2 * solo.c: the number-placing puzzle most popularly known as `Sudoku'.
6 * - reports from users are that `Trivial'-mode puzzles are still
7 * rather hard compared to newspapers' easy ones, so some better
8 * low-end difficulty grading would be nice
9 * + it's possible that really easy puzzles always have
10 * _several_ things you can do, so don't make you hunt too
11 * hard for the one deduction you can currently make
12 * + it's also possible that easy puzzles require fewer
13 * cross-eliminations: perhaps there's a higher incidence of
14 * things you can deduce by looking only at (say) rows,
15 * rather than things you have to check both rows and columns
17 * + but really, what I need to do is find some really easy
18 * puzzles and _play_ them, to see what's actually easy about
20 * + while I'm revamping this area, filling in the _last_
21 * number in a nearly-full row or column should certainly be
22 * permitted even at the lowest difficulty level.
23 * + also Owen noticed that `Basic' grids requiring numeric
24 * elimination are actually very hard, so I wonder if a
25 * difficulty gradation between that and positional-
26 * elimination-only might be in order
27 * + but it's not good to have _too_ many difficulty levels, or
28 * it'll take too long to randomly generate a given level.
30 * - it might still be nice to do some prioritisation on the
31 * removal of numbers from the grid
32 * + one possibility is to try to minimise the maximum number
33 * of filled squares in any block, which in particular ought
34 * to enforce never leaving a completely filled block in the
35 * puzzle as presented.
37 * - alternative interface modes
38 * + sudoku.com's Windows program has a palette of possible
39 * entries; you select a palette entry first and then click
40 * on the square you want it to go in, thus enabling
41 * mouse-only play. Useful for PDAs! I don't think it's
42 * actually incompatible with the current highlight-then-type
43 * approach: you _either_ highlight a palette entry and then
44 * click, _or_ you highlight a square and then type. At most
45 * one thing is ever highlighted at a time, so there's no way
47 * + then again, I don't actually like sudoku.com's interface;
48 * it's too much like a paint package whereas I prefer to
49 * think of Solo as a text editor.
50 * + another PDA-friendly possibility is a drag interface:
51 * _drag_ numbers from the palette into the grid squares.
52 * Thought experiments suggest I'd prefer that to the
53 * sudoku.com approach, but I haven't actually tried it.
57 * Solo puzzles need to be square overall (since each row and each
58 * column must contain one of every digit), but they need not be
59 * subdivided the same way internally. I am going to adopt a
60 * convention whereby I _always_ refer to `r' as the number of rows
61 * of _big_ divisions, and `c' as the number of columns of _big_
62 * divisions. Thus, a 2c by 3r puzzle looks something like this:
66 * ------+------ (Of course, you can't subdivide it the other way
67 * 1 4 5 | 6 3 2 or you'll get clashes; observe that the 4 in the
68 * 3 2 6 | 4 1 5 top left would conflict with the 4 in the second
69 * ------+------ box down on the left-hand side.)
73 * The need for a strong naming convention should now be clear:
74 * each small box is two rows of digits by three columns, while the
75 * overall puzzle has three rows of small boxes by two columns. So
76 * I will (hopefully) consistently use `r' to denote the number of
77 * rows _of small boxes_ (here 3), which is also the number of
78 * columns of digits in each small box; and `c' vice versa (here
81 * I'm also going to choose arbitrarily to list c first wherever
82 * possible: the above is a 2x3 puzzle, not a 3x2 one.
92 #ifdef STANDALONE_SOLVER
94 int solver_show_working
;
100 * To save space, I store digits internally as unsigned char. This
101 * imposes a hard limit of 255 on the order of the puzzle. Since
102 * even a 5x5 takes unacceptably long to generate, I don't see this
103 * as a serious limitation unless something _really_ impressive
104 * happens in computing technology; but here's a typedef anyway for
105 * general good practice.
107 typedef unsigned char digit
;
108 #define ORDER_MAX 255
110 #define PREFERRED_TILE_SIZE 32
111 #define TILE_SIZE (ds->tilesize)
112 #define BORDER (TILE_SIZE / 2)
114 #define FLASH_TIME 0.4F
116 enum { SYMM_NONE
, SYMM_ROT2
, SYMM_ROT4
, SYMM_REF2
, SYMM_REF2D
, SYMM_REF4
,
117 SYMM_REF4D
, SYMM_REF8
};
119 enum { DIFF_BLOCK
, DIFF_SIMPLE
, DIFF_INTERSECT
,
120 DIFF_SET
, DIFF_RECURSIVE
, DIFF_AMBIGUOUS
, DIFF_IMPOSSIBLE
};
134 int c
, r
, symm
, diff
;
140 unsigned char *pencil
; /* c*r*c*r elements */
141 unsigned char *immutable
; /* marks which digits are clues */
142 int completed
, cheated
;
145 static game_params
*default_params(void)
147 game_params
*ret
= snew(game_params
);
150 ret
->symm
= SYMM_ROT2
; /* a plausible default */
151 ret
->diff
= DIFF_BLOCK
; /* so is this */
156 static void free_params(game_params
*params
)
161 static game_params
*dup_params(game_params
*params
)
163 game_params
*ret
= snew(game_params
);
164 *ret
= *params
; /* structure copy */
168 static int game_fetch_preset(int i
, char **name
, game_params
**params
)
174 { "2x2 Trivial", { 2, 2, SYMM_ROT2
, DIFF_BLOCK
} },
175 { "2x3 Basic", { 2, 3, SYMM_ROT2
, DIFF_SIMPLE
} },
176 { "3x3 Trivial", { 3, 3, SYMM_ROT2
, DIFF_BLOCK
} },
177 { "3x3 Basic", { 3, 3, SYMM_ROT2
, DIFF_SIMPLE
} },
178 { "3x3 Intermediate", { 3, 3, SYMM_ROT2
, DIFF_INTERSECT
} },
179 { "3x3 Advanced", { 3, 3, SYMM_ROT2
, DIFF_SET
} },
180 { "3x3 Unreasonable", { 3, 3, SYMM_ROT2
, DIFF_RECURSIVE
} },
182 { "3x4 Basic", { 3, 4, SYMM_ROT2
, DIFF_SIMPLE
} },
183 { "4x4 Basic", { 4, 4, SYMM_ROT2
, DIFF_SIMPLE
} },
187 if (i
< 0 || i
>= lenof(presets
))
190 *name
= dupstr(presets
[i
].title
);
191 *params
= dup_params(&presets
[i
].params
);
196 static void decode_params(game_params
*ret
, char const *string
)
198 ret
->c
= ret
->r
= atoi(string
);
199 while (*string
&& isdigit((unsigned char)*string
)) string
++;
200 if (*string
== 'x') {
202 ret
->r
= atoi(string
);
203 while (*string
&& isdigit((unsigned char)*string
)) string
++;
206 if (*string
== 'r' || *string
== 'm' || *string
== 'a') {
209 if (*string
== 'd') {
216 while (*string
&& isdigit((unsigned char)*string
)) string
++;
217 if (sc
== 'm' && sn
== 8)
218 ret
->symm
= SYMM_REF8
;
219 if (sc
== 'm' && sn
== 4)
220 ret
->symm
= sd ? SYMM_REF4D
: SYMM_REF4
;
221 if (sc
== 'm' && sn
== 2)
222 ret
->symm
= sd ? SYMM_REF2D
: SYMM_REF2
;
223 if (sc
== 'r' && sn
== 4)
224 ret
->symm
= SYMM_ROT4
;
225 if (sc
== 'r' && sn
== 2)
226 ret
->symm
= SYMM_ROT2
;
228 ret
->symm
= SYMM_NONE
;
229 } else if (*string
== 'd') {
231 if (*string
== 't') /* trivial */
232 string
++, ret
->diff
= DIFF_BLOCK
;
233 else if (*string
== 'b') /* basic */
234 string
++, ret
->diff
= DIFF_SIMPLE
;
235 else if (*string
== 'i') /* intermediate */
236 string
++, ret
->diff
= DIFF_INTERSECT
;
237 else if (*string
== 'a') /* advanced */
238 string
++, ret
->diff
= DIFF_SET
;
239 else if (*string
== 'u') /* unreasonable */
240 string
++, ret
->diff
= DIFF_RECURSIVE
;
242 string
++; /* eat unknown character */
246 static char *encode_params(game_params
*params
, int full
)
250 sprintf(str
, "%dx%d", params
->c
, params
->r
);
252 switch (params
->symm
) {
253 case SYMM_REF8
: strcat(str
, "m8"); break;
254 case SYMM_REF4
: strcat(str
, "m4"); break;
255 case SYMM_REF4D
: strcat(str
, "md4"); break;
256 case SYMM_REF2
: strcat(str
, "m2"); break;
257 case SYMM_REF2D
: strcat(str
, "md2"); break;
258 case SYMM_ROT4
: strcat(str
, "r4"); break;
259 /* case SYMM_ROT2: strcat(str, "r2"); break; [default] */
260 case SYMM_NONE
: strcat(str
, "a"); break;
262 switch (params
->diff
) {
263 /* case DIFF_BLOCK: strcat(str, "dt"); break; [default] */
264 case DIFF_SIMPLE
: strcat(str
, "db"); break;
265 case DIFF_INTERSECT
: strcat(str
, "di"); break;
266 case DIFF_SET
: strcat(str
, "da"); break;
267 case DIFF_RECURSIVE
: strcat(str
, "du"); break;
273 static config_item
*game_configure(game_params
*params
)
278 ret
= snewn(5, config_item
);
280 ret
[0].name
= "Columns of sub-blocks";
281 ret
[0].type
= C_STRING
;
282 sprintf(buf
, "%d", params
->c
);
283 ret
[0].sval
= dupstr(buf
);
286 ret
[1].name
= "Rows of sub-blocks";
287 ret
[1].type
= C_STRING
;
288 sprintf(buf
, "%d", params
->r
);
289 ret
[1].sval
= dupstr(buf
);
292 ret
[2].name
= "Symmetry";
293 ret
[2].type
= C_CHOICES
;
294 ret
[2].sval
= ":None:2-way rotation:4-way rotation:2-way mirror:"
295 "2-way diagonal mirror:4-way mirror:4-way diagonal mirror:"
297 ret
[2].ival
= params
->symm
;
299 ret
[3].name
= "Difficulty";
300 ret
[3].type
= C_CHOICES
;
301 ret
[3].sval
= ":Trivial:Basic:Intermediate:Advanced:Unreasonable";
302 ret
[3].ival
= params
->diff
;
312 static game_params
*custom_params(config_item
*cfg
)
314 game_params
*ret
= snew(game_params
);
316 ret
->c
= atoi(cfg
[0].sval
);
317 ret
->r
= atoi(cfg
[1].sval
);
318 ret
->symm
= cfg
[2].ival
;
319 ret
->diff
= cfg
[3].ival
;
324 static char *validate_params(game_params
*params
)
326 if (params
->c
< 2 || params
->r
< 2)
327 return "Both dimensions must be at least 2";
328 if (params
->c
> ORDER_MAX
|| params
->r
> ORDER_MAX
)
329 return "Dimensions greater than "STR(ORDER_MAX
)" are not supported";
333 /* ----------------------------------------------------------------------
334 * Full recursive Solo solver.
336 * The algorithm for this solver is shamelessly copied from a
337 * Python solver written by Andrew Wilkinson (which is GPLed, but
338 * I've reused only ideas and no code). It mostly just does the
339 * obvious recursive thing: pick an empty square, put one of the
340 * possible digits in it, recurse until all squares are filled,
341 * backtrack and change some choices if necessary.
343 * The clever bit is that every time it chooses which square to
344 * fill in next, it does so by counting the number of _possible_
345 * numbers that can go in each square, and it prioritises so that
346 * it picks a square with the _lowest_ number of possibilities. The
347 * idea is that filling in lots of the obvious bits (particularly
348 * any squares with only one possibility) will cut down on the list
349 * of possibilities for other squares and hence reduce the enormous
350 * search space as much as possible as early as possible.
352 * In practice the algorithm appeared to work very well; run on
353 * sample problems from the Times it completed in well under a
354 * second on my G5 even when written in Python, and given an empty
355 * grid (so that in principle it would enumerate _all_ solved
356 * grids!) it found the first valid solution just as quickly. So
357 * with a bit more randomisation I see no reason not to use this as
362 * Internal data structure used in solver to keep track of
365 struct rsolve_coord
{ int x
, y
, r
; };
366 struct rsolve_usage
{
367 int c
, r
, cr
; /* cr == c*r */
368 /* grid is a copy of the input grid, modified as we go along */
370 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
372 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
374 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
376 /* This lists all the empty spaces remaining in the grid. */
377 struct rsolve_coord
*spaces
;
379 /* If we need randomisation in the solve, this is our random state. */
381 /* Number of solutions so far found, and maximum number we care about. */
386 * The real recursive step in the solving function.
388 static void rsolve_real(struct rsolve_usage
*usage
, digit
*grid
)
390 int c
= usage
->c
, r
= usage
->r
, cr
= usage
->cr
;
391 int i
, j
, n
, sx
, sy
, bestm
, bestr
;
395 * Firstly, check for completion! If there are no spaces left
396 * in the grid, we have a solution.
398 if (usage
->nspaces
== 0) {
401 * This is our first solution, so fill in the output grid.
403 memcpy(grid
, usage
->grid
, cr
* cr
);
410 * Otherwise, there must be at least one space. Find the most
411 * constrained space, using the `r' field as a tie-breaker.
413 bestm
= cr
+1; /* so that any space will beat it */
416 for (j
= 0; j
< usage
->nspaces
; j
++) {
417 int x
= usage
->spaces
[j
].x
, y
= usage
->spaces
[j
].y
;
421 * Find the number of digits that could go in this space.
424 for (n
= 0; n
< cr
; n
++)
425 if (!usage
->row
[y
*cr
+n
] && !usage
->col
[x
*cr
+n
] &&
426 !usage
->blk
[((y
/c
)*c
+(x
/r
))*cr
+n
])
429 if (m
< bestm
|| (m
== bestm
&& usage
->spaces
[j
].r
< bestr
)) {
431 bestr
= usage
->spaces
[j
].r
;
439 * Swap that square into the final place in the spaces array,
440 * so that decrementing nspaces will remove it from the list.
442 if (i
!= usage
->nspaces
-1) {
443 struct rsolve_coord t
;
444 t
= usage
->spaces
[usage
->nspaces
-1];
445 usage
->spaces
[usage
->nspaces
-1] = usage
->spaces
[i
];
446 usage
->spaces
[i
] = t
;
450 * Now we've decided which square to start our recursion at,
451 * simply go through all possible values, shuffling them
452 * randomly first if necessary.
454 digits
= snewn(bestm
, int);
456 for (n
= 0; n
< cr
; n
++)
457 if (!usage
->row
[sy
*cr
+n
] && !usage
->col
[sx
*cr
+n
] &&
458 !usage
->blk
[((sy
/c
)*c
+(sx
/r
))*cr
+n
]) {
464 for (i
= j
; i
> 1; i
--) {
465 int p
= random_upto(usage
->rs
, i
);
468 digits
[p
] = digits
[i
-1];
474 /* And finally, go through the digit list and actually recurse. */
475 for (i
= 0; i
< j
; i
++) {
478 /* Update the usage structure to reflect the placing of this digit. */
479 usage
->row
[sy
*cr
+n
-1] = usage
->col
[sx
*cr
+n
-1] =
480 usage
->blk
[((sy
/c
)*c
+(sx
/r
))*cr
+n
-1] = TRUE
;
481 usage
->grid
[sy
*cr
+sx
] = n
;
484 /* Call the solver recursively. */
485 rsolve_real(usage
, grid
);
488 * If we have seen as many solutions as we need, terminate
489 * all processing immediately.
491 if (usage
->solns
>= usage
->maxsolns
)
494 /* Revert the usage structure. */
495 usage
->row
[sy
*cr
+n
-1] = usage
->col
[sx
*cr
+n
-1] =
496 usage
->blk
[((sy
/c
)*c
+(sx
/r
))*cr
+n
-1] = FALSE
;
497 usage
->grid
[sy
*cr
+sx
] = 0;
505 * Entry point to solver. You give it dimensions and a starting
506 * grid, which is simply an array of N^4 digits. In that array, 0
507 * means an empty square, and 1..N mean a clue square.
509 * Return value is the number of solutions found; searching will
510 * stop after the provided `max'. (Thus, you can pass max==1 to
511 * indicate that you only care about finding _one_ solution, or
512 * max==2 to indicate that you want to know the difference between
513 * a unique and non-unique solution.) The input parameter `grid' is
514 * also filled in with the _first_ (or only) solution found by the
517 static int rsolve(int c
, int r
, digit
*grid
, random_state
*rs
, int max
)
519 struct rsolve_usage
*usage
;
524 * Create an rsolve_usage structure.
526 usage
= snew(struct rsolve_usage
);
532 usage
->grid
= snewn(cr
* cr
, digit
);
533 memcpy(usage
->grid
, grid
, cr
* cr
);
535 usage
->row
= snewn(cr
* cr
, unsigned char);
536 usage
->col
= snewn(cr
* cr
, unsigned char);
537 usage
->blk
= snewn(cr
* cr
, unsigned char);
538 memset(usage
->row
, FALSE
, cr
* cr
);
539 memset(usage
->col
, FALSE
, cr
* cr
);
540 memset(usage
->blk
, FALSE
, cr
* cr
);
542 usage
->spaces
= snewn(cr
* cr
, struct rsolve_coord
);
546 usage
->maxsolns
= max
;
551 * Now fill it in with data from the input grid.
553 for (y
= 0; y
< cr
; y
++) {
554 for (x
= 0; x
< cr
; x
++) {
555 int v
= grid
[y
*cr
+x
];
557 usage
->spaces
[usage
->nspaces
].x
= x
;
558 usage
->spaces
[usage
->nspaces
].y
= y
;
560 usage
->spaces
[usage
->nspaces
].r
= random_bits(rs
, 31);
562 usage
->spaces
[usage
->nspaces
].r
= usage
->nspaces
;
565 usage
->row
[y
*cr
+v
-1] = TRUE
;
566 usage
->col
[x
*cr
+v
-1] = TRUE
;
567 usage
->blk
[((y
/c
)*c
+(x
/r
))*cr
+v
-1] = TRUE
;
573 * Run the real recursive solving function.
575 rsolve_real(usage
, grid
);
579 * Clean up the usage structure now we have our answer.
581 sfree(usage
->spaces
);
594 /* ----------------------------------------------------------------------
595 * End of recursive solver code.
598 /* ----------------------------------------------------------------------
599 * Less capable non-recursive solver. This one is used to check
600 * solubility of a grid as we gradually remove numbers from it: by
601 * verifying a grid using this solver we can ensure it isn't _too_
602 * hard (e.g. does not actually require guessing and backtracking).
604 * It supports a variety of specific modes of reasoning. By
605 * enabling or disabling subsets of these modes we can arrange a
606 * range of difficulty levels.
610 * Modes of reasoning currently supported:
612 * - Positional elimination: a number must go in a particular
613 * square because all the other empty squares in a given
614 * row/col/blk are ruled out.
616 * - Numeric elimination: a square must have a particular number
617 * in because all the other numbers that could go in it are
620 * - Intersectional analysis: given two domains which overlap
621 * (hence one must be a block, and the other can be a row or
622 * col), if the possible locations for a particular number in
623 * one of the domains can be narrowed down to the overlap, then
624 * that number can be ruled out everywhere but the overlap in
625 * the other domain too.
627 * - Set elimination: if there is a subset of the empty squares
628 * within a domain such that the union of the possible numbers
629 * in that subset has the same size as the subset itself, then
630 * those numbers can be ruled out everywhere else in the domain.
631 * (For example, if there are five empty squares and the
632 * possible numbers in each are 12, 23, 13, 134 and 1345, then
633 * the first three empty squares form such a subset: the numbers
634 * 1, 2 and 3 _must_ be in those three squares in some
635 * permutation, and hence we can deduce none of them can be in
636 * the fourth or fifth squares.)
637 * + You can also see this the other way round, concentrating
638 * on numbers rather than squares: if there is a subset of
639 * the unplaced numbers within a domain such that the union
640 * of all their possible positions has the same size as the
641 * subset itself, then all other numbers can be ruled out for
642 * those positions. However, it turns out that this is
643 * exactly equivalent to the first formulation at all times:
644 * there is a 1-1 correspondence between suitable subsets of
645 * the unplaced numbers and suitable subsets of the unfilled
646 * places, found by taking the _complement_ of the union of
647 * the numbers' possible positions (or the spaces' possible
652 * Within this solver, I'm going to transform all y-coordinates by
653 * inverting the significance of the block number and the position
654 * within the block. That is, we will start with the top row of
655 * each block in order, then the second row of each block in order,
658 * This transformation has the enormous advantage that it means
659 * every row, column _and_ block is described by an arithmetic
660 * progression of coordinates within the cubic array, so that I can
661 * use the same very simple function to do blockwise, row-wise and
662 * column-wise elimination.
664 #define YTRANS(y) (((y)%c)*r+(y)/c)
665 #define YUNTRANS(y) (((y)%r)*c+(y)/r)
667 struct nsolve_usage
{
670 * We set up a cubic array, indexed by x, y and digit; each
671 * element of this array is TRUE or FALSE according to whether
672 * or not that digit _could_ in principle go in that position.
674 * The way to index this array is cube[(x*cr+y)*cr+n-1].
675 * y-coordinates in here are transformed.
679 * This is the grid in which we write down our final
680 * deductions. y-coordinates in here are _not_ transformed.
684 * Now we keep track, at a slightly higher level, of what we
685 * have yet to work out, to prevent doing the same deduction
688 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
690 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
692 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
695 #define cubepos(x,y,n) (((x)*usage->cr+(y))*usage->cr+(n)-1)
696 #define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
699 * Function called when we are certain that a particular square has
700 * a particular number in it. The y-coordinate passed in here is
703 static void nsolve_place(struct nsolve_usage
*usage
, int x
, int y
, int n
)
705 int c
= usage
->c
, r
= usage
->r
, cr
= usage
->cr
;
711 * Rule out all other numbers in this square.
713 for (i
= 1; i
<= cr
; i
++)
718 * Rule out this number in all other positions in the row.
720 for (i
= 0; i
< cr
; i
++)
725 * Rule out this number in all other positions in the column.
727 for (i
= 0; i
< cr
; i
++)
732 * Rule out this number in all other positions in the block.
736 for (i
= 0; i
< r
; i
++)
737 for (j
= 0; j
< c
; j
++)
738 if (bx
+i
!= x
|| by
+j
*r
!= y
)
739 cube(bx
+i
,by
+j
*r
,n
) = FALSE
;
742 * Enter the number in the result grid.
744 usage
->grid
[YUNTRANS(y
)*cr
+x
] = n
;
747 * Cross out this number from the list of numbers left to place
748 * in its row, its column and its block.
750 usage
->row
[y
*cr
+n
-1] = usage
->col
[x
*cr
+n
-1] =
751 usage
->blk
[((y
%r
)*c
+(x
/r
))*cr
+n
-1] = TRUE
;
754 static int nsolve_elim(struct nsolve_usage
*usage
, int start
, int step
755 #ifdef STANDALONE_SOLVER
760 int c
= usage
->c
, r
= usage
->r
, cr
= c
*r
;
764 * Count the number of set bits within this section of the
769 for (i
= 0; i
< cr
; i
++)
770 if (usage
->cube
[start
+i
*step
]) {
784 if (!usage
->grid
[YUNTRANS(y
)*cr
+x
]) {
785 #ifdef STANDALONE_SOLVER
786 if (solver_show_working
) {
791 printf(":\n placing %d at (%d,%d)\n",
792 n
, 1+x
, 1+YUNTRANS(y
));
795 nsolve_place(usage
, x
, y
, n
);
803 static int nsolve_intersect(struct nsolve_usage
*usage
,
804 int start1
, int step1
, int start2
, int step2
805 #ifdef STANDALONE_SOLVER
810 int c
= usage
->c
, r
= usage
->r
, cr
= c
*r
;
814 * Loop over the first domain and see if there's any set bit
815 * not also in the second.
817 for (i
= 0; i
< cr
; i
++) {
818 int p
= start1
+i
*step1
;
819 if (usage
->cube
[p
] &&
820 !(p
>= start2
&& p
< start2
+cr
*step2
&&
821 (p
- start2
) % step2
== 0))
822 return FALSE
; /* there is, so we can't deduce */
826 * We have determined that all set bits in the first domain are
827 * within its overlap with the second. So loop over the second
828 * domain and remove all set bits that aren't also in that
829 * overlap; return TRUE iff we actually _did_ anything.
832 for (i
= 0; i
< cr
; i
++) {
833 int p
= start2
+i
*step2
;
834 if (usage
->cube
[p
] &&
835 !(p
>= start1
&& p
< start1
+cr
*step1
&& (p
- start1
) % step1
== 0))
837 #ifdef STANDALONE_SOLVER
838 if (solver_show_working
) {
854 printf(" ruling out %d at (%d,%d)\n",
855 pn
, 1+px
, 1+YUNTRANS(py
));
858 ret
= TRUE
; /* we did something */
866 struct nsolve_scratch
{
867 unsigned char *grid
, *rowidx
, *colidx
, *set
;
870 static int nsolve_set(struct nsolve_usage
*usage
,
871 struct nsolve_scratch
*scratch
,
872 int start
, int step1
, int step2
873 #ifdef STANDALONE_SOLVER
878 int c
= usage
->c
, r
= usage
->r
, cr
= c
*r
;
880 unsigned char *grid
= scratch
->grid
;
881 unsigned char *rowidx
= scratch
->rowidx
;
882 unsigned char *colidx
= scratch
->colidx
;
883 unsigned char *set
= scratch
->set
;
886 * We are passed a cr-by-cr matrix of booleans. Our first job
887 * is to winnow it by finding any definite placements - i.e.
888 * any row with a solitary 1 - and discarding that row and the
889 * column containing the 1.
891 memset(rowidx
, TRUE
, cr
);
892 memset(colidx
, TRUE
, cr
);
893 for (i
= 0; i
< cr
; i
++) {
894 int count
= 0, first
= -1;
895 for (j
= 0; j
< cr
; j
++)
896 if (usage
->cube
[start
+i
*step1
+j
*step2
])
900 * This condition actually marks a completely insoluble
901 * (i.e. internally inconsistent) puzzle. We return and
902 * report no progress made.
907 rowidx
[i
] = colidx
[first
] = FALSE
;
911 * Convert each of rowidx/colidx from a list of 0s and 1s to a
912 * list of the indices of the 1s.
914 for (i
= j
= 0; i
< cr
; i
++)
918 for (i
= j
= 0; i
< cr
; i
++)
924 * And create the smaller matrix.
926 for (i
= 0; i
< n
; i
++)
927 for (j
= 0; j
< n
; j
++)
928 grid
[i
*cr
+j
] = usage
->cube
[start
+rowidx
[i
]*step1
+colidx
[j
]*step2
];
931 * Having done that, we now have a matrix in which every row
932 * has at least two 1s in. Now we search to see if we can find
933 * a rectangle of zeroes (in the set-theoretic sense of
934 * `rectangle', i.e. a subset of rows crossed with a subset of
935 * columns) whose width and height add up to n.
942 * We have a candidate set. If its size is <=1 or >=n-1
943 * then we move on immediately.
945 if (count
> 1 && count
< n
-1) {
947 * The number of rows we need is n-count. See if we can
948 * find that many rows which each have a zero in all
949 * the positions listed in `set'.
952 for (i
= 0; i
< n
; i
++) {
954 for (j
= 0; j
< n
; j
++)
955 if (set
[j
] && grid
[i
*cr
+j
]) {
964 * We expect never to be able to get _more_ than
965 * n-count suitable rows: this would imply that (for
966 * example) there are four numbers which between them
967 * have at most three possible positions, and hence it
968 * indicates a faulty deduction before this point or
971 assert(rows
<= n
- count
);
972 if (rows
>= n
- count
) {
973 int progress
= FALSE
;
976 * We've got one! Now, for each row which _doesn't_
977 * satisfy the criterion, eliminate all its set
978 * bits in the positions _not_ listed in `set'.
979 * Return TRUE (meaning progress has been made) if
980 * we successfully eliminated anything at all.
982 * This involves referring back through
983 * rowidx/colidx in order to work out which actual
984 * positions in the cube to meddle with.
986 for (i
= 0; i
< n
; i
++) {
988 for (j
= 0; j
< n
; j
++)
989 if (set
[j
] && grid
[i
*cr
+j
]) {
994 for (j
= 0; j
< n
; j
++)
995 if (!set
[j
] && grid
[i
*cr
+j
]) {
996 int fpos
= (start
+rowidx
[i
]*step1
+
998 #ifdef STANDALONE_SOLVER
999 if (solver_show_working
) {
1015 printf(" ruling out %d at (%d,%d)\n",
1016 pn
, 1+px
, 1+YUNTRANS(py
));
1020 usage
->cube
[fpos
] = FALSE
;
1032 * Binary increment: change the rightmost 0 to a 1, and
1033 * change all 1s to the right of it to 0s.
1036 while (i
> 0 && set
[i
-1])
1037 set
[--i
] = 0, count
--;
1039 set
[--i
] = 1, count
++;
1047 static struct nsolve_scratch
*nsolve_new_scratch(struct nsolve_usage
*usage
)
1049 struct nsolve_scratch
*scratch
= snew(struct nsolve_scratch
);
1051 scratch
->grid
= snewn(cr
*cr
, unsigned char);
1052 scratch
->rowidx
= snewn(cr
, unsigned char);
1053 scratch
->colidx
= snewn(cr
, unsigned char);
1054 scratch
->set
= snewn(cr
, unsigned char);
1058 static void nsolve_free_scratch(struct nsolve_scratch
*scratch
)
1060 sfree(scratch
->set
);
1061 sfree(scratch
->colidx
);
1062 sfree(scratch
->rowidx
);
1063 sfree(scratch
->grid
);
1067 static int nsolve(int c
, int r
, digit
*grid
)
1069 struct nsolve_usage
*usage
;
1070 struct nsolve_scratch
*scratch
;
1073 int diff
= DIFF_BLOCK
;
1076 * Set up a usage structure as a clean slate (everything
1079 usage
= snew(struct nsolve_usage
);
1083 usage
->cube
= snewn(cr
*cr
*cr
, unsigned char);
1084 usage
->grid
= grid
; /* write straight back to the input */
1085 memset(usage
->cube
, TRUE
, cr
*cr
*cr
);
1087 usage
->row
= snewn(cr
* cr
, unsigned char);
1088 usage
->col
= snewn(cr
* cr
, unsigned char);
1089 usage
->blk
= snewn(cr
* cr
, unsigned char);
1090 memset(usage
->row
, FALSE
, cr
* cr
);
1091 memset(usage
->col
, FALSE
, cr
* cr
);
1092 memset(usage
->blk
, FALSE
, cr
* cr
);
1094 scratch
= nsolve_new_scratch(usage
);
1097 * Place all the clue numbers we are given.
1099 for (x
= 0; x
< cr
; x
++)
1100 for (y
= 0; y
< cr
; y
++)
1102 nsolve_place(usage
, x
, YTRANS(y
), grid
[y
*cr
+x
]);
1105 * Now loop over the grid repeatedly trying all permitted modes
1106 * of reasoning. The loop terminates if we complete an
1107 * iteration without making any progress; we then return
1108 * failure or success depending on whether the grid is full or
1113 * I'd like to write `continue;' inside each of the
1114 * following loops, so that the solver returns here after
1115 * making some progress. However, I can't specify that I
1116 * want to continue an outer loop rather than the innermost
1117 * one, so I'm apologetically resorting to a goto.
1122 * Blockwise positional elimination.
1124 for (x
= 0; x
< cr
; x
+= r
)
1125 for (y
= 0; y
< r
; y
++)
1126 for (n
= 1; n
<= cr
; n
++)
1127 if (!usage
->blk
[(y
*c
+(x
/r
))*cr
+n
-1] &&
1128 nsolve_elim(usage
, cubepos(x
,y
,n
), r
*cr
1129 #ifdef STANDALONE_SOLVER
1130 , "positional elimination,"
1131 " block (%d,%d)", 1+x
/r
, 1+y
1134 diff
= max(diff
, DIFF_BLOCK
);
1139 * Row-wise positional elimination.
1141 for (y
= 0; y
< cr
; y
++)
1142 for (n
= 1; n
<= cr
; n
++)
1143 if (!usage
->row
[y
*cr
+n
-1] &&
1144 nsolve_elim(usage
, cubepos(0,y
,n
), cr
*cr
1145 #ifdef STANDALONE_SOLVER
1146 , "positional elimination,"
1147 " row %d", 1+YUNTRANS(y
)
1150 diff
= max(diff
, DIFF_SIMPLE
);
1154 * Column-wise positional elimination.
1156 for (x
= 0; x
< cr
; x
++)
1157 for (n
= 1; n
<= cr
; n
++)
1158 if (!usage
->col
[x
*cr
+n
-1] &&
1159 nsolve_elim(usage
, cubepos(x
,0,n
), cr
1160 #ifdef STANDALONE_SOLVER
1161 , "positional elimination," " column %d", 1+x
1164 diff
= max(diff
, DIFF_SIMPLE
);
1169 * Numeric elimination.
1171 for (x
= 0; x
< cr
; x
++)
1172 for (y
= 0; y
< cr
; y
++)
1173 if (!usage
->grid
[YUNTRANS(y
)*cr
+x
] &&
1174 nsolve_elim(usage
, cubepos(x
,y
,1), 1
1175 #ifdef STANDALONE_SOLVER
1176 , "numeric elimination at (%d,%d)", 1+x
,
1180 diff
= max(diff
, DIFF_SIMPLE
);
1185 * Intersectional analysis, rows vs blocks.
1187 for (y
= 0; y
< cr
; y
++)
1188 for (x
= 0; x
< cr
; x
+= r
)
1189 for (n
= 1; n
<= cr
; n
++)
1190 if (!usage
->row
[y
*cr
+n
-1] &&
1191 !usage
->blk
[((y
%r
)*c
+(x
/r
))*cr
+n
-1] &&
1192 (nsolve_intersect(usage
, cubepos(0,y
,n
), cr
*cr
,
1193 cubepos(x
,y
%r
,n
), r
*cr
1194 #ifdef STANDALONE_SOLVER
1195 , "intersectional analysis,"
1196 " row %d vs block (%d,%d)",
1197 1+YUNTRANS(y
), 1+x
/r
, 1+y
%r
1200 nsolve_intersect(usage
, cubepos(x
,y
%r
,n
), r
*cr
,
1201 cubepos(0,y
,n
), cr
*cr
1202 #ifdef STANDALONE_SOLVER
1203 , "intersectional analysis,"
1204 " block (%d,%d) vs row %d",
1205 1+x
/r
, 1+y
%r
, 1+YUNTRANS(y
)
1208 diff
= max(diff
, DIFF_INTERSECT
);
1213 * Intersectional analysis, columns vs blocks.
1215 for (x
= 0; x
< cr
; x
++)
1216 for (y
= 0; y
< r
; y
++)
1217 for (n
= 1; n
<= cr
; n
++)
1218 if (!usage
->col
[x
*cr
+n
-1] &&
1219 !usage
->blk
[(y
*c
+(x
/r
))*cr
+n
-1] &&
1220 (nsolve_intersect(usage
, cubepos(x
,0,n
), cr
,
1221 cubepos((x
/r
)*r
,y
,n
), r
*cr
1222 #ifdef STANDALONE_SOLVER
1223 , "intersectional analysis,"
1224 " column %d vs block (%d,%d)",
1228 nsolve_intersect(usage
, cubepos((x
/r
)*r
,y
,n
), r
*cr
,
1230 #ifdef STANDALONE_SOLVER
1231 , "intersectional analysis,"
1232 " block (%d,%d) vs column %d",
1236 diff
= max(diff
, DIFF_INTERSECT
);
1241 * Blockwise set elimination.
1243 for (x
= 0; x
< cr
; x
+= r
)
1244 for (y
= 0; y
< r
; y
++)
1245 if (nsolve_set(usage
, scratch
, cubepos(x
,y
,1), r
*cr
, 1
1246 #ifdef STANDALONE_SOLVER
1247 , "set elimination, block (%d,%d)", 1+x
/r
, 1+y
1250 diff
= max(diff
, DIFF_SET
);
1255 * Row-wise set elimination.
1257 for (y
= 0; y
< cr
; y
++)
1258 if (nsolve_set(usage
, scratch
, cubepos(0,y
,1), cr
*cr
, 1
1259 #ifdef STANDALONE_SOLVER
1260 , "set elimination, row %d", 1+YUNTRANS(y
)
1263 diff
= max(diff
, DIFF_SET
);
1268 * Column-wise set elimination.
1270 for (x
= 0; x
< cr
; x
++)
1271 if (nsolve_set(usage
, scratch
, cubepos(x
,0,1), cr
, 1
1272 #ifdef STANDALONE_SOLVER
1273 , "set elimination, column %d", 1+x
1276 diff
= max(diff
, DIFF_SET
);
1281 * If we reach here, we have made no deductions in this
1282 * iteration, so the algorithm terminates.
1287 nsolve_free_scratch(scratch
);
1295 for (x
= 0; x
< cr
; x
++)
1296 for (y
= 0; y
< cr
; y
++)
1298 return DIFF_IMPOSSIBLE
;
1302 /* ----------------------------------------------------------------------
1303 * End of non-recursive solver code.
1307 * Check whether a grid contains a valid complete puzzle.
1309 static int check_valid(int c
, int r
, digit
*grid
)
1312 unsigned char *used
;
1315 used
= snewn(cr
, unsigned char);
1318 * Check that each row contains precisely one of everything.
1320 for (y
= 0; y
< cr
; y
++) {
1321 memset(used
, FALSE
, cr
);
1322 for (x
= 0; x
< cr
; x
++)
1323 if (grid
[y
*cr
+x
] > 0 && grid
[y
*cr
+x
] <= cr
)
1324 used
[grid
[y
*cr
+x
]-1] = TRUE
;
1325 for (n
= 0; n
< cr
; n
++)
1333 * Check that each column contains precisely one of everything.
1335 for (x
= 0; x
< cr
; x
++) {
1336 memset(used
, FALSE
, cr
);
1337 for (y
= 0; y
< cr
; y
++)
1338 if (grid
[y
*cr
+x
] > 0 && grid
[y
*cr
+x
] <= cr
)
1339 used
[grid
[y
*cr
+x
]-1] = TRUE
;
1340 for (n
= 0; n
< cr
; n
++)
1348 * Check that each block contains precisely one of everything.
1350 for (x
= 0; x
< cr
; x
+= r
) {
1351 for (y
= 0; y
< cr
; y
+= c
) {
1353 memset(used
, FALSE
, cr
);
1354 for (xx
= x
; xx
< x
+r
; xx
++)
1355 for (yy
= 0; yy
< y
+c
; yy
++)
1356 if (grid
[yy
*cr
+xx
] > 0 && grid
[yy
*cr
+xx
] <= cr
)
1357 used
[grid
[yy
*cr
+xx
]-1] = TRUE
;
1358 for (n
= 0; n
< cr
; n
++)
1370 static int symmetries(game_params
*params
, int x
, int y
, int *output
, int s
)
1372 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
1375 #define ADD(x,y) (*output++ = (x), *output++ = (y), i++)
1381 break; /* just x,y is all we need */
1383 ADD(cr
- 1 - x
, cr
- 1 - y
);
1388 ADD(cr
- 1 - x
, cr
- 1 - y
);
1399 ADD(cr
- 1 - x
, cr
- 1 - y
);
1403 ADD(cr
- 1 - x
, cr
- 1 - y
);
1404 ADD(cr
- 1 - y
, cr
- 1 - x
);
1409 ADD(cr
- 1 - x
, cr
- 1 - y
);
1413 ADD(cr
- 1 - y
, cr
- 1 - x
);
1422 static char *encode_solve_move(int cr
, digit
*grid
)
1425 char *ret
, *p
, *sep
;
1428 * It's surprisingly easy to work out _exactly_ how long this
1429 * string needs to be. To decimal-encode all the numbers from 1
1432 * - every number has a units digit; total is n.
1433 * - all numbers above 9 have a tens digit; total is max(n-9,0).
1434 * - all numbers above 99 have a hundreds digit; total is max(n-99,0).
1438 for (i
= 1; i
<= cr
; i
*= 10)
1439 len
+= max(cr
- i
+ 1, 0);
1440 len
+= cr
; /* don't forget the commas */
1441 len
*= cr
; /* there are cr rows of these */
1444 * Now len is one bigger than the total size of the
1445 * comma-separated numbers (because we counted an
1446 * additional leading comma). We need to have a leading S
1447 * and a trailing NUL, so we're off by one in total.
1451 ret
= snewn(len
, char);
1455 for (i
= 0; i
< cr
*cr
; i
++) {
1456 p
+= sprintf(p
, "%s%d", sep
, grid
[i
]);
1460 assert(p
- ret
== len
);
1465 static char *new_game_desc(game_params
*params
, random_state
*rs
,
1466 char **aux
, int interactive
)
1468 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
1470 digit
*grid
, *grid2
;
1471 struct xy
{ int x
, y
; } *locs
;
1475 int coords
[16], ncoords
;
1476 int *symmclasses
, nsymmclasses
;
1477 int maxdiff
, recursing
;
1480 * Adjust the maximum difficulty level to be consistent with
1481 * the puzzle size: all 2x2 puzzles appear to be Trivial
1482 * (DIFF_BLOCK) so we cannot hold out for even a Basic
1483 * (DIFF_SIMPLE) one.
1485 maxdiff
= params
->diff
;
1486 if (c
== 2 && r
== 2)
1487 maxdiff
= DIFF_BLOCK
;
1489 grid
= snewn(area
, digit
);
1490 locs
= snewn(area
, struct xy
);
1491 grid2
= snewn(area
, digit
);
1494 * Find the set of equivalence classes of squares permitted
1495 * by the selected symmetry. We do this by enumerating all
1496 * the grid squares which have no symmetric companion
1497 * sorting lower than themselves.
1500 symmclasses
= snewn(cr
* cr
, int);
1504 for (y
= 0; y
< cr
; y
++)
1505 for (x
= 0; x
< cr
; x
++) {
1509 ncoords
= symmetries(params
, x
, y
, coords
, params
->symm
);
1510 for (j
= 0; j
< ncoords
; j
++)
1511 if (coords
[2*j
+1]*cr
+coords
[2*j
] < i
)
1514 symmclasses
[nsymmclasses
++] = i
;
1519 * Loop until we get a grid of the required difficulty. This is
1520 * nasty, but it seems to be unpleasantly hard to generate
1521 * difficult grids otherwise.
1525 * Start the recursive solver with an empty grid to generate a
1526 * random solved state.
1528 memset(grid
, 0, area
);
1529 ret
= rsolve(c
, r
, grid
, rs
, 1);
1531 assert(check_valid(c
, r
, grid
));
1534 * Save the solved grid in aux.
1538 * We might already have written *aux the last time we
1539 * went round this loop, in which case we should free
1540 * the old aux before overwriting it with the new one.
1546 *aux
= encode_solve_move(cr
, grid
);
1550 * Now we have a solved grid, start removing things from it
1551 * while preserving solubility.
1558 * Iterate over the grid and enumerate all the filled
1559 * squares we could empty.
1563 for (i
= 0; i
< nsymmclasses
; i
++) {
1564 x
= symmclasses
[i
] % cr
;
1565 y
= symmclasses
[i
] / cr
;
1574 * Now shuffle that list.
1576 for (i
= nlocs
; i
> 1; i
--) {
1577 int p
= random_upto(rs
, i
);
1579 struct xy t
= locs
[p
];
1580 locs
[p
] = locs
[i
-1];
1586 * Now loop over the shuffled list and, for each element,
1587 * see whether removing that element (and its reflections)
1588 * from the grid will still leave the grid soluble by
1591 for (i
= 0; i
< nlocs
; i
++) {
1597 memcpy(grid2
, grid
, area
);
1598 ncoords
= symmetries(params
, x
, y
, coords
, params
->symm
);
1599 for (j
= 0; j
< ncoords
; j
++)
1600 grid2
[coords
[2*j
+1]*cr
+coords
[2*j
]] = 0;
1603 ret
= (rsolve(c
, r
, grid2
, NULL
, 2) == 1);
1605 ret
= (nsolve(c
, r
, grid2
) <= maxdiff
);
1608 for (j
= 0; j
< ncoords
; j
++)
1609 grid
[coords
[2*j
+1]*cr
+coords
[2*j
]] = 0;
1616 * There was nothing we could remove without
1617 * destroying solvability. If we're trying to
1618 * generate a recursion-only grid and haven't
1619 * switched over to rsolve yet, we now do;
1620 * otherwise we give up.
1622 if (maxdiff
== DIFF_RECURSIVE
&& !recursing
) {
1630 memcpy(grid2
, grid
, area
);
1631 } while (nsolve(c
, r
, grid2
) < maxdiff
);
1639 * Now we have the grid as it will be presented to the user.
1640 * Encode it in a game desc.
1646 desc
= snewn(5 * area
, char);
1649 for (i
= 0; i
<= area
; i
++) {
1650 int n
= (i
< area ? grid
[i
] : -1);
1657 int c
= 'a' - 1 + run
;
1661 run
-= c
- ('a' - 1);
1665 * If there's a number in the very top left or
1666 * bottom right, there's no point putting an
1667 * unnecessary _ before or after it.
1669 if (p
> desc
&& n
> 0)
1673 p
+= sprintf(p
, "%d", n
);
1677 assert(p
- desc
< 5 * area
);
1679 desc
= sresize(desc
, p
- desc
, char);
1687 static char *validate_desc(game_params
*params
, char *desc
)
1689 int area
= params
->r
* params
->r
* params
->c
* params
->c
;
1694 if (n
>= 'a' && n
<= 'z') {
1695 squares
+= n
- 'a' + 1;
1696 } else if (n
== '_') {
1698 } else if (n
> '0' && n
<= '9') {
1700 while (*desc
>= '0' && *desc
<= '9')
1703 return "Invalid character in game description";
1707 return "Not enough data to fill grid";
1710 return "Too much data to fit in grid";
1715 static game_state
*new_game(midend_data
*me
, game_params
*params
, char *desc
)
1717 game_state
*state
= snew(game_state
);
1718 int c
= params
->c
, r
= params
->r
, cr
= c
*r
, area
= cr
* cr
;
1721 state
->c
= params
->c
;
1722 state
->r
= params
->r
;
1724 state
->grid
= snewn(area
, digit
);
1725 state
->pencil
= snewn(area
* cr
, unsigned char);
1726 memset(state
->pencil
, 0, area
* cr
);
1727 state
->immutable
= snewn(area
, unsigned char);
1728 memset(state
->immutable
, FALSE
, area
);
1730 state
->completed
= state
->cheated
= FALSE
;
1735 if (n
>= 'a' && n
<= 'z') {
1736 int run
= n
- 'a' + 1;
1737 assert(i
+ run
<= area
);
1739 state
->grid
[i
++] = 0;
1740 } else if (n
== '_') {
1742 } else if (n
> '0' && n
<= '9') {
1744 state
->immutable
[i
] = TRUE
;
1745 state
->grid
[i
++] = atoi(desc
-1);
1746 while (*desc
>= '0' && *desc
<= '9')
1749 assert(!"We can't get here");
1757 static game_state
*dup_game(game_state
*state
)
1759 game_state
*ret
= snew(game_state
);
1760 int c
= state
->c
, r
= state
->r
, cr
= c
*r
, area
= cr
* cr
;
1765 ret
->grid
= snewn(area
, digit
);
1766 memcpy(ret
->grid
, state
->grid
, area
);
1768 ret
->pencil
= snewn(area
* cr
, unsigned char);
1769 memcpy(ret
->pencil
, state
->pencil
, area
* cr
);
1771 ret
->immutable
= snewn(area
, unsigned char);
1772 memcpy(ret
->immutable
, state
->immutable
, area
);
1774 ret
->completed
= state
->completed
;
1775 ret
->cheated
= state
->cheated
;
1780 static void free_game(game_state
*state
)
1782 sfree(state
->immutable
);
1783 sfree(state
->pencil
);
1788 static char *solve_game(game_state
*state
, game_state
*currstate
,
1789 char *ai
, char **error
)
1791 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
1797 * If we already have the solution in ai, save ourselves some
1803 grid
= snewn(cr
*cr
, digit
);
1804 memcpy(grid
, state
->grid
, cr
*cr
);
1805 rsolve_ret
= rsolve(c
, r
, grid
, NULL
, 2);
1807 if (rsolve_ret
!= 1) {
1809 if (rsolve_ret
== 0)
1810 *error
= "No solution exists for this puzzle";
1812 *error
= "Multiple solutions exist for this puzzle";
1816 ret
= encode_solve_move(cr
, grid
);
1823 static char *grid_text_format(int c
, int r
, digit
*grid
)
1831 * There are cr lines of digits, plus r-1 lines of block
1832 * separators. Each line contains cr digits, cr-1 separating
1833 * spaces, and c-1 two-character block separators. Thus, the
1834 * total length of a line is 2*cr+2*c-3 (not counting the
1835 * newline), and there are cr+r-1 of them.
1837 maxlen
= (cr
+r
-1) * (2*cr
+2*c
-2);
1838 ret
= snewn(maxlen
+1, char);
1841 for (y
= 0; y
< cr
; y
++) {
1842 for (x
= 0; x
< cr
; x
++) {
1843 int ch
= grid
[y
* cr
+ x
];
1853 if ((x
+1) % r
== 0) {
1860 if (y
+1 < cr
&& (y
+1) % c
== 0) {
1861 for (x
= 0; x
< cr
; x
++) {
1865 if ((x
+1) % r
== 0) {
1875 assert(p
- ret
== maxlen
);
1880 static char *game_text_format(game_state
*state
)
1882 return grid_text_format(state
->c
, state
->r
, state
->grid
);
1887 * These are the coordinates of the currently highlighted
1888 * square on the grid, or -1,-1 if there isn't one. When there
1889 * is, pressing a valid number or letter key or Space will
1890 * enter that number or letter in the grid.
1894 * This indicates whether the current highlight is a
1895 * pencil-mark one or a real one.
1900 static game_ui
*new_ui(game_state
*state
)
1902 game_ui
*ui
= snew(game_ui
);
1904 ui
->hx
= ui
->hy
= -1;
1910 static void free_ui(game_ui
*ui
)
1915 static char *encode_ui(game_ui
*ui
)
1920 static void decode_ui(game_ui
*ui
, char *encoding
)
1924 static void game_changed_state(game_ui
*ui
, game_state
*oldstate
,
1925 game_state
*newstate
)
1927 int c
= newstate
->c
, r
= newstate
->r
, cr
= c
*r
;
1929 * We prevent pencil-mode highlighting of a filled square. So
1930 * if the user has just filled in a square which we had a
1931 * pencil-mode highlight in (by Undo, or by Redo, or by Solve),
1932 * then we cancel the highlight.
1934 if (ui
->hx
>= 0 && ui
->hy
>= 0 && ui
->hpencil
&&
1935 newstate
->grid
[ui
->hy
* cr
+ ui
->hx
] != 0) {
1936 ui
->hx
= ui
->hy
= -1;
1940 struct game_drawstate
{
1945 unsigned char *pencil
;
1947 /* This is scratch space used within a single call to game_redraw. */
1951 static char *interpret_move(game_state
*state
, game_ui
*ui
, game_drawstate
*ds
,
1952 int x
, int y
, int button
)
1954 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
1958 button
&= ~MOD_MASK
;
1960 tx
= (x
+ TILE_SIZE
- BORDER
) / TILE_SIZE
- 1;
1961 ty
= (y
+ TILE_SIZE
- BORDER
) / TILE_SIZE
- 1;
1963 if (tx
>= 0 && tx
< cr
&& ty
>= 0 && ty
< cr
) {
1964 if (button
== LEFT_BUTTON
) {
1965 if (state
->immutable
[ty
*cr
+tx
]) {
1966 ui
->hx
= ui
->hy
= -1;
1967 } else if (tx
== ui
->hx
&& ty
== ui
->hy
&& ui
->hpencil
== 0) {
1968 ui
->hx
= ui
->hy
= -1;
1974 return ""; /* UI activity occurred */
1976 if (button
== RIGHT_BUTTON
) {
1978 * Pencil-mode highlighting for non filled squares.
1980 if (state
->grid
[ty
*cr
+tx
] == 0) {
1981 if (tx
== ui
->hx
&& ty
== ui
->hy
&& ui
->hpencil
) {
1982 ui
->hx
= ui
->hy
= -1;
1989 ui
->hx
= ui
->hy
= -1;
1991 return ""; /* UI activity occurred */
1995 if (ui
->hx
!= -1 && ui
->hy
!= -1 &&
1996 ((button
>= '1' && button
<= '9' && button
- '0' <= cr
) ||
1997 (button
>= 'a' && button
<= 'z' && button
- 'a' + 10 <= cr
) ||
1998 (button
>= 'A' && button
<= 'Z' && button
- 'A' + 10 <= cr
) ||
2000 int n
= button
- '0';
2001 if (button
>= 'A' && button
<= 'Z')
2002 n
= button
- 'A' + 10;
2003 if (button
>= 'a' && button
<= 'z')
2004 n
= button
- 'a' + 10;
2009 * Can't overwrite this square. In principle this shouldn't
2010 * happen anyway because we should never have even been
2011 * able to highlight the square, but it never hurts to be
2014 if (state
->immutable
[ui
->hy
*cr
+ui
->hx
])
2018 * Can't make pencil marks in a filled square. In principle
2019 * this shouldn't happen anyway because we should never
2020 * have even been able to pencil-highlight the square, but
2021 * it never hurts to be careful.
2023 if (ui
->hpencil
&& state
->grid
[ui
->hy
*cr
+ui
->hx
])
2026 sprintf(buf
, "%c%d,%d,%d",
2027 ui
->hpencil
&& n
> 0 ?
'P' : 'R', ui
->hx
, ui
->hy
, n
);
2029 ui
->hx
= ui
->hy
= -1;
2037 static game_state
*execute_move(game_state
*from
, char *move
)
2039 int c
= from
->c
, r
= from
->r
, cr
= c
*r
;
2043 if (move
[0] == 'S') {
2046 ret
= dup_game(from
);
2047 ret
->completed
= ret
->cheated
= TRUE
;
2050 for (n
= 0; n
< cr
*cr
; n
++) {
2051 ret
->grid
[n
] = atoi(p
);
2053 if (!*p
|| ret
->grid
[n
] < 1 || ret
->grid
[n
] > cr
) {
2058 while (*p
&& isdigit((unsigned char)*p
)) p
++;
2063 } else if ((move
[0] == 'P' || move
[0] == 'R') &&
2064 sscanf(move
+1, "%d,%d,%d", &x
, &y
, &n
) == 3 &&
2065 x
>= 0 && x
< cr
&& y
>= 0 && y
< cr
&& n
>= 0 && n
<= cr
) {
2067 ret
= dup_game(from
);
2068 if (move
[0] == 'P' && n
> 0) {
2069 int index
= (y
*cr
+x
) * cr
+ (n
-1);
2070 ret
->pencil
[index
] = !ret
->pencil
[index
];
2072 ret
->grid
[y
*cr
+x
] = n
;
2073 memset(ret
->pencil
+ (y
*cr
+x
)*cr
, 0, cr
);
2076 * We've made a real change to the grid. Check to see
2077 * if the game has been completed.
2079 if (!ret
->completed
&& check_valid(c
, r
, ret
->grid
)) {
2080 ret
->completed
= TRUE
;
2085 return NULL
; /* couldn't parse move string */
2088 /* ----------------------------------------------------------------------
2092 #define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
2093 #define GETTILESIZE(cr, w) ( (w-1) / (cr+1) )
2095 static void game_size(game_params
*params
, game_drawstate
*ds
,
2096 int *x
, int *y
, int expand
)
2098 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
2101 ts
= min(GETTILESIZE(cr
, *x
), GETTILESIZE(cr
, *y
));
2105 ds
->tilesize
= min(ts
, PREFERRED_TILE_SIZE
);
2111 static float *game_colours(frontend
*fe
, game_state
*state
, int *ncolours
)
2113 float *ret
= snewn(3 * NCOLOURS
, float);
2115 frontend_default_colour(fe
, &ret
[COL_BACKGROUND
* 3]);
2117 ret
[COL_GRID
* 3 + 0] = 0.0F
;
2118 ret
[COL_GRID
* 3 + 1] = 0.0F
;
2119 ret
[COL_GRID
* 3 + 2] = 0.0F
;
2121 ret
[COL_CLUE
* 3 + 0] = 0.0F
;
2122 ret
[COL_CLUE
* 3 + 1] = 0.0F
;
2123 ret
[COL_CLUE
* 3 + 2] = 0.0F
;
2125 ret
[COL_USER
* 3 + 0] = 0.0F
;
2126 ret
[COL_USER
* 3 + 1] = 0.6F
* ret
[COL_BACKGROUND
* 3 + 1];
2127 ret
[COL_USER
* 3 + 2] = 0.0F
;
2129 ret
[COL_HIGHLIGHT
* 3 + 0] = 0.85F
* ret
[COL_BACKGROUND
* 3 + 0];
2130 ret
[COL_HIGHLIGHT
* 3 + 1] = 0.85F
* ret
[COL_BACKGROUND
* 3 + 1];
2131 ret
[COL_HIGHLIGHT
* 3 + 2] = 0.85F
* ret
[COL_BACKGROUND
* 3 + 2];
2133 ret
[COL_ERROR
* 3 + 0] = 1.0F
;
2134 ret
[COL_ERROR
* 3 + 1] = 0.0F
;
2135 ret
[COL_ERROR
* 3 + 2] = 0.0F
;
2137 ret
[COL_PENCIL
* 3 + 0] = 0.5F
* ret
[COL_BACKGROUND
* 3 + 0];
2138 ret
[COL_PENCIL
* 3 + 1] = 0.5F
* ret
[COL_BACKGROUND
* 3 + 1];
2139 ret
[COL_PENCIL
* 3 + 2] = ret
[COL_BACKGROUND
* 3 + 2];
2141 *ncolours
= NCOLOURS
;
2145 static game_drawstate
*game_new_drawstate(game_state
*state
)
2147 struct game_drawstate
*ds
= snew(struct game_drawstate
);
2148 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
2150 ds
->started
= FALSE
;
2154 ds
->grid
= snewn(cr
*cr
, digit
);
2155 memset(ds
->grid
, 0, cr
*cr
);
2156 ds
->pencil
= snewn(cr
*cr
*cr
, digit
);
2157 memset(ds
->pencil
, 0, cr
*cr
*cr
);
2158 ds
->hl
= snewn(cr
*cr
, unsigned char);
2159 memset(ds
->hl
, 0, cr
*cr
);
2160 ds
->entered_items
= snewn(cr
*cr
, int);
2161 ds
->tilesize
= 0; /* not decided yet */
2165 static void game_free_drawstate(game_drawstate
*ds
)
2170 sfree(ds
->entered_items
);
2174 static void draw_number(frontend
*fe
, game_drawstate
*ds
, game_state
*state
,
2175 int x
, int y
, int hl
)
2177 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
2182 if (ds
->grid
[y
*cr
+x
] == state
->grid
[y
*cr
+x
] &&
2183 ds
->hl
[y
*cr
+x
] == hl
&&
2184 !memcmp(ds
->pencil
+(y
*cr
+x
)*cr
, state
->pencil
+(y
*cr
+x
)*cr
, cr
))
2185 return; /* no change required */
2187 tx
= BORDER
+ x
* TILE_SIZE
+ 2;
2188 ty
= BORDER
+ y
* TILE_SIZE
+ 2;
2204 clip(fe
, cx
, cy
, cw
, ch
);
2206 /* background needs erasing */
2207 draw_rect(fe
, cx
, cy
, cw
, ch
, (hl
& 15) == 1 ? COL_HIGHLIGHT
: COL_BACKGROUND
);
2209 /* pencil-mode highlight */
2210 if ((hl
& 15) == 2) {
2214 coords
[2] = cx
+cw
/2;
2217 coords
[5] = cy
+ch
/2;
2218 draw_polygon(fe
, coords
, 3, TRUE
, COL_HIGHLIGHT
);
2221 /* new number needs drawing? */
2222 if (state
->grid
[y
*cr
+x
]) {
2224 str
[0] = state
->grid
[y
*cr
+x
] + '0';
2226 str
[0] += 'a' - ('9'+1);
2227 draw_text(fe
, tx
+ TILE_SIZE
/2, ty
+ TILE_SIZE
/2,
2228 FONT_VARIABLE
, TILE_SIZE
/2, ALIGN_VCENTRE
| ALIGN_HCENTRE
,
2229 state
->immutable
[y
*cr
+x
] ? COL_CLUE
: (hl
& 16) ? COL_ERROR
: COL_USER
, str
);
2232 int pw
, ph
, pmax
, fontsize
;
2234 /* count the pencil marks required */
2235 for (i
= npencil
= 0; i
< cr
; i
++)
2236 if (state
->pencil
[(y
*cr
+x
)*cr
+i
])
2240 * It's not sensible to arrange pencil marks in the same
2241 * layout as the squares within a block, because this leads
2242 * to the font being too small. Instead, we arrange pencil
2243 * marks in the nearest thing we can to a square layout,
2244 * and we adjust the square layout depending on the number
2245 * of pencil marks in the square.
2247 for (pw
= 1; pw
* pw
< npencil
; pw
++);
2248 if (pw
< 3) pw
= 3; /* otherwise it just looks _silly_ */
2249 ph
= (npencil
+ pw
- 1) / pw
;
2250 if (ph
< 2) ph
= 2; /* likewise */
2252 fontsize
= TILE_SIZE
/(pmax
*(11-pmax
)/8);
2254 for (i
= j
= 0; i
< cr
; i
++)
2255 if (state
->pencil
[(y
*cr
+x
)*cr
+i
]) {
2256 int dx
= j
% pw
, dy
= j
/ pw
;
2261 str
[0] += 'a' - ('9'+1);
2262 draw_text(fe
, tx
+ (4*dx
+3) * TILE_SIZE
/ (4*pw
+2),
2263 ty
+ (4*dy
+3) * TILE_SIZE
/ (4*ph
+2),
2264 FONT_VARIABLE
, fontsize
,
2265 ALIGN_VCENTRE
| ALIGN_HCENTRE
, COL_PENCIL
, str
);
2272 draw_update(fe
, cx
, cy
, cw
, ch
);
2274 ds
->grid
[y
*cr
+x
] = state
->grid
[y
*cr
+x
];
2275 memcpy(ds
->pencil
+(y
*cr
+x
)*cr
, state
->pencil
+(y
*cr
+x
)*cr
, cr
);
2276 ds
->hl
[y
*cr
+x
] = hl
;
2279 static void game_redraw(frontend
*fe
, game_drawstate
*ds
, game_state
*oldstate
,
2280 game_state
*state
, int dir
, game_ui
*ui
,
2281 float animtime
, float flashtime
)
2283 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
2288 * The initial contents of the window are not guaranteed
2289 * and can vary with front ends. To be on the safe side,
2290 * all games should start by drawing a big
2291 * background-colour rectangle covering the whole window.
2293 draw_rect(fe
, 0, 0, SIZE(cr
), SIZE(cr
), COL_BACKGROUND
);
2298 for (x
= 0; x
<= cr
; x
++) {
2299 int thick
= (x
% r ?
0 : 1);
2300 draw_rect(fe
, BORDER
+ x
*TILE_SIZE
- thick
, BORDER
-1,
2301 1+2*thick
, cr
*TILE_SIZE
+3, COL_GRID
);
2303 for (y
= 0; y
<= cr
; y
++) {
2304 int thick
= (y
% c ?
0 : 1);
2305 draw_rect(fe
, BORDER
-1, BORDER
+ y
*TILE_SIZE
- thick
,
2306 cr
*TILE_SIZE
+3, 1+2*thick
, COL_GRID
);
2311 * This array is used to keep track of rows, columns and boxes
2312 * which contain a number more than once.
2314 for (x
= 0; x
< cr
* cr
; x
++)
2315 ds
->entered_items
[x
] = 0;
2316 for (x
= 0; x
< cr
; x
++)
2317 for (y
= 0; y
< cr
; y
++) {
2318 digit d
= state
->grid
[y
*cr
+x
];
2320 int box
= (x
/r
)+(y
/c
)*c
;
2321 ds
->entered_items
[x
*cr
+d
-1] |= ((ds
->entered_items
[x
*cr
+d
-1] & 1) << 1) | 1;
2322 ds
->entered_items
[y
*cr
+d
-1] |= ((ds
->entered_items
[y
*cr
+d
-1] & 4) << 1) | 4;
2323 ds
->entered_items
[box
*cr
+d
-1] |= ((ds
->entered_items
[box
*cr
+d
-1] & 16) << 1) | 16;
2328 * Draw any numbers which need redrawing.
2330 for (x
= 0; x
< cr
; x
++) {
2331 for (y
= 0; y
< cr
; y
++) {
2333 digit d
= state
->grid
[y
*cr
+x
];
2335 if (flashtime
> 0 &&
2336 (flashtime
<= FLASH_TIME
/3 ||
2337 flashtime
>= FLASH_TIME
*2/3))
2340 /* Highlight active input areas. */
2341 if (x
== ui
->hx
&& y
== ui
->hy
)
2342 highlight
= ui
->hpencil ?
2 : 1;
2344 /* Mark obvious errors (ie, numbers which occur more than once
2345 * in a single row, column, or box). */
2346 if (d
&& ((ds
->entered_items
[x
*cr
+d
-1] & 2) ||
2347 (ds
->entered_items
[y
*cr
+d
-1] & 8) ||
2348 (ds
->entered_items
[((x
/r
)+(y
/c
)*c
)*cr
+d
-1] & 32)))
2351 draw_number(fe
, ds
, state
, x
, y
, highlight
);
2356 * Update the _entire_ grid if necessary.
2359 draw_update(fe
, 0, 0, SIZE(cr
), SIZE(cr
));
2364 static float game_anim_length(game_state
*oldstate
, game_state
*newstate
,
2365 int dir
, game_ui
*ui
)
2370 static float game_flash_length(game_state
*oldstate
, game_state
*newstate
,
2371 int dir
, game_ui
*ui
)
2373 if (!oldstate
->completed
&& newstate
->completed
&&
2374 !oldstate
->cheated
&& !newstate
->cheated
)
2379 static int game_wants_statusbar(void)
2384 static int game_timing_state(game_state
*state
)
2390 #define thegame solo
2393 const struct game thegame
= {
2394 "Solo", "games.solo",
2401 TRUE
, game_configure
, custom_params
,
2409 TRUE
, game_text_format
,
2420 game_free_drawstate
,
2424 game_wants_statusbar
,
2425 FALSE
, game_timing_state
,
2426 0, /* mouse_priorities */
2429 #ifdef STANDALONE_SOLVER
2432 * gcc -DSTANDALONE_SOLVER -o solosolver solo.c malloc.c
2435 void frontend_default_colour(frontend
*fe
, float *output
) {}
2436 void draw_text(frontend
*fe
, int x
, int y
, int fonttype
, int fontsize
,
2437 int align
, int colour
, char *text
) {}
2438 void draw_rect(frontend
*fe
, int x
, int y
, int w
, int h
, int colour
) {}
2439 void draw_line(frontend
*fe
, int x1
, int y1
, int x2
, int y2
, int colour
) {}
2440 void draw_polygon(frontend
*fe
, int *coords
, int npoints
,
2441 int fill
, int colour
) {}
2442 void clip(frontend
*fe
, int x
, int y
, int w
, int h
) {}
2443 void unclip(frontend
*fe
) {}
2444 void start_draw(frontend
*fe
) {}
2445 void draw_update(frontend
*fe
, int x
, int y
, int w
, int h
) {}
2446 void end_draw(frontend
*fe
) {}
2447 unsigned long random_bits(random_state
*state
, int bits
)
2448 { assert(!"Shouldn't get randomness"); return 0; }
2449 unsigned long random_upto(random_state
*state
, unsigned long limit
)
2450 { assert(!"Shouldn't get randomness"); return 0; }
2452 void fatal(char *fmt
, ...)
2456 fprintf(stderr
, "fatal error: ");
2459 vfprintf(stderr
, fmt
, ap
);
2462 fprintf(stderr
, "\n");
2466 int main(int argc
, char **argv
)
2471 char *id
= NULL
, *desc
, *err
;
2475 while (--argc
> 0) {
2477 if (!strcmp(p
, "-r")) {
2479 } else if (!strcmp(p
, "-n")) {
2481 } else if (!strcmp(p
, "-v")) {
2482 solver_show_working
= TRUE
;
2484 } else if (!strcmp(p
, "-g")) {
2487 } else if (*p
== '-') {
2488 fprintf(stderr
, "%s: unrecognised option `%s'\n", argv
[0]);
2496 fprintf(stderr
, "usage: %s [-n | -r | -g | -v] <game_id>\n", argv
[0]);
2500 desc
= strchr(id
, ':');
2502 fprintf(stderr
, "%s: game id expects a colon in it\n", argv
[0]);
2507 p
= default_params();
2508 decode_params(p
, id
);
2509 err
= validate_desc(p
, desc
);
2511 fprintf(stderr
, "%s: %s\n", argv
[0], err
);
2514 s
= new_game(NULL
, p
, desc
);
2517 int ret
= rsolve(p
->c
, p
->r
, s
->grid
, NULL
, 2);
2519 fprintf(stderr
, "%s: rsolve: multiple solutions detected\n",
2523 int ret
= nsolve(p
->c
, p
->r
, s
->grid
);
2525 if (ret
== DIFF_IMPOSSIBLE
) {
2527 * Now resort to rsolve to determine whether it's
2530 ret
= rsolve(p
->c
, p
->r
, s
->grid
, NULL
, 2);
2532 ret
= DIFF_IMPOSSIBLE
;
2534 ret
= DIFF_RECURSIVE
;
2536 ret
= DIFF_AMBIGUOUS
;
2538 printf("Difficulty rating: %s\n",
2539 ret
==DIFF_BLOCK ?
"Trivial (blockwise positional elimination only)":
2540 ret
==DIFF_SIMPLE ?
"Basic (row/column/number elimination required)":
2541 ret
==DIFF_INTERSECT ?
"Intermediate (intersectional analysis required)":
2542 ret
==DIFF_SET ?
"Advanced (set elimination required)":
2543 ret
==DIFF_RECURSIVE ?
"Unreasonable (guesswork and backtracking required)":
2544 ret
==DIFF_AMBIGUOUS ?
"Ambiguous (multiple solutions exist)":
2545 ret
==DIFF_IMPOSSIBLE ?
"Impossible (no solution exists)":
2546 "INTERNAL ERROR: unrecognised difficulty code");
2550 printf("%s\n", grid_text_format(p
->c
, p
->r
, s
->grid
));