*
* TODO:
*
- * - can we do anything about nasty centring of text in GTK? It
- * seems to be taking ascenders/descenders into account when
- * centring. Ick.
- *
- * - implement stronger modes of reasoning in nsolve, thus
- * enabling harder puzzles
- * + and having done that, supply configurable difficulty
- * levels
- *
+ * - reports from users are that `Trivial'-mode puzzles are still
+ * rather hard compared to newspapers' easy ones, so some better
+ * low-end difficulty grading would be nice
+ * + it's possible that really easy puzzles always have
+ * _several_ things you can do, so don't make you hunt too
+ * hard for the one deduction you can currently make
+ * + it's also possible that easy puzzles require fewer
+ * cross-eliminations: perhaps there's a higher incidence of
+ * things you can deduce by looking only at (say) rows,
+ * rather than things you have to check both rows and columns
+ * for
+ * + but really, what I need to do is find some really easy
+ * puzzles and _play_ them, to see what's actually easy about
+ * them
+ * + while I'm revamping this area, filling in the _last_
+ * number in a nearly-full row or column should certainly be
+ * permitted even at the lowest difficulty level.
+ * + also Owen noticed that `Basic' grids requiring numeric
+ * elimination are actually very hard, so I wonder if a
+ * difficulty gradation between that and positional-
+ * elimination-only might be in order
+ * + but it's not good to have _too_ many difficulty levels, or
+ * it'll take too long to randomly generate a given level.
+ *
* - it might still be nice to do some prioritisation on the
* removal of numbers from the grid
* + one possibility is to try to minimise the maximum number
* of filled squares in any block, which in particular ought
* to enforce never leaving a completely filled block in the
* puzzle as presented.
- * + be careful of being too clever here, though, until after
- * I've tried implementing difficulty levels. It's not
- * impossible that those might impose much more important
- * constraints on this process.
*
* - alternative interface modes
* + sudoku.com's Windows program has a palette of possible
* click, _or_ you highlight a square and then type. At most
* one thing is ever highlighted at a time, so there's no way
* to confuse the two.
- * + `pencil marks' might be useful for more subtle forms of
- * deduction, once we implement creation of puzzles that
- * require it.
+ * + then again, I don't actually like sudoku.com's interface;
+ * it's too much like a paint package whereas I prefer to
+ * think of Solo as a text editor.
+ * + another PDA-friendly possibility is a drag interface:
+ * _drag_ numbers from the palette into the grid squares.
+ * Thought experiments suggest I'd prefer that to the
+ * sudoku.com approach, but I haven't actually tried it.
*/
/*
#include <ctype.h>
#include <math.h>
+#ifdef STANDALONE_SOLVER
+#include <stdarg.h>
+int solver_show_working, solver_recurse_depth;
+#endif
+
#include "puzzles.h"
/*
typedef unsigned char digit;
#define ORDER_MAX 255
-#define TILE_SIZE 32
-#define BORDER 18
+#define PREFERRED_TILE_SIZE 48
+#define TILE_SIZE (ds->tilesize)
+#define BORDER (TILE_SIZE / 2)
+#define GRIDEXTRA max((TILE_SIZE / 32),1)
#define FLASH_TIME 0.4F
-enum { SYMM_NONE, SYMM_ROT2, SYMM_ROT4, SYMM_REF4 };
+enum { SYMM_NONE, SYMM_ROT2, SYMM_ROT4, SYMM_REF2, SYMM_REF2D, SYMM_REF4,
+ SYMM_REF4D, SYMM_REF8 };
+
+enum { DIFF_BLOCK,
+ DIFF_SIMPLE, DIFF_INTERSECT, DIFF_SET, DIFF_EXTREME, DIFF_RECURSIVE,
+ DIFF_AMBIGUOUS, DIFF_IMPOSSIBLE };
+
+enum { DIFF_KSINGLE, DIFF_KMINMAX, DIFF_KSUMS, DIFF_KINTERSECT };
enum {
COL_BACKGROUND,
+ COL_XDIAGONALS,
COL_GRID,
COL_CLUE,
COL_USER,
COL_HIGHLIGHT,
+ COL_ERROR,
+ COL_PENCIL,
+ COL_KILLER,
NCOLOURS
};
+/*
+ * To determine all possible ways to reach a given sum by adding two or
+ * three numbers from 1..9, each of which occurs exactly once in the sum,
+ * these arrays contain a list of bitmasks for each sum value, where if
+ * bit N is set, it means that N occurs in the sum. Each list is
+ * terminated by a zero if it is shorter than the size of the array.
+ */
+#define MAX_2SUMS 5
+#define MAX_3SUMS 8
+#define MAX_4SUMS 12
+unsigned long sum_bits2[18][MAX_2SUMS];
+unsigned long sum_bits3[25][MAX_3SUMS];
+unsigned long sum_bits4[31][MAX_4SUMS];
+
+static int find_sum_bits(unsigned long *array, int idx, int value_left,
+ int addends_left, int min_addend,
+ unsigned long bitmask_so_far)
+{
+ int i;
+ assert(addends_left >= 2);
+
+ for (i = min_addend; i < value_left; i++) {
+ unsigned long new_bitmask = bitmask_so_far | (1L << i);
+ assert(bitmask_so_far != new_bitmask);
+
+ if (addends_left == 2) {
+ int j = value_left - i;
+ if (j <= i)
+ break;
+ if (j > 9)
+ continue;
+ array[idx++] = new_bitmask | (1L << j);
+ } else
+ idx = find_sum_bits(array, idx, value_left - i,
+ addends_left - 1, i + 1,
+ new_bitmask);
+ }
+ return idx;
+}
+
+static void precompute_sum_bits(void)
+{
+ int i;
+ for (i = 3; i < 31; i++) {
+ int j;
+ if (i < 18) {
+ j = find_sum_bits(sum_bits2[i], 0, i, 2, 1, 0);
+ assert (j <= MAX_2SUMS);
+ if (j < MAX_2SUMS)
+ sum_bits2[i][j] = 0;
+ }
+ if (i < 25) {
+ j = find_sum_bits(sum_bits3[i], 0, i, 3, 1, 0);
+ assert (j <= MAX_3SUMS);
+ if (j < MAX_3SUMS)
+ sum_bits3[i][j] = 0;
+ }
+ j = find_sum_bits(sum_bits4[i], 0, i, 4, 1, 0);
+ assert (j <= MAX_4SUMS);
+ if (j < MAX_4SUMS)
+ sum_bits4[i][j] = 0;
+ }
+}
+
struct game_params {
- int c, r, symm;
+ /*
+ * For a square puzzle, `c' and `r' indicate the puzzle
+ * parameters as described above.
+ *
+ * A jigsaw-style puzzle is indicated by r==1, in which case c
+ * can be whatever it likes (there is no constraint on
+ * compositeness - a 7x7 jigsaw sudoku makes perfect sense).
+ */
+ int c, r, symm, diff, kdiff;
+ int xtype; /* require all digits in X-diagonals */
+ int killer;
+};
+
+struct block_structure {
+ int refcount;
+
+ /*
+ * For text formatting, we do need c and r here.
+ */
+ int c, r, area;
+
+ /*
+ * For any square index, whichblock[i] gives its block index.
+ *
+ * For 0 <= b,i < cr, blocks[b][i] gives the index of the ith
+ * square in block b. nr_squares[b] gives the number of squares
+ * in block b (also the number of valid elements in blocks[b]).
+ *
+ * blocks_data holds the data pointed to by blocks.
+ *
+ * nr_squares may be NULL for block structures where all blocks are
+ * the same size.
+ */
+ int *whichblock, **blocks, *nr_squares, *blocks_data;
+ int nr_blocks, max_nr_squares;
+
+#ifdef STANDALONE_SOLVER
+ /*
+ * Textual descriptions of each block. For normal Sudoku these
+ * are of the form "(1,3)"; for jigsaw they are "starting at
+ * (5,7)". So the sensible usage in both cases is to say
+ * "elimination within block %s" with one of these strings.
+ *
+ * Only blocknames itself needs individually freeing; it's all
+ * one block.
+ */
+ char **blocknames;
+#endif
};
struct game_state {
- int c, r;
- digit *grid;
+ /*
+ * For historical reasons, I use `cr' to denote the overall
+ * width/height of the puzzle. It was a natural notation when
+ * all puzzles were divided into blocks in a grid, but doesn't
+ * really make much sense given jigsaw puzzles. However, the
+ * obvious `n' is heavily used in the solver to describe the
+ * index of a number being placed, so `cr' will have to stay.
+ */
+ int cr;
+ struct block_structure *blocks;
+ struct block_structure *kblocks; /* Blocks for killer puzzles. */
+ int xtype, killer;
+ digit *grid, *kgrid;
+ unsigned char *pencil; /* c*r*c*r elements */
unsigned char *immutable; /* marks which digits are clues */
- int completed;
+ int completed, cheated;
};
static game_params *default_params(void)
game_params *ret = snew(game_params);
ret->c = ret->r = 3;
+ ret->xtype = FALSE;
+ ret->killer = FALSE;
ret->symm = SYMM_ROT2; /* a plausible default */
+ ret->diff = DIFF_BLOCK; /* so is this */
+ ret->kdiff = DIFF_KINTERSECT; /* so is this */
return ret;
}
-static int game_fetch_preset(int i, char **name, game_params **params)
-{
- game_params *ret;
- int c, r;
- char buf[80];
-
- switch (i) {
- case 0: c = 2, r = 2; break;
- case 1: c = 2, r = 3; break;
- case 2: c = 3, r = 3; break;
- case 3: c = 3, r = 4; break;
- case 4: c = 4, r = 4; break;
- default: return FALSE;
- }
-
- sprintf(buf, "%dx%d", c, r);
- *name = dupstr(buf);
- *params = ret = snew(game_params);
- ret->c = c;
- ret->r = r;
- ret->symm = SYMM_ROT2;
- /* FIXME: difficulty presets? */
- return TRUE;
-}
-
static void free_params(game_params *params)
{
sfree(params);
}
-static game_params *dup_params(game_params *params)
+static game_params *dup_params(const game_params *params)
{
game_params *ret = snew(game_params);
*ret = *params; /* structure copy */
return ret;
}
-static game_params *decode_params(char const *string)
+static int game_fetch_preset(int i, char **name, game_params **params)
+{
+ static struct {
+ char *title;
+ game_params params;
+ } presets[] = {
+ { "2x2 Trivial", { 2, 2, SYMM_ROT2, DIFF_BLOCK, DIFF_KMINMAX, FALSE, FALSE } },
+ { "2x3 Basic", { 2, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
+ { "3x3 Trivial", { 3, 3, SYMM_ROT2, DIFF_BLOCK, DIFF_KMINMAX, FALSE, FALSE } },
+ { "3x3 Basic", { 3, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
+ { "3x3 Basic X", { 3, 3, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, TRUE } },
+ { "3x3 Intermediate", { 3, 3, SYMM_ROT2, DIFF_INTERSECT, DIFF_KMINMAX, FALSE, FALSE } },
+ { "3x3 Advanced", { 3, 3, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, FALSE, FALSE } },
+ { "3x3 Advanced X", { 3, 3, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, TRUE } },
+ { "3x3 Extreme", { 3, 3, SYMM_ROT2, DIFF_EXTREME, DIFF_KMINMAX, FALSE, FALSE } },
+ { "3x3 Unreasonable", { 3, 3, SYMM_ROT2, DIFF_RECURSIVE, DIFF_KMINMAX, FALSE, FALSE } },
+ { "3x3 Killer", { 3, 3, SYMM_NONE, DIFF_BLOCK, DIFF_KINTERSECT, FALSE, TRUE } },
+ { "9 Jigsaw Basic", { 9, 1, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
+ { "9 Jigsaw Basic X", { 9, 1, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, TRUE } },
+ { "9 Jigsaw Advanced", { 9, 1, SYMM_ROT2, DIFF_SET, DIFF_KMINMAX, FALSE, FALSE } },
+#ifndef SLOW_SYSTEM
+ { "3x4 Basic", { 3, 4, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
+ { "4x4 Basic", { 4, 4, SYMM_ROT2, DIFF_SIMPLE, DIFF_KMINMAX, FALSE, FALSE } },
+#endif
+ };
+
+ if (i < 0 || i >= lenof(presets))
+ return FALSE;
+
+ *name = dupstr(presets[i].title);
+ *params = dup_params(&presets[i].params);
+
+ return TRUE;
+}
+
+static void decode_params(game_params *ret, char const *string)
{
- game_params *ret = default_params();
+ int seen_r = FALSE;
ret->c = ret->r = atoi(string);
- ret->symm = SYMM_ROT2;
+ ret->xtype = FALSE;
+ ret->killer = FALSE;
while (*string && isdigit((unsigned char)*string)) string++;
if (*string == 'x') {
string++;
ret->r = atoi(string);
+ seen_r = TRUE;
while (*string && isdigit((unsigned char)*string)) string++;
}
- if (*string == 'r' || *string == 'm' || *string == 'a') {
- int sn, sc;
- sc = *string++;
- sn = atoi(string);
- while (*string && isdigit((unsigned char)*string)) string++;
- if (sc == 'm' && sn == 4)
- ret->symm = SYMM_REF4;
- if (sc == 'r' && sn == 4)
- ret->symm = SYMM_ROT4;
- if (sc == 'r' && sn == 2)
- ret->symm = SYMM_ROT2;
- if (sc == 'a')
- ret->symm = SYMM_NONE;
+ while (*string) {
+ if (*string == 'j') {
+ string++;
+ if (seen_r)
+ ret->c *= ret->r;
+ ret->r = 1;
+ } else if (*string == 'x') {
+ string++;
+ ret->xtype = TRUE;
+ } else if (*string == 'k') {
+ string++;
+ ret->killer = TRUE;
+ } else if (*string == 'r' || *string == 'm' || *string == 'a') {
+ int sn, sc, sd;
+ sc = *string++;
+ if (sc == 'm' && *string == 'd') {
+ sd = TRUE;
+ string++;
+ } else {
+ sd = FALSE;
+ }
+ sn = atoi(string);
+ while (*string && isdigit((unsigned char)*string)) string++;
+ if (sc == 'm' && sn == 8)
+ ret->symm = SYMM_REF8;
+ if (sc == 'm' && sn == 4)
+ ret->symm = sd ? SYMM_REF4D : SYMM_REF4;
+ if (sc == 'm' && sn == 2)
+ ret->symm = sd ? SYMM_REF2D : SYMM_REF2;
+ if (sc == 'r' && sn == 4)
+ ret->symm = SYMM_ROT4;
+ if (sc == 'r' && sn == 2)
+ ret->symm = SYMM_ROT2;
+ if (sc == 'a')
+ ret->symm = SYMM_NONE;
+ } else if (*string == 'd') {
+ string++;
+ if (*string == 't') /* trivial */
+ string++, ret->diff = DIFF_BLOCK;
+ else if (*string == 'b') /* basic */
+ string++, ret->diff = DIFF_SIMPLE;
+ else if (*string == 'i') /* intermediate */
+ string++, ret->diff = DIFF_INTERSECT;
+ else if (*string == 'a') /* advanced */
+ string++, ret->diff = DIFF_SET;
+ else if (*string == 'e') /* extreme */
+ string++, ret->diff = DIFF_EXTREME;
+ else if (*string == 'u') /* unreasonable */
+ string++, ret->diff = DIFF_RECURSIVE;
+ } else
+ string++; /* eat unknown character */
}
- /* FIXME: difficulty levels */
-
- return ret;
}
-static char *encode_params(game_params *params)
+static char *encode_params(const game_params *params, int full)
{
char str[80];
- /*
- * Symmetry is a game generation preference and hence is left
- * out of the encoding. Users can add it back in as they see
- * fit.
- */
- sprintf(str, "%dx%d", params->c, params->r);
+ if (params->r > 1)
+ sprintf(str, "%dx%d", params->c, params->r);
+ else
+ sprintf(str, "%dj", params->c);
+ if (params->xtype)
+ strcat(str, "x");
+ if (params->killer)
+ strcat(str, "k");
+
+ if (full) {
+ switch (params->symm) {
+ case SYMM_REF8: strcat(str, "m8"); break;
+ case SYMM_REF4: strcat(str, "m4"); break;
+ case SYMM_REF4D: strcat(str, "md4"); break;
+ case SYMM_REF2: strcat(str, "m2"); break;
+ case SYMM_REF2D: strcat(str, "md2"); break;
+ case SYMM_ROT4: strcat(str, "r4"); break;
+ /* case SYMM_ROT2: strcat(str, "r2"); break; [default] */
+ case SYMM_NONE: strcat(str, "a"); break;
+ }
+ switch (params->diff) {
+ /* case DIFF_BLOCK: strcat(str, "dt"); break; [default] */
+ case DIFF_SIMPLE: strcat(str, "db"); break;
+ case DIFF_INTERSECT: strcat(str, "di"); break;
+ case DIFF_SET: strcat(str, "da"); break;
+ case DIFF_EXTREME: strcat(str, "de"); break;
+ case DIFF_RECURSIVE: strcat(str, "du"); break;
+ }
+ }
return dupstr(str);
}
-static config_item *game_configure(game_params *params)
+static config_item *game_configure(const game_params *params)
{
config_item *ret;
char buf[80];
- ret = snewn(5, config_item);
+ ret = snewn(8, config_item);
ret[0].name = "Columns of sub-blocks";
ret[0].type = C_STRING;
ret[1].sval = dupstr(buf);
ret[1].ival = 0;
- ret[2].name = "Symmetry";
- ret[2].type = C_CHOICES;
- ret[2].sval = ":None:2-way rotation:4-way rotation:4-way mirror";
- ret[2].ival = params->symm;
-
- /*
- * FIXME: difficulty level.
- */
+ ret[2].name = "\"X\" (require every number in each main diagonal)";
+ ret[2].type = C_BOOLEAN;
+ ret[2].sval = NULL;
+ ret[2].ival = params->xtype;
- ret[3].name = NULL;
- ret[3].type = C_END;
+ ret[3].name = "Jigsaw (irregularly shaped sub-blocks)";
+ ret[3].type = C_BOOLEAN;
ret[3].sval = NULL;
- ret[3].ival = 0;
+ ret[3].ival = (params->r == 1);
+
+ ret[4].name = "Killer (digit sums)";
+ ret[4].type = C_BOOLEAN;
+ ret[4].sval = NULL;
+ ret[4].ival = params->killer;
+
+ ret[5].name = "Symmetry";
+ ret[5].type = C_CHOICES;
+ ret[5].sval = ":None:2-way rotation:4-way rotation:2-way mirror:"
+ "2-way diagonal mirror:4-way mirror:4-way diagonal mirror:"
+ "8-way mirror";
+ ret[5].ival = params->symm;
+
+ ret[6].name = "Difficulty";
+ ret[6].type = C_CHOICES;
+ ret[6].sval = ":Trivial:Basic:Intermediate:Advanced:Extreme:Unreasonable";
+ ret[6].ival = params->diff;
+
+ ret[7].name = NULL;
+ ret[7].type = C_END;
+ ret[7].sval = NULL;
+ ret[7].ival = 0;
return ret;
}
-static game_params *custom_params(config_item *cfg)
+static game_params *custom_params(const config_item *cfg)
{
game_params *ret = snew(game_params);
ret->c = atoi(cfg[0].sval);
ret->r = atoi(cfg[1].sval);
- ret->symm = cfg[2].ival;
+ ret->xtype = cfg[2].ival;
+ if (cfg[3].ival) {
+ ret->c *= ret->r;
+ ret->r = 1;
+ }
+ ret->killer = cfg[4].ival;
+ ret->symm = cfg[5].ival;
+ ret->diff = cfg[6].ival;
+ ret->kdiff = DIFF_KINTERSECT;
return ret;
}
-static char *validate_params(game_params *params)
+static char *validate_params(const game_params *params, int full)
{
- if (params->c < 2 || params->r < 2)
+ if (params->c < 2)
return "Both dimensions must be at least 2";
if (params->c > ORDER_MAX || params->r > ORDER_MAX)
return "Dimensions greater than "STR(ORDER_MAX)" are not supported";
+ if ((params->c * params->r) > 31)
+ return "Unable to support more than 31 distinct symbols in a puzzle";
+ if (params->killer && params->c * params->r > 9)
+ return "Killer puzzle dimensions must be smaller than 10.";
return NULL;
}
-/* ----------------------------------------------------------------------
- * Full recursive Solo solver.
- *
- * The algorithm for this solver is shamelessly copied from a
- * Python solver written by Andrew Wilkinson (which is GPLed, but
- * I've reused only ideas and no code). It mostly just does the
- * obvious recursive thing: pick an empty square, put one of the
- * possible digits in it, recurse until all squares are filled,
- * backtrack and change some choices if necessary.
- *
- * The clever bit is that every time it chooses which square to
- * fill in next, it does so by counting the number of _possible_
- * numbers that can go in each square, and it prioritises so that
- * it picks a square with the _lowest_ number of possibilities. The
- * idea is that filling in lots of the obvious bits (particularly
- * any squares with only one possibility) will cut down on the list
- * of possibilities for other squares and hence reduce the enormous
- * search space as much as possible as early as possible.
- *
- * In practice the algorithm appeared to work very well; run on
- * sample problems from the Times it completed in well under a
- * second on my G5 even when written in Python, and given an empty
- * grid (so that in principle it would enumerate _all_ solved
- * grids!) it found the first valid solution just as quickly. So
- * with a bit more randomisation I see no reason not to use this as
- * my grid generator.
- */
-
/*
- * Internal data structure used in solver to keep track of
- * progress.
+ * ----------------------------------------------------------------------
+ * Block structure functions.
*/
-struct rsolve_coord { int x, y, r; };
-struct rsolve_usage {
- int c, r, cr; /* cr == c*r */
- /* grid is a copy of the input grid, modified as we go along */
- digit *grid;
- /* row[y*cr+n-1] TRUE if digit n has been placed in row y */
- unsigned char *row;
- /* col[x*cr+n-1] TRUE if digit n has been placed in row x */
- unsigned char *col;
- /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
- unsigned char *blk;
- /* This lists all the empty spaces remaining in the grid. */
- struct rsolve_coord *spaces;
- int nspaces;
- /* If we need randomisation in the solve, this is our random state. */
- random_state *rs;
- /* Number of solutions so far found, and maximum number we care about. */
- int solns, maxsolns;
-};
-/*
- * The real recursive step in the solving function.
- */
-static void rsolve_real(struct rsolve_usage *usage, digit *grid)
+static struct block_structure *alloc_block_structure(int c, int r, int area,
+ int max_nr_squares,
+ int nr_blocks)
{
- int c = usage->c, r = usage->r, cr = usage->cr;
- int i, j, n, sx, sy, bestm, bestr;
- int *digits;
+ int i;
+ struct block_structure *b = snew(struct block_structure);
+
+ b->refcount = 1;
+ b->nr_blocks = nr_blocks;
+ b->max_nr_squares = max_nr_squares;
+ b->c = c; b->r = r; b->area = area;
+ b->whichblock = snewn(area, int);
+ b->blocks_data = snewn(nr_blocks * max_nr_squares, int);
+ b->blocks = snewn(nr_blocks, int *);
+ b->nr_squares = snewn(nr_blocks, int);
+
+ for (i = 0; i < nr_blocks; i++)
+ b->blocks[i] = b->blocks_data + i*max_nr_squares;
+
+#ifdef STANDALONE_SOLVER
+ b->blocknames = (char **)smalloc(c*r*(sizeof(char *)+80));
+ for (i = 0; i < c * r; i++)
+ b->blocknames[i] = NULL;
+#endif
+ return b;
+}
- /*
- * Firstly, check for completion! If there are no spaces left
- * in the grid, we have a solution.
- */
- if (usage->nspaces == 0) {
- if (!usage->solns) {
- /*
- * This is our first solution, so fill in the output grid.
- */
- memcpy(grid, usage->grid, cr * cr);
- }
- usage->solns++;
- return;
+static void free_block_structure(struct block_structure *b)
+{
+ if (--b->refcount == 0) {
+ sfree(b->whichblock);
+ sfree(b->blocks);
+ sfree(b->blocks_data);
+#ifdef STANDALONE_SOLVER
+ sfree(b->blocknames);
+#endif
+ sfree(b->nr_squares);
+ sfree(b);
}
+}
- /*
- * Otherwise, there must be at least one space. Find the most
- * constrained space, using the `r' field as a tie-breaker.
- */
- bestm = cr+1; /* so that any space will beat it */
- bestr = 0;
- i = sx = sy = -1;
- for (j = 0; j < usage->nspaces; j++) {
- int x = usage->spaces[j].x, y = usage->spaces[j].y;
- int m;
-
- /*
- * Find the number of digits that could go in this space.
- */
- m = 0;
- for (n = 0; n < cr; n++)
- if (!usage->row[y*cr+n] && !usage->col[x*cr+n] &&
- !usage->blk[((y/c)*c+(x/r))*cr+n])
- m++;
-
- if (m < bestm || (m == bestm && usage->spaces[j].r < bestr)) {
- bestm = m;
- bestr = usage->spaces[j].r;
- sx = x;
- sy = y;
- i = j;
- }
- }
+static struct block_structure *dup_block_structure(struct block_structure *b)
+{
+ struct block_structure *nb;
+ int i;
- /*
- * Swap that square into the final place in the spaces array,
- * so that decrementing nspaces will remove it from the list.
- */
- if (i != usage->nspaces-1) {
- struct rsolve_coord t;
- t = usage->spaces[usage->nspaces-1];
- usage->spaces[usage->nspaces-1] = usage->spaces[i];
- usage->spaces[i] = t;
+ nb = alloc_block_structure(b->c, b->r, b->area, b->max_nr_squares,
+ b->nr_blocks);
+ memcpy(nb->nr_squares, b->nr_squares, b->nr_blocks * sizeof *b->nr_squares);
+ memcpy(nb->whichblock, b->whichblock, b->area * sizeof *b->whichblock);
+ memcpy(nb->blocks_data, b->blocks_data,
+ b->nr_blocks * b->max_nr_squares * sizeof *b->blocks_data);
+ for (i = 0; i < b->nr_blocks; i++)
+ nb->blocks[i] = nb->blocks_data + i*nb->max_nr_squares;
+
+#ifdef STANDALONE_SOLVER
+ memcpy(nb->blocknames, b->blocknames, b->c * b->r *(sizeof(char *)+80));
+ {
+ int i;
+ for (i = 0; i < b->c * b->r; i++)
+ if (b->blocknames[i] == NULL)
+ nb->blocknames[i] = NULL;
+ else
+ nb->blocknames[i] = ((char *)nb->blocknames) + (b->blocknames[i] - (char *)b->blocknames);
}
+#endif
+ return nb;
+}
- /*
- * Now we've decided which square to start our recursion at,
- * simply go through all possible values, shuffling them
- * randomly first if necessary.
- */
- digits = snewn(bestm, int);
- j = 0;
- for (n = 0; n < cr; n++)
- if (!usage->row[sy*cr+n] && !usage->col[sx*cr+n] &&
- !usage->blk[((sy/c)*c+(sx/r))*cr+n]) {
- digits[j++] = n+1;
- }
-
- if (usage->rs) {
- /* shuffle */
- for (i = j; i > 1; i--) {
- int p = random_upto(usage->rs, i);
- if (p != i-1) {
- int t = digits[p];
- digits[p] = digits[i-1];
- digits[i-1] = t;
- }
- }
+static void split_block(struct block_structure *b, int *squares, int nr_squares)
+{
+ int i, j;
+ int previous_block = b->whichblock[squares[0]];
+ int newblock = b->nr_blocks;
+
+ assert(b->max_nr_squares >= nr_squares);
+ assert(b->nr_squares[previous_block] > nr_squares);
+
+ b->nr_blocks++;
+ b->blocks_data = sresize(b->blocks_data,
+ b->nr_blocks * b->max_nr_squares, int);
+ b->nr_squares = sresize(b->nr_squares, b->nr_blocks, int);
+ sfree(b->blocks);
+ b->blocks = snewn(b->nr_blocks, int *);
+ for (i = 0; i < b->nr_blocks; i++)
+ b->blocks[i] = b->blocks_data + i*b->max_nr_squares;
+ for (i = 0; i < nr_squares; i++) {
+ assert(b->whichblock[squares[i]] == previous_block);
+ b->whichblock[squares[i]] = newblock;
+ b->blocks[newblock][i] = squares[i];
}
-
- /* And finally, go through the digit list and actually recurse. */
- for (i = 0; i < j; i++) {
- n = digits[i];
-
- /* Update the usage structure to reflect the placing of this digit. */
- usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
- usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = TRUE;
- usage->grid[sy*cr+sx] = n;
- usage->nspaces--;
-
- /* Call the solver recursively. */
- rsolve_real(usage, grid);
-
- /*
- * If we have seen as many solutions as we need, terminate
- * all processing immediately.
- */
- if (usage->solns >= usage->maxsolns)
- break;
-
- /* Revert the usage structure. */
- usage->row[sy*cr+n-1] = usage->col[sx*cr+n-1] =
- usage->blk[((sy/c)*c+(sx/r))*cr+n-1] = FALSE;
- usage->grid[sy*cr+sx] = 0;
- usage->nspaces++;
+ for (i = j = 0; i < b->nr_squares[previous_block]; i++) {
+ int k;
+ int sq = b->blocks[previous_block][i];
+ for (k = 0; k < nr_squares; k++)
+ if (squares[k] == sq)
+ break;
+ if (k == nr_squares)
+ b->blocks[previous_block][j++] = sq;
}
-
- sfree(digits);
+ b->nr_squares[previous_block] -= nr_squares;
+ b->nr_squares[newblock] = nr_squares;
}
-/*
- * Entry point to solver. You give it dimensions and a starting
- * grid, which is simply an array of N^4 digits. In that array, 0
- * means an empty square, and 1..N mean a clue square.
- *
- * Return value is the number of solutions found; searching will
- * stop after the provided `max'. (Thus, you can pass max==1 to
- * indicate that you only care about finding _one_ solution, or
- * max==2 to indicate that you want to know the difference between
- * a unique and non-unique solution.) The input parameter `grid' is
- * also filled in with the _first_ (or only) solution found by the
- * solver.
- */
-static int rsolve(int c, int r, digit *grid, random_state *rs, int max)
+static void remove_from_block(struct block_structure *blocks, int b, int n)
{
- struct rsolve_usage *usage;
- int x, y, cr = c*r;
- int ret;
-
- /*
- * Create an rsolve_usage structure.
- */
- usage = snew(struct rsolve_usage);
-
- usage->c = c;
- usage->r = r;
- usage->cr = cr;
-
- usage->grid = snewn(cr * cr, digit);
- memcpy(usage->grid, grid, cr * cr);
-
- usage->row = snewn(cr * cr, unsigned char);
- usage->col = snewn(cr * cr, unsigned char);
- usage->blk = snewn(cr * cr, unsigned char);
- memset(usage->row, FALSE, cr * cr);
- memset(usage->col, FALSE, cr * cr);
- memset(usage->blk, FALSE, cr * cr);
-
- usage->spaces = snewn(cr * cr, struct rsolve_coord);
- usage->nspaces = 0;
-
- usage->solns = 0;
- usage->maxsolns = max;
-
- usage->rs = rs;
-
- /*
- * Now fill it in with data from the input grid.
- */
- for (y = 0; y < cr; y++) {
- for (x = 0; x < cr; x++) {
- int v = grid[y*cr+x];
- if (v == 0) {
- usage->spaces[usage->nspaces].x = x;
- usage->spaces[usage->nspaces].y = y;
- if (rs)
- usage->spaces[usage->nspaces].r = random_bits(rs, 31);
- else
- usage->spaces[usage->nspaces].r = usage->nspaces;
- usage->nspaces++;
- } else {
- usage->row[y*cr+v-1] = TRUE;
- usage->col[x*cr+v-1] = TRUE;
- usage->blk[((y/c)*c+(x/r))*cr+v-1] = TRUE;
- }
- }
- }
-
- /*
- * Run the real recursive solving function.
- */
- rsolve_real(usage, grid);
- ret = usage->solns;
-
- /*
- * Clean up the usage structure now we have our answer.
- */
- sfree(usage->spaces);
- sfree(usage->blk);
- sfree(usage->col);
- sfree(usage->row);
- sfree(usage->grid);
- sfree(usage);
-
- /*
- * And return.
- */
- return ret;
+ int i, j;
+ blocks->whichblock[n] = -1;
+ for (i = j = 0; i < blocks->nr_squares[b]; i++)
+ if (blocks->blocks[b][i] != n)
+ blocks->blocks[b][j++] = blocks->blocks[b][i];
+ assert(j+1 == i);
+ blocks->nr_squares[b]--;
}
/* ----------------------------------------------------------------------
- * End of recursive solver code.
- */
-
-/* ----------------------------------------------------------------------
- * Less capable non-recursive solver. This one is used to check
- * solubility of a grid as we gradually remove numbers from it: by
- * verifying a grid using this solver we can ensure it isn't _too_
- * hard (e.g. does not actually require guessing and backtracking).
- *
+ * Solver.
+ *
+ * This solver is used for two purposes:
+ * + to check solubility of a grid as we gradually remove numbers
+ * from it
+ * + to solve an externally generated puzzle when the user selects
+ * `Solve'.
+ *
* It supports a variety of specific modes of reasoning. By
* enabling or disabling subsets of these modes we can arrange a
* range of difficulty levels.
* square because all the other empty squares in a given
* row/col/blk are ruled out.
*
+ * - Killer minmax elimination: for killer-type puzzles, a number
+ * is impossible if choosing it would cause the sum in a killer
+ * region to be guaranteed to be too large or too small.
+ *
* - Numeric elimination: a square must have a particular number
* in because all the other numbers that could go in it are
* ruled out.
*
- * More advanced modes of reasoning I'd like to support in future:
- *
- * - Intersectional elimination: given two domains which overlap
+ * - Intersectional analysis: given two domains which overlap
* (hence one must be a block, and the other can be a row or
* col), if the possible locations for a particular number in
* one of the domains can be narrowed down to the overlap, then
* that number can be ruled out everywhere but the overlap in
* the other domain too.
*
- * - Setwise numeric elimination: if there is a subset of the
- * empty squares within a domain such that the union of the
- * possible numbers in that subset has the same size as the
- * subset itself, then those numbers can be ruled out everywhere
- * else in the domain. (For example, if there are five empty
- * squares and the possible numbers in each are 12, 23, 13, 134
- * and 1345, then the first three empty squares form such a
- * subset: the numbers 1, 2 and 3 _must_ be in those three
- * squares in some permutation, and hence we can deduce none of
- * them can be in the fourth or fifth squares.)
- */
-
-/*
- * Within this solver, I'm going to transform all y-coordinates by
- * inverting the significance of the block number and the position
- * within the block. That is, we will start with the top row of
- * each block in order, then the second row of each block in order,
- * etc.
+ * - Set elimination: if there is a subset of the empty squares
+ * within a domain such that the union of the possible numbers
+ * in that subset has the same size as the subset itself, then
+ * those numbers can be ruled out everywhere else in the domain.
+ * (For example, if there are five empty squares and the
+ * possible numbers in each are 12, 23, 13, 134 and 1345, then
+ * the first three empty squares form such a subset: the numbers
+ * 1, 2 and 3 _must_ be in those three squares in some
+ * permutation, and hence we can deduce none of them can be in
+ * the fourth or fifth squares.)
+ * + You can also see this the other way round, concentrating
+ * on numbers rather than squares: if there is a subset of
+ * the unplaced numbers within a domain such that the union
+ * of all their possible positions has the same size as the
+ * subset itself, then all other numbers can be ruled out for
+ * those positions. However, it turns out that this is
+ * exactly equivalent to the first formulation at all times:
+ * there is a 1-1 correspondence between suitable subsets of
+ * the unplaced numbers and suitable subsets of the unfilled
+ * places, found by taking the _complement_ of the union of
+ * the numbers' possible positions (or the spaces' possible
+ * contents).
+ *
+ * - Forcing chains (see comment for solver_forcing().)
*
- * This transformation has the enormous advantage that it means
- * every row, column _and_ block is described by an arithmetic
- * progression of coordinates within the cubic array, so that I can
- * use the same very simple function to do blockwise, row-wise and
- * column-wise elimination.
+ * - Recursion. If all else fails, we pick one of the currently
+ * most constrained empty squares and take a random guess at its
+ * contents, then continue solving on that basis and see if we
+ * get any further.
*/
-#define YTRANS(y) (((y)%c)*r+(y)/c)
-#define YUNTRANS(y) (((y)%r)*c+(y)/r)
-struct nsolve_usage {
- int c, r, cr;
+struct solver_usage {
+ int cr;
+ struct block_structure *blocks, *kblocks, *extra_cages;
/*
* We set up a cubic array, indexed by x, y and digit; each
* element of this array is TRUE or FALSE according to whether
* or not that digit _could_ in principle go in that position.
*
- * The way to index this array is cube[(x*cr+y)*cr+n-1].
- * y-coordinates in here are transformed.
+ * The way to index this array is cube[(y*cr+x)*cr+n-1]; there
+ * are macros below to help with this.
*/
unsigned char *cube;
/*
* deductions. y-coordinates in here are _not_ transformed.
*/
digit *grid;
+ /*
+ * For killer-type puzzles, kclues holds the secondary clue for
+ * each cage. For derived cages, the clue is in extra_clues.
+ */
+ digit *kclues, *extra_clues;
/*
* Now we keep track, at a slightly higher level, of what we
* have yet to work out, to prevent doing the same deduction
unsigned char *row;
/* col[x*cr+n-1] TRUE if digit n has been placed in row x */
unsigned char *col;
- /* blk[(y*c+x)*cr+n-1] TRUE if digit n has been placed in block (x,y) */
+ /* blk[i*cr+n-1] TRUE if digit n has been placed in block i */
unsigned char *blk;
+ /* diag[i*cr+n-1] TRUE if digit n has been placed in diagonal i */
+ unsigned char *diag; /* diag 0 is \, 1 is / */
+
+ int *regions;
+ int nr_regions;
+ int **sq2region;
};
-#define cubepos(x,y,n) (((x)*usage->cr+(y))*usage->cr+(n)-1)
+#define cubepos2(xy,n) ((xy)*usage->cr+(n)-1)
+#define cubepos(x,y,n) cubepos2((y)*usage->cr+(x),n)
#define cube(x,y,n) (usage->cube[cubepos(x,y,n)])
+#define cube2(xy,n) (usage->cube[cubepos2(xy,n)])
+
+#define ondiag0(xy) ((xy) % (cr+1) == 0)
+#define ondiag1(xy) ((xy) % (cr-1) == 0 && (xy) > 0 && (xy) < cr*cr-1)
+#define diag0(i) ((i) * (cr+1))
+#define diag1(i) ((i+1) * (cr-1))
/*
* Function called when we are certain that a particular square has
* a particular number in it. The y-coordinate passed in here is
* transformed.
*/
-static void nsolve_place(struct nsolve_usage *usage, int x, int y, int n)
+static void solver_place(struct solver_usage *usage, int x, int y, int n)
{
- int c = usage->c, r = usage->r, cr = usage->cr;
- int i, j, bx, by;
+ int cr = usage->cr;
+ int sqindex = y*cr+x;
+ int i, bi;
assert(cube(x,y,n));
/*
* Rule out this number in all other positions in the block.
*/
- bx = (x/r)*r;
- by = y % r;
- for (i = 0; i < r; i++)
- for (j = 0; j < c; j++)
- if (bx+i != x || by+j*r != y)
- cube(bx+i,by+j*r,n) = FALSE;
+ bi = usage->blocks->whichblock[sqindex];
+ for (i = 0; i < cr; i++) {
+ int bp = usage->blocks->blocks[bi][i];
+ if (bp != sqindex)
+ cube2(bp,n) = FALSE;
+ }
/*
* Enter the number in the result grid.
*/
- usage->grid[YUNTRANS(y)*cr+x] = n;
+ usage->grid[sqindex] = n;
/*
* Cross out this number from the list of numbers left to place
* in its row, its column and its block.
*/
usage->row[y*cr+n-1] = usage->col[x*cr+n-1] =
- usage->blk[((y/c)*c+(x/r))*cr+n-1] = TRUE;
+ usage->blk[bi*cr+n-1] = TRUE;
+
+ if (usage->diag) {
+ if (ondiag0(sqindex)) {
+ for (i = 0; i < cr; i++)
+ if (diag0(i) != sqindex)
+ cube2(diag0(i),n) = FALSE;
+ usage->diag[n-1] = TRUE;
+ }
+ if (ondiag1(sqindex)) {
+ for (i = 0; i < cr; i++)
+ if (diag1(i) != sqindex)
+ cube2(diag1(i),n) = FALSE;
+ usage->diag[cr+n-1] = TRUE;
+ }
+ }
}
-static int nsolve_elim(struct nsolve_usage *usage, int start, int step)
-{
- int c = usage->c, r = usage->r, cr = c*r;
- int fpos, m, i;
-
- /*
+#if defined STANDALONE_SOLVER && defined __GNUC__
+/*
+ * Forward-declare the functions taking printf-like format arguments
+ * with __attribute__((format)) so as to ensure the argument syntax
+ * gets debugged.
+ */
+struct solver_scratch;
+static int solver_elim(struct solver_usage *usage, int *indices,
+ char *fmt, ...) __attribute__((format(printf,3,4)));
+static int solver_intersect(struct solver_usage *usage,
+ int *indices1, int *indices2, char *fmt, ...)
+ __attribute__((format(printf,4,5)));
+static int solver_set(struct solver_usage *usage,
+ struct solver_scratch *scratch,
+ int *indices, char *fmt, ...)
+ __attribute__((format(printf,4,5)));
+#endif
+
+static int solver_elim(struct solver_usage *usage, int *indices
+#ifdef STANDALONE_SOLVER
+ , char *fmt, ...
+#endif
+ )
+{
+ int cr = usage->cr;
+ int fpos, m, i;
+
+ /*
* Count the number of set bits within this section of the
* cube.
*/
m = 0;
fpos = -1;
for (i = 0; i < cr; i++)
- if (usage->cube[start+i*step]) {
- fpos = start+i*step;
+ if (usage->cube[indices[i]]) {
+ fpos = indices[i];
m++;
}
assert(fpos >= 0);
n = 1 + fpos % cr;
- y = fpos / cr;
- x = y / cr;
- y %= cr;
+ x = fpos / cr;
+ y = x / cr;
+ x %= cr;
+
+ if (!usage->grid[y*cr+x]) {
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ va_list ap;
+ printf("%*s", solver_recurse_depth*4, "");
+ va_start(ap, fmt);
+ vprintf(fmt, ap);
+ va_end(ap);
+ printf(":\n%*s placing %d at (%d,%d)\n",
+ solver_recurse_depth*4, "", n, 1+x, 1+y);
+ }
+#endif
+ solver_place(usage, x, y, n);
+ return +1;
+ }
+ } else if (m == 0) {
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ va_list ap;
+ printf("%*s", solver_recurse_depth*4, "");
+ va_start(ap, fmt);
+ vprintf(fmt, ap);
+ va_end(ap);
+ printf(":\n%*s no possibilities available\n",
+ solver_recurse_depth*4, "");
+ }
+#endif
+ return -1;
+ }
+
+ return 0;
+}
+
+static int solver_intersect(struct solver_usage *usage,
+ int *indices1, int *indices2
+#ifdef STANDALONE_SOLVER
+ , char *fmt, ...
+#endif
+ )
+{
+ int cr = usage->cr;
+ int ret, i, j;
+
+ /*
+ * Loop over the first domain and see if there's any set bit
+ * not also in the second.
+ */
+ for (i = j = 0; i < cr; i++) {
+ int p = indices1[i];
+ while (j < cr && indices2[j] < p)
+ j++;
+ if (usage->cube[p]) {
+ if (j < cr && indices2[j] == p)
+ continue; /* both domains contain this index */
+ else
+ return 0; /* there is, so we can't deduce */
+ }
+ }
+
+ /*
+ * We have determined that all set bits in the first domain are
+ * within its overlap with the second. So loop over the second
+ * domain and remove all set bits that aren't also in that
+ * overlap; return +1 iff we actually _did_ anything.
+ */
+ ret = 0;
+ for (i = j = 0; i < cr; i++) {
+ int p = indices2[i];
+ while (j < cr && indices1[j] < p)
+ j++;
+ if (usage->cube[p] && (j >= cr || indices1[j] != p)) {
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ int px, py, pn;
+
+ if (!ret) {
+ va_list ap;
+ printf("%*s", solver_recurse_depth*4, "");
+ va_start(ap, fmt);
+ vprintf(fmt, ap);
+ va_end(ap);
+ printf(":\n");
+ }
+
+ pn = 1 + p % cr;
+ px = p / cr;
+ py = px / cr;
+ px %= cr;
+
+ printf("%*s ruling out %d at (%d,%d)\n",
+ solver_recurse_depth*4, "", pn, 1+px, 1+py);
+ }
+#endif
+ ret = +1; /* we did something */
+ usage->cube[p] = 0;
+ }
+ }
+
+ return ret;
+}
+
+struct solver_scratch {
+ unsigned char *grid, *rowidx, *colidx, *set;
+ int *neighbours, *bfsqueue;
+ int *indexlist, *indexlist2;
+#ifdef STANDALONE_SOLVER
+ int *bfsprev;
+#endif
+};
+
+static int solver_set(struct solver_usage *usage,
+ struct solver_scratch *scratch,
+ int *indices
+#ifdef STANDALONE_SOLVER
+ , char *fmt, ...
+#endif
+ )
+{
+ int cr = usage->cr;
+ int i, j, n, count;
+ unsigned char *grid = scratch->grid;
+ unsigned char *rowidx = scratch->rowidx;
+ unsigned char *colidx = scratch->colidx;
+ unsigned char *set = scratch->set;
+
+ /*
+ * We are passed a cr-by-cr matrix of booleans. Our first job
+ * is to winnow it by finding any definite placements - i.e.
+ * any row with a solitary 1 - and discarding that row and the
+ * column containing the 1.
+ */
+ memset(rowidx, TRUE, cr);
+ memset(colidx, TRUE, cr);
+ for (i = 0; i < cr; i++) {
+ int count = 0, first = -1;
+ for (j = 0; j < cr; j++)
+ if (usage->cube[indices[i*cr+j]])
+ first = j, count++;
+
+ /*
+ * If count == 0, then there's a row with no 1s at all and
+ * the puzzle is internally inconsistent. However, we ought
+ * to have caught this already during the simpler reasoning
+ * methods, so we can safely fail an assertion if we reach
+ * this point here.
+ */
+ assert(count > 0);
+ if (count == 1)
+ rowidx[i] = colidx[first] = FALSE;
+ }
+
+ /*
+ * Convert each of rowidx/colidx from a list of 0s and 1s to a
+ * list of the indices of the 1s.
+ */
+ for (i = j = 0; i < cr; i++)
+ if (rowidx[i])
+ rowidx[j++] = i;
+ n = j;
+ for (i = j = 0; i < cr; i++)
+ if (colidx[i])
+ colidx[j++] = i;
+ assert(n == j);
+
+ /*
+ * And create the smaller matrix.
+ */
+ for (i = 0; i < n; i++)
+ for (j = 0; j < n; j++)
+ grid[i*cr+j] = usage->cube[indices[rowidx[i]*cr+colidx[j]]];
+
+ /*
+ * Having done that, we now have a matrix in which every row
+ * has at least two 1s in. Now we search to see if we can find
+ * a rectangle of zeroes (in the set-theoretic sense of
+ * `rectangle', i.e. a subset of rows crossed with a subset of
+ * columns) whose width and height add up to n.
+ */
+
+ memset(set, 0, n);
+ count = 0;
+ while (1) {
+ /*
+ * We have a candidate set. If its size is <=1 or >=n-1
+ * then we move on immediately.
+ */
+ if (count > 1 && count < n-1) {
+ /*
+ * The number of rows we need is n-count. See if we can
+ * find that many rows which each have a zero in all
+ * the positions listed in `set'.
+ */
+ int rows = 0;
+ for (i = 0; i < n; i++) {
+ int ok = TRUE;
+ for (j = 0; j < n; j++)
+ if (set[j] && grid[i*cr+j]) {
+ ok = FALSE;
+ break;
+ }
+ if (ok)
+ rows++;
+ }
+
+ /*
+ * We expect never to be able to get _more_ than
+ * n-count suitable rows: this would imply that (for
+ * example) there are four numbers which between them
+ * have at most three possible positions, and hence it
+ * indicates a faulty deduction before this point or
+ * even a bogus clue.
+ */
+ if (rows > n - count) {
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ va_list ap;
+ printf("%*s", solver_recurse_depth*4,
+ "");
+ va_start(ap, fmt);
+ vprintf(fmt, ap);
+ va_end(ap);
+ printf(":\n%*s contradiction reached\n",
+ solver_recurse_depth*4, "");
+ }
+#endif
+ return -1;
+ }
+
+ if (rows >= n - count) {
+ int progress = FALSE;
+
+ /*
+ * We've got one! Now, for each row which _doesn't_
+ * satisfy the criterion, eliminate all its set
+ * bits in the positions _not_ listed in `set'.
+ * Return +1 (meaning progress has been made) if we
+ * successfully eliminated anything at all.
+ *
+ * This involves referring back through
+ * rowidx/colidx in order to work out which actual
+ * positions in the cube to meddle with.
+ */
+ for (i = 0; i < n; i++) {
+ int ok = TRUE;
+ for (j = 0; j < n; j++)
+ if (set[j] && grid[i*cr+j]) {
+ ok = FALSE;
+ break;
+ }
+ if (!ok) {
+ for (j = 0; j < n; j++)
+ if (!set[j] && grid[i*cr+j]) {
+ int fpos = indices[rowidx[i]*cr+colidx[j]];
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ int px, py, pn;
+
+ if (!progress) {
+ va_list ap;
+ printf("%*s", solver_recurse_depth*4,
+ "");
+ va_start(ap, fmt);
+ vprintf(fmt, ap);
+ va_end(ap);
+ printf(":\n");
+ }
+
+ pn = 1 + fpos % cr;
+ px = fpos / cr;
+ py = px / cr;
+ px %= cr;
+
+ printf("%*s ruling out %d at (%d,%d)\n",
+ solver_recurse_depth*4, "",
+ pn, 1+px, 1+py);
+ }
+#endif
+ progress = TRUE;
+ usage->cube[fpos] = FALSE;
+ }
+ }
+ }
+
+ if (progress) {
+ return +1;
+ }
+ }
+ }
+
+ /*
+ * Binary increment: change the rightmost 0 to a 1, and
+ * change all 1s to the right of it to 0s.
+ */
+ i = n;
+ while (i > 0 && set[i-1])
+ set[--i] = 0, count--;
+ if (i > 0)
+ set[--i] = 1, count++;
+ else
+ break; /* done */
+ }
+
+ return 0;
+}
+
+/*
+ * Look for forcing chains. A forcing chain is a path of
+ * pairwise-exclusive squares (i.e. each pair of adjacent squares
+ * in the path are in the same row, column or block) with the
+ * following properties:
+ *
+ * (a) Each square on the path has precisely two possible numbers.
+ *
+ * (b) Each pair of squares which are adjacent on the path share
+ * at least one possible number in common.
+ *
+ * (c) Each square in the middle of the path shares _both_ of its
+ * numbers with at least one of its neighbours (not the same
+ * one with both neighbours).
+ *
+ * These together imply that at least one of the possible number
+ * choices at one end of the path forces _all_ the rest of the
+ * numbers along the path. In order to make real use of this, we
+ * need further properties:
+ *
+ * (c) Ruling out some number N from the square at one end of the
+ * path forces the square at the other end to take the same
+ * number N.
+ *
+ * (d) The two end squares are both in line with some third
+ * square.
+ *
+ * (e) That third square currently has N as a possibility.
+ *
+ * If we can find all of that lot, we can deduce that at least one
+ * of the two ends of the forcing chain has number N, and that
+ * therefore the mutually adjacent third square does not.
+ *
+ * To find forcing chains, we're going to start a bfs at each
+ * suitable square, once for each of its two possible numbers.
+ */
+static int solver_forcing(struct solver_usage *usage,
+ struct solver_scratch *scratch)
+{
+ int cr = usage->cr;
+ int *bfsqueue = scratch->bfsqueue;
+#ifdef STANDALONE_SOLVER
+ int *bfsprev = scratch->bfsprev;
+#endif
+ unsigned char *number = scratch->grid;
+ int *neighbours = scratch->neighbours;
+ int x, y;
+
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++) {
+ int count, t, n;
+
+ /*
+ * If this square doesn't have exactly two candidate
+ * numbers, don't try it.
+ *
+ * In this loop we also sum the candidate numbers,
+ * which is a nasty hack to allow us to quickly find
+ * `the other one' (since we will shortly know there
+ * are exactly two).
+ */
+ for (count = t = 0, n = 1; n <= cr; n++)
+ if (cube(x, y, n))
+ count++, t += n;
+ if (count != 2)
+ continue;
+
+ /*
+ * Now attempt a bfs for each candidate.
+ */
+ for (n = 1; n <= cr; n++)
+ if (cube(x, y, n)) {
+ int orign, currn, head, tail;
+
+ /*
+ * Begin a bfs.
+ */
+ orign = n;
+
+ memset(number, cr+1, cr*cr);
+ head = tail = 0;
+ bfsqueue[tail++] = y*cr+x;
+#ifdef STANDALONE_SOLVER
+ bfsprev[y*cr+x] = -1;
+#endif
+ number[y*cr+x] = t - n;
+
+ while (head < tail) {
+ int xx, yy, nneighbours, xt, yt, i;
+
+ xx = bfsqueue[head++];
+ yy = xx / cr;
+ xx %= cr;
+
+ currn = number[yy*cr+xx];
+
+ /*
+ * Find neighbours of yy,xx.
+ */
+ nneighbours = 0;
+ for (yt = 0; yt < cr; yt++)
+ neighbours[nneighbours++] = yt*cr+xx;
+ for (xt = 0; xt < cr; xt++)
+ neighbours[nneighbours++] = yy*cr+xt;
+ xt = usage->blocks->whichblock[yy*cr+xx];
+ for (yt = 0; yt < cr; yt++)
+ neighbours[nneighbours++] = usage->blocks->blocks[xt][yt];
+ if (usage->diag) {
+ int sqindex = yy*cr+xx;
+ if (ondiag0(sqindex)) {
+ for (i = 0; i < cr; i++)
+ neighbours[nneighbours++] = diag0(i);
+ }
+ if (ondiag1(sqindex)) {
+ for (i = 0; i < cr; i++)
+ neighbours[nneighbours++] = diag1(i);
+ }
+ }
+
+ /*
+ * Try visiting each of those neighbours.
+ */
+ for (i = 0; i < nneighbours; i++) {
+ int cc, tt, nn;
+
+ xt = neighbours[i] % cr;
+ yt = neighbours[i] / cr;
+
+ /*
+ * We need this square to not be
+ * already visited, and to include
+ * currn as a possible number.
+ */
+ if (number[yt*cr+xt] <= cr)
+ continue;
+ if (!cube(xt, yt, currn))
+ continue;
+
+ /*
+ * Don't visit _this_ square a second
+ * time!
+ */
+ if (xt == xx && yt == yy)
+ continue;
+
+ /*
+ * To continue with the bfs, we need
+ * this square to have exactly two
+ * possible numbers.
+ */
+ for (cc = tt = 0, nn = 1; nn <= cr; nn++)
+ if (cube(xt, yt, nn))
+ cc++, tt += nn;
+ if (cc == 2) {
+ bfsqueue[tail++] = yt*cr+xt;
+#ifdef STANDALONE_SOLVER
+ bfsprev[yt*cr+xt] = yy*cr+xx;
+#endif
+ number[yt*cr+xt] = tt - currn;
+ }
+
+ /*
+ * One other possibility is that this
+ * might be the square in which we can
+ * make a real deduction: if it's
+ * adjacent to x,y, and currn is equal
+ * to the original number we ruled out.
+ */
+ if (currn == orign &&
+ (xt == x || yt == y ||
+ (usage->blocks->whichblock[yt*cr+xt] == usage->blocks->whichblock[y*cr+x]) ||
+ (usage->diag && ((ondiag0(yt*cr+xt) && ondiag0(y*cr+x)) ||
+ (ondiag1(yt*cr+xt) && ondiag1(y*cr+x)))))) {
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ char *sep = "";
+ int xl, yl;
+ printf("%*sforcing chain, %d at ends of ",
+ solver_recurse_depth*4, "", orign);
+ xl = xx;
+ yl = yy;
+ while (1) {
+ printf("%s(%d,%d)", sep, 1+xl,
+ 1+yl);
+ xl = bfsprev[yl*cr+xl];
+ if (xl < 0)
+ break;
+ yl = xl / cr;
+ xl %= cr;
+ sep = "-";
+ }
+ printf("\n%*s ruling out %d at (%d,%d)\n",
+ solver_recurse_depth*4, "",
+ orign, 1+xt, 1+yt);
+ }
+#endif
+ cube(xt, yt, orign) = FALSE;
+ return 1;
+ }
+ }
+ }
+ }
+ }
+
+ return 0;
+}
+
+static int solver_killer_minmax(struct solver_usage *usage,
+ struct block_structure *cages, digit *clues,
+ int b
+#ifdef STANDALONE_SOLVER
+ , const char *extra
+#endif
+ )
+{
+ int cr = usage->cr;
+ int i;
+ int ret = 0;
+ int nsquares = cages->nr_squares[b];
+
+ if (clues[b] == 0)
+ return 0;
+
+ for (i = 0; i < nsquares; i++) {
+ int n, x = cages->blocks[b][i];
+
+ for (n = 1; n <= cr; n++)
+ if (cube2(x, n)) {
+ int maxval = 0, minval = 0;
+ int j;
+ for (j = 0; j < nsquares; j++) {
+ int m;
+ int y = cages->blocks[b][j];
+ if (i == j)
+ continue;
+ for (m = 1; m <= cr; m++)
+ if (cube2(y, m)) {
+ minval += m;
+ break;
+ }
+ for (m = cr; m > 0; m--)
+ if (cube2(y, m)) {
+ maxval += m;
+ break;
+ }
+ }
+ if (maxval + n < clues[b]) {
+ cube2(x, n) = FALSE;
+ ret = 1;
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working)
+ printf("%*s ruling out %d at (%d,%d) as too low %s\n",
+ solver_recurse_depth*4, "killer minmax analysis",
+ n, 1 + x%cr, 1 + x/cr, extra);
+#endif
+ }
+ if (minval + n > clues[b]) {
+ cube2(x, n) = FALSE;
+ ret = 1;
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working)
+ printf("%*s ruling out %d at (%d,%d) as too high %s\n",
+ solver_recurse_depth*4, "killer minmax analysis",
+ n, 1 + x%cr, 1 + x/cr, extra);
+#endif
+ }
+ }
+ }
+ return ret;
+}
+
+static int solver_killer_sums(struct solver_usage *usage, int b,
+ struct block_structure *cages, int clue,
+ int cage_is_region
+#ifdef STANDALONE_SOLVER
+ , const char *cage_type
+#endif
+ )
+{
+ int cr = usage->cr;
+ int i, ret, max_sums;
+ int nsquares = cages->nr_squares[b];
+ unsigned long *sumbits, possible_addends;
+
+ if (clue == 0) {
+ assert(nsquares == 0);
+ return 0;
+ }
+ assert(nsquares > 0);
+
+ if (nsquares < 2 || nsquares > 4)
+ return 0;
+
+ if (!cage_is_region) {
+ int known_row = -1, known_col = -1, known_block = -1;
+ /*
+ * Verify that the cage lies entirely within one region,
+ * so that using the precomputed sums is valid.
+ */
+ for (i = 0; i < nsquares; i++) {
+ int x = cages->blocks[b][i];
+
+ assert(usage->grid[x] == 0);
+
+ if (i == 0) {
+ known_row = x/cr;
+ known_col = x%cr;
+ known_block = usage->blocks->whichblock[x];
+ } else {
+ if (known_row != x/cr)
+ known_row = -1;
+ if (known_col != x%cr)
+ known_col = -1;
+ if (known_block != usage->blocks->whichblock[x])
+ known_block = -1;
+ }
+ }
+ if (known_block == -1 && known_col == -1 && known_row == -1)
+ return 0;
+ }
+ if (nsquares == 2) {
+ if (clue < 3 || clue > 17)
+ return -1;
+
+ sumbits = sum_bits2[clue];
+ max_sums = MAX_2SUMS;
+ } else if (nsquares == 3) {
+ if (clue < 6 || clue > 24)
+ return -1;
+
+ sumbits = sum_bits3[clue];
+ max_sums = MAX_3SUMS;
+ } else {
+ if (clue < 10 || clue > 30)
+ return -1;
+
+ sumbits = sum_bits4[clue];
+ max_sums = MAX_4SUMS;
+ }
+ /*
+ * For every possible way to get the sum, see if there is
+ * one square in the cage that disallows all the required
+ * addends. If we find one such square, this way to compute
+ * the sum is impossible.
+ */
+ possible_addends = 0;
+ for (i = 0; i < max_sums; i++) {
+ int j;
+ unsigned long bits = sumbits[i];
+
+ if (bits == 0)
+ break;
+
+ for (j = 0; j < nsquares; j++) {
+ int n;
+ unsigned long square_bits = bits;
+ int x = cages->blocks[b][j];
+ for (n = 1; n <= cr; n++)
+ if (!cube2(x, n))
+ square_bits &= ~(1L << n);
+ if (square_bits == 0) {
+ break;
+ }
+ }
+ if (j == nsquares)
+ possible_addends |= bits;
+ }
+ /*
+ * Now we know which addends can possibly be used to
+ * compute the sum. Remove all other digits from the
+ * set of possibilities.
+ */
+ if (possible_addends == 0)
+ return -1;
+
+ ret = 0;
+ for (i = 0; i < nsquares; i++) {
+ int n;
+ int x = cages->blocks[b][i];
+ for (n = 1; n <= cr; n++) {
+ if (!cube2(x, n))
+ continue;
+ if ((possible_addends & (1 << n)) == 0) {
+ cube2(x, n) = FALSE;
+ ret = 1;
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ printf("%*s using %s\n",
+ solver_recurse_depth*4, "killer sums analysis",
+ cage_type);
+ printf("%*s ruling out %d at (%d,%d) due to impossible %d-sum\n",
+ solver_recurse_depth*4, "",
+ n, 1 + x%cr, 1 + x/cr, nsquares);
+ }
+#endif
+ }
+ }
+ }
+ return ret;
+}
+
+static int filter_whole_cages(struct solver_usage *usage, int *squares, int n,
+ int *filtered_sum)
+{
+ int b, i, j, off;
+ *filtered_sum = 0;
+
+ /* First, filter squares with a clue. */
+ for (i = j = 0; i < n; i++)
+ if (usage->grid[squares[i]])
+ *filtered_sum += usage->grid[squares[i]];
+ else
+ squares[j++] = squares[i];
+ n = j;
+
+ /*
+ * Filter all cages that are covered entirely by the list of
+ * squares.
+ */
+ off = 0;
+ for (b = 0; b < usage->kblocks->nr_blocks && off < n; b++) {
+ int b_squares = usage->kblocks->nr_squares[b];
+ int matched = 0;
+
+ if (b_squares == 0)
+ continue;
+
+ /*
+ * Find all squares of block b that lie in our list,
+ * and make them contiguous at off, which is the current position
+ * in the output list.
+ */
+ for (i = 0; i < b_squares; i++) {
+ for (j = off; j < n; j++)
+ if (squares[j] == usage->kblocks->blocks[b][i]) {
+ int t = squares[off + matched];
+ squares[off + matched] = squares[j];
+ squares[j] = t;
+ matched++;
+ break;
+ }
+ }
+ /* If so, filter out all squares of b from the list. */
+ if (matched != usage->kblocks->nr_squares[b]) {
+ off += matched;
+ continue;
+ }
+ memmove(squares + off, squares + off + matched,
+ (n - off - matched) * sizeof *squares);
+ n -= matched;
+
+ *filtered_sum += usage->kclues[b];
+ }
+ assert(off == n);
+ return off;
+}
+
+static struct solver_scratch *solver_new_scratch(struct solver_usage *usage)
+{
+ struct solver_scratch *scratch = snew(struct solver_scratch);
+ int cr = usage->cr;
+ scratch->grid = snewn(cr*cr, unsigned char);
+ scratch->rowidx = snewn(cr, unsigned char);
+ scratch->colidx = snewn(cr, unsigned char);
+ scratch->set = snewn(cr, unsigned char);
+ scratch->neighbours = snewn(5*cr, int);
+ scratch->bfsqueue = snewn(cr*cr, int);
+#ifdef STANDALONE_SOLVER
+ scratch->bfsprev = snewn(cr*cr, int);
+#endif
+ scratch->indexlist = snewn(cr*cr, int); /* used for set elimination */
+ scratch->indexlist2 = snewn(cr, int); /* only used for intersect() */
+ return scratch;
+}
+
+static void solver_free_scratch(struct solver_scratch *scratch)
+{
+#ifdef STANDALONE_SOLVER
+ sfree(scratch->bfsprev);
+#endif
+ sfree(scratch->bfsqueue);
+ sfree(scratch->neighbours);
+ sfree(scratch->set);
+ sfree(scratch->colidx);
+ sfree(scratch->rowidx);
+ sfree(scratch->grid);
+ sfree(scratch->indexlist);
+ sfree(scratch->indexlist2);
+ sfree(scratch);
+}
+
+/*
+ * Used for passing information about difficulty levels between the solver
+ * and its callers.
+ */
+struct difficulty {
+ /* Maximum levels allowed. */
+ int maxdiff, maxkdiff;
+ /* Levels reached by the solver. */
+ int diff, kdiff;
+};
+
+static void solver(int cr, struct block_structure *blocks,
+ struct block_structure *kblocks, int xtype,
+ digit *grid, digit *kgrid, struct difficulty *dlev)
+{
+ struct solver_usage *usage;
+ struct solver_scratch *scratch;
+ int x, y, b, i, n, ret;
+ int diff = DIFF_BLOCK;
+ int kdiff = DIFF_KSINGLE;
+
+ /*
+ * Set up a usage structure as a clean slate (everything
+ * possible).
+ */
+ usage = snew(struct solver_usage);
+ usage->cr = cr;
+ usage->blocks = blocks;
+ if (kblocks) {
+ usage->kblocks = dup_block_structure(kblocks);
+ usage->extra_cages = alloc_block_structure (kblocks->c, kblocks->r,
+ cr * cr, cr, cr * cr);
+ usage->extra_clues = snewn(cr*cr, digit);
+ } else {
+ usage->kblocks = usage->extra_cages = NULL;
+ usage->extra_clues = NULL;
+ }
+ usage->cube = snewn(cr*cr*cr, unsigned char);
+ usage->grid = grid; /* write straight back to the input */
+ if (kgrid) {
+ int nclues;
+
+ assert(kblocks);
+ nclues = kblocks->nr_blocks;
+ /*
+ * Allow for expansion of the killer regions, the absolute
+ * limit is obviously one region per square.
+ */
+ usage->kclues = snewn(cr*cr, digit);
+ for (i = 0; i < nclues; i++) {
+ for (n = 0; n < kblocks->nr_squares[i]; n++)
+ if (kgrid[kblocks->blocks[i][n]] != 0)
+ usage->kclues[i] = kgrid[kblocks->blocks[i][n]];
+ assert(usage->kclues[i] > 0);
+ }
+ memset(usage->kclues + nclues, 0, cr*cr - nclues);
+ } else {
+ usage->kclues = NULL;
+ }
+
+ memset(usage->cube, TRUE, cr*cr*cr);
+
+ usage->row = snewn(cr * cr, unsigned char);
+ usage->col = snewn(cr * cr, unsigned char);
+ usage->blk = snewn(cr * cr, unsigned char);
+ memset(usage->row, FALSE, cr * cr);
+ memset(usage->col, FALSE, cr * cr);
+ memset(usage->blk, FALSE, cr * cr);
+
+ if (xtype) {
+ usage->diag = snewn(cr * 2, unsigned char);
+ memset(usage->diag, FALSE, cr * 2);
+ } else
+ usage->diag = NULL;
+
+ usage->nr_regions = cr * 3 + (xtype ? 2 : 0);
+ usage->regions = snewn(cr * usage->nr_regions, int);
+ usage->sq2region = snewn(cr * cr * 3, int *);
+
+ for (n = 0; n < cr; n++) {
+ for (i = 0; i < cr; i++) {
+ x = n*cr+i;
+ y = i*cr+n;
+ b = usage->blocks->blocks[n][i];
+ usage->regions[cr*n*3 + i] = x;
+ usage->regions[cr*n*3 + cr + i] = y;
+ usage->regions[cr*n*3 + 2*cr + i] = b;
+ usage->sq2region[x*3] = usage->regions + cr*n*3;
+ usage->sq2region[y*3 + 1] = usage->regions + cr*n*3 + cr;
+ usage->sq2region[b*3 + 2] = usage->regions + cr*n*3 + 2*cr;
+ }
+ }
+
+ scratch = solver_new_scratch(usage);
+
+ /*
+ * Place all the clue numbers we are given.
+ */
+ for (x = 0; x < cr; x++)
+ for (y = 0; y < cr; y++) {
+ int n = grid[y*cr+x];
+ if (n) {
+ if (!cube(x,y,n)) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ solver_place(usage, x, y, grid[y*cr+x]);
+ }
+ }
+
+ /*
+ * Now loop over the grid repeatedly trying all permitted modes
+ * of reasoning. The loop terminates if we complete an
+ * iteration without making any progress; we then return
+ * failure or success depending on whether the grid is full or
+ * not.
+ */
+ while (1) {
+ /*
+ * I'd like to write `continue;' inside each of the
+ * following loops, so that the solver returns here after
+ * making some progress. However, I can't specify that I
+ * want to continue an outer loop rather than the innermost
+ * one, so I'm apologetically resorting to a goto.
+ */
+ cont:
+
+ /*
+ * Blockwise positional elimination.
+ */
+ for (b = 0; b < cr; b++)
+ for (n = 1; n <= cr; n++)
+ if (!usage->blk[b*cr+n-1]) {
+ for (i = 0; i < cr; i++)
+ scratch->indexlist[i] = cubepos2(usage->blocks->blocks[b][i],n);
+ ret = solver_elim(usage, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "positional elimination,"
+ " %d in block %s", n,
+ usage->blocks->blocknames[b]
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_BLOCK);
+ goto cont;
+ }
+ }
+
+ if (usage->kclues != NULL) {
+ int changed = FALSE;
+
+ /*
+ * First, bring the kblocks into a more useful form: remove
+ * all filled-in squares, and reduce the sum by their values.
+ * Walk in reverse order, since otherwise remove_from_block
+ * can move element past our loop counter.
+ */
+ for (b = 0; b < usage->kblocks->nr_blocks; b++)
+ for (i = usage->kblocks->nr_squares[b] -1; i >= 0; i--) {
+ int x = usage->kblocks->blocks[b][i];
+ int t = usage->grid[x];
+
+ if (t == 0)
+ continue;
+ remove_from_block(usage->kblocks, b, x);
+ if (t > usage->kclues[b]) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ usage->kclues[b] -= t;
+ /*
+ * Since cages are regions, this tells us something
+ * about the other squares in the cage.
+ */
+ for (n = 0; n < usage->kblocks->nr_squares[b]; n++) {
+ cube2(usage->kblocks->blocks[b][n], t) = FALSE;
+ }
+ }
+
+ /*
+ * The most trivial kind of solver for killer puzzles: fill
+ * single-square cages.
+ */
+ for (b = 0; b < usage->kblocks->nr_blocks; b++) {
+ int squares = usage->kblocks->nr_squares[b];
+ if (squares == 1) {
+ int v = usage->kclues[b];
+ if (v < 1 || v > cr) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ x = usage->kblocks->blocks[b][0] % cr;
+ y = usage->kblocks->blocks[b][0] / cr;
+ if (!cube(x, y, v)) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ solver_place(usage, x, y, v);
+
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ printf("%*s placing %d at (%d,%d)\n",
+ solver_recurse_depth*4, "killer single-square cage",
+ v, 1 + x%cr, 1 + x/cr);
+ }
+#endif
+ changed = TRUE;
+ }
+ }
+
+ if (changed) {
+ kdiff = max(kdiff, DIFF_KSINGLE);
+ goto cont;
+ }
+ }
+ if (dlev->maxkdiff >= DIFF_KINTERSECT && usage->kclues != NULL) {
+ int changed = FALSE;
+ /*
+ * Now, create the extra_cages information. Every full region
+ * (row, column, or block) has the same sum total (45 for 3x3
+ * puzzles. After we try to cover these regions with cages that
+ * lie entirely within them, any squares that remain must bring
+ * the total to this known value, and so they form additional
+ * cages which aren't immediately evident in the displayed form
+ * of the puzzle.
+ */
+ usage->extra_cages->nr_blocks = 0;
+ for (i = 0; i < 3; i++) {
+ for (n = 0; n < cr; n++) {
+ int *region = usage->regions + cr*n*3 + i*cr;
+ int sum = cr * (cr + 1) / 2;
+ int nsquares = cr;
+ int filtered;
+ int n_extra = usage->extra_cages->nr_blocks;
+ int *extra_list = usage->extra_cages->blocks[n_extra];
+ memcpy(extra_list, region, cr * sizeof *extra_list);
+
+ nsquares = filter_whole_cages(usage, extra_list, nsquares, &filtered);
+ sum -= filtered;
+ if (nsquares == cr || nsquares == 0)
+ continue;
+ if (dlev->maxdiff >= DIFF_RECURSIVE) {
+ if (sum <= 0) {
+ dlev->diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ }
+ assert(sum > 0);
+
+ if (nsquares == 1) {
+ if (sum > cr) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ x = extra_list[0] % cr;
+ y = extra_list[0] / cr;
+ if (!cube(x, y, sum)) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ solver_place(usage, x, y, sum);
+ changed = TRUE;
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ printf("%*s placing %d at (%d,%d)\n",
+ solver_recurse_depth*4, "killer single-square deduced cage",
+ sum, 1 + x, 1 + y);
+ }
+#endif
+ }
+
+ b = usage->kblocks->whichblock[extra_list[0]];
+ for (x = 1; x < nsquares; x++)
+ if (usage->kblocks->whichblock[extra_list[x]] != b)
+ break;
+ if (x == nsquares) {
+ assert(usage->kblocks->nr_squares[b] > nsquares);
+ split_block(usage->kblocks, extra_list, nsquares);
+ assert(usage->kblocks->nr_squares[usage->kblocks->nr_blocks - 1] == nsquares);
+ usage->kclues[usage->kblocks->nr_blocks - 1] = sum;
+ usage->kclues[b] -= sum;
+ } else {
+ usage->extra_cages->nr_squares[n_extra] = nsquares;
+ usage->extra_cages->nr_blocks++;
+ usage->extra_clues[n_extra] = sum;
+ }
+ }
+ }
+ if (changed) {
+ kdiff = max(kdiff, DIFF_KINTERSECT);
+ goto cont;
+ }
+ }
+
+ /*
+ * Another simple killer-type elimination. For every square in a
+ * cage, find the minimum and maximum possible sums of all the
+ * other squares in the same cage, and rule out possibilities
+ * for the given square based on whether they are guaranteed to
+ * cause the sum to be either too high or too low.
+ * This is a special case of trying all possible sums across a
+ * region, which is a recursive algorithm. We should probably
+ * implement it for a higher difficulty level.
+ */
+ if (dlev->maxkdiff >= DIFF_KMINMAX && usage->kclues != NULL) {
+ int changed = FALSE;
+ for (b = 0; b < usage->kblocks->nr_blocks; b++) {
+ int ret = solver_killer_minmax(usage, usage->kblocks,
+ usage->kclues, b
+#ifdef STANDALONE_SOLVER
+ , ""
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0)
+ changed = TRUE;
+ }
+ for (b = 0; b < usage->extra_cages->nr_blocks; b++) {
+ int ret = solver_killer_minmax(usage, usage->extra_cages,
+ usage->extra_clues, b
+#ifdef STANDALONE_SOLVER
+ , "using deduced cages"
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0)
+ changed = TRUE;
+ }
+ if (changed) {
+ kdiff = max(kdiff, DIFF_KMINMAX);
+ goto cont;
+ }
+ }
+
+ /*
+ * Try to use knowledge of which numbers can be used to generate
+ * a given sum.
+ * This can only be used if a cage lies entirely within a region.
+ */
+ if (dlev->maxkdiff >= DIFF_KSUMS && usage->kclues != NULL) {
+ int changed = FALSE;
+
+ for (b = 0; b < usage->kblocks->nr_blocks; b++) {
+ int ret = solver_killer_sums(usage, b, usage->kblocks,
+ usage->kclues[b], TRUE
+#ifdef STANDALONE_SOLVER
+ , "regular clues"
+#endif
+ );
+ if (ret > 0) {
+ changed = TRUE;
+ kdiff = max(kdiff, DIFF_KSUMS);
+ } else if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ }
+
+ for (b = 0; b < usage->extra_cages->nr_blocks; b++) {
+ int ret = solver_killer_sums(usage, b, usage->extra_cages,
+ usage->extra_clues[b], FALSE
+#ifdef STANDALONE_SOLVER
+ , "deduced clues"
+#endif
+ );
+ if (ret > 0) {
+ changed = TRUE;
+ kdiff = max(kdiff, DIFF_KSUMS);
+ } else if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ }
+ }
+
+ if (changed)
+ goto cont;
+ }
+
+ if (dlev->maxdiff <= DIFF_BLOCK)
+ break;
+
+ /*
+ * Row-wise positional elimination.
+ */
+ for (y = 0; y < cr; y++)
+ for (n = 1; n <= cr; n++)
+ if (!usage->row[y*cr+n-1]) {
+ for (x = 0; x < cr; x++)
+ scratch->indexlist[x] = cubepos(x, y, n);
+ ret = solver_elim(usage, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "positional elimination,"
+ " %d in row %d", n, 1+y
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SIMPLE);
+ goto cont;
+ }
+ }
+ /*
+ * Column-wise positional elimination.
+ */
+ for (x = 0; x < cr; x++)
+ for (n = 1; n <= cr; n++)
+ if (!usage->col[x*cr+n-1]) {
+ for (y = 0; y < cr; y++)
+ scratch->indexlist[y] = cubepos(x, y, n);
+ ret = solver_elim(usage, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "positional elimination,"
+ " %d in column %d", n, 1+x
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SIMPLE);
+ goto cont;
+ }
+ }
+
+ /*
+ * X-diagonal positional elimination.
+ */
+ if (usage->diag) {
+ for (n = 1; n <= cr; n++)
+ if (!usage->diag[n-1]) {
+ for (i = 0; i < cr; i++)
+ scratch->indexlist[i] = cubepos2(diag0(i), n);
+ ret = solver_elim(usage, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "positional elimination,"
+ " %d in \\-diagonal", n
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SIMPLE);
+ goto cont;
+ }
+ }
+ for (n = 1; n <= cr; n++)
+ if (!usage->diag[cr+n-1]) {
+ for (i = 0; i < cr; i++)
+ scratch->indexlist[i] = cubepos2(diag1(i), n);
+ ret = solver_elim(usage, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "positional elimination,"
+ " %d in /-diagonal", n
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SIMPLE);
+ goto cont;
+ }
+ }
+ }
+
+ /*
+ * Numeric elimination.
+ */
+ for (x = 0; x < cr; x++)
+ for (y = 0; y < cr; y++)
+ if (!usage->grid[y*cr+x]) {
+ for (n = 1; n <= cr; n++)
+ scratch->indexlist[n-1] = cubepos(x, y, n);
+ ret = solver_elim(usage, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "numeric elimination at (%d,%d)",
+ 1+x, 1+y
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SIMPLE);
+ goto cont;
+ }
+ }
+
+ if (dlev->maxdiff <= DIFF_SIMPLE)
+ break;
+
+ /*
+ * Intersectional analysis, rows vs blocks.
+ */
+ for (y = 0; y < cr; y++)
+ for (b = 0; b < cr; b++)
+ for (n = 1; n <= cr; n++) {
+ if (usage->row[y*cr+n-1] ||
+ usage->blk[b*cr+n-1])
+ continue;
+ for (i = 0; i < cr; i++) {
+ scratch->indexlist[i] = cubepos(i, y, n);
+ scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
+ }
+ /*
+ * solver_intersect() never returns -1.
+ */
+ if (solver_intersect(usage, scratch->indexlist,
+ scratch->indexlist2
+#ifdef STANDALONE_SOLVER
+ , "intersectional analysis,"
+ " %d in row %d vs block %s",
+ n, 1+y, usage->blocks->blocknames[b]
+#endif
+ ) ||
+ solver_intersect(usage, scratch->indexlist2,
+ scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "intersectional analysis,"
+ " %d in block %s vs row %d",
+ n, usage->blocks->blocknames[b], 1+y
+#endif
+ )) {
+ diff = max(diff, DIFF_INTERSECT);
+ goto cont;
+ }
+ }
+
+ /*
+ * Intersectional analysis, columns vs blocks.
+ */
+ for (x = 0; x < cr; x++)
+ for (b = 0; b < cr; b++)
+ for (n = 1; n <= cr; n++) {
+ if (usage->col[x*cr+n-1] ||
+ usage->blk[b*cr+n-1])
+ continue;
+ for (i = 0; i < cr; i++) {
+ scratch->indexlist[i] = cubepos(x, i, n);
+ scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
+ }
+ if (solver_intersect(usage, scratch->indexlist,
+ scratch->indexlist2
+#ifdef STANDALONE_SOLVER
+ , "intersectional analysis,"
+ " %d in column %d vs block %s",
+ n, 1+x, usage->blocks->blocknames[b]
+#endif
+ ) ||
+ solver_intersect(usage, scratch->indexlist2,
+ scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "intersectional analysis,"
+ " %d in block %s vs column %d",
+ n, usage->blocks->blocknames[b], 1+x
+#endif
+ )) {
+ diff = max(diff, DIFF_INTERSECT);
+ goto cont;
+ }
+ }
+
+ if (usage->diag) {
+ /*
+ * Intersectional analysis, \-diagonal vs blocks.
+ */
+ for (b = 0; b < cr; b++)
+ for (n = 1; n <= cr; n++) {
+ if (usage->diag[n-1] ||
+ usage->blk[b*cr+n-1])
+ continue;
+ for (i = 0; i < cr; i++) {
+ scratch->indexlist[i] = cubepos2(diag0(i), n);
+ scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
+ }
+ if (solver_intersect(usage, scratch->indexlist,
+ scratch->indexlist2
+#ifdef STANDALONE_SOLVER
+ , "intersectional analysis,"
+ " %d in \\-diagonal vs block %s",
+ n, usage->blocks->blocknames[b]
+#endif
+ ) ||
+ solver_intersect(usage, scratch->indexlist2,
+ scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "intersectional analysis,"
+ " %d in block %s vs \\-diagonal",
+ n, usage->blocks->blocknames[b]
+#endif
+ )) {
+ diff = max(diff, DIFF_INTERSECT);
+ goto cont;
+ }
+ }
+
+ /*
+ * Intersectional analysis, /-diagonal vs blocks.
+ */
+ for (b = 0; b < cr; b++)
+ for (n = 1; n <= cr; n++) {
+ if (usage->diag[cr+n-1] ||
+ usage->blk[b*cr+n-1])
+ continue;
+ for (i = 0; i < cr; i++) {
+ scratch->indexlist[i] = cubepos2(diag1(i), n);
+ scratch->indexlist2[i] = cubepos2(usage->blocks->blocks[b][i], n);
+ }
+ if (solver_intersect(usage, scratch->indexlist,
+ scratch->indexlist2
+#ifdef STANDALONE_SOLVER
+ , "intersectional analysis,"
+ " %d in /-diagonal vs block %s",
+ n, usage->blocks->blocknames[b]
+#endif
+ ) ||
+ solver_intersect(usage, scratch->indexlist2,
+ scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "intersectional analysis,"
+ " %d in block %s vs /-diagonal",
+ n, usage->blocks->blocknames[b]
+#endif
+ )) {
+ diff = max(diff, DIFF_INTERSECT);
+ goto cont;
+ }
+ }
+ }
+
+ if (dlev->maxdiff <= DIFF_INTERSECT)
+ break;
+
+ /*
+ * Blockwise set elimination.
+ */
+ for (b = 0; b < cr; b++) {
+ for (i = 0; i < cr; i++)
+ for (n = 1; n <= cr; n++)
+ scratch->indexlist[i*cr+n-1] = cubepos2(usage->blocks->blocks[b][i], n);
+ ret = solver_set(usage, scratch, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "set elimination, block %s",
+ usage->blocks->blocknames[b]
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SET);
+ goto cont;
+ }
+ }
+
+ /*
+ * Row-wise set elimination.
+ */
+ for (y = 0; y < cr; y++) {
+ for (x = 0; x < cr; x++)
+ for (n = 1; n <= cr; n++)
+ scratch->indexlist[x*cr+n-1] = cubepos(x, y, n);
+ ret = solver_set(usage, scratch, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "set elimination, row %d", 1+y
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SET);
+ goto cont;
+ }
+ }
+
+ /*
+ * Column-wise set elimination.
+ */
+ for (x = 0; x < cr; x++) {
+ for (y = 0; y < cr; y++)
+ for (n = 1; n <= cr; n++)
+ scratch->indexlist[y*cr+n-1] = cubepos(x, y, n);
+ ret = solver_set(usage, scratch, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "set elimination, column %d", 1+x
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SET);
+ goto cont;
+ }
+ }
+
+ if (usage->diag) {
+ /*
+ * \-diagonal set elimination.
+ */
+ for (i = 0; i < cr; i++)
+ for (n = 1; n <= cr; n++)
+ scratch->indexlist[i*cr+n-1] = cubepos2(diag0(i), n);
+ ret = solver_set(usage, scratch, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "set elimination, \\-diagonal"
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SET);
+ goto cont;
+ }
+
+ /*
+ * /-diagonal set elimination.
+ */
+ for (i = 0; i < cr; i++)
+ for (n = 1; n <= cr; n++)
+ scratch->indexlist[i*cr+n-1] = cubepos2(diag1(i), n);
+ ret = solver_set(usage, scratch, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "set elimination, /-diagonal"
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_SET);
+ goto cont;
+ }
+ }
+
+ if (dlev->maxdiff <= DIFF_SET)
+ break;
+
+ /*
+ * Row-vs-column set elimination on a single number.
+ */
+ for (n = 1; n <= cr; n++) {
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++)
+ scratch->indexlist[y*cr+x] = cubepos(x, y, n);
+ ret = solver_set(usage, scratch, scratch->indexlist
+#ifdef STANDALONE_SOLVER
+ , "positional set elimination, number %d", n
+#endif
+ );
+ if (ret < 0) {
+ diff = DIFF_IMPOSSIBLE;
+ goto got_result;
+ } else if (ret > 0) {
+ diff = max(diff, DIFF_EXTREME);
+ goto cont;
+ }
+ }
+
+ /*
+ * Forcing chains.
+ */
+ if (solver_forcing(usage, scratch)) {
+ diff = max(diff, DIFF_EXTREME);
+ goto cont;
+ }
+
+ /*
+ * If we reach here, we have made no deductions in this
+ * iteration, so the algorithm terminates.
+ */
+ break;
+ }
+
+ /*
+ * Last chance: if we haven't fully solved the puzzle yet, try
+ * recursing based on guesses for a particular square. We pick
+ * one of the most constrained empty squares we can find, which
+ * has the effect of pruning the search tree as much as
+ * possible.
+ */
+ if (dlev->maxdiff >= DIFF_RECURSIVE) {
+ int best, bestcount;
+
+ best = -1;
+ bestcount = cr+1;
+
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++)
+ if (!grid[y*cr+x]) {
+ int count;
+
+ /*
+ * An unfilled square. Count the number of
+ * possible digits in it.
+ */
+ count = 0;
+ for (n = 1; n <= cr; n++)
+ if (cube(x,y,n))
+ count++;
+
+ /*
+ * We should have found any impossibilities
+ * already, so this can safely be an assert.
+ */
+ assert(count > 1);
+
+ if (count < bestcount) {
+ bestcount = count;
+ best = y*cr+x;
+ }
+ }
+
+ if (best != -1) {
+ int i, j;
+ digit *list, *ingrid, *outgrid;
+
+ diff = DIFF_IMPOSSIBLE; /* no solution found yet */
+
+ /*
+ * Attempt recursion.
+ */
+ y = best / cr;
+ x = best % cr;
+
+ list = snewn(cr, digit);
+ ingrid = snewn(cr * cr, digit);
+ outgrid = snewn(cr * cr, digit);
+ memcpy(ingrid, grid, cr * cr);
+
+ /* Make a list of the possible digits. */
+ for (j = 0, n = 1; n <= cr; n++)
+ if (cube(x,y,n))
+ list[j++] = n;
+
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working) {
+ char *sep = "";
+ printf("%*srecursing on (%d,%d) [",
+ solver_recurse_depth*4, "", x + 1, y + 1);
+ for (i = 0; i < j; i++) {
+ printf("%s%d", sep, list[i]);
+ sep = " or ";
+ }
+ printf("]\n");
+ }
+#endif
+
+ /*
+ * And step along the list, recursing back into the
+ * main solver at every stage.
+ */
+ for (i = 0; i < j; i++) {
+ memcpy(outgrid, ingrid, cr * cr);
+ outgrid[y*cr+x] = list[i];
+
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working)
+ printf("%*sguessing %d at (%d,%d)\n",
+ solver_recurse_depth*4, "", list[i], x + 1, y + 1);
+ solver_recurse_depth++;
+#endif
+
+ solver(cr, blocks, kblocks, xtype, outgrid, kgrid, dlev);
+
+#ifdef STANDALONE_SOLVER
+ solver_recurse_depth--;
+ if (solver_show_working) {
+ printf("%*sretracting %d at (%d,%d)\n",
+ solver_recurse_depth*4, "", list[i], x + 1, y + 1);
+ }
+#endif
+
+ /*
+ * If we have our first solution, copy it into the
+ * grid we will return.
+ */
+ if (diff == DIFF_IMPOSSIBLE && dlev->diff != DIFF_IMPOSSIBLE)
+ memcpy(grid, outgrid, cr*cr);
+
+ if (dlev->diff == DIFF_AMBIGUOUS)
+ diff = DIFF_AMBIGUOUS;
+ else if (dlev->diff == DIFF_IMPOSSIBLE)
+ /* do not change our return value */;
+ else {
+ /* the recursion turned up exactly one solution */
+ if (diff == DIFF_IMPOSSIBLE)
+ diff = DIFF_RECURSIVE;
+ else
+ diff = DIFF_AMBIGUOUS;
+ }
+
+ /*
+ * As soon as we've found more than one solution,
+ * give up immediately.
+ */
+ if (diff == DIFF_AMBIGUOUS)
+ break;
+ }
+
+ sfree(outgrid);
+ sfree(ingrid);
+ sfree(list);
+ }
+
+ } else {
+ /*
+ * We're forbidden to use recursion, so we just see whether
+ * our grid is fully solved, and return DIFF_IMPOSSIBLE
+ * otherwise.
+ */
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++)
+ if (!grid[y*cr+x])
+ diff = DIFF_IMPOSSIBLE;
+ }
+
+ got_result:
+ dlev->diff = diff;
+ dlev->kdiff = kdiff;
+
+#ifdef STANDALONE_SOLVER
+ if (solver_show_working)
+ printf("%*s%s found\n",
+ solver_recurse_depth*4, "",
+ diff == DIFF_IMPOSSIBLE ? "no solution" :
+ diff == DIFF_AMBIGUOUS ? "multiple solutions" :
+ "one solution");
+#endif
+
+ sfree(usage->sq2region);
+ sfree(usage->regions);
+ sfree(usage->cube);
+ sfree(usage->row);
+ sfree(usage->col);
+ sfree(usage->blk);
+ if (usage->kblocks) {
+ free_block_structure(usage->kblocks);
+ free_block_structure(usage->extra_cages);
+ sfree(usage->extra_clues);
+ }
+ if (usage->kclues) sfree(usage->kclues);
+ sfree(usage);
+
+ solver_free_scratch(scratch);
+}
+
+/* ----------------------------------------------------------------------
+ * End of solver code.
+ */
+
+/* ----------------------------------------------------------------------
+ * Killer set generator.
+ */
+
+/* ----------------------------------------------------------------------
+ * Solo filled-grid generator.
+ *
+ * This grid generator works by essentially trying to solve a grid
+ * starting from no clues, and not worrying that there's more than
+ * one possible solution. Unfortunately, it isn't computationally
+ * feasible to do this by calling the above solver with an empty
+ * grid, because that one needs to allocate a lot of scratch space
+ * at every recursion level. Instead, I have a much simpler
+ * algorithm which I shamelessly copied from a Python solver
+ * written by Andrew Wilkinson (which is GPLed, but I've reused
+ * only ideas and no code). It mostly just does the obvious
+ * recursive thing: pick an empty square, put one of the possible
+ * digits in it, recurse until all squares are filled, backtrack
+ * and change some choices if necessary.
+ *
+ * The clever bit is that every time it chooses which square to
+ * fill in next, it does so by counting the number of _possible_
+ * numbers that can go in each square, and it prioritises so that
+ * it picks a square with the _lowest_ number of possibilities. The
+ * idea is that filling in lots of the obvious bits (particularly
+ * any squares with only one possibility) will cut down on the list
+ * of possibilities for other squares and hence reduce the enormous
+ * search space as much as possible as early as possible.
+ *
+ * The use of bit sets implies that we support puzzles up to a size of
+ * 32x32 (less if anyone finds a 16-bit machine to compile this on).
+ */
+
+/*
+ * Internal data structure used in gridgen to keep track of
+ * progress.
+ */
+struct gridgen_coord { int x, y, r; };
+struct gridgen_usage {
+ int cr;
+ struct block_structure *blocks, *kblocks;
+ /* grid is a copy of the input grid, modified as we go along */
+ digit *grid;
+ /*
+ * Bitsets. In each of them, bit n is set if digit n has been placed
+ * in the corresponding region. row, col and blk are used for all
+ * puzzles. cge is used only for killer puzzles, and diag is used
+ * only for x-type puzzles.
+ * All of these have cr entries, except diag which only has 2,
+ * and cge, which has as many entries as kblocks.
+ */
+ unsigned int *row, *col, *blk, *cge, *diag;
+ /* This lists all the empty spaces remaining in the grid. */
+ struct gridgen_coord *spaces;
+ int nspaces;
+ /* If we need randomisation in the solve, this is our random state. */
+ random_state *rs;
+};
+
+static void gridgen_place(struct gridgen_usage *usage, int x, int y, digit n)
+{
+ unsigned int bit = 1 << n;
+ int cr = usage->cr;
+ usage->row[y] |= bit;
+ usage->col[x] |= bit;
+ usage->blk[usage->blocks->whichblock[y*cr+x]] |= bit;
+ if (usage->cge)
+ usage->cge[usage->kblocks->whichblock[y*cr+x]] |= bit;
+ if (usage->diag) {
+ if (ondiag0(y*cr+x))
+ usage->diag[0] |= bit;
+ if (ondiag1(y*cr+x))
+ usage->diag[1] |= bit;
+ }
+ usage->grid[y*cr+x] = n;
+}
+
+static void gridgen_remove(struct gridgen_usage *usage, int x, int y, digit n)
+{
+ unsigned int mask = ~(1 << n);
+ int cr = usage->cr;
+ usage->row[y] &= mask;
+ usage->col[x] &= mask;
+ usage->blk[usage->blocks->whichblock[y*cr+x]] &= mask;
+ if (usage->cge)
+ usage->cge[usage->kblocks->whichblock[y*cr+x]] &= mask;
+ if (usage->diag) {
+ if (ondiag0(y*cr+x))
+ usage->diag[0] &= mask;
+ if (ondiag1(y*cr+x))
+ usage->diag[1] &= mask;
+ }
+ usage->grid[y*cr+x] = 0;
+}
+
+#define N_SINGLE 32
+
+/*
+ * The real recursive step in the generating function.
+ *
+ * Return values: 1 means solution found, 0 means no solution
+ * found on this branch.
+ */
+static int gridgen_real(struct gridgen_usage *usage, digit *grid, int *steps)
+{
+ int cr = usage->cr;
+ int i, j, n, sx, sy, bestm, bestr, ret;
+ int *digits;
+ unsigned int used;
+
+ /*
+ * Firstly, check for completion! If there are no spaces left
+ * in the grid, we have a solution.
+ */
+ if (usage->nspaces == 0)
+ return TRUE;
+
+ /*
+ * Next, abandon generation if we went over our steps limit.
+ */
+ if (*steps <= 0)
+ return FALSE;
+ (*steps)--;
+
+ /*
+ * Otherwise, there must be at least one space. Find the most
+ * constrained space, using the `r' field as a tie-breaker.
+ */
+ bestm = cr+1; /* so that any space will beat it */
+ bestr = 0;
+ used = ~0;
+ i = sx = sy = -1;
+ for (j = 0; j < usage->nspaces; j++) {
+ int x = usage->spaces[j].x, y = usage->spaces[j].y;
+ unsigned int used_xy;
+ int m;
+
+ m = usage->blocks->whichblock[y*cr+x];
+ used_xy = usage->row[y] | usage->col[x] | usage->blk[m];
+ if (usage->cge != NULL)
+ used_xy |= usage->cge[usage->kblocks->whichblock[y*cr+x]];
+ if (usage->cge != NULL)
+ used_xy |= usage->cge[usage->kblocks->whichblock[y*cr+x]];
+ if (usage->diag != NULL) {
+ if (ondiag0(y*cr+x))
+ used_xy |= usage->diag[0];
+ if (ondiag1(y*cr+x))
+ used_xy |= usage->diag[1];
+ }
+
+ /*
+ * Find the number of digits that could go in this space.
+ */
+ m = 0;
+ for (n = 1; n <= cr; n++) {
+ unsigned int bit = 1 << n;
+ if ((used_xy & bit) == 0)
+ m++;
+ }
+ if (m < bestm || (m == bestm && usage->spaces[j].r < bestr)) {
+ bestm = m;
+ bestr = usage->spaces[j].r;
+ sx = x;
+ sy = y;
+ i = j;
+ used = used_xy;
+ }
+ }
+
+ /*
+ * Swap that square into the final place in the spaces array,
+ * so that decrementing nspaces will remove it from the list.
+ */
+ if (i != usage->nspaces-1) {
+ struct gridgen_coord t;
+ t = usage->spaces[usage->nspaces-1];
+ usage->spaces[usage->nspaces-1] = usage->spaces[i];
+ usage->spaces[i] = t;
+ }
+
+ /*
+ * Now we've decided which square to start our recursion at,
+ * simply go through all possible values, shuffling them
+ * randomly first if necessary.
+ */
+ digits = snewn(bestm, int);
+
+ j = 0;
+ for (n = 1; n <= cr; n++) {
+ unsigned int bit = 1 << n;
+
+ if ((used & bit) == 0)
+ digits[j++] = n;
+ }
+
+ if (usage->rs)
+ shuffle(digits, j, sizeof(*digits), usage->rs);
+
+ /* And finally, go through the digit list and actually recurse. */
+ ret = FALSE;
+ for (i = 0; i < j; i++) {
+ n = digits[i];
+
+ /* Update the usage structure to reflect the placing of this digit. */
+ gridgen_place(usage, sx, sy, n);
+ usage->nspaces--;
+
+ /* Call the solver recursively. Stop when we find a solution. */
+ if (gridgen_real(usage, grid, steps)) {
+ ret = TRUE;
+ break;
+ }
- nsolve_place(usage, x, y, n);
- return TRUE;
+ /* Revert the usage structure. */
+ gridgen_remove(usage, sx, sy, n);
+ usage->nspaces++;
}
- return FALSE;
+ sfree(digits);
+ return ret;
}
-static int nsolve(int c, int r, digit *grid)
+/*
+ * Entry point to generator. You give it parameters and a starting
+ * grid, which is simply an array of cr*cr digits.
+ */
+static int gridgen(int cr, struct block_structure *blocks,
+ struct block_structure *kblocks, int xtype,
+ digit *grid, random_state *rs, int maxsteps)
{
- struct nsolve_usage *usage;
- int cr = c*r;
- int x, y, n;
+ struct gridgen_usage *usage;
+ int x, y, ret;
/*
- * Set up a usage structure as a clean slate (everything
- * possible).
+ * Clear the grid to start with.
*/
- usage = snew(struct nsolve_usage);
- usage->c = c;
- usage->r = r;
- usage->cr = cr;
- usage->cube = snewn(cr*cr*cr, unsigned char);
- usage->grid = grid; /* write straight back to the input */
- memset(usage->cube, TRUE, cr*cr*cr);
-
- usage->row = snewn(cr * cr, unsigned char);
- usage->col = snewn(cr * cr, unsigned char);
- usage->blk = snewn(cr * cr, unsigned char);
- memset(usage->row, FALSE, cr * cr);
- memset(usage->col, FALSE, cr * cr);
- memset(usage->blk, FALSE, cr * cr);
+ memset(grid, 0, cr*cr);
/*
- * Place all the clue numbers we are given.
+ * Create a gridgen_usage structure.
*/
- for (x = 0; x < cr; x++)
- for (y = 0; y < cr; y++)
- if (grid[y*cr+x])
- nsolve_place(usage, x, YTRANS(y), grid[y*cr+x]);
+ usage = snew(struct gridgen_usage);
+
+ usage->cr = cr;
+ usage->blocks = blocks;
+
+ usage->grid = grid;
+
+ usage->row = snewn(cr, unsigned int);
+ usage->col = snewn(cr, unsigned int);
+ usage->blk = snewn(cr, unsigned int);
+ if (kblocks != NULL) {
+ usage->kblocks = kblocks;
+ usage->cge = snewn(usage->kblocks->nr_blocks, unsigned int);
+ memset(usage->cge, FALSE, kblocks->nr_blocks * sizeof *usage->cge);
+ } else {
+ usage->cge = NULL;
+ }
+
+ memset(usage->row, 0, cr * sizeof *usage->row);
+ memset(usage->col, 0, cr * sizeof *usage->col);
+ memset(usage->blk, 0, cr * sizeof *usage->blk);
+
+ if (xtype) {
+ usage->diag = snewn(2, unsigned int);
+ memset(usage->diag, 0, 2 * sizeof *usage->diag);
+ } else {
+ usage->diag = NULL;
+ }
/*
- * Now loop over the grid repeatedly trying all permitted modes
- * of reasoning. The loop terminates if we complete an
- * iteration without making any progress; we then return
- * failure or success depending on whether the grid is full or
- * not.
+ * Begin by filling in the whole top row with randomly chosen
+ * numbers. This cannot introduce any bias or restriction on
+ * the available grids, since we already know those numbers
+ * are all distinct so all we're doing is choosing their
+ * labels.
*/
- while (1) {
- /*
- * Blockwise positional elimination.
- */
- for (x = 0; x < cr; x += r)
- for (y = 0; y < r; y++)
- for (n = 1; n <= cr; n++)
- if (!usage->blk[(y*c+(x/r))*cr+n-1] &&
- nsolve_elim(usage, cubepos(x,y,n), r*cr))
- continue;
+ for (x = 0; x < cr; x++)
+ grid[x] = x+1;
+ shuffle(grid, cr, sizeof(*grid), rs);
+ for (x = 0; x < cr; x++)
+ gridgen_place(usage, x, 0, grid[x]);
- /*
- * Row-wise positional elimination.
- */
- for (y = 0; y < cr; y++)
- for (n = 1; n <= cr; n++)
- if (!usage->row[y*cr+n-1] &&
- nsolve_elim(usage, cubepos(0,y,n), cr*cr))
- continue;
- /*
- * Column-wise positional elimination.
- */
- for (x = 0; x < cr; x++)
- for (n = 1; n <= cr; n++)
- if (!usage->col[x*cr+n-1] &&
- nsolve_elim(usage, cubepos(x,0,n), cr))
- continue;
+ usage->spaces = snewn(cr * cr, struct gridgen_coord);
+ usage->nspaces = 0;
- /*
- * Numeric elimination.
- */
- for (x = 0; x < cr; x++)
- for (y = 0; y < cr; y++)
- if (!usage->grid[YUNTRANS(y)*cr+x] &&
- nsolve_elim(usage, cubepos(x,y,1), 1))
- continue;
+ usage->rs = rs;
- /*
- * If we reach here, we have made no deductions in this
- * iteration, so the algorithm terminates.
- */
- break;
+ /*
+ * Initialise the list of grid spaces, taking care to leave
+ * out the row I've already filled in above.
+ */
+ for (y = 1; y < cr; y++) {
+ for (x = 0; x < cr; x++) {
+ usage->spaces[usage->nspaces].x = x;
+ usage->spaces[usage->nspaces].y = y;
+ usage->spaces[usage->nspaces].r = random_bits(rs, 31);
+ usage->nspaces++;
+ }
}
- sfree(usage->cube);
- sfree(usage->row);
- sfree(usage->col);
+ /*
+ * Run the real generator function.
+ */
+ ret = gridgen_real(usage, grid, &maxsteps);
+
+ /*
+ * Clean up the usage structure now we have our answer.
+ */
+ sfree(usage->spaces);
+ sfree(usage->cge);
sfree(usage->blk);
+ sfree(usage->col);
+ sfree(usage->row);
sfree(usage);
- for (x = 0; x < cr; x++)
- for (y = 0; y < cr; y++)
- if (!grid[y*cr+x])
- return FALSE;
- return TRUE;
+ return ret;
}
/* ----------------------------------------------------------------------
- * End of non-recursive solver code.
+ * End of grid generator code.
*/
+static int check_killer_cage_sum(struct block_structure *kblocks,
+ digit *kgrid, digit *grid, int blk)
+{
+ /*
+ * Returns: -1 if the cage has any empty square; 0 if all squares
+ * are full but the sum is wrong; +1 if all squares are full and
+ * they have the right sum.
+ *
+ * Does not check uniqueness of numbers within the cage; that's
+ * done elsewhere (because in error highlighting it needs to be
+ * detected separately so as to flag the error in a visually
+ * different way).
+ */
+ int n_squares = kblocks->nr_squares[blk];
+ int sum = 0, clue = 0;
+ int i;
+
+ for (i = 0; i < n_squares; i++) {
+ int xy = kblocks->blocks[blk][i];
+
+ if (grid[xy] == 0)
+ return -1;
+ sum += grid[xy];
+
+ if (kgrid[xy]) {
+ assert(clue == 0);
+ clue = kgrid[xy];
+ }
+ }
+
+ assert(clue != 0);
+ return sum == clue;
+}
+
/*
* Check whether a grid contains a valid complete puzzle.
*/
-static int check_valid(int c, int r, digit *grid)
+static int check_valid(int cr, struct block_structure *blocks,
+ struct block_structure *kblocks,
+ digit *kgrid, int xtype, digit *grid)
{
- int cr = c*r;
unsigned char *used;
- int x, y, n;
+ int x, y, i, j, n;
used = snewn(cr, unsigned char);
/*
* Check that each block contains precisely one of everything.
*/
- for (x = 0; x < cr; x += r) {
- for (y = 0; y < cr; y += c) {
- int xx, yy;
+ for (i = 0; i < cr; i++) {
+ memset(used, FALSE, cr);
+ for (j = 0; j < cr; j++)
+ if (grid[blocks->blocks[i][j]] > 0 &&
+ grid[blocks->blocks[i][j]] <= cr)
+ used[grid[blocks->blocks[i][j]]-1] = TRUE;
+ for (n = 0; n < cr; n++)
+ if (!used[n]) {
+ sfree(used);
+ return FALSE;
+ }
+ }
+
+ /*
+ * Check that each Killer cage, if any, contains at most one of
+ * everything. If we also know the clues for those cages (which we
+ * might not, when this function is called early in puzzle
+ * generation), we also check that they all have the right sum.
+ */
+ if (kblocks) {
+ for (i = 0; i < kblocks->nr_blocks; i++) {
memset(used, FALSE, cr);
- for (xx = x; xx < x+r; xx++)
- for (yy = 0; yy < y+c; yy++)
- if (grid[yy*cr+xx] > 0 && grid[yy*cr+xx] <= cr)
- used[grid[yy*cr+xx]-1] = TRUE;
- for (n = 0; n < cr; n++)
- if (!used[n]) {
- sfree(used);
- return FALSE;
+ for (j = 0; j < kblocks->nr_squares[i]; j++)
+ if (grid[kblocks->blocks[i][j]] > 0 &&
+ grid[kblocks->blocks[i][j]] <= cr) {
+ if (used[grid[kblocks->blocks[i][j]]-1]) {
+ sfree(used);
+ return FALSE;
+ }
+ used[grid[kblocks->blocks[i][j]]-1] = TRUE;
}
+
+ if (kgrid && check_killer_cage_sum(kblocks, kgrid, grid, i) != 1) {
+ sfree(used);
+ return FALSE;
+ }
}
}
+ /*
+ * Check that each diagonal contains precisely one of everything.
+ */
+ if (xtype) {
+ memset(used, FALSE, cr);
+ for (i = 0; i < cr; i++)
+ if (grid[diag0(i)] > 0 && grid[diag0(i)] <= cr)
+ used[grid[diag0(i)]-1] = TRUE;
+ for (n = 0; n < cr; n++)
+ if (!used[n]) {
+ sfree(used);
+ return FALSE;
+ }
+ for (i = 0; i < cr; i++)
+ if (grid[diag1(i)] > 0 && grid[diag1(i)] <= cr)
+ used[grid[diag1(i)]-1] = TRUE;
+ for (n = 0; n < cr; n++)
+ if (!used[n]) {
+ sfree(used);
+ return FALSE;
+ }
+ }
+
sfree(used);
return TRUE;
}
-static void symmetry_limit(game_params *params, int *xlim, int *ylim, int s)
+static int symmetries(const game_params *params, int x, int y,
+ int *output, int s)
{
int c = params->c, r = params->r, cr = c*r;
+ int i = 0;
+
+#define ADD(x,y) (*output++ = (x), *output++ = (y), i++)
+
+ ADD(x, y);
switch (s) {
case SYMM_NONE:
- *xlim = *ylim = cr;
- break;
+ break; /* just x,y is all we need */
case SYMM_ROT2:
- *xlim = (cr+1) / 2;
- *ylim = cr;
- break;
- case SYMM_REF4:
+ ADD(cr - 1 - x, cr - 1 - y);
+ break;
case SYMM_ROT4:
- *xlim = *ylim = (cr+1) / 2;
- break;
+ ADD(cr - 1 - y, x);
+ ADD(y, cr - 1 - x);
+ ADD(cr - 1 - x, cr - 1 - y);
+ break;
+ case SYMM_REF2:
+ ADD(cr - 1 - x, y);
+ break;
+ case SYMM_REF2D:
+ ADD(y, x);
+ break;
+ case SYMM_REF4:
+ ADD(cr - 1 - x, y);
+ ADD(x, cr - 1 - y);
+ ADD(cr - 1 - x, cr - 1 - y);
+ break;
+ case SYMM_REF4D:
+ ADD(y, x);
+ ADD(cr - 1 - x, cr - 1 - y);
+ ADD(cr - 1 - y, cr - 1 - x);
+ break;
+ case SYMM_REF8:
+ ADD(cr - 1 - x, y);
+ ADD(x, cr - 1 - y);
+ ADD(cr - 1 - x, cr - 1 - y);
+ ADD(y, x);
+ ADD(y, cr - 1 - x);
+ ADD(cr - 1 - y, x);
+ ADD(cr - 1 - y, cr - 1 - x);
+ break;
+ }
+
+#undef ADD
+
+ return i;
+}
+
+static char *encode_solve_move(int cr, digit *grid)
+{
+ int i, len;
+ char *ret, *p, *sep;
+
+ /*
+ * It's surprisingly easy to work out _exactly_ how long this
+ * string needs to be. To decimal-encode all the numbers from 1
+ * to n:
+ *
+ * - every number has a units digit; total is n.
+ * - all numbers above 9 have a tens digit; total is max(n-9,0).
+ * - all numbers above 99 have a hundreds digit; total is max(n-99,0).
+ * - and so on.
+ */
+ len = 0;
+ for (i = 1; i <= cr; i *= 10)
+ len += max(cr - i + 1, 0);
+ len += cr; /* don't forget the commas */
+ len *= cr; /* there are cr rows of these */
+
+ /*
+ * Now len is one bigger than the total size of the
+ * comma-separated numbers (because we counted an
+ * additional leading comma). We need to have a leading S
+ * and a trailing NUL, so we're off by one in total.
+ */
+ len++;
+
+ ret = snewn(len, char);
+ p = ret;
+ *p++ = 'S';
+ sep = "";
+ for (i = 0; i < cr*cr; i++) {
+ p += sprintf(p, "%s%d", sep, grid[i]);
+ sep = ",";
+ }
+ *p++ = '\0';
+ assert(p - ret == len);
+
+ return ret;
+}
+
+static void dsf_to_blocks(int *dsf, struct block_structure *blocks,
+ int min_expected, int max_expected)
+{
+ int cr = blocks->c * blocks->r, area = cr * cr;
+ int i, nb = 0;
+
+ for (i = 0; i < area; i++)
+ blocks->whichblock[i] = -1;
+ for (i = 0; i < area; i++) {
+ int j = dsf_canonify(dsf, i);
+ if (blocks->whichblock[j] < 0)
+ blocks->whichblock[j] = nb++;
+ blocks->whichblock[i] = blocks->whichblock[j];
+ }
+ assert(nb >= min_expected && nb <= max_expected);
+ blocks->nr_blocks = nb;
+}
+
+static void make_blocks_from_whichblock(struct block_structure *blocks)
+{
+ int i;
+
+ for (i = 0; i < blocks->nr_blocks; i++) {
+ blocks->blocks[i][blocks->max_nr_squares-1] = 0;
+ blocks->nr_squares[i] = 0;
+ }
+ for (i = 0; i < blocks->area; i++) {
+ int b = blocks->whichblock[i];
+ int j = blocks->blocks[b][blocks->max_nr_squares-1]++;
+ assert(j < blocks->max_nr_squares);
+ blocks->blocks[b][j] = i;
+ blocks->nr_squares[b]++;
+ }
+}
+
+static char *encode_block_structure_desc(char *p, struct block_structure *blocks)
+{
+ int i, currrun = 0;
+ int c = blocks->c, r = blocks->r, cr = c * r;
+
+ /*
+ * Encode the block structure. We do this by encoding
+ * the pattern of dividing lines: first we iterate
+ * over the cr*(cr-1) internal vertical grid lines in
+ * ordinary reading order, then over the cr*(cr-1)
+ * internal horizontal ones in transposed reading
+ * order.
+ *
+ * We encode the number of non-lines between the
+ * lines; _ means zero (two adjacent divisions), a
+ * means 1, ..., y means 25, and z means 25 non-lines
+ * _and no following line_ (so that za means 26, zb 27
+ * etc).
+ */
+ for (i = 0; i <= 2*cr*(cr-1); i++) {
+ int x, y, p0, p1, edge;
+
+ if (i == 2*cr*(cr-1)) {
+ edge = TRUE; /* terminating virtual edge */
+ } else {
+ if (i < cr*(cr-1)) {
+ y = i/(cr-1);
+ x = i%(cr-1);
+ p0 = y*cr+x;
+ p1 = y*cr+x+1;
+ } else {
+ x = i/(cr-1) - cr;
+ y = i%(cr-1);
+ p0 = y*cr+x;
+ p1 = (y+1)*cr+x;
+ }
+ edge = (blocks->whichblock[p0] != blocks->whichblock[p1]);
+ }
+
+ if (edge) {
+ while (currrun > 25)
+ *p++ = 'z', currrun -= 25;
+ if (currrun)
+ *p++ = 'a'-1 + currrun;
+ else
+ *p++ = '_';
+ currrun = 0;
+ } else
+ currrun++;
+ }
+ return p;
+}
+
+static char *encode_grid(char *desc, digit *grid, int area)
+{
+ int run, i;
+ char *p = desc;
+
+ run = 0;
+ for (i = 0; i <= area; i++) {
+ int n = (i < area ? grid[i] : -1);
+
+ if (!n)
+ run++;
+ else {
+ if (run) {
+ while (run > 0) {
+ int c = 'a' - 1 + run;
+ if (run > 26)
+ c = 'z';
+ *p++ = c;
+ run -= c - ('a' - 1);
+ }
+ } else {
+ /*
+ * If there's a number in the very top left or
+ * bottom right, there's no point putting an
+ * unnecessary _ before or after it.
+ */
+ if (p > desc && n > 0)
+ *p++ = '_';
+ }
+ if (n > 0)
+ p += sprintf(p, "%d", n);
+ run = 0;
+ }
}
+ return p;
+}
+
+/*
+ * Conservatively stimate the number of characters required for
+ * encoding a grid of a certain area.
+ */
+static int grid_encode_space (int area)
+{
+ int t, count;
+ for (count = 1, t = area; t > 26; t -= 26)
+ count++;
+ return count * area;
+}
+
+/*
+ * Conservatively stimate the number of characters required for
+ * encoding a given blocks structure.
+ */
+static int blocks_encode_space(struct block_structure *blocks)
+{
+ int cr = blocks->c * blocks->r, area = cr * cr;
+ return grid_encode_space(area);
}
-static int symmetries(game_params *params, int x, int y, int *output, int s)
+static char *encode_puzzle_desc(const game_params *params, digit *grid,
+ struct block_structure *blocks,
+ digit *kgrid,
+ struct block_structure *kblocks)
{
int c = params->c, r = params->r, cr = c*r;
- int i = 0;
+ int area = cr*cr;
+ char *p, *desc;
+ int space;
+
+ space = grid_encode_space(area) + 1;
+ if (r == 1)
+ space += blocks_encode_space(blocks) + 1;
+ if (params->killer) {
+ space += blocks_encode_space(kblocks) + 1;
+ space += grid_encode_space(area) + 1;
+ }
+ desc = snewn(space, char);
+ p = encode_grid(desc, grid, area);
- *output++ = x;
- *output++ = y;
- i++;
+ if (r == 1) {
+ *p++ = ',';
+ p = encode_block_structure_desc(p, blocks);
+ }
+ if (params->killer) {
+ *p++ = ',';
+ p = encode_block_structure_desc(p, kblocks);
+ *p++ = ',';
+ p = encode_grid(p, kgrid, area);
+ }
+ assert(p - desc < space);
+ *p++ = '\0';
+ desc = sresize(desc, p - desc, char);
- switch (s) {
- case SYMM_NONE:
- break; /* just x,y is all we need */
- case SYMM_REF4:
- case SYMM_ROT4:
- switch (s) {
- case SYMM_REF4:
- *output++ = cr - 1 - x;
- *output++ = y;
- i++;
-
- *output++ = x;
- *output++ = cr - 1 - y;
- i++;
- break;
- case SYMM_ROT4:
- *output++ = cr - 1 - y;
- *output++ = x;
- i++;
-
- *output++ = y;
- *output++ = cr - 1 - x;
- i++;
- break;
+ return desc;
+}
+
+static void merge_blocks(struct block_structure *b, int n1, int n2)
+{
+ int i;
+ /* Move data towards the lower block number. */
+ if (n2 < n1) {
+ int t = n2;
+ n2 = n1;
+ n1 = t;
+ }
+
+ /* Merge n2 into n1, and move the last block into n2's position. */
+ for (i = 0; i < b->nr_squares[n2]; i++)
+ b->whichblock[b->blocks[n2][i]] = n1;
+ memcpy(b->blocks[n1] + b->nr_squares[n1], b->blocks[n2],
+ b->nr_squares[n2] * sizeof **b->blocks);
+ b->nr_squares[n1] += b->nr_squares[n2];
+
+ n1 = b->nr_blocks - 1;
+ if (n2 != n1) {
+ memcpy(b->blocks[n2], b->blocks[n1],
+ b->nr_squares[n1] * sizeof **b->blocks);
+ for (i = 0; i < b->nr_squares[n1]; i++)
+ b->whichblock[b->blocks[n1][i]] = n2;
+ b->nr_squares[n2] = b->nr_squares[n1];
+ }
+ b->nr_blocks = n1;
+}
+
+static int merge_some_cages(struct block_structure *b, int cr, int area,
+ digit *grid, random_state *rs)
+{
+ /*
+ * Make a list of all the pairs of adjacent blocks.
+ */
+ int i, j, k;
+ struct pair {
+ int b1, b2;
+ } *pairs;
+ int npairs;
+
+ pairs = snewn(b->nr_blocks * b->nr_blocks, struct pair);
+ npairs = 0;
+
+ for (i = 0; i < b->nr_blocks; i++) {
+ for (j = i+1; j < b->nr_blocks; j++) {
+
+ /*
+ * Rule the merger out of consideration if it's
+ * obviously not viable.
+ */
+ if (b->nr_squares[i] + b->nr_squares[j] > b->max_nr_squares)
+ continue; /* we couldn't merge these anyway */
+
+ /*
+ * See if these two blocks have a pair of squares
+ * adjacent to each other.
+ */
+ for (k = 0; k < b->nr_squares[i]; k++) {
+ int xy = b->blocks[i][k];
+ int y = xy / cr, x = xy % cr;
+ if ((y > 0 && b->whichblock[xy - cr] == j) ||
+ (y+1 < cr && b->whichblock[xy + cr] == j) ||
+ (x > 0 && b->whichblock[xy - 1] == j) ||
+ (x+1 < cr && b->whichblock[xy + 1] == j)) {
+ /*
+ * Yes! Add this pair to our list.
+ */
+ pairs[npairs].b1 = i;
+ pairs[npairs].b2 = j;
+ break;
+ }
+ }
+ }
+ }
+
+ /*
+ * Now go through that list in random order until we find a pair
+ * of blocks we can merge.
+ */
+ while (npairs > 0) {
+ int n1, n2;
+ unsigned int digits_found;
+
+ /*
+ * Pick a random pair, and remove it from the list.
+ */
+ i = random_upto(rs, npairs);
+ n1 = pairs[i].b1;
+ n2 = pairs[i].b2;
+ if (i != npairs-1)
+ pairs[i] = pairs[npairs-1];
+ npairs--;
+
+ /* Guarantee that the merged cage would still be a region. */
+ digits_found = 0;
+ for (i = 0; i < b->nr_squares[n1]; i++)
+ digits_found |= 1 << grid[b->blocks[n1][i]];
+ for (i = 0; i < b->nr_squares[n2]; i++)
+ if (digits_found & (1 << grid[b->blocks[n2][i]]))
+ break;
+ if (i != b->nr_squares[n2])
+ continue;
+
+ /*
+ * Got one! Do the merge.
+ */
+ merge_blocks(b, n1, n2);
+ sfree(pairs);
+ return TRUE;
+ }
+
+ sfree(pairs);
+ return FALSE;
+}
+
+static void compute_kclues(struct block_structure *cages, digit *kclues,
+ digit *grid, int area)
+{
+ int i;
+ memset(kclues, 0, area * sizeof *kclues);
+ for (i = 0; i < cages->nr_blocks; i++) {
+ int j, sum = 0;
+ for (j = 0; j < area; j++)
+ if (cages->whichblock[j] == i)
+ sum += grid[j];
+ for (j = 0; j < area; j++)
+ if (cages->whichblock[j] == i)
+ break;
+ assert (j != area);
+ kclues[j] = sum;
+ }
+}
+
+static struct block_structure *gen_killer_cages(int cr, random_state *rs,
+ int remove_singletons)
+{
+ int nr;
+ int x, y, area = cr * cr;
+ int n_singletons = 0;
+ struct block_structure *b = alloc_block_structure (1, cr, area, cr, area);
+
+ for (x = 0; x < area; x++)
+ b->whichblock[x] = -1;
+ nr = 0;
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++) {
+ int rnd;
+ int xy = y*cr+x;
+ if (b->whichblock[xy] != -1)
+ continue;
+ b->whichblock[xy] = nr;
+
+ rnd = random_bits(rs, 4);
+ if (xy + 1 < area && (rnd >= 4 || (!remove_singletons && rnd >= 1))) {
+ int xy2 = xy + 1;
+ if (x + 1 == cr || b->whichblock[xy2] != -1 ||
+ (xy + cr < area && random_bits(rs, 1) == 0))
+ xy2 = xy + cr;
+ if (xy2 >= area)
+ n_singletons++;
+ else
+ b->whichblock[xy2] = nr;
+ } else
+ n_singletons++;
+ nr++;
}
- /* fall through */
- case SYMM_ROT2:
- *output++ = cr - 1 - x;
- *output++ = cr - 1 - y;
- i++;
- break;
- }
- return i;
+ b->nr_blocks = nr;
+ make_blocks_from_whichblock(b);
+
+ for (x = y = 0; x < b->nr_blocks; x++)
+ if (b->nr_squares[x] == 1)
+ y++;
+ assert(y == n_singletons);
+
+ if (n_singletons > 0 && remove_singletons) {
+ int n;
+ for (n = 0; n < b->nr_blocks;) {
+ int xy, x, y, xy2, other;
+ if (b->nr_squares[n] > 1) {
+ n++;
+ continue;
+ }
+ xy = b->blocks[n][0];
+ x = xy % cr;
+ y = xy / cr;
+ if (xy + 1 == area)
+ xy2 = xy - 1;
+ else if (x + 1 < cr && (y + 1 == cr || random_bits(rs, 1) == 0))
+ xy2 = xy + 1;
+ else
+ xy2 = xy + cr;
+ other = b->whichblock[xy2];
+
+ if (b->nr_squares[other] == 1)
+ n_singletons--;
+ n_singletons--;
+ merge_blocks(b, n, other);
+ if (n < other)
+ n++;
+ }
+ assert(n_singletons == 0);
+ }
+ return b;
}
-static char *new_game_seed(game_params *params, random_state *rs)
+static char *new_game_desc(const game_params *params, random_state *rs,
+ char **aux, int interactive)
{
int c = params->c, r = params->r, cr = c*r;
int area = cr*cr;
- digit *grid, *grid2;
+ struct block_structure *blocks, *kblocks;
+ digit *grid, *grid2, *kgrid;
struct xy { int x, y; } *locs;
int nlocs;
- int ret;
- char *seed;
+ char *desc;
int coords[16], ncoords;
- int xlim, ylim;
+ int x, y, i, j;
+ struct difficulty dlev;
+
+ precompute_sum_bits();
/*
- * Start the recursive solver with an empty grid to generate a
- * random solved state.
+ * Adjust the maximum difficulty level to be consistent with
+ * the puzzle size: all 2x2 puzzles appear to be Trivial
+ * (DIFF_BLOCK) so we cannot hold out for even a Basic
+ * (DIFF_SIMPLE) one.
*/
+ dlev.maxdiff = params->diff;
+ dlev.maxkdiff = params->kdiff;
+ if (c == 2 && r == 2)
+ dlev.maxdiff = DIFF_BLOCK;
+
grid = snewn(area, digit);
- memset(grid, 0, area);
- ret = rsolve(c, r, grid, rs, 1);
- assert(ret == 1);
- assert(check_valid(c, r, grid));
-
-#ifdef DEBUG
- memcpy(grid,
- "\x0\x1\x0\x0\x6\x0\x0\x0\x0"
- "\x5\x0\x0\x7\x0\x4\x0\x2\x0"
- "\x0\x0\x6\x1\x0\x0\x0\x0\x0"
- "\x8\x9\x7\x0\x0\x0\x0\x0\x0"
- "\x0\x0\x3\x0\x4\x0\x9\x0\x0"
- "\x0\x0\x0\x0\x0\x0\x8\x7\x6"
- "\x0\x0\x0\x0\x0\x9\x1\x0\x0"
- "\x0\x3\x0\x6\x0\x5\x0\x0\x7"
- "\x0\x0\x0\x0\x8\x0\x0\x5\x0"
- , area);
+ locs = snewn(area, struct xy);
+ grid2 = snewn(area, digit);
- {
- int y, x;
- for (y = 0; y < cr; y++) {
- for (x = 0; x < cr; x++) {
- printf("%2.0d", grid[y*cr+x]);
- }
- printf("\n");
- }
- printf("\n");
- }
+ blocks = alloc_block_structure (c, r, area, cr, cr);
- nsolve(c, r, grid);
+ kblocks = NULL;
+ kgrid = (params->killer) ? snewn(area, digit) : NULL;
- {
- int y, x;
- for (y = 0; y < cr; y++) {
- for (x = 0; x < cr; x++) {
- printf("%2.0d", grid[y*cr+x]);
- }
- printf("\n");
- }
- printf("\n");
- }
+#ifdef STANDALONE_SOLVER
+ assert(!"This should never happen, so we don't need to create blocknames");
#endif
/*
- * Now we have a solved grid, start removing things from it
- * while preserving solubility.
+ * Loop until we get a grid of the required difficulty. This is
+ * nasty, but it seems to be unpleasantly hard to generate
+ * difficult grids otherwise.
*/
- locs = snewn(area, struct xy);
- grid2 = snewn(area, digit);
- symmetry_limit(params, &xlim, &ylim, params->symm);
while (1) {
- int x, y, i, j;
+ /*
+ * Generate a random solved state, starting by
+ * constructing the block structure.
+ */
+ if (r == 1) { /* jigsaw mode */
+ int *dsf = divvy_rectangle(cr, cr, cr, rs);
- /*
- * Iterate over the grid and enumerate all the filled
- * squares we could empty.
- */
- nlocs = 0;
-
- for (x = 0; x < xlim; x++)
- for (y = 0; y < ylim; y++)
- if (grid[y*cr+x]) {
- locs[nlocs].x = x;
- locs[nlocs].y = y;
- nlocs++;
- }
+ dsf_to_blocks (dsf, blocks, cr, cr);
+
+ sfree(dsf);
+ } else { /* basic Sudoku mode */
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++)
+ blocks->whichblock[y*cr+x] = (y/c) * c + (x/r);
+ }
+ make_blocks_from_whichblock(blocks);
+
+ if (params->killer) {
+ if (kblocks) free_block_structure(kblocks);
+ kblocks = gen_killer_cages(cr, rs, params->kdiff > DIFF_KSINGLE);
+ }
+
+ if (!gridgen(cr, blocks, kblocks, params->xtype, grid, rs, area*area))
+ continue;
+ assert(check_valid(cr, blocks, kblocks, NULL, params->xtype, grid));
/*
- * Now shuffle that list.
+ * Save the solved grid in aux.
*/
- for (i = nlocs; i > 1; i--) {
- int p = random_upto(rs, i);
- if (p != i-1) {
- struct xy t = locs[p];
- locs[p] = locs[i-1];
- locs[i-1] = t;
- }
+ {
+ /*
+ * We might already have written *aux the last time we
+ * went round this loop, in which case we should free
+ * the old aux before overwriting it with the new one.
+ */
+ if (*aux) {
+ sfree(*aux);
+ }
+
+ *aux = encode_solve_move(cr, grid);
}
/*
- * Now loop over the shuffled list and, for each element,
- * see whether removing that element (and its reflections)
- * from the grid will still leave the grid soluble by
- * nsolve.
+ * Now we have a solved grid. For normal puzzles, we start removing
+ * things from it while preserving solubility. Killer puzzles are
+ * different: we just pass the empty grid to the solver, and use
+ * the puzzle if it comes back solved.
*/
- for (i = 0; i < nlocs; i++) {
- x = locs[i].x;
- y = locs[i].y;
-
- memcpy(grid2, grid, area);
- ncoords = symmetries(params, x, y, coords, params->symm);
- for (j = 0; j < ncoords; j++)
- grid2[coords[2*j+1]*cr+coords[2*j]] = 0;
-
- if (nsolve(c, r, grid2)) {
- for (j = 0; j < ncoords; j++)
- grid[coords[2*j+1]*cr+coords[2*j]] = 0;
+
+ if (params->killer) {
+ struct block_structure *good_cages = NULL;
+ struct block_structure *last_cages = NULL;
+ int ntries = 0;
+
+ memcpy(grid2, grid, area);
+
+ for (;;) {
+ compute_kclues(kblocks, kgrid, grid2, area);
+
+ memset(grid, 0, area * sizeof *grid);
+ solver(cr, blocks, kblocks, params->xtype, grid, kgrid, &dlev);
+ if (dlev.diff == dlev.maxdiff && dlev.kdiff == dlev.maxkdiff) {
+ /*
+ * We have one that matches our difficulty. Store it for
+ * later, but keep going.
+ */
+ if (good_cages)
+ free_block_structure(good_cages);
+ ntries = 0;
+ good_cages = dup_block_structure(kblocks);
+ if (!merge_some_cages(kblocks, cr, area, grid2, rs))
+ break;
+ } else if (dlev.diff > dlev.maxdiff || dlev.kdiff > dlev.maxkdiff) {
+ /*
+ * Give up after too many tries and either use the good one we
+ * found, or generate a new grid.
+ */
+ if (++ntries > 50)
+ break;
+ /*
+ * The difficulty level got too high. If we have a good
+ * one, use it, otherwise go back to the last one that
+ * was at a lower difficulty and restart the process from
+ * there.
+ */
+ if (good_cages != NULL) {
+ free_block_structure(kblocks);
+ kblocks = dup_block_structure(good_cages);
+ if (!merge_some_cages(kblocks, cr, area, grid2, rs))
+ break;
+ } else {
+ if (last_cages == NULL)
+ break;
+ free_block_structure(kblocks);
+ kblocks = last_cages;
+ last_cages = NULL;
+ }
+ } else {
+ if (last_cages)
+ free_block_structure(last_cages);
+ last_cages = dup_block_structure(kblocks);
+ if (!merge_some_cages(kblocks, cr, area, grid2, rs))
+ break;
+ }
+ }
+ if (last_cages)
+ free_block_structure(last_cages);
+ if (good_cages != NULL) {
+ free_block_structure(kblocks);
+ kblocks = good_cages;
+ compute_kclues(kblocks, kgrid, grid2, area);
+ memset(grid, 0, area * sizeof *grid);
break;
}
+ continue;
}
- if (i == nlocs) {
- /*
- * There was nothing we could remove without destroying
- * solvability.
- */
- break;
- }
+ /*
+ * Find the set of equivalence classes of squares permitted
+ * by the selected symmetry. We do this by enumerating all
+ * the grid squares which have no symmetric companion
+ * sorting lower than themselves.
+ */
+ nlocs = 0;
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++) {
+ int i = y*cr+x;
+ int j;
+
+ ncoords = symmetries(params, x, y, coords, params->symm);
+ for (j = 0; j < ncoords; j++)
+ if (coords[2*j+1]*cr+coords[2*j] < i)
+ break;
+ if (j == ncoords) {
+ locs[nlocs].x = x;
+ locs[nlocs].y = y;
+ nlocs++;
+ }
+ }
+
+ /*
+ * Now shuffle that list.
+ */
+ shuffle(locs, nlocs, sizeof(*locs), rs);
+
+ /*
+ * Now loop over the shuffled list and, for each element,
+ * see whether removing that element (and its reflections)
+ * from the grid will still leave the grid soluble.
+ */
+ for (i = 0; i < nlocs; i++) {
+ x = locs[i].x;
+ y = locs[i].y;
+
+ memcpy(grid2, grid, area);
+ ncoords = symmetries(params, x, y, coords, params->symm);
+ for (j = 0; j < ncoords; j++)
+ grid2[coords[2*j+1]*cr+coords[2*j]] = 0;
+
+ solver(cr, blocks, kblocks, params->xtype, grid2, kgrid, &dlev);
+ if (dlev.diff <= dlev.maxdiff &&
+ (!params->killer || dlev.kdiff <= dlev.maxkdiff)) {
+ for (j = 0; j < ncoords; j++)
+ grid[coords[2*j+1]*cr+coords[2*j]] = 0;
+ }
+ }
+
+ memcpy(grid2, grid, area);
+
+ solver(cr, blocks, kblocks, params->xtype, grid2, kgrid, &dlev);
+ if (dlev.diff == dlev.maxdiff &&
+ (!params->killer || dlev.kdiff == dlev.maxkdiff))
+ break; /* found one! */
}
+
sfree(grid2);
sfree(locs);
-#ifdef DEBUG
- {
- int y, x;
- for (y = 0; y < cr; y++) {
- for (x = 0; x < cr; x++) {
- printf("%2.0d", grid[y*cr+x]);
- }
- printf("\n");
- }
- printf("\n");
- }
-#endif
-
/*
* Now we have the grid as it will be presented to the user.
- * Encode it in a game seed.
+ * Encode it in a game desc.
*/
- {
- char *p;
- int run, i;
-
- seed = snewn(5 * area, char);
- p = seed;
- run = 0;
- for (i = 0; i <= area; i++) {
- int n = (i < area ? grid[i] : -1);
-
- if (!n)
- run++;
- else {
- if (run) {
- while (run > 0) {
- int c = 'a' - 1 + run;
- if (run > 26)
- c = 'z';
- *p++ = c;
- run -= c - ('a' - 1);
- }
- } else {
- /*
- * If there's a number in the very top left or
- * bottom right, there's no point putting an
- * unnecessary _ before or after it.
- */
- if (p > seed && n > 0)
- *p++ = '_';
- }
- if (n > 0)
- p += sprintf(p, "%d", n);
- run = 0;
+ desc = encode_puzzle_desc(params, grid, blocks, kgrid, kblocks);
+
+ sfree(grid);
+ free_block_structure(blocks);
+ if (params->killer) {
+ free_block_structure(kblocks);
+ sfree(kgrid);
+ }
+
+ return desc;
+}
+
+static const char *spec_to_grid(const char *desc, digit *grid, int area)
+{
+ int i = 0;
+ while (*desc && *desc != ',') {
+ int n = *desc++;
+ if (n >= 'a' && n <= 'z') {
+ int run = n - 'a' + 1;
+ assert(i + run <= area);
+ while (run-- > 0)
+ grid[i++] = 0;
+ } else if (n == '_') {
+ /* do nothing */;
+ } else if (n > '0' && n <= '9') {
+ assert(i < area);
+ grid[i++] = atoi(desc-1);
+ while (*desc >= '0' && *desc <= '9')
+ desc++;
+ } else {
+ assert(!"We can't get here");
+ }
+ }
+ assert(i == area);
+ return desc;
+}
+
+/*
+ * Create a DSF from a spec found in *pdesc. Update this to point past the
+ * end of the block spec, and return an error string or NULL if everything
+ * is OK. The DSF is stored in *PDSF.
+ */
+static char *spec_to_dsf(const char **pdesc, int **pdsf, int cr, int area)
+{
+ const char *desc = *pdesc;
+ int pos = 0;
+ int *dsf;
+
+ *pdsf = dsf = snew_dsf(area);
+
+ while (*desc && *desc != ',') {
+ int c, adv;
+
+ if (*desc == '_')
+ c = 0;
+ else if (*desc >= 'a' && *desc <= 'z')
+ c = *desc - 'a' + 1;
+ else {
+ sfree(dsf);
+ return "Invalid character in game description";
+ }
+ desc++;
+
+ adv = (c != 26); /* 'z' is a special case */
+
+ while (c-- > 0) {
+ int p0, p1;
+
+ /*
+ * Non-edge; merge the two dsf classes on either
+ * side of it.
+ */
+ if (pos >= 2*cr*(cr-1)) {
+ sfree(dsf);
+ return "Too much data in block structure specification";
+ }
+
+ if (pos < cr*(cr-1)) {
+ int y = pos/(cr-1);
+ int x = pos%(cr-1);
+ p0 = y*cr+x;
+ p1 = y*cr+x+1;
+ } else {
+ int x = pos/(cr-1) - cr;
+ int y = pos%(cr-1);
+ p0 = y*cr+x;
+ p1 = (y+1)*cr+x;
}
+ dsf_merge(dsf, p0, p1);
+
+ pos++;
}
- assert(p - seed < 5 * area);
- *p++ = '\0';
- seed = sresize(seed, p - seed, char);
+ if (adv)
+ pos++;
}
+ *pdesc = desc;
- sfree(grid);
+ /*
+ * When desc is exhausted, we expect to have gone exactly
+ * one space _past_ the end of the grid, due to the dummy
+ * edge at the end.
+ */
+ if (pos != 2*cr*(cr-1)+1) {
+ sfree(dsf);
+ return "Not enough data in block structure specification";
+ }
- return seed;
+ return NULL;
}
-static char *validate_seed(game_params *params, char *seed)
+static char *validate_grid_desc(const char **pdesc, int range, int area)
{
- int area = params->r * params->r * params->c * params->c;
+ const char *desc = *pdesc;
int squares = 0;
-
- while (*seed) {
- int n = *seed++;
+ while (*desc && *desc != ',') {
+ int n = *desc++;
if (n >= 'a' && n <= 'z') {
squares += n - 'a' + 1;
} else if (n == '_') {
/* do nothing */;
} else if (n > '0' && n <= '9') {
+ int val = atoi(desc-1);
+ if (val < 1 || val > range)
+ return "Out-of-range number in game description";
squares++;
- while (*seed >= '0' && *seed <= '9')
- seed++;
+ while (*desc >= '0' && *desc <= '9')
+ desc++;
} else
- return "Invalid character in game specification";
+ return "Invalid character in game description";
}
if (squares < area)
if (squares > area)
return "Too much data to fit in grid";
+ *pdesc = desc;
+ return NULL;
+}
+
+static char *validate_block_desc(const char **pdesc, int cr, int area,
+ int min_nr_blocks, int max_nr_blocks,
+ int min_nr_squares, int max_nr_squares)
+{
+ char *err;
+ int *dsf;
+
+ err = spec_to_dsf(pdesc, &dsf, cr, area);
+ if (err) {
+ return err;
+ }
+
+ if (min_nr_squares == max_nr_squares) {
+ assert(min_nr_blocks == max_nr_blocks);
+ assert(min_nr_blocks * min_nr_squares == area);
+ }
+ /*
+ * Now we've got our dsf. Verify that it matches
+ * expectations.
+ */
+ {
+ int *canons, *counts;
+ int i, j, c, ncanons = 0;
+
+ canons = snewn(max_nr_blocks, int);
+ counts = snewn(max_nr_blocks, int);
+
+ for (i = 0; i < area; i++) {
+ j = dsf_canonify(dsf, i);
+
+ for (c = 0; c < ncanons; c++)
+ if (canons[c] == j) {
+ counts[c]++;
+ if (counts[c] > max_nr_squares) {
+ sfree(dsf);
+ sfree(canons);
+ sfree(counts);
+ return "A jigsaw block is too big";
+ }
+ break;
+ }
+
+ if (c == ncanons) {
+ if (ncanons >= max_nr_blocks) {
+ sfree(dsf);
+ sfree(canons);
+ sfree(counts);
+ return "Too many distinct jigsaw blocks";
+ }
+ canons[ncanons] = j;
+ counts[ncanons] = 1;
+ ncanons++;
+ }
+ }
+
+ if (ncanons < min_nr_blocks) {
+ sfree(dsf);
+ sfree(canons);
+ sfree(counts);
+ return "Not enough distinct jigsaw blocks";
+ }
+ for (c = 0; c < ncanons; c++) {
+ if (counts[c] < min_nr_squares) {
+ sfree(dsf);
+ sfree(canons);
+ sfree(counts);
+ return "A jigsaw block is too small";
+ }
+ }
+ sfree(canons);
+ sfree(counts);
+ }
+
+ sfree(dsf);
+ return NULL;
+}
+
+static char *validate_desc(const game_params *params, const char *desc)
+{
+ int cr = params->c * params->r, area = cr*cr;
+ char *err;
+
+ err = validate_grid_desc(&desc, cr, area);
+ if (err)
+ return err;
+
+ if (params->r == 1) {
+ /*
+ * Now we expect a suffix giving the jigsaw block
+ * structure. Parse it and validate that it divides the
+ * grid into the right number of regions which are the
+ * right size.
+ */
+ if (*desc != ',')
+ return "Expected jigsaw block structure in game description";
+ desc++;
+ err = validate_block_desc(&desc, cr, area, cr, cr, cr, cr);
+ if (err)
+ return err;
+
+ }
+ if (params->killer) {
+ if (*desc != ',')
+ return "Expected killer block structure in game description";
+ desc++;
+ err = validate_block_desc(&desc, cr, area, cr, area, 2, cr);
+ if (err)
+ return err;
+ if (*desc != ',')
+ return "Expected killer clue grid in game description";
+ desc++;
+ err = validate_grid_desc(&desc, cr * area, area);
+ if (err)
+ return err;
+ }
+ if (*desc)
+ return "Unexpected data at end of game description";
return NULL;
}
-static game_state *new_game(game_params *params, char *seed)
+static game_state *new_game(midend *me, const game_params *params,
+ const char *desc)
{
game_state *state = snew(game_state);
int c = params->c, r = params->r, cr = c*r, area = cr * cr;
int i;
- state->c = params->c;
- state->r = params->r;
+ precompute_sum_bits();
+
+ state->cr = cr;
+ state->xtype = params->xtype;
+ state->killer = params->killer;
state->grid = snewn(area, digit);
+ state->pencil = snewn(area * cr, unsigned char);
+ memset(state->pencil, 0, area * cr);
state->immutable = snewn(area, unsigned char);
memset(state->immutable, FALSE, area);
- state->completed = FALSE;
+ state->blocks = alloc_block_structure (c, r, area, cr, cr);
- i = 0;
- while (*seed) {
- int n = *seed++;
- if (n >= 'a' && n <= 'z') {
- int run = n - 'a' + 1;
- assert(i + run <= area);
- while (run-- > 0)
- state->grid[i++] = 0;
- } else if (n == '_') {
- /* do nothing */;
- } else if (n > '0' && n <= '9') {
- assert(i < area);
+ if (params->killer) {
+ state->kblocks = alloc_block_structure (c, r, area, cr, area);
+ state->kgrid = snewn(area, digit);
+ } else {
+ state->kblocks = NULL;
+ state->kgrid = NULL;
+ }
+ state->completed = state->cheated = FALSE;
+
+ desc = spec_to_grid(desc, state->grid, area);
+ for (i = 0; i < area; i++)
+ if (state->grid[i] != 0)
state->immutable[i] = TRUE;
- state->grid[i++] = atoi(seed-1);
- while (*seed >= '0' && *seed <= '9')
- seed++;
- } else {
- assert(!"We can't get here");
- }
+
+ if (r == 1) {
+ char *err;
+ int *dsf;
+ assert(*desc == ',');
+ desc++;
+ err = spec_to_dsf(&desc, &dsf, cr, area);
+ assert(err == NULL);
+ dsf_to_blocks(dsf, state->blocks, cr, cr);
+ sfree(dsf);
+ } else {
+ int x, y;
+
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++)
+ state->blocks->whichblock[y*cr+x] = (y/c) * c + (x/r);
}
- assert(i == area);
+ make_blocks_from_whichblock(state->blocks);
+
+ if (params->killer) {
+ char *err;
+ int *dsf;
+ assert(*desc == ',');
+ desc++;
+ err = spec_to_dsf(&desc, &dsf, cr, area);
+ assert(err == NULL);
+ dsf_to_blocks(dsf, state->kblocks, cr, area);
+ sfree(dsf);
+ make_blocks_from_whichblock(state->kblocks);
+
+ assert(*desc == ',');
+ desc++;
+ desc = spec_to_grid(desc, state->kgrid, area);
+ }
+ assert(!*desc);
+
+#ifdef STANDALONE_SOLVER
+ /*
+ * Set up the block names for solver diagnostic output.
+ */
+ {
+ char *p = (char *)(state->blocks->blocknames + cr);
+
+ if (r == 1) {
+ for (i = 0; i < area; i++) {
+ int j = state->blocks->whichblock[i];
+ if (!state->blocks->blocknames[j]) {
+ state->blocks->blocknames[j] = p;
+ p += 1 + sprintf(p, "starting at (%d,%d)",
+ 1 + i%cr, 1 + i/cr);
+ }
+ }
+ } else {
+ int bx, by;
+ for (by = 0; by < r; by++)
+ for (bx = 0; bx < c; bx++) {
+ state->blocks->blocknames[by*c+bx] = p;
+ p += 1 + sprintf(p, "(%d,%d)", bx+1, by+1);
+ }
+ }
+ assert(p - (char *)state->blocks->blocknames < (int)(cr*(sizeof(char *)+80)));
+ for (i = 0; i < cr; i++)
+ assert(state->blocks->blocknames[i]);
+ }
+#endif
return state;
}
-static game_state *dup_game(game_state *state)
+static game_state *dup_game(const game_state *state)
{
game_state *ret = snew(game_state);
- int c = state->c, r = state->r, cr = c*r, area = cr * cr;
+ int cr = state->cr, area = cr * cr;
+
+ ret->cr = state->cr;
+ ret->xtype = state->xtype;
+ ret->killer = state->killer;
- ret->c = state->c;
- ret->r = state->r;
+ ret->blocks = state->blocks;
+ ret->blocks->refcount++;
+
+ ret->kblocks = state->kblocks;
+ if (ret->kblocks)
+ ret->kblocks->refcount++;
ret->grid = snewn(area, digit);
memcpy(ret->grid, state->grid, area);
- ret->immutable = snewn(area, unsigned char);
- memcpy(ret->immutable, state->immutable, area);
+ if (state->killer) {
+ ret->kgrid = snewn(area, digit);
+ memcpy(ret->kgrid, state->kgrid, area);
+ } else
+ ret->kgrid = NULL;
+
+ ret->pencil = snewn(area * cr, unsigned char);
+ memcpy(ret->pencil, state->pencil, area * cr);
+
+ ret->immutable = snewn(area, unsigned char);
+ memcpy(ret->immutable, state->immutable, area);
+
+ ret->completed = state->completed;
+ ret->cheated = state->cheated;
+
+ return ret;
+}
+
+static void free_game(game_state *state)
+{
+ free_block_structure(state->blocks);
+ if (state->kblocks)
+ free_block_structure(state->kblocks);
+
+ sfree(state->immutable);
+ sfree(state->pencil);
+ sfree(state->grid);
+ if (state->kgrid) sfree(state->kgrid);
+ sfree(state);
+}
+
+static char *solve_game(const game_state *state, const game_state *currstate,
+ const char *ai, char **error)
+{
+ int cr = state->cr;
+ char *ret;
+ digit *grid;
+ struct difficulty dlev;
+
+ /*
+ * If we already have the solution in ai, save ourselves some
+ * time.
+ */
+ if (ai)
+ return dupstr(ai);
+
+ grid = snewn(cr*cr, digit);
+ memcpy(grid, state->grid, cr*cr);
+ dlev.maxdiff = DIFF_RECURSIVE;
+ dlev.maxkdiff = DIFF_KINTERSECT;
+ solver(cr, state->blocks, state->kblocks, state->xtype, grid,
+ state->kgrid, &dlev);
+
+ *error = NULL;
+
+ if (dlev.diff == DIFF_IMPOSSIBLE)
+ *error = "No solution exists for this puzzle";
+ else if (dlev.diff == DIFF_AMBIGUOUS)
+ *error = "Multiple solutions exist for this puzzle";
+
+ if (*error) {
+ sfree(grid);
+ return NULL;
+ }
+
+ ret = encode_solve_move(cr, grid);
+
+ sfree(grid);
+
+ return ret;
+}
+
+static char *grid_text_format(int cr, struct block_structure *blocks,
+ int xtype, digit *grid)
+{
+ int vmod, hmod;
+ int x, y;
+ int totallen, linelen, nlines;
+ char *ret, *p, ch;
+
+ /*
+ * For non-jigsaw Sudoku, we format in the way we always have,
+ * by having the digits unevenly spaced so that the dividing
+ * lines can fit in:
+ *
+ * . . | . .
+ * . . | . .
+ * ----+----
+ * . . | . .
+ * . . | . .
+ *
+ * For jigsaw puzzles, however, we must leave space between
+ * _all_ pairs of digits for an optional dividing line, so we
+ * have to move to the rather ugly
+ *
+ * . . . .
+ * ------+------
+ * . . | . .
+ * +---+
+ * . . | . | .
+ * ------+ |
+ * . . . | .
+ *
+ * We deal with both cases using the same formatting code; we
+ * simply invent a vmod value such that there's a vertical
+ * dividing line before column i iff i is divisible by vmod
+ * (so it's r in the first case and 1 in the second), and hmod
+ * likewise for horizontal dividing lines.
+ */
+
+ if (blocks->r != 1) {
+ vmod = blocks->r;
+ hmod = blocks->c;
+ } else {
+ vmod = hmod = 1;
+ }
+
+ /*
+ * Line length: we have cr digits, each with a space after it,
+ * and (cr-1)/vmod dividing lines, each with a space after it.
+ * The final space is replaced by a newline, but that doesn't
+ * affect the length.
+ */
+ linelen = 2*(cr + (cr-1)/vmod);
+
+ /*
+ * Number of lines: we have cr rows of digits, and (cr-1)/hmod
+ * dividing rows.
+ */
+ nlines = cr + (cr-1)/hmod;
+
+ /*
+ * Allocate the space.
+ */
+ totallen = linelen * nlines;
+ ret = snewn(totallen+1, char); /* leave room for terminating NUL */
+
+ /*
+ * Write the text.
+ */
+ p = ret;
+ for (y = 0; y < cr; y++) {
+ /*
+ * Row of digits.
+ */
+ for (x = 0; x < cr; x++) {
+ /*
+ * Digit.
+ */
+ digit d = grid[y*cr+x];
+
+ if (d == 0) {
+ /*
+ * Empty space: we usually write a dot, but we'll
+ * highlight spaces on the X-diagonals (in X mode)
+ * by using underscores instead.
+ */
+ if (xtype && (ondiag0(y*cr+x) || ondiag1(y*cr+x)))
+ ch = '_';
+ else
+ ch = '.';
+ } else if (d <= 9) {
+ ch = '0' + d;
+ } else {
+ ch = 'a' + d-10;
+ }
+
+ *p++ = ch;
+ if (x == cr-1) {
+ *p++ = '\n';
+ continue;
+ }
+ *p++ = ' ';
+
+ if ((x+1) % vmod)
+ continue;
+
+ /*
+ * Optional dividing line.
+ */
+ if (blocks->whichblock[y*cr+x] != blocks->whichblock[y*cr+x+1])
+ ch = '|';
+ else
+ ch = ' ';
+ *p++ = ch;
+ *p++ = ' ';
+ }
+ if (y == cr-1 || (y+1) % hmod)
+ continue;
+
+ /*
+ * Dividing row.
+ */
+ for (x = 0; x < cr; x++) {
+ int dwid;
+ int tl, tr, bl, br;
+
+ /*
+ * Division between two squares. This varies
+ * complicatedly in length.
+ */
+ dwid = 2; /* digit and its following space */
+ if (x == cr-1)
+ dwid--; /* no following space at end of line */
+ if (x > 0 && x % vmod == 0)
+ dwid++; /* preceding space after a divider */
+
+ if (blocks->whichblock[y*cr+x] != blocks->whichblock[(y+1)*cr+x])
+ ch = '-';
+ else
+ ch = ' ';
+
+ while (dwid-- > 0)
+ *p++ = ch;
+
+ if (x == cr-1) {
+ *p++ = '\n';
+ break;
+ }
+
+ if ((x+1) % vmod)
+ continue;
- ret->completed = state->completed;
+ /*
+ * Corner square. This is:
+ * - a space if all four surrounding squares are in
+ * the same block
+ * - a vertical line if the two left ones are in one
+ * block and the two right in another
+ * - a horizontal line if the two top ones are in one
+ * block and the two bottom in another
+ * - a plus sign in all other cases. (If we had a
+ * richer character set available we could break
+ * this case up further by doing fun things with
+ * line-drawing T-pieces.)
+ */
+ tl = blocks->whichblock[y*cr+x];
+ tr = blocks->whichblock[y*cr+x+1];
+ bl = blocks->whichblock[(y+1)*cr+x];
+ br = blocks->whichblock[(y+1)*cr+x+1];
+
+ if (tl == tr && tr == bl && bl == br)
+ ch = ' ';
+ else if (tl == bl && tr == br)
+ ch = '|';
+ else if (tl == tr && bl == br)
+ ch = '-';
+ else
+ ch = '+';
+
+ *p++ = ch;
+ }
+ }
+ assert(p - ret == totallen);
+ *p = '\0';
return ret;
}
-static void free_game(game_state *state)
+static int game_can_format_as_text_now(const game_params *params)
{
- sfree(state->immutable);
- sfree(state->grid);
- sfree(state);
+ /*
+ * Formatting Killer puzzles as text is currently unsupported. I
+ * can't think of any sensible way of doing it which doesn't
+ * involve expanding the puzzle to such a large scale as to make
+ * it unusable.
+ */
+ if (params->killer)
+ return FALSE;
+ return TRUE;
+}
+
+static char *game_text_format(const game_state *state)
+{
+ assert(!state->kblocks);
+ return grid_text_format(state->cr, state->blocks, state->xtype,
+ state->grid);
}
struct game_ui {
/*
* These are the coordinates of the currently highlighted
- * square on the grid, or -1,-1 if there isn't one. When there
- * is, pressing a valid number or letter key or Space will
- * enter that number or letter in the grid.
+ * square on the grid, if hshow = 1.
*/
int hx, hy;
+ /*
+ * This indicates whether the current highlight is a
+ * pencil-mark one or a real one.
+ */
+ int hpencil;
+ /*
+ * This indicates whether or not we're showing the highlight
+ * (used to be hx = hy = -1); important so that when we're
+ * using the cursor keys it doesn't keep coming back at a
+ * fixed position. When hshow = 1, pressing a valid number
+ * or letter key or Space will enter that number or letter in the grid.
+ */
+ int hshow;
+ /*
+ * This indicates whether we're using the highlight as a cursor;
+ * it means that it doesn't vanish on a keypress, and that it is
+ * allowed on immutable squares.
+ */
+ int hcursor;
};
-static game_ui *new_ui(game_state *state)
+static game_ui *new_ui(const game_state *state)
{
game_ui *ui = snew(game_ui);
- ui->hx = ui->hy = -1;
+ ui->hx = ui->hy = 0;
+ ui->hpencil = ui->hshow = ui->hcursor = 0;
return ui;
}
sfree(ui);
}
-static game_state *make_move(game_state *from, game_ui *ui, int x, int y,
- int button)
+static char *encode_ui(const game_ui *ui)
{
- int c = from->c, r = from->r, cr = c*r;
- int tx, ty;
- game_state *ret;
+ return NULL;
+}
- tx = (x - BORDER) / TILE_SIZE;
- ty = (y - BORDER) / TILE_SIZE;
+static void decode_ui(game_ui *ui, const char *encoding)
+{
+}
- if (tx >= 0 && tx < cr && ty >= 0 && ty < cr && button == LEFT_BUTTON) {
- if (tx == ui->hx && ty == ui->hy) {
- ui->hx = ui->hy = -1;
- } else {
- ui->hx = tx;
- ui->hy = ty;
- }
- return from; /* UI activity occurred */
+static void game_changed_state(game_ui *ui, const game_state *oldstate,
+ const game_state *newstate)
+{
+ int cr = newstate->cr;
+ /*
+ * We prevent pencil-mode highlighting of a filled square, unless
+ * we're using the cursor keys. So if the user has just filled in
+ * a square which we had a pencil-mode highlight in (by Undo, or
+ * by Redo, or by Solve), then we cancel the highlight.
+ */
+ if (ui->hshow && ui->hpencil && !ui->hcursor &&
+ newstate->grid[ui->hy * cr + ui->hx] != 0) {
+ ui->hshow = 0;
+ }
+}
+
+struct game_drawstate {
+ int started;
+ int cr, xtype;
+ int tilesize;
+ digit *grid;
+ unsigned char *pencil;
+ unsigned char *hl;
+ /* This is scratch space used within a single call to game_redraw. */
+ int nregions, *entered_items;
+};
+
+static char *interpret_move(const game_state *state, game_ui *ui,
+ const game_drawstate *ds,
+ int x, int y, int button)
+{
+ int cr = state->cr;
+ int tx, ty;
+ char buf[80];
+
+ button &= ~MOD_MASK;
+
+ tx = (x + TILE_SIZE - BORDER) / TILE_SIZE - 1;
+ ty = (y + TILE_SIZE - BORDER) / TILE_SIZE - 1;
+
+ if (tx >= 0 && tx < cr && ty >= 0 && ty < cr) {
+ if (button == LEFT_BUTTON) {
+ if (state->immutable[ty*cr+tx]) {
+ ui->hshow = 0;
+ } else if (tx == ui->hx && ty == ui->hy &&
+ ui->hshow && ui->hpencil == 0) {
+ ui->hshow = 0;
+ } else {
+ ui->hx = tx;
+ ui->hy = ty;
+ ui->hshow = 1;
+ ui->hpencil = 0;
+ }
+ ui->hcursor = 0;
+ return ""; /* UI activity occurred */
+ }
+ if (button == RIGHT_BUTTON) {
+ /*
+ * Pencil-mode highlighting for non filled squares.
+ */
+ if (state->grid[ty*cr+tx] == 0) {
+ if (tx == ui->hx && ty == ui->hy &&
+ ui->hshow && ui->hpencil) {
+ ui->hshow = 0;
+ } else {
+ ui->hpencil = 1;
+ ui->hx = tx;
+ ui->hy = ty;
+ ui->hshow = 1;
+ }
+ } else {
+ ui->hshow = 0;
+ }
+ ui->hcursor = 0;
+ return ""; /* UI activity occurred */
+ }
+ }
+ if (IS_CURSOR_MOVE(button)) {
+ move_cursor(button, &ui->hx, &ui->hy, cr, cr, 0);
+ ui->hshow = ui->hcursor = 1;
+ return "";
+ }
+ if (ui->hshow &&
+ (button == CURSOR_SELECT)) {
+ ui->hpencil = 1 - ui->hpencil;
+ ui->hcursor = 1;
+ return "";
}
- if (ui->hx != -1 && ui->hy != -1 &&
- ((button >= '1' && button <= '9' && button - '0' <= cr) ||
+ if (ui->hshow &&
+ ((button >= '0' && button <= '9' && button - '0' <= cr) ||
(button >= 'a' && button <= 'z' && button - 'a' + 10 <= cr) ||
(button >= 'A' && button <= 'Z' && button - 'A' + 10 <= cr) ||
- button == ' ')) {
+ button == CURSOR_SELECT2 || button == '\b')) {
int n = button - '0';
if (button >= 'A' && button <= 'Z')
n = button - 'A' + 10;
if (button >= 'a' && button <= 'z')
n = button - 'a' + 10;
- if (button == ' ')
+ if (button == CURSOR_SELECT2 || button == '\b')
n = 0;
- if (from->immutable[ui->hy*cr+ui->hx])
- return NULL; /* can't overwrite this square */
+ /*
+ * Can't overwrite this square. This can only happen here
+ * if we're using the cursor keys.
+ */
+ if (state->immutable[ui->hy*cr+ui->hx])
+ return NULL;
- ret = dup_game(from);
- ret->grid[ui->hy*cr+ui->hx] = n;
- ui->hx = ui->hy = -1;
+ /*
+ * Can't make pencil marks in a filled square. Again, this
+ * can only become highlighted if we're using cursor keys.
+ */
+ if (ui->hpencil && state->grid[ui->hy*cr+ui->hx])
+ return NULL;
- /*
- * We've made a real change to the grid. Check to see
- * if the game has been completed.
- */
- if (!ret->completed && check_valid(c, r, ret->grid)) {
- ret->completed = TRUE;
- }
+ sprintf(buf, "%c%d,%d,%d",
+ (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n);
- return ret; /* made a valid move */
+ if (!ui->hcursor) ui->hshow = 0;
+
+ return dupstr(buf);
}
+ if (button == 'M' || button == 'm')
+ return dupstr("M");
+
return NULL;
}
+static game_state *execute_move(const game_state *from, const char *move)
+{
+ int cr = from->cr;
+ game_state *ret;
+ int x, y, n;
+
+ if (move[0] == 'S') {
+ const char *p;
+
+ ret = dup_game(from);
+ ret->completed = ret->cheated = TRUE;
+
+ p = move+1;
+ for (n = 0; n < cr*cr; n++) {
+ ret->grid[n] = atoi(p);
+
+ if (!*p || ret->grid[n] < 1 || ret->grid[n] > cr) {
+ free_game(ret);
+ return NULL;
+ }
+
+ while (*p && isdigit((unsigned char)*p)) p++;
+ if (*p == ',') p++;
+ }
+
+ return ret;
+ } else if ((move[0] == 'P' || move[0] == 'R') &&
+ sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
+ x >= 0 && x < cr && y >= 0 && y < cr && n >= 0 && n <= cr) {
+
+ ret = dup_game(from);
+ if (move[0] == 'P' && n > 0) {
+ int index = (y*cr+x) * cr + (n-1);
+ ret->pencil[index] = !ret->pencil[index];
+ } else {
+ ret->grid[y*cr+x] = n;
+ memset(ret->pencil + (y*cr+x)*cr, 0, cr);
+
+ /*
+ * We've made a real change to the grid. Check to see
+ * if the game has been completed.
+ */
+ if (!ret->completed && check_valid(
+ cr, ret->blocks, ret->kblocks, ret->kgrid,
+ ret->xtype, ret->grid)) {
+ ret->completed = TRUE;
+ }
+ }
+ return ret;
+ } else if (move[0] == 'M') {
+ /*
+ * Fill in absolutely all pencil marks in unfilled squares,
+ * for those who like to play by the rigorous approach of
+ * starting off in that state and eliminating things.
+ */
+ ret = dup_game(from);
+ for (y = 0; y < cr; y++) {
+ for (x = 0; x < cr; x++) {
+ if (!ret->grid[y*cr+x]) {
+ memset(ret->pencil + (y*cr+x)*cr, 1, cr);
+ }
+ }
+ }
+ return ret;
+ } else
+ return NULL; /* couldn't parse move string */
+}
+
/* ----------------------------------------------------------------------
* Drawing routines.
*/
-struct game_drawstate {
- int started;
- int c, r, cr;
- digit *grid;
- unsigned char *hl;
-};
-
-#define XSIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
-#define YSIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
+#define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1)
+#define GETTILESIZE(cr, w) ( (double)(w-1) / (double)(cr+1) )
-static void game_size(game_params *params, int *x, int *y)
+static void game_compute_size(const game_params *params, int tilesize,
+ int *x, int *y)
{
- int c = params->c, r = params->r, cr = c*r;
+ /* Ick: fake up `ds->tilesize' for macro expansion purposes */
+ struct { int tilesize; } ads, *ds = &ads;
+ ads.tilesize = tilesize;
+
+ *x = SIZE(params->c * params->r);
+ *y = SIZE(params->c * params->r);
+}
- *x = XSIZE(cr);
- *y = YSIZE(cr);
+static void game_set_size(drawing *dr, game_drawstate *ds,
+ const game_params *params, int tilesize)
+{
+ ds->tilesize = tilesize;
}
-static float *game_colours(frontend *fe, game_state *state, int *ncolours)
+static float *game_colours(frontend *fe, int *ncolours)
{
float *ret = snewn(3 * NCOLOURS, float);
frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
+ ret[COL_XDIAGONALS * 3 + 0] = 0.9F * ret[COL_BACKGROUND * 3 + 0];
+ ret[COL_XDIAGONALS * 3 + 1] = 0.9F * ret[COL_BACKGROUND * 3 + 1];
+ ret[COL_XDIAGONALS * 3 + 2] = 0.9F * ret[COL_BACKGROUND * 3 + 2];
+
ret[COL_GRID * 3 + 0] = 0.0F;
ret[COL_GRID * 3 + 1] = 0.0F;
ret[COL_GRID * 3 + 2] = 0.0F;
ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
ret[COL_USER * 3 + 2] = 0.0F;
- ret[COL_HIGHLIGHT * 3 + 0] = 0.85F * ret[COL_BACKGROUND * 3 + 0];
- ret[COL_HIGHLIGHT * 3 + 1] = 0.85F * ret[COL_BACKGROUND * 3 + 1];
- ret[COL_HIGHLIGHT * 3 + 2] = 0.85F * ret[COL_BACKGROUND * 3 + 2];
+ ret[COL_HIGHLIGHT * 3 + 0] = 0.78F * ret[COL_BACKGROUND * 3 + 0];
+ ret[COL_HIGHLIGHT * 3 + 1] = 0.78F * ret[COL_BACKGROUND * 3 + 1];
+ ret[COL_HIGHLIGHT * 3 + 2] = 0.78F * ret[COL_BACKGROUND * 3 + 2];
+
+ ret[COL_ERROR * 3 + 0] = 1.0F;
+ ret[COL_ERROR * 3 + 1] = 0.0F;
+ ret[COL_ERROR * 3 + 2] = 0.0F;
+
+ ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
+ ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
+ ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
+
+ ret[COL_KILLER * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
+ ret[COL_KILLER * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
+ ret[COL_KILLER * 3 + 2] = 0.1F * ret[COL_BACKGROUND * 3 + 2];
*ncolours = NCOLOURS;
return ret;
}
-static game_drawstate *game_new_drawstate(game_state *state)
+static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
{
struct game_drawstate *ds = snew(struct game_drawstate);
- int c = state->c, r = state->r, cr = c*r;
+ int cr = state->cr;
ds->started = FALSE;
- ds->c = c;
- ds->r = r;
ds->cr = cr;
+ ds->xtype = state->xtype;
ds->grid = snewn(cr*cr, digit);
- memset(ds->grid, 0, cr*cr);
+ memset(ds->grid, cr+2, cr*cr);
+ ds->pencil = snewn(cr*cr*cr, digit);
+ memset(ds->pencil, 0, cr*cr*cr);
ds->hl = snewn(cr*cr, unsigned char);
memset(ds->hl, 0, cr*cr);
-
+ /*
+ * ds->entered_items needs one row of cr entries per entity in
+ * which digits may not be duplicated. That's one for each row,
+ * each column, each block, each diagonal, and each Killer cage.
+ */
+ ds->nregions = cr*3 + 2;
+ if (state->kblocks)
+ ds->nregions += state->kblocks->nr_blocks;
+ ds->entered_items = snewn(cr * ds->nregions, int);
+ ds->tilesize = 0; /* not decided yet */
return ds;
}
-static void game_free_drawstate(game_drawstate *ds)
+static void game_free_drawstate(drawing *dr, game_drawstate *ds)
{
sfree(ds->hl);
+ sfree(ds->pencil);
sfree(ds->grid);
+ sfree(ds->entered_items);
sfree(ds);
}
-static void draw_number(frontend *fe, game_drawstate *ds, game_state *state,
- int x, int y, int hl)
+static void draw_number(drawing *dr, game_drawstate *ds,
+ const game_state *state, int x, int y, int hl)
{
- int c = state->c, r = state->r, cr = c*r;
- int tx, ty;
+ int cr = state->cr;
+ int tx, ty, tw, th;
int cx, cy, cw, ch;
- char str[2];
+ int col_killer = (hl & 32 ? COL_ERROR : COL_KILLER);
+ char str[20];
- if (ds->grid[y*cr+x] == state->grid[y*cr+x] && ds->hl[y*cr+x] == hl)
+ if (ds->grid[y*cr+x] == state->grid[y*cr+x] &&
+ ds->hl[y*cr+x] == hl &&
+ !memcmp(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr))
return; /* no change required */
- tx = BORDER + x * TILE_SIZE + 2;
- ty = BORDER + y * TILE_SIZE + 2;
+ tx = BORDER + x * TILE_SIZE + 1 + GRIDEXTRA;
+ ty = BORDER + y * TILE_SIZE + 1 + GRIDEXTRA;
cx = tx;
cy = ty;
- cw = TILE_SIZE-3;
- ch = TILE_SIZE-3;
+ cw = tw = TILE_SIZE-1-2*GRIDEXTRA;
+ ch = th = TILE_SIZE-1-2*GRIDEXTRA;
+
+ if (x > 0 && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[y*cr+x-1])
+ cx -= GRIDEXTRA, cw += GRIDEXTRA;
+ if (x+1 < cr && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[y*cr+x+1])
+ cw += GRIDEXTRA;
+ if (y > 0 && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[(y-1)*cr+x])
+ cy -= GRIDEXTRA, ch += GRIDEXTRA;
+ if (y+1 < cr && state->blocks->whichblock[y*cr+x] == state->blocks->whichblock[(y+1)*cr+x])
+ ch += GRIDEXTRA;
+
+ clip(dr, cx, cy, cw, ch);
+
+ /* background needs erasing */
+ draw_rect(dr, cx, cy, cw, ch,
+ ((hl & 15) == 1 ? COL_HIGHLIGHT :
+ (ds->xtype && (ondiag0(y*cr+x) || ondiag1(y*cr+x))) ? COL_XDIAGONALS :
+ COL_BACKGROUND));
+
+ /*
+ * Draw the corners of thick lines in corner-adjacent squares,
+ * which jut into this square by one pixel.
+ */
+ if (x > 0 && y > 0 && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y-1)*cr+x-1])
+ draw_rect(dr, tx-GRIDEXTRA, ty-GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
+ if (x+1 < cr && y > 0 && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y-1)*cr+x+1])
+ draw_rect(dr, tx+TILE_SIZE-1-2*GRIDEXTRA, ty-GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
+ if (x > 0 && y+1 < cr && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y+1)*cr+x-1])
+ draw_rect(dr, tx-GRIDEXTRA, ty+TILE_SIZE-1-2*GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
+ if (x+1 < cr && y+1 < cr && state->blocks->whichblock[y*cr+x] != state->blocks->whichblock[(y+1)*cr+x+1])
+ draw_rect(dr, tx+TILE_SIZE-1-2*GRIDEXTRA, ty+TILE_SIZE-1-2*GRIDEXTRA, GRIDEXTRA, GRIDEXTRA, COL_GRID);
+
+ /* pencil-mode highlight */
+ if ((hl & 15) == 2) {
+ int coords[6];
+ coords[0] = cx;
+ coords[1] = cy;
+ coords[2] = cx+cw/2;
+ coords[3] = cy;
+ coords[4] = cx;
+ coords[5] = cy+ch/2;
+ draw_polygon(dr, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
+ }
+
+ if (state->kblocks) {
+ int t = GRIDEXTRA * 3;
+ int kcx, kcy, kcw, kch;
+ int kl, kt, kr, kb;
+ int has_left = 0, has_right = 0, has_top = 0, has_bottom = 0;
+
+ /*
+ * In non-jigsaw mode, the Killer cages are placed at a
+ * fixed offset from the outer edge of the cell dividing
+ * lines, so that they look right whether those lines are
+ * thick or thin. In jigsaw mode, however, doing this will
+ * sometimes cause the cage outlines in adjacent squares to
+ * fail to match up with each other, so we must offset a
+ * fixed amount from the _centre_ of the cell dividing
+ * lines.
+ */
+ if (state->blocks->r == 1) {
+ kcx = tx;
+ kcy = ty;
+ kcw = tw;
+ kch = th;
+ } else {
+ kcx = cx;
+ kcy = cy;
+ kcw = cw;
+ kch = ch;
+ }
+ kl = kcx - 1;
+ kt = kcy - 1;
+ kr = kcx + kcw;
+ kb = kcy + kch;
- if (x % r)
- cx--, cw++;
- if ((x+1) % r)
- cw++;
- if (y % c)
- cy--, ch++;
- if ((y+1) % c)
- ch++;
+ /*
+ * First, draw the lines dividing this area from neighbouring
+ * different areas.
+ */
+ if (x == 0 || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[y*cr+x-1])
+ has_left = 1, kl += t;
+ if (x+1 >= cr || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[y*cr+x+1])
+ has_right = 1, kr -= t;
+ if (y == 0 || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x])
+ has_top = 1, kt += t;
+ if (y+1 >= cr || state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x])
+ has_bottom = 1, kb -= t;
+ if (has_top)
+ draw_line(dr, kl, kt, kr, kt, col_killer);
+ if (has_bottom)
+ draw_line(dr, kl, kb, kr, kb, col_killer);
+ if (has_left)
+ draw_line(dr, kl, kt, kl, kb, col_killer);
+ if (has_right)
+ draw_line(dr, kr, kt, kr, kb, col_killer);
+ /*
+ * Now, take care of the corners (just as for the normal borders).
+ * We only need a corner if there wasn't a full edge.
+ */
+ if (x > 0 && y > 0 && !has_left && !has_top
+ && state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x-1])
+ {
+ draw_line(dr, kl, kt + t, kl + t, kt + t, col_killer);
+ draw_line(dr, kl + t, kt, kl + t, kt + t, col_killer);
+ }
+ if (x+1 < cr && y > 0 && !has_right && !has_top
+ && state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y-1)*cr+x+1])
+ {
+ draw_line(dr, kcx + kcw - t, kt + t, kcx + kcw, kt + t, col_killer);
+ draw_line(dr, kcx + kcw - t, kt, kcx + kcw - t, kt + t, col_killer);
+ }
+ if (x > 0 && y+1 < cr && !has_left && !has_bottom
+ && state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x-1])
+ {
+ draw_line(dr, kl, kcy + kch - t, kl + t, kcy + kch - t, col_killer);
+ draw_line(dr, kl + t, kcy + kch - t, kl + t, kcy + kch, col_killer);
+ }
+ if (x+1 < cr && y+1 < cr && !has_right && !has_bottom
+ && state->kblocks->whichblock[y*cr+x] != state->kblocks->whichblock[(y+1)*cr+x+1])
+ {
+ draw_line(dr, kcx + kcw - t, kcy + kch - t, kcx + kcw - t, kcy + kch, col_killer);
+ draw_line(dr, kcx + kcw - t, kcy + kch - t, kcx + kcw, kcy + kch - t, col_killer);
+ }
- clip(fe, cx, cy, cw, ch);
+ }
- /* background needs erasing? */
- if (ds->grid[y*cr+x] || ds->hl[y*cr+x] != hl)
- draw_rect(fe, cx, cy, cw, ch, hl ? COL_HIGHLIGHT : COL_BACKGROUND);
+ if (state->killer && state->kgrid[y*cr+x]) {
+ sprintf (str, "%d", state->kgrid[y*cr+x]);
+ draw_text(dr, tx + GRIDEXTRA * 4, ty + GRIDEXTRA * 4 + TILE_SIZE/4,
+ FONT_VARIABLE, TILE_SIZE/4, ALIGN_VNORMAL | ALIGN_HLEFT,
+ col_killer, str);
+ }
/* new number needs drawing? */
if (state->grid[y*cr+x]) {
str[0] = state->grid[y*cr+x] + '0';
if (str[0] > '9')
str[0] += 'a' - ('9'+1);
- draw_text(fe, tx + TILE_SIZE/2, ty + TILE_SIZE/2,
+ draw_text(dr, tx + TILE_SIZE/2, ty + TILE_SIZE/2,
FONT_VARIABLE, TILE_SIZE/2, ALIGN_VCENTRE | ALIGN_HCENTRE,
- state->immutable[y*cr+x] ? COL_CLUE : COL_USER, str);
+ state->immutable[y*cr+x] ? COL_CLUE : (hl & 16) ? COL_ERROR : COL_USER, str);
+ } else {
+ int i, j, npencil;
+ int pl, pr, pt, pb;
+ float bestsize;
+ int pw, ph, minph, pbest, fontsize;
+
+ /* Count the pencil marks required. */
+ for (i = npencil = 0; i < cr; i++)
+ if (state->pencil[(y*cr+x)*cr+i])
+ npencil++;
+ if (npencil) {
+
+ minph = 2;
+
+ /*
+ * Determine the bounding rectangle within which we're going
+ * to put the pencil marks.
+ */
+ /* Start with the whole square */
+ pl = tx + GRIDEXTRA;
+ pr = pl + TILE_SIZE - GRIDEXTRA;
+ pt = ty + GRIDEXTRA;
+ pb = pt + TILE_SIZE - GRIDEXTRA;
+ if (state->killer) {
+ /*
+ * Make space for the Killer cages. We do this
+ * unconditionally, for uniformity between squares,
+ * rather than making it depend on whether a Killer
+ * cage edge is actually present on any given side.
+ */
+ pl += GRIDEXTRA * 3;
+ pr -= GRIDEXTRA * 3;
+ pt += GRIDEXTRA * 3;
+ pb -= GRIDEXTRA * 3;
+ if (state->kgrid[y*cr+x] != 0) {
+ /* Make further space for the Killer number. */
+ pt += TILE_SIZE/4;
+ /* minph--; */
+ }
+ }
+
+ /*
+ * We arrange our pencil marks in a grid layout, with
+ * the number of rows and columns adjusted to allow the
+ * maximum font size.
+ *
+ * So now we work out what the grid size ought to be.
+ */
+ bestsize = 0.0;
+ pbest = 0;
+ /* Minimum */
+ for (pw = 3; pw < max(npencil,4); pw++) {
+ float fw, fh, fs;
+
+ ph = (npencil + pw - 1) / pw;
+ ph = max(ph, minph);
+ fw = (pr - pl) / (float)pw;
+ fh = (pb - pt) / (float)ph;
+ fs = min(fw, fh);
+ if (fs > bestsize) {
+ bestsize = fs;
+ pbest = pw;
+ }
+ }
+ assert(pbest > 0);
+ pw = pbest;
+ ph = (npencil + pw - 1) / pw;
+ ph = max(ph, minph);
+
+ /*
+ * Now we've got our grid dimensions, work out the pixel
+ * size of a grid element, and round it to the nearest
+ * pixel. (We don't want rounding errors to make the
+ * grid look uneven at low pixel sizes.)
+ */
+ fontsize = min((pr - pl) / pw, (pb - pt) / ph);
+
+ /*
+ * Centre the resulting figure in the square.
+ */
+ pl = tx + (TILE_SIZE - fontsize * pw) / 2;
+ pt = ty + (TILE_SIZE - fontsize * ph) / 2;
+
+ /*
+ * And move it down a bit if it's collided with the
+ * Killer cage number.
+ */
+ if (state->killer && state->kgrid[y*cr+x] != 0) {
+ pt = max(pt, ty + GRIDEXTRA * 3 + TILE_SIZE/4);
+ }
+
+ /*
+ * Now actually draw the pencil marks.
+ */
+ for (i = j = 0; i < cr; i++)
+ if (state->pencil[(y*cr+x)*cr+i]) {
+ int dx = j % pw, dy = j / pw;
+
+ str[1] = '\0';
+ str[0] = i + '1';
+ if (str[0] > '9')
+ str[0] += 'a' - ('9'+1);
+ draw_text(dr, pl + fontsize * (2*dx+1) / 2,
+ pt + fontsize * (2*dy+1) / 2,
+ FONT_VARIABLE, fontsize,
+ ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
+ j++;
+ }
+ }
}
- unclip(fe);
+ unclip(dr);
- draw_update(fe, cx, cy, cw, ch);
+ draw_update(dr, cx, cy, cw, ch);
ds->grid[y*cr+x] = state->grid[y*cr+x];
+ memcpy(ds->pencil+(y*cr+x)*cr, state->pencil+(y*cr+x)*cr, cr);
ds->hl[y*cr+x] = hl;
}
-static void game_redraw(frontend *fe, game_drawstate *ds, game_state *oldstate,
- game_state *state, int dir, game_ui *ui,
- float animtime, float flashtime)
+static void game_redraw(drawing *dr, game_drawstate *ds,
+ const game_state *oldstate, const game_state *state,
+ int dir, const game_ui *ui,
+ float animtime, float flashtime)
{
- int c = state->c, r = state->r, cr = c*r;
+ int cr = state->cr;
int x, y;
if (!ds->started) {
* all games should start by drawing a big
* background-colour rectangle covering the whole window.
*/
- draw_rect(fe, 0, 0, XSIZE(cr), YSIZE(cr), COL_BACKGROUND);
+ draw_rect(dr, 0, 0, SIZE(cr), SIZE(cr), COL_BACKGROUND);
/*
- * Draw the grid.
+ * Draw the grid. We draw it as a big thick rectangle of
+ * COL_GRID initially; individual calls to draw_number()
+ * will poke the right-shaped holes in it.
*/
- for (x = 0; x <= cr; x++) {
- int thick = (x % r ? 0 : 1);
- draw_rect(fe, BORDER + x*TILE_SIZE - thick, BORDER-1,
- 1+2*thick, cr*TILE_SIZE+3, COL_GRID);
- }
- for (y = 0; y <= cr; y++) {
- int thick = (y % c ? 0 : 1);
- draw_rect(fe, BORDER-1, BORDER + y*TILE_SIZE - thick,
- cr*TILE_SIZE+3, 1+2*thick, COL_GRID);
- }
+ draw_rect(dr, BORDER-GRIDEXTRA, BORDER-GRIDEXTRA,
+ cr*TILE_SIZE+1+2*GRIDEXTRA, cr*TILE_SIZE+1+2*GRIDEXTRA,
+ COL_GRID);
}
+ /*
+ * This array is used to keep track of rows, columns and boxes
+ * which contain a number more than once.
+ */
+ for (x = 0; x < cr * ds->nregions; x++)
+ ds->entered_items[x] = 0;
+ for (x = 0; x < cr; x++)
+ for (y = 0; y < cr; y++) {
+ digit d = state->grid[y*cr+x];
+ if (d) {
+ int box, kbox;
+
+ /* Rows */
+ ds->entered_items[x*cr+d-1]++;
+
+ /* Columns */
+ ds->entered_items[(y+cr)*cr+d-1]++;
+
+ /* Blocks */
+ box = state->blocks->whichblock[y*cr+x];
+ ds->entered_items[(box+2*cr)*cr+d-1]++;
+
+ /* Diagonals */
+ if (ds->xtype) {
+ if (ondiag0(y*cr+x))
+ ds->entered_items[(3*cr)*cr+d-1]++;
+ if (ondiag1(y*cr+x))
+ ds->entered_items[(3*cr+1)*cr+d-1]++;
+ }
+
+ /* Killer cages */
+ if (state->kblocks) {
+ kbox = state->kblocks->whichblock[y*cr+x];
+ ds->entered_items[(kbox+3*cr+2)*cr+d-1]++;
+ }
+ }
+ }
+
/*
* Draw any numbers which need redrawing.
*/
for (x = 0; x < cr; x++) {
for (y = 0; y < cr; y++) {
- draw_number(fe, ds, state, x, y,
- (x == ui->hx && y == ui->hy) ||
- (flashtime > 0 &&
- (flashtime <= FLASH_TIME/3 ||
- flashtime >= FLASH_TIME*2/3)));
+ int highlight = 0;
+ digit d = state->grid[y*cr+x];
+
+ if (flashtime > 0 &&
+ (flashtime <= FLASH_TIME/3 ||
+ flashtime >= FLASH_TIME*2/3))
+ highlight = 1;
+
+ /* Highlight active input areas. */
+ if (x == ui->hx && y == ui->hy && ui->hshow)
+ highlight = ui->hpencil ? 2 : 1;
+
+ /* Mark obvious errors (ie, numbers which occur more than once
+ * in a single row, column, or box). */
+ if (d && (ds->entered_items[x*cr+d-1] > 1 ||
+ ds->entered_items[(y+cr)*cr+d-1] > 1 ||
+ ds->entered_items[(state->blocks->whichblock[y*cr+x]
+ +2*cr)*cr+d-1] > 1 ||
+ (ds->xtype && ((ondiag0(y*cr+x) &&
+ ds->entered_items[(3*cr)*cr+d-1] > 1) ||
+ (ondiag1(y*cr+x) &&
+ ds->entered_items[(3*cr+1)*cr+d-1]>1)))||
+ (state->kblocks &&
+ ds->entered_items[(state->kblocks->whichblock[y*cr+x]
+ +3*cr+2)*cr+d-1] > 1)))
+ highlight |= 16;
+
+ if (d && state->kblocks) {
+ if (check_killer_cage_sum(
+ state->kblocks, state->kgrid, state->grid,
+ state->kblocks->whichblock[y*cr+x]) == 0)
+ highlight |= 32;
+ }
+
+ draw_number(dr, ds, state, x, y, highlight);
}
}
* Update the _entire_ grid if necessary.
*/
if (!ds->started) {
- draw_update(fe, 0, 0, XSIZE(cr), YSIZE(cr));
+ draw_update(dr, 0, 0, SIZE(cr), SIZE(cr));
ds->started = TRUE;
}
}
-static float game_anim_length(game_state *oldstate, game_state *newstate,
- int dir)
+static float game_anim_length(const game_state *oldstate,
+ const game_state *newstate, int dir, game_ui *ui)
{
return 0.0F;
}
-static float game_flash_length(game_state *oldstate, game_state *newstate,
- int dir)
+static float game_flash_length(const game_state *oldstate,
+ const game_state *newstate, int dir, game_ui *ui)
{
- if (!oldstate->completed && newstate->completed)
+ if (!oldstate->completed && newstate->completed &&
+ !oldstate->cheated && !newstate->cheated)
return FLASH_TIME;
return 0.0F;
}
-static int game_wants_statusbar(void)
+static int game_status(const game_state *state)
{
- return FALSE;
+ return state->completed ? +1 : 0;
+}
+
+static int game_timing_state(const game_state *state, game_ui *ui)
+{
+ if (state->completed)
+ return FALSE;
+ return TRUE;
+}
+
+static void game_print_size(const game_params *params, float *x, float *y)
+{
+ int pw, ph;
+
+ /*
+ * I'll use 9mm squares by default. They should be quite big
+ * for this game, because players will want to jot down no end
+ * of pencil marks in the squares.
+ */
+ game_compute_size(params, 900, &pw, &ph);
+ *x = pw / 100.0F;
+ *y = ph / 100.0F;
+}
+
+/*
+ * Subfunction to draw the thick lines between cells. In order to do
+ * this using the line-drawing rather than rectangle-drawing API (so
+ * as to get line thicknesses to scale correctly) and yet have
+ * correctly mitred joins between lines, we must do this by tracing
+ * the boundary of each sub-block and drawing it in one go as a
+ * single polygon.
+ *
+ * This subfunction is also reused with thinner dotted lines to
+ * outline the Killer cages, this time offsetting the outline toward
+ * the interior of the affected squares.
+ */
+static void outline_block_structure(drawing *dr, game_drawstate *ds,
+ const game_state *state,
+ struct block_structure *blocks,
+ int ink, int inset)
+{
+ int cr = state->cr;
+ int *coords;
+ int bi, i, n;
+ int x, y, dx, dy, sx, sy, sdx, sdy;
+
+ /*
+ * Maximum perimeter of a k-omino is 2k+2. (Proof: start
+ * with k unconnected squares, with total perimeter 4k.
+ * Now repeatedly join two disconnected components
+ * together into a larger one; every time you do so you
+ * remove at least two unit edges, and you require k-1 of
+ * these operations to create a single connected piece, so
+ * you must have at most 4k-2(k-1) = 2k+2 unit edges left
+ * afterwards.)
+ */
+ coords = snewn(4*cr+4, int); /* 2k+2 points, 2 coords per point */
+
+ /*
+ * Iterate over all the blocks.
+ */
+ for (bi = 0; bi < blocks->nr_blocks; bi++) {
+ if (blocks->nr_squares[bi] == 0)
+ continue;
+
+ /*
+ * For each block, find a starting square within it
+ * which has a boundary at the left.
+ */
+ for (i = 0; i < cr; i++) {
+ int j = blocks->blocks[bi][i];
+ if (j % cr == 0 || blocks->whichblock[j-1] != bi)
+ break;
+ }
+ assert(i < cr); /* every block must have _some_ leftmost square */
+ x = blocks->blocks[bi][i] % cr;
+ y = blocks->blocks[bi][i] / cr;
+ dx = -1;
+ dy = 0;
+
+ /*
+ * Now begin tracing round the perimeter. At all
+ * times, (x,y) describes some square within the
+ * block, and (x+dx,y+dy) is some adjacent square
+ * outside it; so the edge between those two squares
+ * is always an edge of the block.
+ */
+ sx = x, sy = y, sdx = dx, sdy = dy; /* save starting position */
+ n = 0;
+ do {
+ int cx, cy, tx, ty, nin;
+
+ /*
+ * Advance to the next edge, by looking at the two
+ * squares beyond it. If they're both outside the block,
+ * we turn right (by leaving x,y the same and rotating
+ * dx,dy clockwise); if they're both inside, we turn
+ * left (by rotating dx,dy anticlockwise and contriving
+ * to leave x+dx,y+dy unchanged); if one of each, we go
+ * straight on (and may enforce by assertion that
+ * they're one of each the _right_ way round).
+ */
+ nin = 0;
+ tx = x - dy + dx;
+ ty = y + dx + dy;
+ nin += (tx >= 0 && tx < cr && ty >= 0 && ty < cr &&
+ blocks->whichblock[ty*cr+tx] == bi);
+ tx = x - dy;
+ ty = y + dx;
+ nin += (tx >= 0 && tx < cr && ty >= 0 && ty < cr &&
+ blocks->whichblock[ty*cr+tx] == bi);
+ if (nin == 0) {
+ /*
+ * Turn right.
+ */
+ int tmp;
+ tmp = dx;
+ dx = -dy;
+ dy = tmp;
+ } else if (nin == 2) {
+ /*
+ * Turn left.
+ */
+ int tmp;
+
+ x += dx;
+ y += dy;
+
+ tmp = dx;
+ dx = dy;
+ dy = -tmp;
+
+ x -= dx;
+ y -= dy;
+ } else {
+ /*
+ * Go straight on.
+ */
+ x -= dy;
+ y += dx;
+ }
+
+ /*
+ * Now enforce by assertion that we ended up
+ * somewhere sensible.
+ */
+ assert(x >= 0 && x < cr && y >= 0 && y < cr &&
+ blocks->whichblock[y*cr+x] == bi);
+ assert(x+dx < 0 || x+dx >= cr || y+dy < 0 || y+dy >= cr ||
+ blocks->whichblock[(y+dy)*cr+(x+dx)] != bi);
+
+ /*
+ * Record the point we just went past at one end of the
+ * edge. To do this, we translate (x,y) down and right
+ * by half a unit (so they're describing a point in the
+ * _centre_ of the square) and then translate back again
+ * in a manner rotated by dy and dx.
+ */
+ assert(n < 2*cr+2);
+ cx = ((2*x+1) + dy + dx) / 2;
+ cy = ((2*y+1) - dx + dy) / 2;
+ coords[2*n+0] = BORDER + cx * TILE_SIZE;
+ coords[2*n+1] = BORDER + cy * TILE_SIZE;
+ coords[2*n+0] -= dx * inset;
+ coords[2*n+1] -= dy * inset;
+ if (nin == 0) {
+ /*
+ * We turned right, so inset this corner back along
+ * the edge towards the centre of the square.
+ */
+ coords[2*n+0] -= dy * inset;
+ coords[2*n+1] += dx * inset;
+ } else if (nin == 2) {
+ /*
+ * We turned left, so inset this corner further
+ * _out_ along the edge into the next square.
+ */
+ coords[2*n+0] += dy * inset;
+ coords[2*n+1] -= dx * inset;
+ }
+ n++;
+
+ } while (x != sx || y != sy || dx != sdx || dy != sdy);
+
+ /*
+ * That's our polygon; now draw it.
+ */
+ draw_polygon(dr, coords, n, -1, ink);
+ }
+
+ sfree(coords);
+}
+
+static void game_print(drawing *dr, const game_state *state, int tilesize)
+{
+ int cr = state->cr;
+ int ink = print_mono_colour(dr, 0);
+ int x, y;
+
+ /* Ick: fake up `ds->tilesize' for macro expansion purposes */
+ game_drawstate ads, *ds = &ads;
+ game_set_size(dr, ds, NULL, tilesize);
+
+ /*
+ * Border.
+ */
+ print_line_width(dr, 3 * TILE_SIZE / 40);
+ draw_rect_outline(dr, BORDER, BORDER, cr*TILE_SIZE, cr*TILE_SIZE, ink);
+
+ /*
+ * Highlight X-diagonal squares.
+ */
+ if (state->xtype) {
+ int i;
+ int xhighlight = print_grey_colour(dr, 0.90F);
+
+ for (i = 0; i < cr; i++)
+ draw_rect(dr, BORDER + i*TILE_SIZE, BORDER + i*TILE_SIZE,
+ TILE_SIZE, TILE_SIZE, xhighlight);
+ for (i = 0; i < cr; i++)
+ if (i*2 != cr-1) /* avoid redoing centre square, just for fun */
+ draw_rect(dr, BORDER + i*TILE_SIZE,
+ BORDER + (cr-1-i)*TILE_SIZE,
+ TILE_SIZE, TILE_SIZE, xhighlight);
+ }
+
+ /*
+ * Main grid.
+ */
+ for (x = 1; x < cr; x++) {
+ print_line_width(dr, TILE_SIZE / 40);
+ draw_line(dr, BORDER+x*TILE_SIZE, BORDER,
+ BORDER+x*TILE_SIZE, BORDER+cr*TILE_SIZE, ink);
+ }
+ for (y = 1; y < cr; y++) {
+ print_line_width(dr, TILE_SIZE / 40);
+ draw_line(dr, BORDER, BORDER+y*TILE_SIZE,
+ BORDER+cr*TILE_SIZE, BORDER+y*TILE_SIZE, ink);
+ }
+
+ /*
+ * Thick lines between cells.
+ */
+ print_line_width(dr, 3 * TILE_SIZE / 40);
+ outline_block_structure(dr, ds, state, state->blocks, ink, 0);
+
+ /*
+ * Killer cages and their totals.
+ */
+ if (state->kblocks) {
+ print_line_width(dr, TILE_SIZE / 40);
+ print_line_dotted(dr, TRUE);
+ outline_block_structure(dr, ds, state, state->kblocks, ink,
+ 5 * TILE_SIZE / 40);
+ print_line_dotted(dr, FALSE);
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++)
+ if (state->kgrid[y*cr+x]) {
+ char str[20];
+ sprintf(str, "%d", state->kgrid[y*cr+x]);
+ draw_text(dr,
+ BORDER+x*TILE_SIZE + 7*TILE_SIZE/40,
+ BORDER+y*TILE_SIZE + 16*TILE_SIZE/40,
+ FONT_VARIABLE, TILE_SIZE/4,
+ ALIGN_VNORMAL | ALIGN_HLEFT,
+ ink, str);
+ }
+ }
+
+ /*
+ * Standard (non-Killer) clue numbers.
+ */
+ for (y = 0; y < cr; y++)
+ for (x = 0; x < cr; x++)
+ if (state->grid[y*cr+x]) {
+ char str[2];
+ str[1] = '\0';
+ str[0] = state->grid[y*cr+x] + '0';
+ if (str[0] > '9')
+ str[0] += 'a' - ('9'+1);
+ draw_text(dr, BORDER + x*TILE_SIZE + TILE_SIZE/2,
+ BORDER + y*TILE_SIZE + TILE_SIZE/2,
+ FONT_VARIABLE, TILE_SIZE/2,
+ ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
+ }
}
#ifdef COMBINED
#endif
const struct game thegame = {
- "Solo", "games.solo", TRUE,
+ "Solo", "games.solo", "solo",
default_params,
game_fetch_preset,
decode_params,
encode_params,
free_params,
dup_params,
- game_configure,
- custom_params,
+ TRUE, game_configure, custom_params,
validate_params,
- new_game_seed,
- validate_seed,
+ new_game_desc,
+ validate_desc,
new_game,
dup_game,
free_game,
+ TRUE, solve_game,
+ TRUE, game_can_format_as_text_now, game_text_format,
new_ui,
free_ui,
- make_move,
- game_size,
+ encode_ui,
+ decode_ui,
+ game_changed_state,
+ interpret_move,
+ execute_move,
+ PREFERRED_TILE_SIZE, game_compute_size, game_set_size,
game_colours,
game_new_drawstate,
game_free_drawstate,
game_redraw,
game_anim_length,
game_flash_length,
- game_wants_statusbar,
+ game_status,
+ TRUE, FALSE, game_print_size, game_print,
+ FALSE, /* wants_statusbar */
+ FALSE, game_timing_state,
+ REQUIRE_RBUTTON | REQUIRE_NUMPAD, /* flags */
};
+
+#ifdef STANDALONE_SOLVER
+
+int main(int argc, char **argv)
+{
+ game_params *p;
+ game_state *s;
+ char *id = NULL, *desc, *err;
+ int grade = FALSE;
+ struct difficulty dlev;
+
+ while (--argc > 0) {
+ char *p = *++argv;
+ if (!strcmp(p, "-v")) {
+ solver_show_working = TRUE;
+ } else if (!strcmp(p, "-g")) {
+ grade = TRUE;
+ } else if (*p == '-') {
+ fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
+ return 1;
+ } else {
+ id = p;
+ }
+ }
+
+ if (!id) {
+ fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
+ return 1;
+ }
+
+ desc = strchr(id, ':');
+ if (!desc) {
+ fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
+ return 1;
+ }
+ *desc++ = '\0';
+
+ p = default_params();
+ decode_params(p, id);
+ err = validate_desc(p, desc);
+ if (err) {
+ fprintf(stderr, "%s: %s\n", argv[0], err);
+ return 1;
+ }
+ s = new_game(NULL, p, desc);
+
+ dlev.maxdiff = DIFF_RECURSIVE;
+ dlev.maxkdiff = DIFF_KINTERSECT;
+ solver(s->cr, s->blocks, s->kblocks, s->xtype, s->grid, s->kgrid, &dlev);
+ if (grade) {
+ printf("Difficulty rating: %s\n",
+ dlev.diff==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)":
+ dlev.diff==DIFF_SIMPLE ? "Basic (row/column/number elimination required)":
+ dlev.diff==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)":
+ dlev.diff==DIFF_SET ? "Advanced (set elimination required)":
+ dlev.diff==DIFF_EXTREME ? "Extreme (complex non-recursive techniques required)":
+ dlev.diff==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)":
+ dlev.diff==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)":
+ dlev.diff==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)":
+ "INTERNAL ERROR: unrecognised difficulty code");
+ if (p->killer)
+ printf("Killer difficulty: %s\n",
+ dlev.kdiff==DIFF_KSINGLE ? "Trivial (single square cages only)":
+ dlev.kdiff==DIFF_KMINMAX ? "Simple (maximum sum analysis required)":
+ dlev.kdiff==DIFF_KSUMS ? "Intermediate (sum possibilities)":
+ dlev.kdiff==DIFF_KINTERSECT ? "Advanced (sum region intersections)":
+ "INTERNAL ERROR: unrecognised difficulty code");
+ } else {
+ printf("%s\n", grid_text_format(s->cr, s->blocks, s->xtype, s->grid));
+ }
+
+ return 0;
+}
+
+#endif
+
+/* vim: set shiftwidth=4 tabstop=8: */
~ian / sgt-puzzles.git / blobdiff