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
113 #define FLASH_TIME 0.4F
115 enum { SYMM_NONE
, SYMM_ROT2
, SYMM_ROT4
, SYMM_REF4
};
117 enum { DIFF_BLOCK
, DIFF_SIMPLE
, DIFF_INTERSECT
,
118 DIFF_SET
, DIFF_RECURSIVE
, DIFF_AMBIGUOUS
, DIFF_IMPOSSIBLE
};
132 int c
, r
, symm
, diff
;
138 unsigned char *pencil
; /* c*r*c*r elements */
139 unsigned char *immutable
; /* marks which digits are clues */
140 int completed
, cheated
;
143 static game_params
*default_params(void)
145 game_params
*ret
= snew(game_params
);
148 ret
->symm
= SYMM_ROT2
; /* a plausible default */
149 ret
->diff
= DIFF_BLOCK
; /* so is this */
154 static void free_params(game_params
*params
)
159 static game_params
*dup_params(game_params
*params
)
161 game_params
*ret
= snew(game_params
);
162 *ret
= *params
; /* structure copy */
166 static int game_fetch_preset(int i
, char **name
, game_params
**params
)
172 { "2x2 Trivial", { 2, 2, SYMM_ROT2
, DIFF_BLOCK
} },
173 { "2x3 Basic", { 2, 3, SYMM_ROT2
, DIFF_SIMPLE
} },
174 { "3x3 Trivial", { 3, 3, SYMM_ROT2
, DIFF_BLOCK
} },
175 { "3x3 Basic", { 3, 3, SYMM_ROT2
, DIFF_SIMPLE
} },
176 { "3x3 Intermediate", { 3, 3, SYMM_ROT2
, DIFF_INTERSECT
} },
177 { "3x3 Advanced", { 3, 3, SYMM_ROT2
, DIFF_SET
} },
178 { "3x3 Unreasonable", { 3, 3, SYMM_ROT2
, DIFF_RECURSIVE
} },
180 { "3x4 Basic", { 3, 4, SYMM_ROT2
, DIFF_SIMPLE
} },
181 { "4x4 Basic", { 4, 4, SYMM_ROT2
, DIFF_SIMPLE
} },
185 if (i
< 0 || i
>= lenof(presets
))
188 *name
= dupstr(presets
[i
].title
);
189 *params
= dup_params(&presets
[i
].params
);
194 static void decode_params(game_params
*ret
, char const *string
)
196 ret
->c
= ret
->r
= atoi(string
);
197 while (*string
&& isdigit((unsigned char)*string
)) string
++;
198 if (*string
== 'x') {
200 ret
->r
= atoi(string
);
201 while (*string
&& isdigit((unsigned char)*string
)) string
++;
204 if (*string
== 'r' || *string
== 'm' || *string
== 'a') {
208 while (*string
&& isdigit((unsigned char)*string
)) string
++;
209 if (sc
== 'm' && sn
== 4)
210 ret
->symm
= SYMM_REF4
;
211 if (sc
== 'r' && sn
== 4)
212 ret
->symm
= SYMM_ROT4
;
213 if (sc
== 'r' && sn
== 2)
214 ret
->symm
= SYMM_ROT2
;
216 ret
->symm
= SYMM_NONE
;
217 } else if (*string
== 'd') {
219 if (*string
== 't') /* trivial */
220 string
++, ret
->diff
= DIFF_BLOCK
;
221 else if (*string
== 'b') /* basic */
222 string
++, ret
->diff
= DIFF_SIMPLE
;
223 else if (*string
== 'i') /* intermediate */
224 string
++, ret
->diff
= DIFF_INTERSECT
;
225 else if (*string
== 'a') /* advanced */
226 string
++, ret
->diff
= DIFF_SET
;
227 else if (*string
== 'u') /* unreasonable */
228 string
++, ret
->diff
= DIFF_RECURSIVE
;
230 string
++; /* eat unknown character */
234 static char *encode_params(game_params
*params
, int full
)
238 sprintf(str
, "%dx%d", params
->c
, params
->r
);
240 switch (params
->symm
) {
241 case SYMM_REF4
: strcat(str
, "m4"); break;
242 case SYMM_ROT4
: strcat(str
, "r4"); break;
243 /* case SYMM_ROT2: strcat(str, "r2"); break; [default] */
244 case SYMM_NONE
: strcat(str
, "a"); break;
246 switch (params
->diff
) {
247 /* case DIFF_BLOCK: strcat(str, "dt"); break; [default] */
248 case DIFF_SIMPLE
: strcat(str
, "db"); break;
249 case DIFF_INTERSECT
: strcat(str
, "di"); break;
250 case DIFF_SET
: strcat(str
, "da"); break;
251 case DIFF_RECURSIVE
: strcat(str
, "du"); break;
257 static config_item
*game_configure(game_params
*params
)
262 ret
= snewn(5, config_item
);
264 ret
[0].name
= "Columns of sub-blocks";
265 ret
[0].type
= C_STRING
;
266 sprintf(buf
, "%d", params
->c
);
267 ret
[0].sval
= dupstr(buf
);
270 ret
[1].name
= "Rows of sub-blocks";
271 ret
[1].type
= C_STRING
;
272 sprintf(buf
, "%d", params
->r
);
273 ret
[1].sval
= dupstr(buf
);
276 ret
[2].name
= "Symmetry";
277 ret
[2].type
= C_CHOICES
;
278 ret
[2].sval
= ":None:2-way rotation:4-way rotation:4-way mirror";
279 ret
[2].ival
= params
->symm
;
281 ret
[3].name
= "Difficulty";
282 ret
[3].type
= C_CHOICES
;
283 ret
[3].sval
= ":Trivial:Basic:Intermediate:Advanced:Unreasonable";
284 ret
[3].ival
= params
->diff
;
294 static game_params
*custom_params(config_item
*cfg
)
296 game_params
*ret
= snew(game_params
);
298 ret
->c
= atoi(cfg
[0].sval
);
299 ret
->r
= atoi(cfg
[1].sval
);
300 ret
->symm
= cfg
[2].ival
;
301 ret
->diff
= cfg
[3].ival
;
306 static char *validate_params(game_params
*params
)
308 if (params
->c
< 2 || params
->r
< 2)
309 return "Both dimensions must be at least 2";
310 if (params
->c
> ORDER_MAX
|| params
->r
> ORDER_MAX
)
311 return "Dimensions greater than "STR(ORDER_MAX
)" are not supported";
315 /* ----------------------------------------------------------------------
316 * Full recursive Solo solver.
318 * The algorithm for this solver is shamelessly copied from a
319 * Python solver written by Andrew Wilkinson (which is GPLed, but
320 * I've reused only ideas and no code). It mostly just does the
321 * obvious recursive thing: pick an empty square, put one of the
322 * possible digits in it, recurse until all squares are filled,
323 * backtrack and change some choices if necessary.
325 * The clever bit is that every time it chooses which square to
326 * fill in next, it does so by counting the number of _possible_
327 * numbers that can go in each square, and it prioritises so that
328 * it picks a square with the _lowest_ number of possibilities. The
329 * idea is that filling in lots of the obvious bits (particularly
330 * any squares with only one possibility) will cut down on the list
331 * of possibilities for other squares and hence reduce the enormous
332 * search space as much as possible as early as possible.
334 * In practice the algorithm appeared to work very well; run on
335 * sample problems from the Times it completed in well under a
336 * second on my G5 even when written in Python, and given an empty
337 * grid (so that in principle it would enumerate _all_ solved
338 * grids!) it found the first valid solution just as quickly. So
339 * with a bit more randomisation I see no reason not to use this as
344 * Internal data structure used in solver to keep track of
347 struct rsolve_coord
{ int x
, y
, r
; };
348 struct rsolve_usage
{
349 int c
, r
, cr
; /* cr == c*r */
350 /* grid is a copy of the input grid, modified as we go along */
352 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
354 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
356 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
358 /* This lists all the empty spaces remaining in the grid. */
359 struct rsolve_coord
*spaces
;
361 /* If we need randomisation in the solve, this is our random state. */
363 /* Number of solutions so far found, and maximum number we care about. */
368 * The real recursive step in the solving function.
370 static void rsolve_real(struct rsolve_usage
*usage
, digit
*grid
)
372 int c
= usage
->c
, r
= usage
->r
, cr
= usage
->cr
;
373 int i
, j
, n
, sx
, sy
, bestm
, bestr
;
377 * Firstly, check for completion! If there are no spaces left
378 * in the grid, we have a solution.
380 if (usage
->nspaces
== 0) {
383 * This is our first solution, so fill in the output grid.
385 memcpy(grid
, usage
->grid
, cr
* cr
);
392 * Otherwise, there must be at least one space. Find the most
393 * constrained space, using the `r' field as a tie-breaker.
395 bestm
= cr
+1; /* so that any space will beat it */
398 for (j
= 0; j
< usage
->nspaces
; j
++) {
399 int x
= usage
->spaces
[j
].x
, y
= usage
->spaces
[j
].y
;
403 * Find the number of digits that could go in this space.
406 for (n
= 0; n
< cr
; n
++)
407 if (!usage
->row
[y
*cr
+n
] && !usage
->col
[x
*cr
+n
] &&
408 !usage
->blk
[((y
/c
)*c
+(x
/r
))*cr
+n
])
411 if (m
< bestm
|| (m
== bestm
&& usage
->spaces
[j
].r
< bestr
)) {
413 bestr
= usage
->spaces
[j
].r
;
421 * Swap that square into the final place in the spaces array,
422 * so that decrementing nspaces will remove it from the list.
424 if (i
!= usage
->nspaces
-1) {
425 struct rsolve_coord t
;
426 t
= usage
->spaces
[usage
->nspaces
-1];
427 usage
->spaces
[usage
->nspaces
-1] = usage
->spaces
[i
];
428 usage
->spaces
[i
] = t
;
432 * Now we've decided which square to start our recursion at,
433 * simply go through all possible values, shuffling them
434 * randomly first if necessary.
436 digits
= snewn(bestm
, int);
438 for (n
= 0; n
< cr
; n
++)
439 if (!usage
->row
[sy
*cr
+n
] && !usage
->col
[sx
*cr
+n
] &&
440 !usage
->blk
[((sy
/c
)*c
+(sx
/r
))*cr
+n
]) {
446 for (i
= j
; i
> 1; i
--) {
447 int p
= random_upto(usage
->rs
, i
);
450 digits
[p
] = digits
[i
-1];
456 /* And finally, go through the digit list and actually recurse. */
457 for (i
= 0; i
< j
; i
++) {
460 /* Update the usage structure to reflect the placing of this digit. */
461 usage
->row
[sy
*cr
+n
-1] = usage
->col
[sx
*cr
+n
-1] =
462 usage
->blk
[((sy
/c
)*c
+(sx
/r
))*cr
+n
-1] = TRUE
;
463 usage
->grid
[sy
*cr
+sx
] = n
;
466 /* Call the solver recursively. */
467 rsolve_real(usage
, grid
);
470 * If we have seen as many solutions as we need, terminate
471 * all processing immediately.
473 if (usage
->solns
>= usage
->maxsolns
)
476 /* Revert the usage structure. */
477 usage
->row
[sy
*cr
+n
-1] = usage
->col
[sx
*cr
+n
-1] =
478 usage
->blk
[((sy
/c
)*c
+(sx
/r
))*cr
+n
-1] = FALSE
;
479 usage
->grid
[sy
*cr
+sx
] = 0;
487 * Entry point to solver. You give it dimensions and a starting
488 * grid, which is simply an array of N^4 digits. In that array, 0
489 * means an empty square, and 1..N mean a clue square.
491 * Return value is the number of solutions found; searching will
492 * stop after the provided `max'. (Thus, you can pass max==1 to
493 * indicate that you only care about finding _one_ solution, or
494 * max==2 to indicate that you want to know the difference between
495 * a unique and non-unique solution.) The input parameter `grid' is
496 * also filled in with the _first_ (or only) solution found by the
499 static int rsolve(int c
, int r
, digit
*grid
, random_state
*rs
, int max
)
501 struct rsolve_usage
*usage
;
506 * Create an rsolve_usage structure.
508 usage
= snew(struct rsolve_usage
);
514 usage
->grid
= snewn(cr
* cr
, digit
);
515 memcpy(usage
->grid
, grid
, cr
* cr
);
517 usage
->row
= snewn(cr
* cr
, unsigned char);
518 usage
->col
= snewn(cr
* cr
, unsigned char);
519 usage
->blk
= snewn(cr
* cr
, unsigned char);
520 memset(usage
->row
, FALSE
, cr
* cr
);
521 memset(usage
->col
, FALSE
, cr
* cr
);
522 memset(usage
->blk
, FALSE
, cr
* cr
);
524 usage
->spaces
= snewn(cr
* cr
, struct rsolve_coord
);
528 usage
->maxsolns
= max
;
533 * Now fill it in with data from the input grid.
535 for (y
= 0; y
< cr
; y
++) {
536 for (x
= 0; x
< cr
; x
++) {
537 int v
= grid
[y
*cr
+x
];
539 usage
->spaces
[usage
->nspaces
].x
= x
;
540 usage
->spaces
[usage
->nspaces
].y
= y
;
542 usage
->spaces
[usage
->nspaces
].r
= random_bits(rs
, 31);
544 usage
->spaces
[usage
->nspaces
].r
= usage
->nspaces
;
547 usage
->row
[y
*cr
+v
-1] = TRUE
;
548 usage
->col
[x
*cr
+v
-1] = TRUE
;
549 usage
->blk
[((y
/c
)*c
+(x
/r
))*cr
+v
-1] = TRUE
;
555 * Run the real recursive solving function.
557 rsolve_real(usage
, grid
);
561 * Clean up the usage structure now we have our answer.
563 sfree(usage
->spaces
);
576 /* ----------------------------------------------------------------------
577 * End of recursive solver code.
580 /* ----------------------------------------------------------------------
581 * Less capable non-recursive solver. This one is used to check
582 * solubility of a grid as we gradually remove numbers from it: by
583 * verifying a grid using this solver we can ensure it isn't _too_
584 * hard (e.g. does not actually require guessing and backtracking).
586 * It supports a variety of specific modes of reasoning. By
587 * enabling or disabling subsets of these modes we can arrange a
588 * range of difficulty levels.
592 * Modes of reasoning currently supported:
594 * - Positional elimination: a number must go in a particular
595 * square because all the other empty squares in a given
596 * row/col/blk are ruled out.
598 * - Numeric elimination: a square must have a particular number
599 * in because all the other numbers that could go in it are
602 * - Intersectional analysis: given two domains which overlap
603 * (hence one must be a block, and the other can be a row or
604 * col), if the possible locations for a particular number in
605 * one of the domains can be narrowed down to the overlap, then
606 * that number can be ruled out everywhere but the overlap in
607 * the other domain too.
609 * - Set elimination: if there is a subset of the empty squares
610 * within a domain such that the union of the possible numbers
611 * in that subset has the same size as the subset itself, then
612 * those numbers can be ruled out everywhere else in the domain.
613 * (For example, if there are five empty squares and the
614 * possible numbers in each are 12, 23, 13, 134 and 1345, then
615 * the first three empty squares form such a subset: the numbers
616 * 1, 2 and 3 _must_ be in those three squares in some
617 * permutation, and hence we can deduce none of them can be in
618 * the fourth or fifth squares.)
619 * + You can also see this the other way round, concentrating
620 * on numbers rather than squares: if there is a subset of
621 * the unplaced numbers within a domain such that the union
622 * of all their possible positions has the same size as the
623 * subset itself, then all other numbers can be ruled out for
624 * those positions. However, it turns out that this is
625 * exactly equivalent to the first formulation at all times:
626 * there is a 1-1 correspondence between suitable subsets of
627 * the unplaced numbers and suitable subsets of the unfilled
628 * places, found by taking the _complement_ of the union of
629 * the numbers' possible positions (or the spaces' possible
634 * Within this solver, I'm going to transform all y-coordinates by
635 * inverting the significance of the block number and the position
636 * within the block. That is, we will start with the top row of
637 * each block in order, then the second row of each block in order,
640 * This transformation has the enormous advantage that it means
641 * every row, column _and_ block is described by an arithmetic
642 * progression of coordinates within the cubic array, so that I can
643 * use the same very simple function to do blockwise, row-wise and
644 * column-wise elimination.
646 #define YTRANS(y) (((y)%c)*r+(y)/c)
647 #define YUNTRANS(y) (((y)%r)*c+(y)/r)
649 struct nsolve_usage
{
652 * We set up a cubic array, indexed by x, y and digit; each
653 * element of this array is TRUE or FALSE according to whether
654 * or not that digit _could_ in principle go in that position.
656 * The way to index this array is cube[(x*cr+y)*cr+n-1].
657 * y-coordinates in here are transformed.
661 * This is the grid in which we write down our final
662 * deductions. y-coordinates in here are _not_ transformed.
666 * Now we keep track, at a slightly higher level, of what we
667 * have yet to work out, to prevent doing the same deduction
670 /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
672 /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
674 /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
677 #define cubepos(x,y,n) (((x)*usage->cr+(y))*usage->cr+(n)-1)
678 #define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
681 * Function called when we are certain that a particular square has
682 * a particular number in it. The y-coordinate passed in here is
685 static void nsolve_place(struct nsolve_usage
*usage
, int x
, int y
, int n
)
687 int c
= usage
->c
, r
= usage
->r
, cr
= usage
->cr
;
693 * Rule out all other numbers in this square.
695 for (i
= 1; i
<= cr
; i
++)
700 * Rule out this number in all other positions in the row.
702 for (i
= 0; i
< cr
; i
++)
707 * Rule out this number in all other positions in the column.
709 for (i
= 0; i
< cr
; i
++)
714 * Rule out this number in all other positions in the block.
718 for (i
= 0; i
< r
; i
++)
719 for (j
= 0; j
< c
; j
++)
720 if (bx
+i
!= x
|| by
+j
*r
!= y
)
721 cube(bx
+i
,by
+j
*r
,n
) = FALSE
;
724 * Enter the number in the result grid.
726 usage
->grid
[YUNTRANS(y
)*cr
+x
] = n
;
729 * Cross out this number from the list of numbers left to place
730 * in its row, its column and its block.
732 usage
->row
[y
*cr
+n
-1] = usage
->col
[x
*cr
+n
-1] =
733 usage
->blk
[((y
%r
)*c
+(x
/r
))*cr
+n
-1] = TRUE
;
736 static int nsolve_elim(struct nsolve_usage
*usage
, int start
, int step
737 #ifdef STANDALONE_SOLVER
742 int c
= usage
->c
, r
= usage
->r
, cr
= c
*r
;
746 * Count the number of set bits within this section of the
751 for (i
= 0; i
< cr
; i
++)
752 if (usage
->cube
[start
+i
*step
]) {
766 if (!usage
->grid
[YUNTRANS(y
)*cr
+x
]) {
767 #ifdef STANDALONE_SOLVER
768 if (solver_show_working
) {
773 printf(":\n placing %d at (%d,%d)\n",
774 n
, 1+x
, 1+YUNTRANS(y
));
777 nsolve_place(usage
, x
, y
, n
);
785 static int nsolve_intersect(struct nsolve_usage
*usage
,
786 int start1
, int step1
, int start2
, int step2
787 #ifdef STANDALONE_SOLVER
792 int c
= usage
->c
, r
= usage
->r
, cr
= c
*r
;
796 * Loop over the first domain and see if there's any set bit
797 * not also in the second.
799 for (i
= 0; i
< cr
; i
++) {
800 int p
= start1
+i
*step1
;
801 if (usage
->cube
[p
] &&
802 !(p
>= start2
&& p
< start2
+cr
*step2
&&
803 (p
- start2
) % step2
== 0))
804 return FALSE
; /* there is, so we can't deduce */
808 * We have determined that all set bits in the first domain are
809 * within its overlap with the second. So loop over the second
810 * domain and remove all set bits that aren't also in that
811 * overlap; return TRUE iff we actually _did_ anything.
814 for (i
= 0; i
< cr
; i
++) {
815 int p
= start2
+i
*step2
;
816 if (usage
->cube
[p
] &&
817 !(p
>= start1
&& p
< start1
+cr
*step1
&& (p
- start1
) % step1
== 0))
819 #ifdef STANDALONE_SOLVER
820 if (solver_show_working
) {
836 printf(" ruling out %d at (%d,%d)\n",
837 pn
, 1+px
, 1+YUNTRANS(py
));
840 ret
= TRUE
; /* we did something */
848 struct nsolve_scratch
{
849 unsigned char *grid
, *rowidx
, *colidx
, *set
;
852 static int nsolve_set(struct nsolve_usage
*usage
,
853 struct nsolve_scratch
*scratch
,
854 int start
, int step1
, int step2
855 #ifdef STANDALONE_SOLVER
860 int c
= usage
->c
, r
= usage
->r
, cr
= c
*r
;
862 unsigned char *grid
= scratch
->grid
;
863 unsigned char *rowidx
= scratch
->rowidx
;
864 unsigned char *colidx
= scratch
->colidx
;
865 unsigned char *set
= scratch
->set
;
868 * We are passed a cr-by-cr matrix of booleans. Our first job
869 * is to winnow it by finding any definite placements - i.e.
870 * any row with a solitary 1 - and discarding that row and the
871 * column containing the 1.
873 memset(rowidx
, TRUE
, cr
);
874 memset(colidx
, TRUE
, cr
);
875 for (i
= 0; i
< cr
; i
++) {
876 int count
= 0, first
= -1;
877 for (j
= 0; j
< cr
; j
++)
878 if (usage
->cube
[start
+i
*step1
+j
*step2
])
882 * This condition actually marks a completely insoluble
883 * (i.e. internally inconsistent) puzzle. We return and
884 * report no progress made.
889 rowidx
[i
] = colidx
[first
] = FALSE
;
893 * Convert each of rowidx/colidx from a list of 0s and 1s to a
894 * list of the indices of the 1s.
896 for (i
= j
= 0; i
< cr
; i
++)
900 for (i
= j
= 0; i
< cr
; i
++)
906 * And create the smaller matrix.
908 for (i
= 0; i
< n
; i
++)
909 for (j
= 0; j
< n
; j
++)
910 grid
[i
*cr
+j
] = usage
->cube
[start
+rowidx
[i
]*step1
+colidx
[j
]*step2
];
913 * Having done that, we now have a matrix in which every row
914 * has at least two 1s in. Now we search to see if we can find
915 * a rectangle of zeroes (in the set-theoretic sense of
916 * `rectangle', i.e. a subset of rows crossed with a subset of
917 * columns) whose width and height add up to n.
924 * We have a candidate set. If its size is <=1 or >=n-1
925 * then we move on immediately.
927 if (count
> 1 && count
< n
-1) {
929 * The number of rows we need is n-count. See if we can
930 * find that many rows which each have a zero in all
931 * the positions listed in `set'.
934 for (i
= 0; i
< n
; i
++) {
936 for (j
= 0; j
< n
; j
++)
937 if (set
[j
] && grid
[i
*cr
+j
]) {
946 * We expect never to be able to get _more_ than
947 * n-count suitable rows: this would imply that (for
948 * example) there are four numbers which between them
949 * have at most three possible positions, and hence it
950 * indicates a faulty deduction before this point or
953 assert(rows
<= n
- count
);
954 if (rows
>= n
- count
) {
955 int progress
= FALSE
;
958 * We've got one! Now, for each row which _doesn't_
959 * satisfy the criterion, eliminate all its set
960 * bits in the positions _not_ listed in `set'.
961 * Return TRUE (meaning progress has been made) if
962 * we successfully eliminated anything at all.
964 * This involves referring back through
965 * rowidx/colidx in order to work out which actual
966 * positions in the cube to meddle with.
968 for (i
= 0; i
< n
; i
++) {
970 for (j
= 0; j
< n
; j
++)
971 if (set
[j
] && grid
[i
*cr
+j
]) {
976 for (j
= 0; j
< n
; j
++)
977 if (!set
[j
] && grid
[i
*cr
+j
]) {
978 int fpos
= (start
+rowidx
[i
]*step1
+
980 #ifdef STANDALONE_SOLVER
981 if (solver_show_working
) {
997 printf(" ruling out %d at (%d,%d)\n",
998 pn
, 1+px
, 1+YUNTRANS(py
));
1002 usage
->cube
[fpos
] = FALSE
;
1014 * Binary increment: change the rightmost 0 to a 1, and
1015 * change all 1s to the right of it to 0s.
1018 while (i
> 0 && set
[i
-1])
1019 set
[--i
] = 0, count
--;
1021 set
[--i
] = 1, count
++;
1029 static struct nsolve_scratch
*nsolve_new_scratch(struct nsolve_usage
*usage
)
1031 struct nsolve_scratch
*scratch
= snew(struct nsolve_scratch
);
1033 scratch
->grid
= snewn(cr
*cr
, unsigned char);
1034 scratch
->rowidx
= snewn(cr
, unsigned char);
1035 scratch
->colidx
= snewn(cr
, unsigned char);
1036 scratch
->set
= snewn(cr
, unsigned char);
1040 static void nsolve_free_scratch(struct nsolve_scratch
*scratch
)
1042 sfree(scratch
->set
);
1043 sfree(scratch
->colidx
);
1044 sfree(scratch
->rowidx
);
1045 sfree(scratch
->grid
);
1049 static int nsolve(int c
, int r
, digit
*grid
)
1051 struct nsolve_usage
*usage
;
1052 struct nsolve_scratch
*scratch
;
1055 int diff
= DIFF_BLOCK
;
1058 * Set up a usage structure as a clean slate (everything
1061 usage
= snew(struct nsolve_usage
);
1065 usage
->cube
= snewn(cr
*cr
*cr
, unsigned char);
1066 usage
->grid
= grid
; /* write straight back to the input */
1067 memset(usage
->cube
, TRUE
, cr
*cr
*cr
);
1069 usage
->row
= snewn(cr
* cr
, unsigned char);
1070 usage
->col
= snewn(cr
* cr
, unsigned char);
1071 usage
->blk
= snewn(cr
* cr
, unsigned char);
1072 memset(usage
->row
, FALSE
, cr
* cr
);
1073 memset(usage
->col
, FALSE
, cr
* cr
);
1074 memset(usage
->blk
, FALSE
, cr
* cr
);
1076 scratch
= nsolve_new_scratch(usage
);
1079 * Place all the clue numbers we are given.
1081 for (x
= 0; x
< cr
; x
++)
1082 for (y
= 0; y
< cr
; y
++)
1084 nsolve_place(usage
, x
, YTRANS(y
), grid
[y
*cr
+x
]);
1087 * Now loop over the grid repeatedly trying all permitted modes
1088 * of reasoning. The loop terminates if we complete an
1089 * iteration without making any progress; we then return
1090 * failure or success depending on whether the grid is full or
1095 * I'd like to write `continue;' inside each of the
1096 * following loops, so that the solver returns here after
1097 * making some progress. However, I can't specify that I
1098 * want to continue an outer loop rather than the innermost
1099 * one, so I'm apologetically resorting to a goto.
1104 * Blockwise positional elimination.
1106 for (x
= 0; x
< cr
; x
+= r
)
1107 for (y
= 0; y
< r
; y
++)
1108 for (n
= 1; n
<= cr
; n
++)
1109 if (!usage
->blk
[(y
*c
+(x
/r
))*cr
+n
-1] &&
1110 nsolve_elim(usage
, cubepos(x
,y
,n
), r
*cr
1111 #ifdef STANDALONE_SOLVER
1112 , "positional elimination,"
1113 " block (%d,%d)", 1+x
/r
, 1+y
1116 diff
= max(diff
, DIFF_BLOCK
);
1121 * Row-wise positional elimination.
1123 for (y
= 0; y
< cr
; y
++)
1124 for (n
= 1; n
<= cr
; n
++)
1125 if (!usage
->row
[y
*cr
+n
-1] &&
1126 nsolve_elim(usage
, cubepos(0,y
,n
), cr
*cr
1127 #ifdef STANDALONE_SOLVER
1128 , "positional elimination,"
1129 " row %d", 1+YUNTRANS(y
)
1132 diff
= max(diff
, DIFF_SIMPLE
);
1136 * Column-wise positional elimination.
1138 for (x
= 0; x
< cr
; x
++)
1139 for (n
= 1; n
<= cr
; n
++)
1140 if (!usage
->col
[x
*cr
+n
-1] &&
1141 nsolve_elim(usage
, cubepos(x
,0,n
), cr
1142 #ifdef STANDALONE_SOLVER
1143 , "positional elimination," " column %d", 1+x
1146 diff
= max(diff
, DIFF_SIMPLE
);
1151 * Numeric elimination.
1153 for (x
= 0; x
< cr
; x
++)
1154 for (y
= 0; y
< cr
; y
++)
1155 if (!usage
->grid
[YUNTRANS(y
)*cr
+x
] &&
1156 nsolve_elim(usage
, cubepos(x
,y
,1), 1
1157 #ifdef STANDALONE_SOLVER
1158 , "numeric elimination at (%d,%d)", 1+x
,
1162 diff
= max(diff
, DIFF_SIMPLE
);
1167 * Intersectional analysis, rows vs blocks.
1169 for (y
= 0; y
< cr
; y
++)
1170 for (x
= 0; x
< cr
; x
+= r
)
1171 for (n
= 1; n
<= cr
; n
++)
1172 if (!usage
->row
[y
*cr
+n
-1] &&
1173 !usage
->blk
[((y
%r
)*c
+(x
/r
))*cr
+n
-1] &&
1174 (nsolve_intersect(usage
, cubepos(0,y
,n
), cr
*cr
,
1175 cubepos(x
,y
%r
,n
), r
*cr
1176 #ifdef STANDALONE_SOLVER
1177 , "intersectional analysis,"
1178 " row %d vs block (%d,%d)",
1179 1+YUNTRANS(y
), 1+x
/r
, 1+y
%r
1182 nsolve_intersect(usage
, cubepos(x
,y
%r
,n
), r
*cr
,
1183 cubepos(0,y
,n
), cr
*cr
1184 #ifdef STANDALONE_SOLVER
1185 , "intersectional analysis,"
1186 " block (%d,%d) vs row %d",
1187 1+x
/r
, 1+y
%r
, 1+YUNTRANS(y
)
1190 diff
= max(diff
, DIFF_INTERSECT
);
1195 * Intersectional analysis, columns vs blocks.
1197 for (x
= 0; x
< cr
; x
++)
1198 for (y
= 0; y
< r
; y
++)
1199 for (n
= 1; n
<= cr
; n
++)
1200 if (!usage
->col
[x
*cr
+n
-1] &&
1201 !usage
->blk
[(y
*c
+(x
/r
))*cr
+n
-1] &&
1202 (nsolve_intersect(usage
, cubepos(x
,0,n
), cr
,
1203 cubepos((x
/r
)*r
,y
,n
), r
*cr
1204 #ifdef STANDALONE_SOLVER
1205 , "intersectional analysis,"
1206 " column %d vs block (%d,%d)",
1210 nsolve_intersect(usage
, cubepos((x
/r
)*r
,y
,n
), r
*cr
,
1212 #ifdef STANDALONE_SOLVER
1213 , "intersectional analysis,"
1214 " block (%d,%d) vs column %d",
1218 diff
= max(diff
, DIFF_INTERSECT
);
1223 * Blockwise set elimination.
1225 for (x
= 0; x
< cr
; x
+= r
)
1226 for (y
= 0; y
< r
; y
++)
1227 if (nsolve_set(usage
, scratch
, cubepos(x
,y
,1), r
*cr
, 1
1228 #ifdef STANDALONE_SOLVER
1229 , "set elimination, block (%d,%d)", 1+x
/r
, 1+y
1232 diff
= max(diff
, DIFF_SET
);
1237 * Row-wise set elimination.
1239 for (y
= 0; y
< cr
; y
++)
1240 if (nsolve_set(usage
, scratch
, cubepos(0,y
,1), cr
*cr
, 1
1241 #ifdef STANDALONE_SOLVER
1242 , "set elimination, row %d", 1+YUNTRANS(y
)
1245 diff
= max(diff
, DIFF_SET
);
1250 * Column-wise set elimination.
1252 for (x
= 0; x
< cr
; x
++)
1253 if (nsolve_set(usage
, scratch
, cubepos(x
,0,1), cr
, 1
1254 #ifdef STANDALONE_SOLVER
1255 , "set elimination, column %d", 1+x
1258 diff
= max(diff
, DIFF_SET
);
1263 * If we reach here, we have made no deductions in this
1264 * iteration, so the algorithm terminates.
1269 nsolve_free_scratch(scratch
);
1277 for (x
= 0; x
< cr
; x
++)
1278 for (y
= 0; y
< cr
; y
++)
1280 return DIFF_IMPOSSIBLE
;
1284 /* ----------------------------------------------------------------------
1285 * End of non-recursive solver code.
1289 * Check whether a grid contains a valid complete puzzle.
1291 static int check_valid(int c
, int r
, digit
*grid
)
1294 unsigned char *used
;
1297 used
= snewn(cr
, unsigned char);
1300 * Check that each row contains precisely one of everything.
1302 for (y
= 0; y
< cr
; y
++) {
1303 memset(used
, FALSE
, cr
);
1304 for (x
= 0; x
< cr
; x
++)
1305 if (grid
[y
*cr
+x
] > 0 && grid
[y
*cr
+x
] <= cr
)
1306 used
[grid
[y
*cr
+x
]-1] = TRUE
;
1307 for (n
= 0; n
< cr
; n
++)
1315 * Check that each column contains precisely one of everything.
1317 for (x
= 0; x
< cr
; x
++) {
1318 memset(used
, FALSE
, cr
);
1319 for (y
= 0; y
< cr
; y
++)
1320 if (grid
[y
*cr
+x
] > 0 && grid
[y
*cr
+x
] <= cr
)
1321 used
[grid
[y
*cr
+x
]-1] = TRUE
;
1322 for (n
= 0; n
< cr
; n
++)
1330 * Check that each block contains precisely one of everything.
1332 for (x
= 0; x
< cr
; x
+= r
) {
1333 for (y
= 0; y
< cr
; y
+= c
) {
1335 memset(used
, FALSE
, cr
);
1336 for (xx
= x
; xx
< x
+r
; xx
++)
1337 for (yy
= 0; yy
< y
+c
; yy
++)
1338 if (grid
[yy
*cr
+xx
] > 0 && grid
[yy
*cr
+xx
] <= cr
)
1339 used
[grid
[yy
*cr
+xx
]-1] = TRUE
;
1340 for (n
= 0; n
< cr
; n
++)
1352 static void symmetry_limit(game_params
*params
, int *xlim
, int *ylim
, int s
)
1354 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
1366 *xlim
= *ylim
= (cr
+1) / 2;
1371 static int symmetries(game_params
*params
, int x
, int y
, int *output
, int s
)
1373 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
1382 break; /* just x,y is all we need */
1387 *output
++ = cr
- 1 - x
;
1392 *output
++ = cr
- 1 - y
;
1396 *output
++ = cr
- 1 - y
;
1401 *output
++ = cr
- 1 - x
;
1407 *output
++ = cr
- 1 - x
;
1408 *output
++ = cr
- 1 - y
;
1416 struct game_aux_info
{
1421 static char *new_game_desc(game_params
*params
, random_state
*rs
,
1422 game_aux_info
**aux
, int interactive
)
1424 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
1426 digit
*grid
, *grid2
;
1427 struct xy
{ int x
, y
; } *locs
;
1431 int coords
[16], ncoords
;
1433 int maxdiff
, recursing
;
1436 * Adjust the maximum difficulty level to be consistent with
1437 * the puzzle size: all 2x2 puzzles appear to be Trivial
1438 * (DIFF_BLOCK) so we cannot hold out for even a Basic
1439 * (DIFF_SIMPLE) one.
1441 maxdiff
= params
->diff
;
1442 if (c
== 2 && r
== 2)
1443 maxdiff
= DIFF_BLOCK
;
1445 grid
= snewn(area
, digit
);
1446 locs
= snewn(area
, struct xy
);
1447 grid2
= snewn(area
, digit
);
1450 * Loop until we get a grid of the required difficulty. This is
1451 * nasty, but it seems to be unpleasantly hard to generate
1452 * difficult grids otherwise.
1456 * Start the recursive solver with an empty grid to generate a
1457 * random solved state.
1459 memset(grid
, 0, area
);
1460 ret
= rsolve(c
, r
, grid
, rs
, 1);
1462 assert(check_valid(c
, r
, grid
));
1465 * Save the solved grid in the aux_info.
1468 game_aux_info
*ai
= snew(game_aux_info
);
1471 ai
->grid
= snewn(cr
* cr
, digit
);
1472 memcpy(ai
->grid
, grid
, cr
* cr
* sizeof(digit
));
1474 * We might already have written *aux the last time we
1475 * went round this loop, in which case we should free
1476 * the old aux_info before overwriting it with the new
1480 sfree((*aux
)->grid
);
1487 * Now we have a solved grid, start removing things from it
1488 * while preserving solubility.
1490 symmetry_limit(params
, &xlim
, &ylim
, params
->symm
);
1496 * Iterate over the grid and enumerate all the filled
1497 * squares we could empty.
1501 for (x
= 0; x
< xlim
; x
++)
1502 for (y
= 0; y
< ylim
; y
++)
1510 * Now shuffle that list.
1512 for (i
= nlocs
; i
> 1; i
--) {
1513 int p
= random_upto(rs
, i
);
1515 struct xy t
= locs
[p
];
1516 locs
[p
] = locs
[i
-1];
1522 * Now loop over the shuffled list and, for each element,
1523 * see whether removing that element (and its reflections)
1524 * from the grid will still leave the grid soluble by
1527 for (i
= 0; i
< nlocs
; i
++) {
1533 memcpy(grid2
, grid
, area
);
1534 ncoords
= symmetries(params
, x
, y
, coords
, params
->symm
);
1535 for (j
= 0; j
< ncoords
; j
++)
1536 grid2
[coords
[2*j
+1]*cr
+coords
[2*j
]] = 0;
1539 ret
= (rsolve(c
, r
, grid2
, NULL
, 2) == 1);
1541 ret
= (nsolve(c
, r
, grid2
) <= maxdiff
);
1544 for (j
= 0; j
< ncoords
; j
++)
1545 grid
[coords
[2*j
+1]*cr
+coords
[2*j
]] = 0;
1552 * There was nothing we could remove without
1553 * destroying solvability. If we're trying to
1554 * generate a recursion-only grid and haven't
1555 * switched over to rsolve yet, we now do;
1556 * otherwise we give up.
1558 if (maxdiff
== DIFF_RECURSIVE
&& !recursing
) {
1566 memcpy(grid2
, grid
, area
);
1567 } while (nsolve(c
, r
, grid2
) < maxdiff
);
1573 * Now we have the grid as it will be presented to the user.
1574 * Encode it in a game desc.
1580 desc
= snewn(5 * area
, char);
1583 for (i
= 0; i
<= area
; i
++) {
1584 int n
= (i
< area ? grid
[i
] : -1);
1591 int c
= 'a' - 1 + run
;
1595 run
-= c
- ('a' - 1);
1599 * If there's a number in the very top left or
1600 * bottom right, there's no point putting an
1601 * unnecessary _ before or after it.
1603 if (p
> desc
&& n
> 0)
1607 p
+= sprintf(p
, "%d", n
);
1611 assert(p
- desc
< 5 * area
);
1613 desc
= sresize(desc
, p
- desc
, char);
1621 static void game_free_aux_info(game_aux_info
*aux
)
1627 static char *validate_desc(game_params
*params
, char *desc
)
1629 int area
= params
->r
* params
->r
* params
->c
* params
->c
;
1634 if (n
>= 'a' && n
<= 'z') {
1635 squares
+= n
- 'a' + 1;
1636 } else if (n
== '_') {
1638 } else if (n
> '0' && n
<= '9') {
1640 while (*desc
>= '0' && *desc
<= '9')
1643 return "Invalid character in game description";
1647 return "Not enough data to fill grid";
1650 return "Too much data to fit in grid";
1655 static game_state
*new_game(midend_data
*me
, game_params
*params
, char *desc
)
1657 game_state
*state
= snew(game_state
);
1658 int c
= params
->c
, r
= params
->r
, cr
= c
*r
, area
= cr
* cr
;
1661 state
->c
= params
->c
;
1662 state
->r
= params
->r
;
1664 state
->grid
= snewn(area
, digit
);
1665 state
->pencil
= snewn(area
* cr
, unsigned char);
1666 memset(state
->pencil
, 0, area
* cr
);
1667 state
->immutable
= snewn(area
, unsigned char);
1668 memset(state
->immutable
, FALSE
, area
);
1670 state
->completed
= state
->cheated
= FALSE
;
1675 if (n
>= 'a' && n
<= 'z') {
1676 int run
= n
- 'a' + 1;
1677 assert(i
+ run
<= area
);
1679 state
->grid
[i
++] = 0;
1680 } else if (n
== '_') {
1682 } else if (n
> '0' && n
<= '9') {
1684 state
->immutable
[i
] = TRUE
;
1685 state
->grid
[i
++] = atoi(desc
-1);
1686 while (*desc
>= '0' && *desc
<= '9')
1689 assert(!"We can't get here");
1697 static game_state
*dup_game(game_state
*state
)
1699 game_state
*ret
= snew(game_state
);
1700 int c
= state
->c
, r
= state
->r
, cr
= c
*r
, area
= cr
* cr
;
1705 ret
->grid
= snewn(area
, digit
);
1706 memcpy(ret
->grid
, state
->grid
, area
);
1708 ret
->pencil
= snewn(area
* cr
, unsigned char);
1709 memcpy(ret
->pencil
, state
->pencil
, area
* cr
);
1711 ret
->immutable
= snewn(area
, unsigned char);
1712 memcpy(ret
->immutable
, state
->immutable
, area
);
1714 ret
->completed
= state
->completed
;
1715 ret
->cheated
= state
->cheated
;
1720 static void free_game(game_state
*state
)
1722 sfree(state
->immutable
);
1723 sfree(state
->pencil
);
1728 static game_state
*solve_game(game_state
*state
, game_aux_info
*ai
,
1732 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
1735 ret
= dup_game(state
);
1736 ret
->completed
= ret
->cheated
= TRUE
;
1739 * If we already have the solution in the aux_info, save
1740 * ourselves some time.
1746 memcpy(ret
->grid
, ai
->grid
, cr
* cr
* sizeof(digit
));
1749 rsolve_ret
= rsolve(c
, r
, ret
->grid
, NULL
, 2);
1751 if (rsolve_ret
!= 1) {
1753 if (rsolve_ret
== 0)
1754 *error
= "No solution exists for this puzzle";
1756 *error
= "Multiple solutions exist for this puzzle";
1764 static char *grid_text_format(int c
, int r
, digit
*grid
)
1772 * There are cr lines of digits, plus r-1 lines of block
1773 * separators. Each line contains cr digits, cr-1 separating
1774 * spaces, and c-1 two-character block separators. Thus, the
1775 * total length of a line is 2*cr+2*c-3 (not counting the
1776 * newline), and there are cr+r-1 of them.
1778 maxlen
= (cr
+r
-1) * (2*cr
+2*c
-2);
1779 ret
= snewn(maxlen
+1, char);
1782 for (y
= 0; y
< cr
; y
++) {
1783 for (x
= 0; x
< cr
; x
++) {
1784 int ch
= grid
[y
* cr
+ x
];
1794 if ((x
+1) % r
== 0) {
1801 if (y
+1 < cr
&& (y
+1) % c
== 0) {
1802 for (x
= 0; x
< cr
; x
++) {
1806 if ((x
+1) % r
== 0) {
1816 assert(p
- ret
== maxlen
);
1821 static char *game_text_format(game_state
*state
)
1823 return grid_text_format(state
->c
, state
->r
, state
->grid
);
1828 * These are the coordinates of the currently highlighted
1829 * square on the grid, or -1,-1 if there isn't one. When there
1830 * is, pressing a valid number or letter key or Space will
1831 * enter that number or letter in the grid.
1835 * This indicates whether the current highlight is a
1836 * pencil-mark one or a real one.
1841 static game_ui
*new_ui(game_state
*state
)
1843 game_ui
*ui
= snew(game_ui
);
1845 ui
->hx
= ui
->hy
= -1;
1851 static void free_ui(game_ui
*ui
)
1856 static void game_changed_state(game_ui
*ui
, game_state
*oldstate
,
1857 game_state
*newstate
)
1859 int c
= newstate
->c
, r
= newstate
->r
, cr
= c
*r
;
1861 * We prevent pencil-mode highlighting of a filled square. So
1862 * if the user has just filled in a square which we had a
1863 * pencil-mode highlight in (by Undo, or by Redo, or by Solve),
1864 * then we cancel the highlight.
1866 if (ui
->hx
>= 0 && ui
->hy
>= 0 && ui
->hpencil
&&
1867 newstate
->grid
[ui
->hy
* cr
+ ui
->hx
] != 0) {
1868 ui
->hx
= ui
->hy
= -1;
1872 static game_state
*make_move(game_state
*from
, game_ui
*ui
, game_drawstate
*ds
,
1873 int x
, int y
, int button
)
1875 int c
= from
->c
, r
= from
->r
, cr
= c
*r
;
1879 button
&= ~MOD_MASK
;
1881 tx
= (x
+ TILE_SIZE
- BORDER
) / TILE_SIZE
- 1;
1882 ty
= (y
+ TILE_SIZE
- BORDER
) / TILE_SIZE
- 1;
1884 if (tx
>= 0 && tx
< cr
&& ty
>= 0 && ty
< cr
) {
1885 if (button
== LEFT_BUTTON
) {
1886 if (from
->immutable
[ty
*cr
+tx
]) {
1887 ui
->hx
= ui
->hy
= -1;
1888 } else if (tx
== ui
->hx
&& ty
== ui
->hy
&& ui
->hpencil
== 0) {
1889 ui
->hx
= ui
->hy
= -1;
1895 return from
; /* UI activity occurred */
1897 if (button
== RIGHT_BUTTON
) {
1899 * Pencil-mode highlighting for non filled squares.
1901 if (from
->grid
[ty
*cr
+tx
] == 0) {
1902 if (tx
== ui
->hx
&& ty
== ui
->hy
&& ui
->hpencil
) {
1903 ui
->hx
= ui
->hy
= -1;
1910 ui
->hx
= ui
->hy
= -1;
1912 return from
; /* UI activity occurred */
1916 if (ui
->hx
!= -1 && ui
->hy
!= -1 &&
1917 ((button
>= '1' && button
<= '9' && button
- '0' <= cr
) ||
1918 (button
>= 'a' && button
<= 'z' && button
- 'a' + 10 <= cr
) ||
1919 (button
>= 'A' && button
<= 'Z' && button
- 'A' + 10 <= cr
) ||
1921 int n
= button
- '0';
1922 if (button
>= 'A' && button
<= 'Z')
1923 n
= button
- 'A' + 10;
1924 if (button
>= 'a' && button
<= 'z')
1925 n
= button
- 'a' + 10;
1930 * Can't overwrite this square. In principle this shouldn't
1931 * happen anyway because we should never have even been
1932 * able to highlight the square, but it never hurts to be
1935 if (from
->immutable
[ui
->hy
*cr
+ui
->hx
])
1939 * Can't make pencil marks in a filled square. In principle
1940 * this shouldn't happen anyway because we should never
1941 * have even been able to pencil-highlight the square, but
1942 * it never hurts to be careful.
1944 if (ui
->hpencil
&& from
->grid
[ui
->hy
*cr
+ui
->hx
])
1947 ret
= dup_game(from
);
1948 if (ui
->hpencil
&& n
> 0) {
1949 int index
= (ui
->hy
*cr
+ui
->hx
) * cr
+ (n
-1);
1950 ret
->pencil
[index
] = !ret
->pencil
[index
];
1952 ret
->grid
[ui
->hy
*cr
+ui
->hx
] = n
;
1953 memset(ret
->pencil
+ (ui
->hy
*cr
+ui
->hx
)*cr
, 0, cr
);
1956 * We've made a real change to the grid. Check to see
1957 * if the game has been completed.
1959 if (!ret
->completed
&& check_valid(c
, r
, ret
->grid
)) {
1960 ret
->completed
= TRUE
;
1963 ui
->hx
= ui
->hy
= -1;
1965 return ret
; /* made a valid move */
1971 /* ----------------------------------------------------------------------
1975 struct game_drawstate
{
1979 unsigned char *pencil
;
1981 /* This is scratch space used within a single call to game_redraw. */
1985 #define XSIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
1986 #define YSIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
1988 static void game_size(game_params
*params
, int *x
, int *y
)
1990 int c
= params
->c
, r
= params
->r
, cr
= c
*r
;
1996 static float *game_colours(frontend
*fe
, game_state
*state
, int *ncolours
)
1998 float *ret
= snewn(3 * NCOLOURS
, float);
2000 frontend_default_colour(fe
, &ret
[COL_BACKGROUND
* 3]);
2002 ret
[COL_GRID
* 3 + 0] = 0.0F
;
2003 ret
[COL_GRID
* 3 + 1] = 0.0F
;
2004 ret
[COL_GRID
* 3 + 2] = 0.0F
;
2006 ret
[COL_CLUE
* 3 + 0] = 0.0F
;
2007 ret
[COL_CLUE
* 3 + 1] = 0.0F
;
2008 ret
[COL_CLUE
* 3 + 2] = 0.0F
;
2010 ret
[COL_USER
* 3 + 0] = 0.0F
;
2011 ret
[COL_USER
* 3 + 1] = 0.6F
* ret
[COL_BACKGROUND
* 3 + 1];
2012 ret
[COL_USER
* 3 + 2] = 0.0F
;
2014 ret
[COL_HIGHLIGHT
* 3 + 0] = 0.85F
* ret
[COL_BACKGROUND
* 3 + 0];
2015 ret
[COL_HIGHLIGHT
* 3 + 1] = 0.85F
* ret
[COL_BACKGROUND
* 3 + 1];
2016 ret
[COL_HIGHLIGHT
* 3 + 2] = 0.85F
* ret
[COL_BACKGROUND
* 3 + 2];
2018 ret
[COL_ERROR
* 3 + 0] = 1.0F
;
2019 ret
[COL_ERROR
* 3 + 1] = 0.0F
;
2020 ret
[COL_ERROR
* 3 + 2] = 0.0F
;
2022 ret
[COL_PENCIL
* 3 + 0] = 0.5F
* ret
[COL_BACKGROUND
* 3 + 0];
2023 ret
[COL_PENCIL
* 3 + 1] = 0.5F
* ret
[COL_BACKGROUND
* 3 + 1];
2024 ret
[COL_PENCIL
* 3 + 2] = ret
[COL_BACKGROUND
* 3 + 2];
2026 *ncolours
= NCOLOURS
;
2030 static game_drawstate
*game_new_drawstate(game_state
*state
)
2032 struct game_drawstate
*ds
= snew(struct game_drawstate
);
2033 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
2035 ds
->started
= FALSE
;
2039 ds
->grid
= snewn(cr
*cr
, digit
);
2040 memset(ds
->grid
, 0, cr
*cr
);
2041 ds
->pencil
= snewn(cr
*cr
*cr
, digit
);
2042 memset(ds
->pencil
, 0, cr
*cr
*cr
);
2043 ds
->hl
= snewn(cr
*cr
, unsigned char);
2044 memset(ds
->hl
, 0, cr
*cr
);
2045 ds
->entered_items
= snewn(cr
*cr
, int);
2049 static void game_free_drawstate(game_drawstate
*ds
)
2054 sfree(ds
->entered_items
);
2058 static void draw_number(frontend
*fe
, game_drawstate
*ds
, game_state
*state
,
2059 int x
, int y
, int hl
)
2061 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
2066 if (ds
->grid
[y
*cr
+x
] == state
->grid
[y
*cr
+x
] &&
2067 ds
->hl
[y
*cr
+x
] == hl
&&
2068 !memcmp(ds
->pencil
+(y
*cr
+x
)*cr
, state
->pencil
+(y
*cr
+x
)*cr
, cr
))
2069 return; /* no change required */
2071 tx
= BORDER
+ x
* TILE_SIZE
+ 2;
2072 ty
= BORDER
+ y
* TILE_SIZE
+ 2;
2088 clip(fe
, cx
, cy
, cw
, ch
);
2090 /* background needs erasing */
2091 draw_rect(fe
, cx
, cy
, cw
, ch
, (hl
& 15) == 1 ? COL_HIGHLIGHT
: COL_BACKGROUND
);
2093 /* pencil-mode highlight */
2094 if ((hl
& 15) == 2) {
2098 coords
[2] = cx
+cw
/2;
2101 coords
[5] = cy
+ch
/2;
2102 draw_polygon(fe
, coords
, 3, TRUE
, COL_HIGHLIGHT
);
2105 /* new number needs drawing? */
2106 if (state
->grid
[y
*cr
+x
]) {
2108 str
[0] = state
->grid
[y
*cr
+x
] + '0';
2110 str
[0] += 'a' - ('9'+1);
2111 draw_text(fe
, tx
+ TILE_SIZE
/2, ty
+ TILE_SIZE
/2,
2112 FONT_VARIABLE
, TILE_SIZE
/2, ALIGN_VCENTRE
| ALIGN_HCENTRE
,
2113 state
->immutable
[y
*cr
+x
] ? COL_CLUE
: (hl
& 16) ? COL_ERROR
: COL_USER
, str
);
2116 int pw
, ph
, pmax
, fontsize
;
2118 /* count the pencil marks required */
2119 for (i
= npencil
= 0; i
< cr
; i
++)
2120 if (state
->pencil
[(y
*cr
+x
)*cr
+i
])
2124 * It's not sensible to arrange pencil marks in the same
2125 * layout as the squares within a block, because this leads
2126 * to the font being too small. Instead, we arrange pencil
2127 * marks in the nearest thing we can to a square layout,
2128 * and we adjust the square layout depending on the number
2129 * of pencil marks in the square.
2131 for (pw
= 1; pw
* pw
< npencil
; pw
++);
2132 if (pw
< 3) pw
= 3; /* otherwise it just looks _silly_ */
2133 ph
= (npencil
+ pw
- 1) / pw
;
2134 if (ph
< 2) ph
= 2; /* likewise */
2136 fontsize
= TILE_SIZE
/(pmax
*(11-pmax
)/8);
2138 for (i
= j
= 0; i
< cr
; i
++)
2139 if (state
->pencil
[(y
*cr
+x
)*cr
+i
]) {
2140 int dx
= j
% pw
, dy
= j
/ pw
;
2145 str
[0] += 'a' - ('9'+1);
2146 draw_text(fe
, tx
+ (4*dx
+3) * TILE_SIZE
/ (4*pw
+2),
2147 ty
+ (4*dy
+3) * TILE_SIZE
/ (4*ph
+2),
2148 FONT_VARIABLE
, fontsize
,
2149 ALIGN_VCENTRE
| ALIGN_HCENTRE
, COL_PENCIL
, str
);
2156 draw_update(fe
, cx
, cy
, cw
, ch
);
2158 ds
->grid
[y
*cr
+x
] = state
->grid
[y
*cr
+x
];
2159 memcpy(ds
->pencil
+(y
*cr
+x
)*cr
, state
->pencil
+(y
*cr
+x
)*cr
, cr
);
2160 ds
->hl
[y
*cr
+x
] = hl
;
2163 static void game_redraw(frontend
*fe
, game_drawstate
*ds
, game_state
*oldstate
,
2164 game_state
*state
, int dir
, game_ui
*ui
,
2165 float animtime
, float flashtime
)
2167 int c
= state
->c
, r
= state
->r
, cr
= c
*r
;
2172 * The initial contents of the window are not guaranteed
2173 * and can vary with front ends. To be on the safe side,
2174 * all games should start by drawing a big
2175 * background-colour rectangle covering the whole window.
2177 draw_rect(fe
, 0, 0, XSIZE(cr
), YSIZE(cr
), COL_BACKGROUND
);
2182 for (x
= 0; x
<= cr
; x
++) {
2183 int thick
= (x
% r ?
0 : 1);
2184 draw_rect(fe
, BORDER
+ x
*TILE_SIZE
- thick
, BORDER
-1,
2185 1+2*thick
, cr
*TILE_SIZE
+3, COL_GRID
);
2187 for (y
= 0; y
<= cr
; y
++) {
2188 int thick
= (y
% c ?
0 : 1);
2189 draw_rect(fe
, BORDER
-1, BORDER
+ y
*TILE_SIZE
- thick
,
2190 cr
*TILE_SIZE
+3, 1+2*thick
, COL_GRID
);
2195 * This array is used to keep track of rows, columns and boxes
2196 * which contain a number more than once.
2198 for (x
= 0; x
< cr
* cr
; x
++)
2199 ds
->entered_items
[x
] = 0;
2200 for (x
= 0; x
< cr
; x
++)
2201 for (y
= 0; y
< cr
; y
++) {
2202 digit d
= state
->grid
[y
*cr
+x
];
2204 int box
= (x
/r
)+(y
/c
)*c
;
2205 ds
->entered_items
[x
*cr
+d
-1] |= ((ds
->entered_items
[x
*cr
+d
-1] & 1) << 1) | 1;
2206 ds
->entered_items
[y
*cr
+d
-1] |= ((ds
->entered_items
[y
*cr
+d
-1] & 4) << 1) | 4;
2207 ds
->entered_items
[box
*cr
+d
-1] |= ((ds
->entered_items
[box
*cr
+d
-1] & 16) << 1) | 16;
2212 * Draw any numbers which need redrawing.
2214 for (x
= 0; x
< cr
; x
++) {
2215 for (y
= 0; y
< cr
; y
++) {
2217 digit d
= state
->grid
[y
*cr
+x
];
2219 if (flashtime
> 0 &&
2220 (flashtime
<= FLASH_TIME
/3 ||
2221 flashtime
>= FLASH_TIME
*2/3))
2224 /* Highlight active input areas. */
2225 if (x
== ui
->hx
&& y
== ui
->hy
)
2226 highlight
= ui
->hpencil ?
2 : 1;
2228 /* Mark obvious errors (ie, numbers which occur more than once
2229 * in a single row, column, or box). */
2230 if ((ds
->entered_items
[x
*cr
+d
-1] & 2) ||
2231 (ds
->entered_items
[y
*cr
+d
-1] & 8) ||
2232 (ds
->entered_items
[((x
/r
)+(y
/c
)*c
)*cr
+d
-1] & 32))
2235 draw_number(fe
, ds
, state
, x
, y
, highlight
);
2240 * Update the _entire_ grid if necessary.
2243 draw_update(fe
, 0, 0, XSIZE(cr
), YSIZE(cr
));
2248 static float game_anim_length(game_state
*oldstate
, game_state
*newstate
,
2249 int dir
, game_ui
*ui
)
2254 static float game_flash_length(game_state
*oldstate
, game_state
*newstate
,
2255 int dir
, game_ui
*ui
)
2257 if (!oldstate
->completed
&& newstate
->completed
&&
2258 !oldstate
->cheated
&& !newstate
->cheated
)
2263 static int game_wants_statusbar(void)
2268 static int game_timing_state(game_state
*state
)
2274 #define thegame solo
2277 const struct game thegame
= {
2278 "Solo", "games.solo",
2285 TRUE
, game_configure
, custom_params
,
2294 TRUE
, game_text_format
,
2302 game_free_drawstate
,
2306 game_wants_statusbar
,
2307 FALSE
, game_timing_state
,
2308 0, /* mouse_priorities */
2311 #ifdef STANDALONE_SOLVER
2314 * gcc -DSTANDALONE_SOLVER -o solosolver solo.c malloc.c
2317 void frontend_default_colour(frontend
*fe
, float *output
) {}
2318 void draw_text(frontend
*fe
, int x
, int y
, int fonttype
, int fontsize
,
2319 int align
, int colour
, char *text
) {}
2320 void draw_rect(frontend
*fe
, int x
, int y
, int w
, int h
, int colour
) {}
2321 void draw_line(frontend
*fe
, int x1
, int y1
, int x2
, int y2
, int colour
) {}
2322 void draw_polygon(frontend
*fe
, int *coords
, int npoints
,
2323 int fill
, int colour
) {}
2324 void clip(frontend
*fe
, int x
, int y
, int w
, int h
) {}
2325 void unclip(frontend
*fe
) {}
2326 void start_draw(frontend
*fe
) {}
2327 void draw_update(frontend
*fe
, int x
, int y
, int w
, int h
) {}
2328 void end_draw(frontend
*fe
) {}
2329 unsigned long random_bits(random_state
*state
, int bits
)
2330 { assert(!"Shouldn't get randomness"); return 0; }
2331 unsigned long random_upto(random_state
*state
, unsigned long limit
)
2332 { assert(!"Shouldn't get randomness"); return 0; }
2334 void fatal(char *fmt
, ...)
2338 fprintf(stderr
, "fatal error: ");
2341 vfprintf(stderr
, fmt
, ap
);
2344 fprintf(stderr
, "\n");
2348 int main(int argc
, char **argv
)
2353 char *id
= NULL
, *desc
, *err
;
2357 while (--argc
> 0) {
2359 if (!strcmp(p
, "-r")) {
2361 } else if (!strcmp(p
, "-n")) {
2363 } else if (!strcmp(p
, "-v")) {
2364 solver_show_working
= TRUE
;
2366 } else if (!strcmp(p
, "-g")) {
2369 } else if (*p
== '-') {
2370 fprintf(stderr
, "%s: unrecognised option `%s'\n", argv
[0]);
2378 fprintf(stderr
, "usage: %s [-n | -r | -g | -v] <game_id>\n", argv
[0]);
2382 desc
= strchr(id
, ':');
2384 fprintf(stderr
, "%s: game id expects a colon in it\n", argv
[0]);
2389 p
= default_params();
2390 decode_params(p
, id
);
2391 err
= validate_desc(p
, desc
);
2393 fprintf(stderr
, "%s: %s\n", argv
[0], err
);
2396 s
= new_game(NULL
, p
, desc
);
2399 int ret
= rsolve(p
->c
, p
->r
, s
->grid
, NULL
, 2);
2401 fprintf(stderr
, "%s: rsolve: multiple solutions detected\n",
2405 int ret
= nsolve(p
->c
, p
->r
, s
->grid
);
2407 if (ret
== DIFF_IMPOSSIBLE
) {
2409 * Now resort to rsolve to determine whether it's
2412 ret
= rsolve(p
->c
, p
->r
, s
->grid
, NULL
, 2);
2414 ret
= DIFF_IMPOSSIBLE
;
2416 ret
= DIFF_RECURSIVE
;
2418 ret
= DIFF_AMBIGUOUS
;
2420 printf("Difficulty rating: %s\n",
2421 ret
==DIFF_BLOCK ?
"Trivial (blockwise positional elimination only)":
2422 ret
==DIFF_SIMPLE ?
"Basic (row/column/number elimination required)":
2423 ret
==DIFF_INTERSECT ?
"Intermediate (intersectional analysis required)":
2424 ret
==DIFF_SET ?
"Advanced (set elimination required)":
2425 ret
==DIFF_RECURSIVE ?
"Unreasonable (guesswork and backtracking required)":
2426 ret
==DIFF_AMBIGUOUS ?
"Ambiguous (multiple solutions exist)":
2427 ret
==DIFF_IMPOSSIBLE ?
"Impossible (no solution exists)":
2428 "INTERNAL ERROR: unrecognised difficulty code");
2432 printf("%s\n", grid_text_format(p
->c
, p
->r
, s
->grid
));