X-Git-Url: https://git.distorted.org.uk/~mdw/sgt/puzzles/blobdiff_plain/844f605fe87ffa1c30cc4a18d2b705495f612b5b..1f608c7c964dccc40e32f7138235cce85ad5be82:/solo.c diff --git a/solo.c b/solo.c index bbe0c31..f8d8d6b 100644 --- a/solo.c +++ b/solo.c @@ -91,7 +91,7 @@ #ifdef STANDALONE_SOLVER #include -int solver_show_working; +int solver_show_working, solver_recurse_depth; #endif #include "puzzles.h" @@ -321,286 +321,28 @@ static game_params *custom_params(config_item *cfg) 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) 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) > 36) + return "Unable to support more than 36 distinct symbols in a puzzle"; 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. - */ -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) -{ - int c = usage->c, r = usage->r, cr = usage->cr; - int i, j, n, sx, sy, bestm, bestr; - int *digits; - - /* - * 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; - } - - /* - * 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; - } - } - - /* - * 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; - } - - /* - * 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; - } - } - } - - /* 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++; - } - - sfree(digits); -} - -/* - * 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) -{ - 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; -} - -/* ---------------------------------------------------------------------- - * 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 several purposes: + * + to generate filled grids as the basis for new puzzles (by + * supplying no clue squares at all) + * + 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. @@ -646,6 +388,11 @@ static int rsolve(int c, int r, digit *grid, random_state *rs, int max) * places, found by taking the _complement_ of the union of * the numbers' possible positions (or the spaces' possible * contents). + * + * - 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. */ /* @@ -664,7 +411,7 @@ static int rsolve(int c, int r, digit *grid, random_state *rs, int max) #define YTRANS(y) (((y)%c)*r+(y)/c) #define YUNTRANS(y) (((y)%r)*c+(y)/r) -struct nsolve_usage { +struct solver_usage { int c, r, cr; /* * We set up a cubic array, indexed by x, y and digit; each @@ -700,7 +447,7 @@ struct nsolve_usage { * 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; @@ -751,7 +498,7 @@ static void nsolve_place(struct nsolve_usage *usage, int x, int y, int n) usage->blk[((y%r)*c+(x/r))*cr+n-1] = TRUE; } -static int nsolve_elim(struct nsolve_usage *usage, int start, int step +static int solver_elim(struct solver_usage *usage, int start, int step #ifdef STANDALONE_SOLVER , char *fmt, ... #endif @@ -785,22 +532,36 @@ static int nsolve_elim(struct nsolve_usage *usage, int start, int step #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 placing %d at (%d,%d)\n", - n, 1+x, 1+YUNTRANS(y)); + printf(":\n%*s placing %d at (%d,%d)\n", + solver_recurse_depth*4, "", n, 1+x, 1+YUNTRANS(y)); } #endif - nsolve_place(usage, x, y, n); - return TRUE; + 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 FALSE; + return 0; } -static int nsolve_intersect(struct nsolve_usage *usage, +static int solver_intersect(struct solver_usage *usage, int start1, int step1, int start2, int step2 #ifdef STANDALONE_SOLVER , char *fmt, ... @@ -819,16 +580,16 @@ static int nsolve_intersect(struct nsolve_usage *usage, if (usage->cube[p] && !(p >= start2 && p < start2+cr*step2 && (p - start2) % step2 == 0)) - return FALSE; /* there is, so we can't deduce */ + 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 TRUE iff we actually _did_ anything. + * overlap; return +1 iff we actually _did_ anything. */ - ret = FALSE; + ret = 0; for (i = 0; i < cr; i++) { int p = start2+i*step2; if (usage->cube[p] && @@ -840,6 +601,7 @@ static int nsolve_intersect(struct nsolve_usage *usage, if (!ret) { va_list ap; + printf("%*s", solver_recurse_depth*4, ""); va_start(ap, fmt); vprintf(fmt, ap); va_end(ap); @@ -851,11 +613,11 @@ static int nsolve_intersect(struct nsolve_usage *usage, px = py / cr; py %= cr; - printf(" ruling out %d at (%d,%d)\n", - pn, 1+px, 1+YUNTRANS(py)); + printf("%*s ruling out %d at (%d,%d)\n", + solver_recurse_depth*4, "", pn, 1+px, 1+YUNTRANS(py)); } #endif - ret = TRUE; /* we did something */ + ret = +1; /* we did something */ usage->cube[p] = 0; } } @@ -863,12 +625,12 @@ static int nsolve_intersect(struct nsolve_usage *usage, return ret; } -struct nsolve_scratch { +struct solver_scratch { unsigned char *grid, *rowidx, *colidx, *set; }; -static int nsolve_set(struct nsolve_usage *usage, - struct nsolve_scratch *scratch, +static int solver_set(struct solver_usage *usage, + struct solver_scratch *scratch, int start, int step1, int step2 #ifdef STANDALONE_SOLVER , char *fmt, ... @@ -895,14 +657,15 @@ static int nsolve_set(struct nsolve_usage *usage, for (j = 0; j < cr; j++) if (usage->cube[start+i*step1+j*step2]) first = j, count++; - if (count == 0) { - /* - * This condition actually marks a completely insoluble - * (i.e. internally inconsistent) puzzle. We return and - * report no progress made. - */ - return FALSE; - } + + /* + * 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; } @@ -968,7 +731,22 @@ static int nsolve_set(struct nsolve_usage *usage, * indicates a faulty deduction before this point or * even a bogus clue. */ - assert(rows <= n - count); + 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; @@ -976,8 +754,8 @@ static int nsolve_set(struct nsolve_usage *usage, * 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 TRUE (meaning progress has been made) if - * we successfully eliminated anything at all. + * 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 @@ -998,9 +776,11 @@ static int nsolve_set(struct nsolve_usage *usage, #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); @@ -1012,7 +792,8 @@ static int nsolve_set(struct nsolve_usage *usage, px = py / cr; py %= cr; - printf(" ruling out %d at (%d,%d)\n", + printf("%*s ruling out %d at (%d,%d)\n", + solver_recurse_depth*4, "", pn, 1+px, 1+YUNTRANS(py)); } #endif @@ -1023,7 +804,7 @@ static int nsolve_set(struct nsolve_usage *usage, } if (progress) { - return TRUE; + return +1; } } } @@ -1041,12 +822,12 @@ static int nsolve_set(struct nsolve_usage *usage, break; /* done */ } - return FALSE; + return 0; } -static struct nsolve_scratch *nsolve_new_scratch(struct nsolve_usage *usage) +static struct solver_scratch *solver_new_scratch(struct solver_usage *usage) { - struct nsolve_scratch *scratch = snew(struct nsolve_scratch); + 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); @@ -1055,7 +836,7 @@ static struct nsolve_scratch *nsolve_new_scratch(struct nsolve_usage *usage) return scratch; } -static void nsolve_free_scratch(struct nsolve_scratch *scratch) +static void solver_free_scratch(struct solver_scratch *scratch) { sfree(scratch->set); sfree(scratch->colidx); @@ -1064,19 +845,19 @@ static void nsolve_free_scratch(struct nsolve_scratch *scratch) sfree(scratch); } -static int nsolve(int c, int r, digit *grid) +static int solver(int c, int r, digit *grid, int maxdiff) { - struct nsolve_usage *usage; - struct nsolve_scratch *scratch; + struct solver_usage *usage; + struct solver_scratch *scratch; int cr = c*r; - int x, y, n; + int x, y, n, ret; int diff = DIFF_BLOCK; /* * Set up a usage structure as a clean slate (everything * possible). */ - usage = snew(struct nsolve_usage); + usage = snew(struct solver_usage); usage->c = c; usage->r = r; usage->cr = cr; @@ -1091,7 +872,7 @@ static int nsolve(int c, int r, digit *grid) memset(usage->col, FALSE, cr * cr); memset(usage->blk, FALSE, cr * cr); - scratch = nsolve_new_scratch(usage); + scratch = solver_new_scratch(usage); /* * Place all the clue numbers we are given. @@ -1099,7 +880,7 @@ static int nsolve(int c, int r, digit *grid) 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]); + solver_place(usage, x, YTRANS(y), grid[y*cr+x]); /* * Now loop over the grid repeatedly trying all permitted modes @@ -1124,45 +905,64 @@ static int nsolve(int c, int r, digit *grid) 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 + if (!usage->blk[(y*c+(x/r))*cr+n-1]) { + ret = solver_elim(usage, cubepos(x,y,n), r*cr #ifdef STANDALONE_SOLVER - , "positional elimination," - " block (%d,%d)", 1+x/r, 1+y + , "positional elimination," + " %d in block (%d,%d)", n, 1+x/r, 1+y #endif - )) { - diff = max(diff, DIFF_BLOCK); - goto cont; + ); + if (ret < 0) { + diff = DIFF_IMPOSSIBLE; + goto got_result; + } else if (ret > 0) { + diff = max(diff, DIFF_BLOCK); + goto cont; + } } + if (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] && - nsolve_elim(usage, cubepos(0,y,n), cr*cr + if (!usage->row[y*cr+n-1]) { + ret = solver_elim(usage, cubepos(0,y,n), cr*cr #ifdef STANDALONE_SOLVER - , "positional elimination," - " row %d", 1+YUNTRANS(y) + , "positional elimination," + " %d in row %d", n, 1+YUNTRANS(y) #endif - )) { - diff = max(diff, DIFF_SIMPLE); - goto cont; + ); + 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] && - nsolve_elim(usage, cubepos(x,0,n), cr + if (!usage->col[x*cr+n-1]) { + ret = solver_elim(usage, cubepos(x,0,n), cr #ifdef STANDALONE_SOLVER - , "positional elimination," " column %d", 1+x + , "positional elimination," + " %d in column %d", n, 1+x #endif - )) { - diff = max(diff, DIFF_SIMPLE); - goto cont; + ); + if (ret < 0) { + diff = DIFF_IMPOSSIBLE; + goto got_result; + } else if (ret > 0) { + diff = max(diff, DIFF_SIMPLE); + goto cont; + } } /* @@ -1170,39 +970,50 @@ static int nsolve(int c, int r, digit *grid) */ 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 + if (!usage->grid[YUNTRANS(y)*cr+x]) { + ret = solver_elim(usage, cubepos(x,y,1), 1 #ifdef STANDALONE_SOLVER - , "numeric elimination at (%d,%d)", 1+x, - 1+YUNTRANS(y) + , "numeric elimination at (%d,%d)", 1+x, + 1+YUNTRANS(y) #endif - )) { - diff = max(diff, DIFF_SIMPLE); - goto cont; + ); + if (ret < 0) { + diff = DIFF_IMPOSSIBLE; + goto got_result; + } else if (ret > 0) { + diff = max(diff, DIFF_SIMPLE); + goto cont; + } } + if (maxdiff <= DIFF_SIMPLE) + break; + /* * Intersectional analysis, rows vs blocks. */ for (y = 0; y < cr; y++) for (x = 0; x < cr; x += r) for (n = 1; n <= cr; n++) + /* + * solver_intersect() never returns -1. + */ if (!usage->row[y*cr+n-1] && !usage->blk[((y%r)*c+(x/r))*cr+n-1] && - (nsolve_intersect(usage, cubepos(0,y,n), cr*cr, + (solver_intersect(usage, cubepos(0,y,n), cr*cr, cubepos(x,y%r,n), r*cr #ifdef STANDALONE_SOLVER , "intersectional analysis," - " row %d vs block (%d,%d)", - 1+YUNTRANS(y), 1+x/r, 1+y%r + " %d in row %d vs block (%d,%d)", + n, 1+YUNTRANS(y), 1+x/r, 1+y%r #endif ) || - nsolve_intersect(usage, cubepos(x,y%r,n), r*cr, + solver_intersect(usage, cubepos(x,y%r,n), r*cr, cubepos(0,y,n), cr*cr #ifdef STANDALONE_SOLVER , "intersectional analysis," - " block (%d,%d) vs row %d", - 1+x/r, 1+y%r, 1+YUNTRANS(y) + " %d in block (%d,%d) vs row %d", + n, 1+x/r, 1+y%r, 1+YUNTRANS(y) #endif ))) { diff = max(diff, DIFF_INTERSECT); @@ -1217,65 +1028,83 @@ static int nsolve(int c, int r, digit *grid) for (n = 1; n <= cr; n++) if (!usage->col[x*cr+n-1] && !usage->blk[(y*c+(x/r))*cr+n-1] && - (nsolve_intersect(usage, cubepos(x,0,n), cr, + (solver_intersect(usage, cubepos(x,0,n), cr, cubepos((x/r)*r,y,n), r*cr #ifdef STANDALONE_SOLVER , "intersectional analysis," - " column %d vs block (%d,%d)", - 1+x, 1+x/r, 1+y + " %d in column %d vs block (%d,%d)", + n, 1+x, 1+x/r, 1+y #endif ) || - nsolve_intersect(usage, cubepos((x/r)*r,y,n), r*cr, + solver_intersect(usage, cubepos((x/r)*r,y,n), r*cr, cubepos(x,0,n), cr #ifdef STANDALONE_SOLVER , "intersectional analysis," - " block (%d,%d) vs column %d", - 1+x/r, 1+y, 1+x + " %d in block (%d,%d) vs column %d", + n, 1+x/r, 1+y, 1+x #endif ))) { diff = max(diff, DIFF_INTERSECT); goto cont; } + if (maxdiff <= DIFF_INTERSECT) + break; + /* * Blockwise set elimination. */ for (x = 0; x < cr; x += r) - for (y = 0; y < r; y++) - if (nsolve_set(usage, scratch, cubepos(x,y,1), r*cr, 1 + for (y = 0; y < r; y++) { + ret = solver_set(usage, scratch, cubepos(x,y,1), r*cr, 1 #ifdef STANDALONE_SOLVER - , "set elimination, block (%d,%d)", 1+x/r, 1+y + , "set elimination, block (%d,%d)", 1+x/r, 1+y #endif - )) { - diff = max(diff, DIFF_SET); - goto cont; - } + ); + 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++) - if (nsolve_set(usage, scratch, cubepos(0,y,1), cr*cr, 1 + for (y = 0; y < cr; y++) { + ret = solver_set(usage, scratch, cubepos(0,y,1), cr*cr, 1 #ifdef STANDALONE_SOLVER - , "set elimination, row %d", 1+YUNTRANS(y) + , "set elimination, row %d", 1+YUNTRANS(y) #endif - )) { - diff = max(diff, DIFF_SET); - goto cont; - } + ); + 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++) - if (nsolve_set(usage, scratch, cubepos(x,0,1), cr, 1 + for (x = 0; x < cr; x++) { + ret = solver_set(usage, scratch, cubepos(x,0,1), cr, 1 #ifdef STANDALONE_SOLVER - , "set elimination, column %d", 1+x + , "set elimination, column %d", 1+x #endif - )) { - diff = max(diff, DIFF_SET); - goto cont; - } + ); + if (ret < 0) { + diff = DIFF_IMPOSSIBLE; + goto got_result; + } else if (ret > 0) { + diff = max(diff, DIFF_SET); + goto cont; + } + } /* * If we reach here, we have made no deductions in this @@ -1284,7 +1113,161 @@ static int nsolve(int c, int r, digit *grid) break; } - nsolve_free_scratch(scratch); + /* + * 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 (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,YTRANS(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,YTRANS(y),n)) + list[j++] = n; + +#ifdef STANDALONE_SOLVER + if (solver_show_working) { + char *sep = ""; + printf("%*srecursing on (%d,%d) [", + solver_recurse_depth*4, "", x, y); + 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++) { + int ret; + + 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, y); + solver_recurse_depth++; +#endif + + ret = solver(c, r, outgrid, maxdiff); + +#ifdef STANDALONE_SOLVER + solver_recurse_depth--; + if (solver_show_working) { + printf("%*sretracting %d at (%d,%d)\n", + solver_recurse_depth*4, "", list[i], x, y); + } +#endif + + /* + * If we have our first solution, copy it into the + * grid we will return. + */ + if (diff == DIFF_IMPOSSIBLE && ret != DIFF_IMPOSSIBLE) + memcpy(grid, outgrid, cr*cr); + + if (ret == DIFF_AMBIGUOUS) + diff = DIFF_AMBIGUOUS; + else if (ret == 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:; + +#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->cube); sfree(usage->row); @@ -1292,15 +1275,234 @@ static int nsolve(int c, int r, digit *grid) sfree(usage->blk); sfree(usage); - for (x = 0; x < cr; x++) - for (y = 0; y < cr; y++) - if (!grid[y*cr+x]) - return DIFF_IMPOSSIBLE; + solver_free_scratch(scratch); + return diff; } /* ---------------------------------------------------------------------- - * End of non-recursive solver code. + * End of solver code. + */ + +/* ---------------------------------------------------------------------- + * 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. + */ + +/* + * Internal data structure used in gridgen to keep track of + * progress. + */ +struct gridgen_coord { int x, y, r; }; +struct gridgen_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 gridgen_coord *spaces; + int nspaces; + /* If we need randomisation in the solve, this is our random state. */ + random_state *rs; +}; + +/* + * The real recursive step in the generating function. + */ +static int gridgen_real(struct gridgen_usage *usage, digit *grid) +{ + int c = usage->c, r = usage->r, cr = usage->cr; + int i, j, n, sx, sy, bestm, bestr, ret; + int *digits; + + /* + * Firstly, check for completion! If there are no spaces left + * in the grid, we have a solution. + */ + if (usage->nspaces == 0) { + memcpy(grid, usage->grid, cr * cr); + return TRUE; + } + + /* + * 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; + } + } + + /* + * 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 = 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(digits, j, sizeof(*digits), usage->rs); + + /* And finally, go through the digit list and actually recurse. */ + ret = FALSE; + for (i = 0; i < j; i++) { + n = digits[i]; + + /* Update the usage structure to reflect the placing of this digit. */ + 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. Stop when we find a solution. */ + if (gridgen_real(usage, grid)) + ret = TRUE; + + /* 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++; + + if (ret) + break; + } + + sfree(digits); + return ret; +} + +/* + * Entry point to generator. You give it dimensions and a starting + * grid, which is simply an array of cr*cr digits. + */ +static void gridgen(int c, int r, digit *grid, random_state *rs) +{ + struct gridgen_usage *usage; + int x, y, cr = c*r; + + /* + * Clear the grid to start with. + */ + memset(grid, 0, cr*cr); + + /* + * Create a gridgen_usage structure. + */ + usage = snew(struct gridgen_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 gridgen_coord); + usage->nspaces = 0; + + usage->rs = rs; + + /* + * Initialise the list of grid spaces. + */ + for (y = 0; 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++; + } + } + + /* + * Run the real generator function. + */ + gridgen_real(usage, grid); + + /* + * 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); +} + +/* ---------------------------------------------------------------------- + * End of grid generator code. */ /* @@ -1470,7 +1672,6 @@ static char *new_game_desc(game_params *params, random_state *rs, digit *grid, *grid2; struct xy { int x, y; } *locs; int nlocs; - int ret; char *desc; int coords[16], ncoords; int *symmclasses, nsymmclasses; @@ -1522,12 +1723,9 @@ static char *new_game_desc(game_params *params, random_state *rs, */ do { /* - * Start the recursive solver with an empty grid to generate a - * random solved state. + * Generate a random solved state. */ - memset(grid, 0, area); - ret = rsolve(c, r, grid, rs, 1); - assert(ret == 1); + gridgen(c, r, grid, rs); assert(check_valid(c, r, grid)); /* @@ -1573,20 +1771,13 @@ static char *new_game_desc(game_params *params, random_state *rs, /* * Now shuffle that list. */ - 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; - } - } + 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 by - * nsolve. + * solver. */ for (i = 0; i < nlocs; i++) { int ret; @@ -1599,12 +1790,8 @@ static char *new_game_desc(game_params *params, random_state *rs, for (j = 0; j < ncoords; j++) grid2[coords[2*j+1]*cr+coords[2*j]] = 0; - if (recursing) - ret = (rsolve(c, r, grid2, NULL, 2) == 1); - else - ret = (nsolve(c, r, grid2) <= maxdiff); - - if (ret) { + ret = solver(c, r, grid2, maxdiff); + if (ret != DIFF_IMPOSSIBLE && ret != DIFF_AMBIGUOUS) { for (j = 0; j < ncoords; j++) grid[coords[2*j+1]*cr+coords[2*j]] = 0; break; @@ -1614,21 +1801,14 @@ static char *new_game_desc(game_params *params, random_state *rs, if (i == nlocs) { /* * There was nothing we could remove without - * destroying solvability. If we're trying to - * generate a recursion-only grid and haven't - * switched over to rsolve yet, we now do; - * otherwise we give up. + * destroying solvability. Give up. */ - if (maxdiff == DIFF_RECURSIVE && !recursing) { - recursing = TRUE; - } else { - break; - } + break; } } memcpy(grid2, grid, area); - } while (nsolve(c, r, grid2) < maxdiff); + } while (solver(c, r, grid2, maxdiff) < maxdiff); sfree(grid2); sfree(locs); @@ -1791,7 +1971,7 @@ static char *solve_game(game_state *state, game_state *currstate, int c = state->c, r = state->r, cr = c*r; char *ret; digit *grid; - int rsolve_ret; + int solve_ret; /* * If we already have the solution in ai, save ourselves some @@ -1802,14 +1982,17 @@ static char *solve_game(game_state *state, game_state *currstate, grid = snewn(cr*cr, digit); memcpy(grid, state->grid, cr*cr); - rsolve_ret = rsolve(c, r, grid, NULL, 2); + solve_ret = solver(c, r, grid, DIFF_RECURSIVE); + + *error = NULL; + + if (solve_ret == DIFF_IMPOSSIBLE) + *error = "No solution exists for this puzzle"; + else if (solve_ret == DIFF_AMBIGUOUS) + *error = "Multiple solutions exist for this puzzle"; - if (rsolve_ret != 1) { + if (*error) { sfree(grid); - if (rsolve_ret == 0) - *error = "No solution exists for this puzzle"; - else - *error = "Multiple solutions exist for this puzzle"; return NULL; } @@ -2024,7 +2207,7 @@ static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds, return NULL; sprintf(buf, "%c%d,%d,%d", - ui->hpencil && n > 0 ? 'P' : 'R', ui->hx, ui->hy, n); + (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n); ui->hx = ui->hy = -1; @@ -2090,22 +2273,23 @@ static game_state *execute_move(game_state *from, char *move) */ #define SIZE(cr) ((cr) * TILE_SIZE + 2*BORDER + 1) -#define GETTILESIZE(cr, w) ( (w-1) / (cr+1) ) +#define GETTILESIZE(cr, w) ( (double)(w-1) / (double)(cr+1) ) -static void game_size(game_params *params, game_drawstate *ds, - int *x, int *y, int expand) +static void game_compute_size(game_params *params, int tilesize, + int *x, int *y) { - int c = params->c, r = params->r, cr = c*r; - int ts; + /* Ick: fake up `ds->tilesize' for macro expansion purposes */ + struct { int tilesize; } ads, *ds = &ads; + ads.tilesize = tilesize; - ts = min(GETTILESIZE(cr, *x), GETTILESIZE(cr, *y)); - if (expand) - ds->tilesize = ts; - else - ds->tilesize = min(ts, PREFERRED_TILE_SIZE); + *x = SIZE(params->c * params->r); + *y = SIZE(params->c * params->r); +} - *x = SIZE(cr); - *y = SIZE(cr); +static void game_set_size(game_drawstate *ds, game_params *params, + int tilesize) +{ + ds->tilesize = tilesize; } static float *game_colours(frontend *fe, game_state *state, int *ncolours) @@ -2215,7 +2399,7 @@ static void draw_number(frontend *fe, game_drawstate *ds, game_state *state, coords[3] = cy; coords[4] = cx; coords[5] = cy+ch/2; - draw_polygon(fe, coords, 3, TRUE, COL_HIGHLIGHT); + draw_polygon(fe, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT); } /* new number needs drawing? */ @@ -2381,7 +2565,7 @@ static int game_wants_statusbar(void) return FALSE; } -static int game_timing_state(game_state *state) +static int game_timing_state(game_state *state, game_ui *ui) { return TRUE; } @@ -2414,7 +2598,7 @@ const struct game thegame = { game_changed_state, interpret_move, execute_move, - game_size, + PREFERRED_TILE_SIZE, game_compute_size, game_set_size, game_colours, game_new_drawstate, game_free_drawstate, @@ -2438,7 +2622,7 @@ void draw_text(frontend *fe, int x, int y, int fonttype, int fontsize, void draw_rect(frontend *fe, int x, int y, int w, int h, int colour) {} void draw_line(frontend *fe, int x1, int y1, int x2, int y2, int colour) {} void draw_polygon(frontend *fe, int *coords, int npoints, - int fill, int colour) {} + int fillcolour, int outlinecolour) {} void clip(frontend *fe, int x, int y, int w, int h) {} void unclip(frontend *fe) {} void start_draw(frontend *fe) {} @@ -2448,6 +2632,8 @@ unsigned long random_bits(random_state *state, int bits) { assert(!"Shouldn't get randomness"); return 0; } unsigned long random_upto(random_state *state, unsigned long limit) { assert(!"Shouldn't get randomness"); return 0; } +void shuffle(void *array, int nelts, int eltsize, random_state *rs) +{ assert(!"Shouldn't get randomness"); } void fatal(char *fmt, ...) { @@ -2467,25 +2653,18 @@ int main(int argc, char **argv) { game_params *p; game_state *s; - int recurse = TRUE; char *id = NULL, *desc, *err; - int y, x; int grade = FALSE; + int ret; while (--argc > 0) { char *p = *++argv; - if (!strcmp(p, "-r")) { - recurse = TRUE; - } else if (!strcmp(p, "-n")) { - recurse = FALSE; - } else if (!strcmp(p, "-v")) { + if (!strcmp(p, "-v")) { solver_show_working = TRUE; - recurse = FALSE; } else if (!strcmp(p, "-g")) { grade = TRUE; - recurse = FALSE; } else if (*p == '-') { - fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0]); + fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p); return 1; } else { id = p; @@ -2493,7 +2672,7 @@ int main(int argc, char **argv) } if (!id) { - fprintf(stderr, "usage: %s [-n | -r | -g | -v] \n", argv[0]); + fprintf(stderr, "usage: %s [-g | -v] \n", argv[0]); return 1; } @@ -2513,42 +2692,21 @@ int main(int argc, char **argv) } s = new_game(NULL, p, desc); - if (recurse) { - int ret = rsolve(p->c, p->r, s->grid, NULL, 2); - if (ret > 1) { - fprintf(stderr, "%s: rsolve: multiple solutions detected\n", - argv[0]); - } + ret = solver(p->c, p->r, s->grid, DIFF_RECURSIVE); + if (grade) { + printf("Difficulty rating: %s\n", + ret==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)": + ret==DIFF_SIMPLE ? "Basic (row/column/number elimination required)": + ret==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)": + ret==DIFF_SET ? "Advanced (set elimination required)": + ret==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)": + ret==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)": + ret==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)": + "INTERNAL ERROR: unrecognised difficulty code"); } else { - int ret = nsolve(p->c, p->r, s->grid); - if (grade) { - if (ret == DIFF_IMPOSSIBLE) { - /* - * Now resort to rsolve to determine whether it's - * really soluble. - */ - ret = rsolve(p->c, p->r, s->grid, NULL, 2); - if (ret == 0) - ret = DIFF_IMPOSSIBLE; - else if (ret == 1) - ret = DIFF_RECURSIVE; - else - ret = DIFF_AMBIGUOUS; - } - printf("Difficulty rating: %s\n", - ret==DIFF_BLOCK ? "Trivial (blockwise positional elimination only)": - ret==DIFF_SIMPLE ? "Basic (row/column/number elimination required)": - ret==DIFF_INTERSECT ? "Intermediate (intersectional analysis required)": - ret==DIFF_SET ? "Advanced (set elimination required)": - ret==DIFF_RECURSIVE ? "Unreasonable (guesswork and backtracking required)": - ret==DIFF_AMBIGUOUS ? "Ambiguous (multiple solutions exist)": - ret==DIFF_IMPOSSIBLE ? "Impossible (no solution exists)": - "INTERNAL ERROR: unrecognised difficulty code"); - } + printf("%s\n", grid_text_format(p->c, p->r, s->grid)); } - printf("%s\n", grid_text_format(p->c, p->r, s->grid)); - return 0; }