + 2] = 0.1F
* ret
[COL_BACKGROUND
* 3 + 2];
4647 *ncolours
= NCOLOURS
;
4651 static game_drawstate
*game_new_drawstate(drawing
*dr
, game_state
*state
)
4653 struct game_drawstate
*ds
= snew(struct game_drawstate
);
4656 ds
->started
= FALSE
;
4658 ds
->xtype
= state
->xtype
;
4659 ds
->grid
= snewn(cr
*cr
, digit
);
4660 memset(ds
->grid
, cr
+2, cr
*cr
);
4661 ds
->pencil
= snewn(cr
*cr
*cr
, digit
);
4662 memset(ds
->pencil
, 0, cr
*cr
*cr
);
4663 ds
->hl
= snewn(cr
*cr
, unsigned char);
4664 memset(ds
->hl
, 0, cr
*cr
);
4666 * ds->entered_items needs one row of cr entries per entity in
4667 * which digits may not be duplicated. That's one for each row,
4668 * each column, each block, each diagonal, and each Killer cage.
4670 ds
->nregions
= cr
*3 + 2;
4672 ds
->nregions
+= state
->kblocks
->nr_blocks
;
4673 ds
->entered_items
= snewn(cr
* ds
->nregions
, int);
4674 ds
->tilesize
= 0; /* not decided yet */
4678 static void game_free_drawstate(drawing
*dr
, game_drawstate
*ds
)
4683 sfree(ds
->entered_items
);
4687 static void draw_number(drawing
*dr
, game_drawstate
*ds
, game_state
*state
,
4688 int x
, int y
, int hl
)
4693 int col_killer
= (hl
& 32 ? COL_ERROR
: COL_KILLER
);
4696 if (ds
->grid
[y
*cr
+x
] == state
->grid
[y
*cr
+x
] &&
4697 ds
->hl
[y
*cr
+x
] == hl
&&
4698 !memcmp(ds
->pencil
+(y
*cr
+x
)*cr
, state
->pencil
+(y
*cr
+x
)*cr
, cr
))
4699 return; /* no change required */
4701 tx
= BORDER
+ x
* TILE_SIZE
+ 1 + GRIDEXTRA
;
4702 ty
= BORDER
+ y
* TILE_SIZE
+ 1 + GRIDEXTRA
;
4706 cw
= tw
= TILE_SIZE
-1-2*GRIDEXTRA
;
4707 ch
= th
= TILE_SIZE
-1-2*GRIDEXTRA
;
4709 if (x
> 0 && state
->blocks
->whichblock
[y
*cr
+x
] == state
->blocks
->whichblock
[y
*cr
+x
-1])
4710 cx
-= GRIDEXTRA
, cw
+= GRIDEXTRA
;
4711 if (x
+1 < cr
&& state
->blocks
->whichblock
[y
*cr
+x
] == state
->blocks
->whichblock
[y
*cr
+x
+1])
4713 if (y
> 0 && state
->blocks
->whichblock
[y
*cr
+x
] == state
->blocks
->whichblock
[(y
-1)*cr
+x
])
4714 cy
-= GRIDEXTRA
, ch
+= GRIDEXTRA
;
4715 if (y
+1 < cr
&& state
->blocks
->whichblock
[y
*cr
+x
] == state
->blocks
->whichblock
[(y
+1)*cr
+x
])
4718 clip(dr
, cx
, cy
, cw
, ch
);
4720 /* background needs erasing */
4721 draw_rect(dr
, cx
, cy
, cw
, ch
,
4722 ((hl
& 15) == 1 ? COL_HIGHLIGHT
:
4723 (ds
->xtype
&& (ondiag0(y
*cr
+x
) || ondiag1(y
*cr
+x
))) ? COL_XDIAGONALS
:
4727 * Draw the corners of thick lines in corner-adjacent squares,
4728 * which jut into this square by one pixel.
4730 if (x
> 0 && y
> 0 && state
->blocks
->whichblock
[y
*cr
+x
] != state
->blocks
->whichblock
[(y
-1)*cr
+x
-1])
4731 draw_rect(dr
, tx
-GRIDEXTRA
, ty
-GRIDEXTRA
, GRIDEXTRA
, GRIDEXTRA
, COL_GRID
);
4732 if (x
+1 < cr
&& y
> 0 && state
->blocks
->whichblock
[y
*cr
+x
] != state
->blocks
->whichblock
[(y
-1)*cr
+x
+1])
4733 draw_rect(dr
, tx
+TILE_SIZE
-1-2*GRIDEXTRA
, ty
-GRIDEXTRA
, GRIDEXTRA
, GRIDEXTRA
, COL_GRID
);
4734 if (x
> 0 && y
+1 < cr
&& state
->blocks
->whichblock
[y
*cr
+x
] != state
->blocks
->whichblock
[(y
+1)*cr
+x
-1])
4735 draw_rect(dr
, tx
-GRIDEXTRA
, ty
+TILE_SIZE
-1-2*GRIDEXTRA
, GRIDEXTRA
, GRIDEXTRA
, COL_GRID
);
4736 if (x
+1 < cr
&& y
+1 < cr
&& state
->blocks
->whichblock
[y
*cr
+x
] != state
->blocks
->whichblock
[(y
+1)*cr
+x
+1])
4737 draw_rect(dr
, tx
+TILE_SIZE
-1-2*GRIDEXTRA
, ty
+TILE_SIZE
-1-2*GRIDEXTRA
, GRIDEXTRA
, GRIDEXTRA
, COL_GRID
);
4739 /* pencil-mode highlight */
4740 if ((hl
& 15) == 2) {
4744 coords
[2] = cx
+cw
/2;
4747 coords
[5] = cy
+ch
/2;
4748 draw_polygon(dr
, coords
, 3, COL_HIGHLIGHT
, COL_HIGHLIGHT
);
4751 if (state
->kblocks
) {
4752 int t
= GRIDEXTRA
* 3;
4753 int kcx
, kcy
, kcw
, kch
;
4755 int has_left
= 0, has_right
= 0, has_top
= 0, has_bottom
= 0;
4758 * In non-jigsaw mode, the Killer cages are placed at a
4759 * fixed offset from the outer edge of the cell dividing
4760 * lines, so that they look right whether those lines are
4761 * thick or thin. In jigsaw mode, however, doing this will
4762 * sometimes cause the cage outlines in adjacent squares to
4763 * fail to match up with each other, so we must offset a
4764 * fixed amount from the _centre_ of the cell dividing
4767 if (state
->blocks
->r
== 1) {
4784 * First, draw the lines dividing this area from neighbouring
4787 if (x
== 0 || state
->kblocks
->whichblock
[y
*cr
+x
] != state
->kblocks
->whichblock
[y
*cr
+x
-1])
4788 has_left
= 1, kl
+= t
;
4789 if (x
+1 >= cr
|| state
->kblocks
->whichblock
[y
*cr
+x
] != state
->kblocks
->whichblock
[y
*cr
+x
+1])
4790 has_right
= 1, kr
-= t
;
4791 if (y
== 0 || state
->kblocks
->whichblock
[y
*cr
+x
] != state
->kblocks
->whichblock
[(y
-1)*cr
+x
])
4792 has_top
= 1, kt
+= t
;
4793 if (y
+1 >= cr
|| state
->kblocks
->whichblock
[y
*cr
+x
] != state
->kblocks
->whichblock
[(y
+1)*cr
+x
])
4794 has_bottom
= 1, kb
-= t
;
4796 draw_line(dr
, kl
, kt
, kr
, kt
, col_killer
);
4798 draw_line(dr
, kl
, kb
, kr
, kb
, col_killer
);
4800 draw_line(dr
, kl
, kt
, kl
, kb
, col_killer
);
4802 draw_line(dr
, kr
, kt
, kr
, kb
, col_killer
);
4804 * Now, take care of the corners (just as for the normal borders).
4805 * We only need a corner if there wasn't a full edge.
4807 if (x
> 0 && y
> 0 && !has_left
&& !has_top
4808 && state
->kblocks
->whichblock
[y
*cr
+x
] != state
->kblocks
->whichblock
[(y
-1)*cr
+x
-1])
4810 draw_line(dr
, kl
, kt
+ t
, kl
+ t
, kt
+ t
, col_killer
);
4811 draw_line(dr
, kl
+ t
, kt
, kl
+ t
, kt
+ t
, col_killer
);
4813 if (x
+1 < cr
&& y
> 0 && !has_right
&& !has_top
4814 && state
->kblocks
->whichblock
[y
*cr
+x
] != state
->kblocks
->whichblock
[(y
-1)*cr
+x
+1])
4816 draw_line(dr
, kcx
+ kcw
- t
, kt
+ t
, kcx
+ kcw
, kt
+ t
, col_killer
);
4817 draw_line(dr
, kcx
+ kcw
- t
, kt
, kcx
+ kcw
- t
, kt
+ t
, col_killer
);
4819 if (x
> 0 && y
+1 < cr
&& !has_left
&& !has_bottom
4820 && state
->kblocks
->whichblock
[y
*cr
+x
] != state
->kblocks
->whichblock
[(y
+1)*cr
+x
-1])
4822 draw_line(dr
, kl
, kcy
+ kch
- t
, kl
+ t
, kcy
+ kch
- t
, col_killer
);
4823 draw_line(dr
, kl
+ t
, kcy
+ kch
- t
, kl
+ t
, kcy
+ kch
, col_killer
);
4825 if (x
+1 < cr
&& y
+1 < cr
&& !has_right
&& !has_bottom
4826 && state
->kblocks
->whichblock
[y
*cr
+x
] != state
->kblocks
->whichblock
[(y
+1)*cr
+x
+1])
4828 draw_line(dr
, kcx
+ kcw
- t
, kcy
+ kch
- t
, kcx
+ kcw
- t
, kcy
+ kch
, col_killer
);
4829 draw_line(dr
, kcx
+ kcw
- t
, kcy
+ kch
- t
, kcx
+ kcw
, kcy
+ kch
- t
, col_killer
);
4834 if (state
->killer
&& state
->kgrid
[y
*cr
+x
]) {
4835 sprintf (str
, "%d", state
->kgrid
[y
*cr
+x
]);
4836 draw_text(dr
, tx
+ GRIDEXTRA
* 4, ty
+ GRIDEXTRA
* 4 + TILE_SIZE
/4,
4837 FONT_VARIABLE
, TILE_SIZE
/4, ALIGN_VNORMAL
| ALIGN_HLEFT
,
4841 /* new number needs drawing? */
4842 if (state
->grid
[y
*cr
+x
]) {
4844 str
[0] = state
->grid
[y
*cr
+x
] + '0';
4846 str
[0] += 'a' - ('9'+1);
4847 draw_text(dr
, tx
+ TILE_SIZE
/2, ty
+ TILE_SIZE
/2,
4848 FONT_VARIABLE
, TILE_SIZE
/2, ALIGN_VCENTRE
| ALIGN_HCENTRE
,
4849 state
->immutable
[y
*cr
+x
] ? COL_CLUE
: (hl
& 16) ? COL_ERROR
: COL_USER
, str
);
4854 int pw
, ph
, minph
, pbest
, fontsize
;
4856 /* Count the pencil marks required. */
4857 for (i
= npencil
= 0; i
< cr
; i
++)
4858 if (state
->pencil
[(y
*cr
+x
)*cr
+i
])
4865 * Determine the bounding rectangle within which we're going
4866 * to put the pencil marks.
4868 /* Start with the whole square */
4869 pl
= tx
+ GRIDEXTRA
;
4870 pr
= pl
+ TILE_SIZE
- GRIDEXTRA
;
4871 pt
= ty
+ GRIDEXTRA
;
4872 pb
= pt
+ TILE_SIZE
- GRIDEXTRA
;
4873 if (state
->killer
) {
4875 * Make space for the Killer cages. We do this
4876 * unconditionally, for uniformity between squares,
4877 * rather than making it depend on whether a Killer
4878 * cage edge is actually present on any given side.
4880 pl
+= GRIDEXTRA
* 3;
4881 pr
-= GRIDEXTRA
* 3;
4882 pt
+= GRIDEXTRA
* 3;
4883 pb
-= GRIDEXTRA
* 3;
4884 if (state
->kgrid
[y
*cr
+x
] != 0) {
4885 /* Make further space for the Killer number. */
4892 * We arrange our pencil marks in a grid layout, with
4893 * the number of rows and columns adjusted to allow the
4894 * maximum font size.
4896 * So now we work out what the grid size ought to be.
4901 for (pw
= 3; pw
< max(npencil
,4); pw
++) {
4904 ph
= (npencil
+ pw
- 1) / pw
;
4905 ph
= max(ph
, minph
);
4906 fw
= (pr
- pl
) / (float)pw
;
4907 fh
= (pb
- pt
) / (float)ph
;
4909 if (fs
> bestsize
) {
4916 ph
= (npencil
+ pw
- 1) / pw
;
4917 ph
= max(ph
, minph
);
4920 * Now we've got our grid dimensions, work out the pixel
4921 * size of a grid element, and round it to the nearest
4922 * pixel. (We don't want rounding errors to make the
4923 * grid look uneven at low pixel sizes.)
4925 fontsize
= min((pr
- pl
) / pw
, (pb
- pt
) / ph
);
4928 * Centre the resulting figure in the square.
4930 pl
= tx
+ (TILE_SIZE
- fontsize
* pw
) / 2;
4931 pt
= ty
+ (TILE_SIZE
- fontsize
* ph
) / 2;
4934 * And move it down a bit if it's collided with the
4935 * Killer cage number.
4937 if (state
->killer
&& state
->kgrid
[y
*cr
+x
] != 0) {
4938 pt
= max(pt
, ty
+ GRIDEXTRA
* 3 + TILE_SIZE
/4);
4942 * Now actually draw the pencil marks.
4944 for (i
= j
= 0; i
< cr
; i
++)
4945 if (state
->pencil
[(y
*cr
+x
)*cr
+i
]) {
4946 int dx
= j
% pw
, dy
= j
/ pw
;
4951 str
[0] += 'a' - ('9'+1);
4952 draw_text(dr
, pl
+ fontsize
* (2*dx
+1) / 2,
4953 pt
+ fontsize
* (2*dy
+1) / 2,
4954 FONT_VARIABLE
, fontsize
,
4955 ALIGN_VCENTRE
| ALIGN_HCENTRE
, COL_PENCIL
, str
);
4963 draw_update(dr
, cx
, cy
, cw
, ch
);
4965 ds
->grid
[y
*cr
+x
] = state
->grid
[y
*cr
+x
];
4966 memcpy(ds
->pencil
+(y
*cr
+x
)*cr
, state
->pencil
+(y
*cr
+x
)*cr
, cr
);
4967 ds
->hl
[y
*cr
+x
] = hl
;
4970 static void game_redraw(drawing
*dr
, game_drawstate
*ds
, game_state
*oldstate
,
4971 game_state
*state
, int dir
, game_ui
*ui
,
4972 float animtime
, float flashtime
)
4979 * The initial contents of the window are not guaranteed
4980 * and can vary with front ends. To be on the safe side,
4981 * all games should start by drawing a big
4982 * background-colour rectangle covering the whole window.
4984 draw_rect(dr
, 0, 0, SIZE(cr
), SIZE(cr
), COL_BACKGROUND
);
4987 * Draw the grid. We draw it as a big thick rectangle of
4988 * COL_GRID initially; individual calls to draw_number()
4989 * will poke the right-shaped holes in it.
4991 draw_rect(dr
, BORDER
-GRIDEXTRA
, BORDER
-GRIDEXTRA
,
4992 cr
*TILE_SIZE
+1+2*GRIDEXTRA
, cr
*TILE_SIZE
+1+2*GRIDEXTRA
,
4997 * This array is used to keep track of rows, columns and boxes
4998 * which contain a number more than once.
5000 for (x
= 0; x
< cr
* ds
->nregions
; x
++)
5001 ds
->entered_items
[x
] = 0;
5002 for (x
= 0; x
< cr
; x
++)
5003 for (y
= 0; y
< cr
; y
++) {
5004 digit d
= state
->grid
[y
*cr
+x
];
5009 ds
->entered_items
[x
*cr
+d
-1]++;
5012 ds
->entered_items
[(y
+cr
)*cr
+d
-1]++;
5015 box
= state
->blocks
->whichblock
[y
*cr
+x
];
5016 ds
->entered_items
[(box
+2*cr
)*cr
+d
-1]++;
5020 if (ondiag0(y
*cr
+x
))
5021 ds
->entered_items
[(3*cr
)*cr
+d
-1]++;
5022 if (ondiag1(y
*cr
+x
))
5023 ds
->entered_items
[(3*cr
+1)*cr
+d
-1]++;
5027 if (state
->kblocks
) {
5028 kbox
= state
->kblocks
->whichblock
[y
*cr
+x
];
5029 ds
->entered_items
[(kbox
+3*cr
+2)*cr
+d
-1]++;
5035 * Draw any numbers which need redrawing.
5037 for (x
= 0; x
< cr
; x
++) {
5038 for (y
= 0; y
< cr
; y
++) {
5040 digit d
= state
->grid
[y
*cr
+x
];
5042 if (flashtime
> 0 &&
5043 (flashtime
<= FLASH_TIME
/3 ||
5044 flashtime
>= FLASH_TIME
*2/3))
5047 /* Highlight active input areas. */
5048 if (x
== ui
->hx
&& y
== ui
->hy
&& ui
->hshow
)
5049 highlight
= ui
->hpencil ?
2 : 1;
5051 /* Mark obvious errors (ie, numbers which occur more than once
5052 * in a single row, column, or box). */
5053 if (d
&& (ds
->entered_items
[x
*cr
+d
-1] > 1 ||
5054 ds
->entered_items
[(y
+cr
)*cr
+d
-1] > 1 ||
5055 ds
->entered_items
[(state
->blocks
->whichblock
[y
*cr
+x
]
5056 +2*cr
)*cr
+d
-1] > 1 ||
5057 (ds
->xtype
&& ((ondiag0(y
*cr
+x
) &&
5058 ds
->entered_items
[(3*cr
)*cr
+d
-1] > 1) ||
5060 ds
->entered_items
[(3*cr
+1)*cr
+d
-1]>1)))||
5062 ds
->entered_items
[(state
->kblocks
->whichblock
[y
*cr
+x
]
5063 +3*cr
+2)*cr
+d
-1] > 1)))
5066 if (d
&& state
->kblocks
) {
5067 int i
, b
= state
->kblocks
->whichblock
[y
*cr
+x
];
5068 int n_squares
= state
->kblocks
->nr_squares
[b
];
5069 int sum
= 0, clue
= 0;
5070 for (i
= 0; i
< n_squares
; i
++) {
5071 int xy
= state
->kblocks
->blocks
[b
][i
];
5072 if (state
->grid
[xy
] == 0)
5075 sum
+= state
->grid
[xy
];
5076 if (state
->kgrid
[xy
]) {
5078 clue
= state
->kgrid
[xy
];
5082 if (i
== n_squares
) {
5089 draw_number(dr
, ds
, state
, x
, y
, highlight
);
5094 * Update the _entire_ grid if necessary.
5097 draw_update(dr
, 0, 0, SIZE(cr
), SIZE(cr
));
5102 static float game_anim_length(game_state
*oldstate
, game_state
*newstate
,
5103 int dir
, game_ui
*ui
)
5108 static float game_flash_length(game_state
*oldstate
, game_state
*newstate
,
5109 int dir
, game_ui
*ui
)
5111 if (!oldstate
->completed
&& newstate
->completed
&&
5112 !oldstate
->cheated
&& !newstate
->cheated
)
5117 static int game_timing_state(game_state
*state
, game_ui
*ui
)
5119 if (state
->completed
)
5124 static void game_print_size(game_params
*params
, float *x
, float *y
)
5129 * I'll use 9mm squares by default. They should be quite big
5130 * for this game, because players will want to jot down no end
5131 * of pencil marks in the squares.
5133 game_compute_size(params
, 900, &pw
, &ph
);
5139 * Subfunction to draw the thick lines between cells. In order to do
5140 * this using the line-drawing rather than rectangle-drawing API (so
5141 * as to get line thicknesses to scale correctly) and yet have
5142 * correctly mitred joins between lines, we must do this by tracing
5143 * the boundary of each sub-block and drawing it in one go as a
5146 * This subfunction is also reused with thinner dotted lines to
5147 * outline the Killer cages, this time offsetting the outline toward
5148 * the interior of the affected squares.
5150 static void outline_block_structure(drawing
*dr
, game_drawstate
*ds
,
5152 struct block_structure
*blocks
,
5158 int x
, y
, dx
, dy
, sx
, sy
, sdx
, sdy
;
5161 * Maximum perimeter of a k-omino is 2k+2. (Proof: start
5162 * with k unconnected squares, with total perimeter 4k.
5163 * Now repeatedly join two disconnected components
5164 * together into a larger one; every time you do so you
5165 * remove at least two unit edges, and you require k-1 of
5166 * these operations to create a single connected piece, so
5167 * you must have at most 4k-2(k-1) = 2k+2 unit edges left
5170 coords
= snewn(4*cr
+4, int); /* 2k+2 points, 2 coords per point */
5173 * Iterate over all the blocks.
5175 for (bi
= 0; bi
< blocks
->nr_blocks
; bi
++) {
5176 if (blocks
->nr_squares
[bi
] == 0)
5180 * For each block, find a starting square within it
5181 * which has a boundary at the left.
5183 for (i
= 0; i
< cr
; i
++) {
5184 int j
= blocks
->blocks
[bi
][i
];
5185 if (j
% cr
== 0 || blocks
->whichblock
[j
-1] != bi
)
5188 assert(i
< cr
); /* every block must have _some_ leftmost square */
5189 x
= blocks
->blocks
[bi
][i
] % cr
;
5190 y
= blocks
->blocks
[bi
][i
] / cr
;
5195 * Now begin tracing round the perimeter. At all
5196 * times, (x,y) describes some square within the
5197 * block, and (x+dx,y+dy) is some adjacent square
5198 * outside it; so the edge between those two squares
5199 * is always an edge of the block.
5201 sx
= x
, sy
= y
, sdx
= dx
, sdy
= dy
; /* save starting position */
5204 int cx
, cy
, tx
, ty
, nin
;
5207 * Advance to the next edge, by looking at the two
5208 * squares beyond it. If they're both outside the block,
5209 * we turn right (by leaving x,y the same and rotating
5210 * dx,dy clockwise); if they're both inside, we turn
5211 * left (by rotating dx,dy anticlockwise and contriving
5212 * to leave x+dx,y+dy unchanged); if one of each, we go
5213 * straight on (and may enforce by assertion that
5214 * they're one of each the _right_ way round).
5219 nin
+= (tx
>= 0 && tx
< cr
&& ty
>= 0 && ty
< cr
&&
5220 blocks
->whichblock
[ty
*cr
+tx
] == bi
);
5223 nin
+= (tx
>= 0 && tx
< cr
&& ty
>= 0 && ty
< cr
&&
5224 blocks
->whichblock
[ty
*cr
+tx
] == bi
);
5233 } else if (nin
== 2) {
5257 * Now enforce by assertion that we ended up
5258 * somewhere sensible.
5260 assert(x
>= 0 && x
< cr
&& y
>= 0 && y
< cr
&&
5261 blocks
->whichblock
[y
*cr
+x
] == bi
);
5262 assert(x
+dx
< 0 || x
+dx
>= cr
|| y
+dy
< 0 || y
+dy
>= cr
||
5263 blocks
->whichblock
[(y
+dy
)*cr
+(x
+dx
)] != bi
);
5266 * Record the point we just went past at one end of the
5267 * edge. To do this, we translate (x,y) down and right
5268 * by half a unit (so they're describing a point in the
5269 * _centre_ of the square) and then translate back again
5270 * in a manner rotated by dy and dx.
5273 cx
= ((2*x
+1) + dy
+ dx
) / 2;
5274 cy
= ((2*y
+1) - dx
+ dy
) / 2;
5275 coords
[2*n
+0] = BORDER
+ cx
* TILE_SIZE
;
5276 coords
[2*n
+1] = BORDER
+ cy
* TILE_SIZE
;
5277 coords
[2*n
+0] -= dx
* inset
;
5278 coords
[2*n
+1] -= dy
* inset
;
5281 * We turned right, so inset this corner back along
5282 * the edge towards the centre of the square.
5284 coords
[2*n
+0] -= dy
* inset
;
5285 coords
[2*n
+1] += dx
* inset
;
5286 } else if (nin
== 2) {
5288 * We turned left, so inset this corner further
5289 * _out_ along the edge into the next square.
5291 coords
[2*n
+0] += dy
* inset
;
5292 coords
[2*n
+1] -= dx
* inset
;
5296 } while (x
!= sx
|| y
!= sy
|| dx
!= sdx
|| dy
!= sdy
);
5299 * That's our polygon; now draw it.
5301 draw_polygon(dr
, coords
, n
, -1, ink
);
5307 static void game_print(drawing
*dr
, game_state
*state
, int tilesize
)
5310 int ink
= print_mono_colour(dr
, 0);
5313 /* Ick: fake up `ds->tilesize' for macro expansion purposes */
5314 game_drawstate ads
, *ds
= &ads
;
5315 game_set_size(dr
, ds
, NULL
, tilesize
);
5320 print_line_width(dr
, 3 * TILE_SIZE
/ 40);
5321 draw_rect_outline(dr
, BORDER
, BORDER
, cr
*TILE_SIZE
, cr
*TILE_SIZE
, ink
);
5324 * Highlight X-diagonal squares.
5328 int xhighlight
= print_grey_colour(dr
, 0.90F
);
5330 for (i
= 0; i
< cr
; i
++)
5331 draw_rect(dr
, BORDER
+ i
*TILE_SIZE
, BORDER
+ i
*TILE_SIZE
,
5332 TILE_SIZE
, TILE_SIZE
, xhighlight
);
5333 for (i
= 0; i
< cr
; i
++)
5334 if (i
*2 != cr
-1) /* avoid redoing centre square, just for fun */
5335 draw_rect(dr
, BORDER
+ i
*TILE_SIZE
,
5336 BORDER
+ (cr
-1-i
)*TILE_SIZE
,
5337 TILE_SIZE
, TILE_SIZE
, xhighlight
);
5343 for (x
= 1; x
< cr
; x
++) {
5344 print_line_width(dr
, TILE_SIZE
/ 40);
5345 draw_line(dr
, BORDER
+x
*TILE_SIZE
, BORDER
,
5346 BORDER
+x
*TILE_SIZE
, BORDER
+cr
*TILE_SIZE
, ink
);
5348 for (y
= 1; y
< cr
; y
++) {
5349 print_line_width(dr
, TILE_SIZE
/ 40);
5350 draw_line(dr
, BORDER
, BORDER
+y
*TILE_SIZE
,
5351 BORDER
+cr
*TILE_SIZE
, BORDER
+y
*TILE_SIZE
, ink
);
5355 * Thick lines between cells.
5357 print_line_width(dr
, 3 * TILE_SIZE
/ 40);
5358 outline_block_structure(dr
, ds
, state
, state
->blocks
, ink
, 0);
5361 * Killer cages and their totals.
5363 if (state
->kblocks
) {
5364 print_line_width(dr
, TILE_SIZE
/ 40);
5365 print_line_dotted(dr
, TRUE
);
5366 outline_block_structure(dr
, ds
, state
, state
->kblocks
, ink
,
5367 5 * TILE_SIZE
/ 40);
5368 print_line_dotted(dr
, FALSE
);
5369 for (y
= 0; y
< cr
; y
++)
5370 for (x
= 0; x
< cr
; x
++)
5371 if (state
->kgrid
[y
*cr
+x
]) {
5373 sprintf(str
, "%d", state
->kgrid
[y
*cr
+x
]);
5375 BORDER
+x
*TILE_SIZE
+ 7*TILE_SIZE
/40,
5376 BORDER
+y
*TILE_SIZE
+ 16*TILE_SIZE
/40,
5377 FONT_VARIABLE
, TILE_SIZE
/4,
5378 ALIGN_VNORMAL
| ALIGN_HLEFT
,
5384 * Standard (non-Killer) clue numbers.
5386 for (y
= 0; y
< cr
; y
++)
5387 for (x
= 0; x
< cr
; x
++)
5388 if (state
->grid
[y
*cr
+x
]) {
5391 str
[0] = state
->grid
[y
*cr
+x
] + '0';
5393 str
[0] += 'a' - ('9'+1);
5394 draw_text(dr
, BORDER
+ x
*TILE_SIZE
+ TILE_SIZE
/2,
5395 BORDER
+ y
*TILE_SIZE
+ TILE_SIZE
/2,
5396 FONT_VARIABLE
, TILE_SIZE
/2,
5397 ALIGN_VCENTRE
| ALIGN_HCENTRE
, ink
, str
);
5402 #define thegame solo
5405 const struct game thegame
= {
5406 "Solo", "games.solo", "solo",
5413 TRUE
, game_configure
, custom_params
,
5421 TRUE
, game_can_format_as_text_now
, game_text_format
,
5429 PREFERRED_TILE_SIZE
, game_compute_size
, game_set_size
,
5432 game_free_drawstate
,
5436 TRUE
, FALSE
, game_print_size
, game_print
,
5437 FALSE
, /* wants_statusbar */
5438 FALSE
, game_timing_state
,
5439 REQUIRE_RBUTTON
| REQUIRE_NUMPAD
, /* flags */
5442 #ifdef STANDALONE_SOLVER
5444 int main(int argc
, char **argv
)
5448 char *id
= NULL
, *desc
, *err
;
5450 struct difficulty dlev
;
5452 while (--argc
> 0) {
5454 if (!strcmp(p
, "-v")) {
5455 solver_show_working
= TRUE
;
5456 } else if (!strcmp(p
, "-g")) {
5458 } else if (*p
== '-') {
5459 fprintf(stderr
, "%s: unrecognised option `%s'\n", argv
[0], p
);
5467 fprintf(stderr
, "usage: %s [-g | -v] <game_id>\n", argv
[0]);
5471 desc
= strchr(id
, ':');
5473 fprintf(stderr
, "%s: game id expects a colon in it\n", argv
[0]);
5478 p
= default_params();
5479 decode_params(p
, id
);
5480 err
= validate_desc(p
, desc
);
5482 fprintf(stderr
, "%s: %s\n", argv
[0], err
);
5485 s
= new_game(NULL
, p
, desc
);
5487 dlev
.maxdiff
= DIFF_RECURSIVE
;
5488 dlev
.maxkdiff
= DIFF_KINTERSECT
;
5489 solver(s
->cr
, s
->blocks
, s
->kblocks
, s
->xtype
, s
->grid
, s
->kgrid
, &dlev
);
5491 printf("Difficulty rating: %s\n",
5492 dlev
.diff
==DIFF_BLOCK ?
"Trivial (blockwise positional elimination only)":
5493 dlev
.diff
==DIFF_SIMPLE ?
"Basic (row/column/number elimination required)":
5494 dlev
.diff
==DIFF_INTERSECT ?
"Intermediate (intersectional analysis required)":
5495 dlev
.diff
==DIFF_SET ?
"Advanced (set elimination required)":
5496 dlev
.diff
==DIFF_EXTREME ?
"Extreme (complex non-recursive techniques required)":
5497 dlev
.diff
==DIFF_RECURSIVE ?
"Unreasonable (guesswork and backtracking required)":
5498 dlev
.diff
==DIFF_AMBIGUOUS ?
"Ambiguous (multiple solutions exist)":
5499 dlev
.diff
==DIFF_IMPOSSIBLE ?
"Impossible (no solution exists)":
5500 "INTERNAL ERROR: unrecognised difficulty code");
5502 printf("Killer diffculty: %s\n",
5503 dlev
.kdiff
==DIFF_KSINGLE ?
"Trivial (single square cages only)":
5504 dlev
.kdiff
==DIFF_KMINMAX ?
"Simple (maximum sum analysis required)":
5505 dlev
.kdiff
==DIFF_KSUMS ?
"Intermediate (sum possibilities)":
5506 dlev
.kdiff
==DIFF_KINTERSECT ?
"Advanced (sum region intersections)":
5507 "INTERNAL ERROR: unrecognised difficulty code");
5509 printf("%s\n", grid_text_format(s
->cr
, s
->blocks
, s
->xtype
, s
->grid
));
5517 /* vim: set shiftwidth=4 tabstop=8: */