X-Git-Url: https://git.distorted.org.uk/~mdw/sgt/puzzles/blobdiff_plain/4846f788f861e4c7d895831ba77c497f6875d998..HEAD:/solo.c diff --git a/solo.c b/solo.c index 70eaa99..d9bf18d 100644 --- a/solo.c +++ b/solo.c @@ -3,25 +3,36 @@ * * 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 @@ -33,9 +44,13 @@ * 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. */ /* @@ -74,6 +89,11 @@ #include #include +#ifdef STANDALONE_SOLVER +#include +int solver_show_working, solver_recurse_depth; +#endif + #include "puzzles.h" /* @@ -87,31 +107,167 @@ 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) @@ -119,36 +275,15 @@ 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); @@ -161,47 +296,142 @@ static game_params *dup_params(game_params *params) 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(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); } @@ -210,7 +440,7 @@ static config_item *game_configure(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; @@ -224,19 +454,37 @@ static config_item *game_configure(game_params *params) 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; } @@ -247,291 +495,161 @@ static game_params *custom_params(config_item *cfg) 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(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. @@ -544,56 +662,62 @@ static int rsolve(int c, int r, digit *grid, random_state *rs, int max) * 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; /* @@ -602,6 +726,11 @@ struct nsolve_usage { */ 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 * many times. @@ -610,21 +739,35 @@ struct nsolve_usage { 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)); @@ -652,168 +795,2179 @@ static void nsolve_place(struct nsolve_usage *usage, int x, int y, int 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++; } - if (m == 1) { - int x, y, n; - assert(fpos >= 0); + if (m == 1) { + int x, y, n; + assert(fpos >= 0); + + n = 1 + fpos % 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]; - n = 1 + fpos % cr; - y = fpos / cr; - x = y / cr; - y %= cr; + /* Update the usage structure to reflect the placing of this digit. */ + gridgen_place(usage, sx, sy, n); + usage->nspaces--; - nsolve_place(usage, x, y, n); - return TRUE; + /* Call the solver recursively. Stop when we find a solution. */ + if (gridgen_real(usage, grid, steps)) { + ret = TRUE; + break; + } + + /* 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. */ /* * 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, 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); @@ -850,298 +3004,903 @@ static int check_valid(int c, int r, digit *grid) /* * 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 (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; } } } + /* + * 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(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 int symmetries(game_params *params, int x, int y, int *output, int s) +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 char *encode_puzzle_desc(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(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, 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 char *spec_to_grid(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(char **pdesc, int **pdsf, int cr, int area) +{ + 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 != 25); /* 'z' is a special case */ + + while (c-- > 0) { + int p0, p1; + + /* + * Non-edge; merge the two dsf classes on either + * side of it. + */ + assert(pos < 2*cr*(cr-1)); + 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(char **pdesc, int range, int area) { - int area = params->r * params->r * params->c * params->c; + 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) @@ -1149,46 +3908,229 @@ static char *validate_seed(game_params *params, char *seed) if (squares > area) return "Too much data to fit in grid"; + *pdesc = desc; + return NULL; +} + +static char *validate_block_desc(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(game_params *params, 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, game_params *params, 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; } @@ -1196,44 +4138,334 @@ static game_state *new_game(game_params *params, char *seed) static game_state *dup_game(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(game_state *state, game_state *currstate, + 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(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(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) { 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; } @@ -1243,88 +4475,227 @@ static void free_ui(game_ui *ui) sfree(ui); } -static game_state *make_move(game_state *from, game_ui *ui, int x, int y, - int button) +static char *encode_ui(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, 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, game_state *oldstate, + 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(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); } return NULL; } +static game_state *execute_move(game_state *from, char *move) +{ + int cr = from->cr; + game_state *ret; + int x, y, n; + + if (move[0] == 'S') { + 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->xtype, ret->grid)) { + ret->completed = TRUE; + } + } + 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(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, + 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; @@ -1337,71 +4708,215 @@ static float *game_colours(frontend *fe, game_state *state, int *ncolours) 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, 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, +static void draw_number(drawing *dr, game_drawstate *ds, 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]) { @@ -1409,24 +4924,134 @@ static void draw_number(frontend *fe, game_drawstate *ds, game_state *state, 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, +static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate, game_state *state, int dir, 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) { @@ -1436,33 +5061,112 @@ static void game_redraw(frontend *fe, game_drawstate *ds, game_state *oldstate, * 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) { + int i, b = state->kblocks->whichblock[y*cr+x]; + int n_squares = state->kblocks->nr_squares[b]; + int sum = 0, clue = 0; + for (i = 0; i < n_squares; i++) { + int xy = state->kblocks->blocks[b][i]; + if (state->grid[xy] == 0) + break; + + sum += state->grid[xy]; + if (state->kgrid[xy]) { + assert(clue == 0); + clue = state->kgrid[xy]; + } + } + + if (i == n_squares) { + assert(clue != 0); + if (sum != clue) + highlight |= 32; + } + } + + draw_number(dr, ds, state, x, y, highlight); } } @@ -1470,28 +5174,313 @@ static void game_redraw(frontend *fe, game_drawstate *ds, game_state *oldstate, * 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) + int dir, game_ui *ui) { return 0.0F; } static float game_flash_length(game_state *oldstate, game_state *newstate, - int dir) + 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(game_state *state) { - return FALSE; + return state->completed ? +1 : 0; +} + +static int game_timing_state(game_state *state, game_ui *ui) +{ + if (state->completed) + return FALSE; + return TRUE; +} + +static void game_print_size(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, + 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, 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 @@ -1499,30 +5488,116 @@ static int game_wants_statusbar(void) #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] \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: */