towers.c

   1 /*
   2  * towers.c: the puzzle also known as 'Skyscrapers'.
   3  *
   4  * Possible future work:
   5  *
   6  *  - Relax the upper bound on grid size at 9?
   7  *     + I'd need TOCHAR and FROMCHAR macros a bit like group's, to
   8  *       be used wherever this code has +'0' or -'0'
   9  *     + the pencil marks in the drawstate would need a separate
  10  *       word to live in
  11  *     + the clues outside the grid would have to cope with being
  12  *       multi-digit, meaning in particular that the text formatting
  13  *       would become more unpleasant
  14  *     + most importantly, though, the solver just isn't fast
  15  *       enough. Even at size 9 it can't really do the solver_hard
  16  *       factorial-time enumeration at a sensible rate. Easy puzzles
  17  *       higher than that would be possible, but more latin-squarey
  18  *       than skyscrapery, as it were.
  19  *
  20  *  - UI work?
  21  *     + Allow the user to mark a clue as 'spent' in some way once
  22  *       it's no longer interesting (typically because no
  23  *       arrangement of the remaining possibilities _can_ violate
  24  *       it)?
  25  */
  26
  27 #include <stdio.h>
  28 #include <stdlib.h>
  29 #include <string.h>
  30 #include <assert.h>
  31 #include <ctype.h>
  32 #include <math.h>
  33
  34 #include "puzzles.h"
  35 #include "latin.h"
  36
  37 /*
  38  * Difficulty levels. I do some macro ickery here to ensure that my
  39  * enum and the various forms of my name list always match up.
  40  */
  41 #define DIFFLIST(A) \
  42     A(EASY,Easy,solver_easy,e) \
  43     A(HARD,Hard,solver_hard,h) \
  44     A(EXTREME,Extreme,NULL,x) \
  45     A(UNREASONABLE,Unreasonable,NULL,u)
  46 #define ENUM(upper,title,func,lower) DIFF_ ## upper,
  47 #define TITLE(upper,title,func,lower) #title,
  48 #define ENCODE(upper,title,func,lower) #lower
  49 #define CONFIG(upper,title,func,lower) ":" #title
  50 enum { DIFFLIST(ENUM) DIFFCOUNT };
  51 static char const *const towers_diffnames[] = { DIFFLIST(TITLE) };
  52 static char const towers_diffchars[] = DIFFLIST(ENCODE);
  53 #define DIFFCONFIG DIFFLIST(CONFIG)
  54
  55 enum {
  56     COL_BACKGROUND,
  57     COL_GRID,
  58     COL_USER,
  59     COL_HIGHLIGHT,
  60     COL_ERROR,
  61     COL_PENCIL,
  62     NCOLOURS
  63 };
  64
  65 struct game_params {
  66     int w, diff;
  67 };
  68
  69 struct clues {
  70     int refcount;
  71     int w;
  72     /*
  73      * An array of 4w integers, of which:
  74      *  - the first w run across the top
  75      *  - the next w across the bottom
  76      *  - the third w down the left
  77      *  - the last w down the right.
  78      */
  79     int *clues;
  80
  81     /*
  82      * An array of w*w digits.
  83      */
  84     digit *immutable;
  85 };
  86
  87 /*
  88  * Macros to compute clue indices and coordinates.
  89  */
  90 #define STARTSTEP(start, step, index, w) do { \
  91     if (index < w) \
  92         start = index, step = w; \
  93     else if (index < 2*w) \
  94         start = (w-1)*w+(index-w), step = -w; \
  95     else if (index < 3*w) \
  96         start = w*(index-2*w), step = 1; \
  97     else \
  98         start = w*(index-3*w)+(w-1), step = -1; \
  99 } while (0)
 100 #define CSTARTSTEP(start, step, index, w) \
 101     STARTSTEP(start, step, (((index)+2*w)%(4*w)), w)
 102 #define CLUEPOS(x, y, index, w) do { \
 103     if (index < w) \
 104         x = index, y = -1; \
 105     else if (index < 2*w) \
 106         x = index-w, y = w; \
 107     else if (index < 3*w) \
 108         x = -1, y = index-2*w; \
 109     else \
 110         x = w, y = index-3*w; \
 111 } while (0)
 112
 113 #ifdef STANDALONE_SOLVER
 114 static const char *const cluepos[] = {
 115     "above column", "below column", "left of row", "right of row"
 116 };
 117 #endif
 118
 119 struct game_state {
 120     game_params par;
 121     struct clues *clues;
 122     digit *grid;
 123     int *pencil;                       /* bitmaps using bits 1<<1..1<<n */
 124     int completed, cheated;
 125 };
 126
 127 static game_params *default_params(void)
 128 {
 129     game_params *ret = snew(game_params);
 130
 131     ret->w = 5;
 132     ret->diff = DIFF_EASY;
 133
 134     return ret;
 135 }
 136
 137 const static struct game_params towers_presets[] = {
 138     {  4, DIFF_EASY         },
 139     {  5, DIFF_EASY         },
 140     {  5, DIFF_HARD         },
 141     {  6, DIFF_EASY         },
 142     {  6, DIFF_HARD         },
 143     {  6, DIFF_EXTREME      },
 144     {  6, DIFF_UNREASONABLE },
 145 };
 146
 147 static int game_fetch_preset(int i, char **name, game_params **params)
 148 {
 149     game_params *ret;
 150     char buf[80];
 151
 152     if (i < 0 || i >= lenof(towers_presets))
 153         return FALSE;
 154
 155     ret = snew(game_params);
 156     *ret = towers_presets[i]; /* structure copy */
 157
 158     sprintf(buf, "%dx%d %s", ret->w, ret->w, towers_diffnames[ret->diff]);
 159
 160     *name = dupstr(buf);
 161     *params = ret;
 162     return TRUE;
 163 }
 164
 165 static void free_params(game_params *params)
 166 {
 167     sfree(params);
 168 }
 169
 170 static game_params *dup_params(game_params *params)
 171 {
 172     game_params *ret = snew(game_params);
 173     *ret = *params;                    /* structure copy */
 174     return ret;
 175 }
 176
 177 static void decode_params(game_params *params, char const *string)
 178 {
 179     char const *p = string;
 180
 181     params->w = atoi(p);
 182     while (*p && isdigit((unsigned char)*p)) p++;
 183
 184     if (*p == 'd') {
 185         int i;
 186         p++;
 187         params->diff = DIFFCOUNT+1; /* ...which is invalid */
 188         if (*p) {
 189             for (i = 0; i < DIFFCOUNT; i++) {
 190                 if (*p == towers_diffchars[i])
 191                     params->diff = i;
 192             }
 193             p++;
 194         }
 195     }
 196 }
 197
 198 static char *encode_params(game_params *params, int full)
 199 {
 200     char ret[80];
 201
 202     sprintf(ret, "%d", params->w);
 203     if (full)
 204         sprintf(ret + strlen(ret), "d%c", towers_diffchars[params->diff]);
 205
 206     return dupstr(ret);
 207 }
 208
 209 static config_item *game_configure(game_params *params)
 210 {
 211     config_item *ret;
 212     char buf[80];
 213
 214     ret = snewn(3, config_item);
 215
 216     ret[0].name = "Grid size";
 217     ret[0].type = C_STRING;
 218     sprintf(buf, "%d", params->w);
 219     ret[0].sval = dupstr(buf);
 220     ret[0].ival = 0;
 221
 222     ret[1].name = "Difficulty";
 223     ret[1].type = C_CHOICES;
 224     ret[1].sval = DIFFCONFIG;
 225     ret[1].ival = params->diff;
 226
 227     ret[2].name = NULL;
 228     ret[2].type = C_END;
 229     ret[2].sval = NULL;
 230     ret[2].ival = 0;
 231
 232     return ret;
 233 }
 234
 235 static game_params *custom_params(config_item *cfg)
 236 {
 237     game_params *ret = snew(game_params);
 238
 239     ret->w = atoi(cfg[0].sval);
 240     ret->diff = cfg[1].ival;
 241
 242     return ret;
 243 }
 244
 245 static char *validate_params(game_params *params, int full)
 246 {
 247     if (params->w < 3 || params->w > 9)
 248         return "Grid size must be between 3 and 9";
 249     if (params->diff >= DIFFCOUNT)
 250         return "Unknown difficulty rating";
 251     return NULL;
 252 }
 253
 254 /* ----------------------------------------------------------------------
 255  * Solver.
 256  */
 257
 258 struct solver_ctx {
 259     int w, diff;
 260     int started;
 261     int *clues;
 262     long *iscratch;
 263     int *dscratch;
 264 };
 265
 266 static int solver_easy(struct latin_solver *solver, void *vctx)
 267 {
 268     struct solver_ctx *ctx = (struct solver_ctx *)vctx;
 269     int w = ctx->w;
 270     int c, i, j, n, m, furthest;
 271     int start, step, cstart, cstep, clue, pos, cpos;
 272     int ret = 0;
 273 #ifdef STANDALONE_SOLVER
 274     char prefix[256];
 275 #endif
 276
 277     if (!ctx->started) {
 278         ctx->started = TRUE;
 279         /*
 280          * One-off loop to help get started: when a pair of facing
 281          * clues sum to w+1, it must mean that the row consists of
 282          * two increasing sequences back to back, so we can
 283          * immediately place the highest digit by knowing the
 284          * lengths of those two sequences.
 285          */
 286         for (c = 0; c < 3*w; c = (c == w-1 ? 2*w : c+1)) {
 287             int c2 = c + w;
 288
 289             if (ctx->clues[c] && ctx->clues[c2] &&
 290                 ctx->clues[c] + ctx->clues[c2] == w+1) {
 291                 STARTSTEP(start, step, c, w);
 292                 CSTARTSTEP(cstart, cstep, c, w);
 293                 pos = start + (ctx->clues[c]-1)*step;
 294                 cpos = cstart + (ctx->clues[c]-1)*cstep;
 295                 if (solver->cube[cpos*w+w-1]) {
 296 #ifdef STANDALONE_SOLVER
 297                     if (solver_show_working) {
 298                         printf("%*sfacing clues on %s %d are maximal:\n",
 299                                solver_recurse_depth*4, "",
 300                                c>=2*w ? "row" : "column", c % w + 1);
 301                         printf("%*s  placing %d at (%d,%d)\n",
 302                                solver_recurse_depth*4, "",
 303                                w, pos%w+1, pos/w+1);
 304                     }
 305 #endif
 306                     latin_solver_place(solver, pos%w, pos/w, w);
 307                     ret = 1;
 308                 } else {
 309                     ret = -1;
 310                 }
 311             }
 312         }
 313
 314         if (ret)
 315             return ret;
 316     }
 317
 318     /*
 319      * Go over every clue doing reasonably simple heuristic
 320      * deductions.
 321      */
 322     for (c = 0; c < 4*w; c++) {
 323         clue = ctx->clues[c];
 324         if (!clue)
 325             continue;
 326         STARTSTEP(start, step, c, w);
 327         CSTARTSTEP(cstart, cstep, c, w);
 328
 329         /* Find the location of each number in the row. */
 330         for (i = 0; i < w; i++)
 331             ctx->dscratch[i] = w;
 332         for (i = 0; i < w; i++)
 333             if (solver->grid[start+i*step])
 334                 ctx->dscratch[solver->grid[start+i*step]-1] = i;
 335
 336         n = m = 0;
 337         furthest = w;
 338         for (i = w; i >= 1; i--) {
 339             if (ctx->dscratch[i-1] == w) {
 340                 break;
 341             } else if (ctx->dscratch[i-1] < furthest) {
 342                 furthest = ctx->dscratch[i-1];
 343                 m = i;
 344                 n++;
 345             }
 346         }
 347         if (clue == n+1 && furthest > 1) {
 348 #ifdef STANDALONE_SOLVER
 349             if (solver_show_working)
 350                 sprintf(prefix, "%*sclue %s %d is nearly filled:\n",
 351                         solver_recurse_depth*4, "",
 352                         cluepos[c/w], c%w+1);
 353             else
 354                 prefix[0] = '\0';              /* placate optimiser */
 355 #endif
 356             /*
 357              * We can already see an increasing sequence of the very
 358              * highest numbers, of length one less than that
 359              * specified in the clue. All of those numbers _must_ be
 360              * part of the clue sequence, so the number right next
 361              * to the clue must be the final one - i.e. it must be
 362              * bigger than any of the numbers between it and m. This
 363              * allows us to rule out small numbers in that square.
 364              *
 365              * (This is a generalisation of the obvious deduction
 366              * that when you see a clue saying 1, it must be right
 367              * next to the largest possible number; and similarly,
 368              * when you see a clue saying 2 opposite that, it must
 369              * be right next to the second-largest.)
 370              */
 371             j = furthest-1;  /* number of small numbers we can rule out */
 372             for (i = 1; i <= w && j > 0; i++) {
 373                 if (ctx->dscratch[i-1] < w && ctx->dscratch[i-1] >= furthest)
 374                     continue;          /* skip this number, it's elsewhere */
 375                 j--;
 376                 if (solver->cube[cstart*w+i-1]) {
 377 #ifdef STANDALONE_SOLVER
 378                     if (solver_show_working) {
 379                         printf("%s%*s  ruling out %d at (%d,%d)\n",
 380                                prefix, solver_recurse_depth*4, "",
 381                                i, start%w+1, start/w+1);
 382                         prefix[0] = '\0';
 383                     }
 384 #endif
 385                     solver->cube[cstart*w+i-1] = 0;
 386                     ret = 1;
 387                 }
 388             }
 389         }
 390
 391         if (ret)
 392             return ret;
 393
 394 #ifdef STANDALONE_SOLVER
 395             if (solver_show_working)
 396                 sprintf(prefix, "%*slower bounds for clue %s %d:\n",
 397                         solver_recurse_depth*4, "",
 398                         cluepos[c/w], c%w+1);
 399             else
 400                 prefix[0] = '\0';              /* placate optimiser */
 401 #endif
 402
 403         i = 0;
 404         for (n = w; n > 0; n--) {
 405             /*
 406              * The largest number cannot occur in the first (clue-1)
 407              * squares of the row, or else there wouldn't be space
 408              * for a sufficiently long increasing sequence which it
 409              * terminated. The second-largest number (not counting
 410              * any that are known to be on the far side of a larger
 411              * number and hence excluded from this sequence) cannot
 412              * occur in the first (clue-2) squares, similarly, and
 413              * so on.
 414              */
 415
 416             if (ctx->dscratch[n-1] < w) {
 417                 for (m = n+1; m < w; m++)
 418                     if (ctx->dscratch[m] < ctx->dscratch[n-1])
 419                         break;
 420                 if (m < w)
 421                     continue;          /* this number doesn't count */
 422             }
 423
 424             for (j = 0; j < clue - i - 1; j++)
 425                 if (solver->cube[(cstart + j*cstep)*w+n-1]) {
 426 #ifdef STANDALONE_SOLVER
 427                     if (solver_show_working) {
 428                         int pos = start+j*step;
 429                         printf("%s%*s  ruling out %d at (%d,%d)\n",
 430                                prefix, solver_recurse_depth*4, "",
 431                                n, pos%w+1, pos/w+1);
 432                         prefix[0] = '\0';
 433                     }
 434 #endif
 435                     solver->cube[(cstart + j*cstep)*w+n-1] = 0;
 436                     ret = 1;
 437                 }
 438             i++;
 439         }
 440     }
 441
 442     if (ret)
 443         return ret;
 444
 445     return 0;
 446 }
 447
 448 static int solver_hard(struct latin_solver *solver, void *vctx)
 449 {
 450     struct solver_ctx *ctx = (struct solver_ctx *)vctx;
 451     int w = ctx->w;
 452     int c, i, j, n, best, clue, start, step, ret;
 453     long bitmap;
 454 #ifdef STANDALONE_SOLVER
 455     char prefix[256];
 456 #endif
 457
 458     /*
 459      * Go over every clue analysing all possibilities.
 460      */
 461     for (c = 0; c < 4*w; c++) {
 462         clue = ctx->clues[c];
 463         if (!clue)
 464             continue;
 465         CSTARTSTEP(start, step, c, w);
 466
 467         for (i = 0; i < w; i++)
 468             ctx->iscratch[i] = 0;
 469
 470         /*
 471          * Instead of a tedious physical recursion, I iterate in the
 472          * scratch array through all possibilities. At any given
 473          * moment, i indexes the element of the box that will next
 474          * be incremented.
 475          */
 476         i = 0;
 477         ctx->dscratch[i] = 0;
 478         best = n = 0;
 479         bitmap = 0;
 480
 481         while (1) {
 482             if (i < w) {
 483                 /*
 484                  * Find the next valid value for cell i.
 485                  */
 486                 int limit = (n == clue ? best : w);
 487                 int pos = start + step * i;
 488                 for (j = ctx->dscratch[i] + 1; j <= limit; j++) {
 489                     if (bitmap & (1L << j))
 490                         continue;      /* used this one already */
 491                     if (!solver->cube[pos*w+j-1])
 492                         continue;      /* ruled out already */
 493
 494                     /* Found one. */
 495                     break;
 496                 }
 497
 498                 if (j > limit) {
 499                     /* No valid values left; drop back. */
 500                     i--;
 501                     if (i < 0)
 502                         break;         /* overall iteration is finished */
 503                     bitmap &= ~(1L << ctx->dscratch[i]);
 504                     if (ctx->dscratch[i] == best) {
 505                         n--;
 506                         best = 0;
 507                         for (j = 0; j < i; j++)
 508                             if (best < ctx->dscratch[j])
 509                                 best = ctx->dscratch[j];
 510                     }
 511                 } else {
 512                     /* Got a valid value; store it and move on. */
 513                     bitmap |= 1L << j;
 514                     ctx->dscratch[i++] = j;
 515                     if (j > best) {
 516                         best = j;
 517                         n++;
 518                     }
 519                     ctx->dscratch[i] = 0;
 520                 }
 521             } else {
 522                 if (n == clue) {
 523                     for (j = 0; j < w; j++)
 524                         ctx->iscratch[j] |= 1L << ctx->dscratch[j];
 525                 }
 526                 i--;
 527                 bitmap &= ~(1L << ctx->dscratch[i]);
 528                 if (ctx->dscratch[i] == best) {
 529                     n--;
 530                     best = 0;
 531                     for (j = 0; j < i; j++)
 532                         if (best < ctx->dscratch[j])
 533                             best = ctx->dscratch[j];
 534                 }
 535             }
 536         }
 537
 538 #ifdef STANDALONE_SOLVER
 539         if (solver_show_working)
 540             sprintf(prefix, "%*sexhaustive analysis of clue %s %d:\n",
 541                     solver_recurse_depth*4, "",
 542                     cluepos[c/w], c%w+1);
 543         else
 544             prefix[0] = '\0';          /* placate optimiser */
 545 #endif
 546
 547         ret = 0;
 548
 549         for (i = 0; i < w; i++) {
 550             int pos = start + step * i;
 551             for (j = 1; j <= w; j++) {
 552                 if (solver->cube[pos*w+j-1] &&
 553                     !(ctx->iscratch[i] & (1L << j))) {
 554 #ifdef STANDALONE_SOLVER
 555                     if (solver_show_working) {
 556                         printf("%s%*s  ruling out %d at (%d,%d)\n",
 557                                prefix, solver_recurse_depth*4, "",
 558                                j, pos/w+1, pos%w+1);
 559                         prefix[0] = '\0';
 560                     }
 561 #endif
 562                     solver->cube[pos*w+j-1] = 0;
 563                     ret = 1;
 564                 }
 565             }
 566
 567             /*
 568              * Once we find one clue we can do something with in
 569              * this way, revert to trying easier deductions, so as
 570              * not to generate solver diagnostics that make the
 571              * problem look harder than it is.
 572              */
 573             if (ret)
 574                 return ret;
 575         }
 576     }
 577
 578     return 0;
 579 }
 580
 581 #define SOLVER(upper,title,func,lower) func,
 582 static usersolver_t const towers_solvers[] = { DIFFLIST(SOLVER) };
 583
 584 static int solver(int w, int *clues, digit *soln, int maxdiff)
 585 {
 586     int ret;
 587     struct solver_ctx ctx;
 588
 589     ctx.w = w;
 590     ctx.diff = maxdiff;
 591     ctx.clues = clues;
 592     ctx.started = FALSE;
 593     ctx.iscratch = snewn(w, long);
 594     ctx.dscratch = snewn(w+1, int);
 595
 596     ret = latin_solver(soln, w, maxdiff,
 597                        DIFF_EASY, DIFF_HARD, DIFF_EXTREME,
 598                        DIFF_EXTREME, DIFF_UNREASONABLE,
 599                        towers_solvers, &ctx, NULL, NULL);
 600
 601     sfree(ctx.iscratch);
 602     sfree(ctx.dscratch);
 603
 604     return ret;
 605 }
 606
 607 /* ----------------------------------------------------------------------
 608  * Grid generation.
 609  */
 610
 611 static char *new_game_desc(game_params *params, random_state *rs,
 612                            char **aux, int interactive)
 613 {
 614     int w = params->w, a = w*w;
 615     digit *grid, *soln, *soln2;
 616     int *clues, *order;
 617     int i, ret;
 618     int diff = params->diff;
 619     char *desc, *p;
 620
 621     /*
 622      * Difficulty exceptions: some combinations of size and
 623      * difficulty cannot be satisfied, because all puzzles of at
 624      * most that difficulty are actually even easier.
 625      *
 626      * Remember to re-test this whenever a change is made to the
 627      * solver logic!
 628      *
 629      * I tested it using the following shell command:
 630
 631 for d in e h x u; do
 632   for i in {3..9}; do
 633     echo -n "./towers --generate 1 ${i}d${d}: "
 634     perl -e 'alarm 30; exec @ARGV' ./towers --generate 1 ${i}d${d} >/dev/null \
 635       && echo ok
 636   done
 637 done
 638
 639      * Of course, it's better to do that after taking the exceptions
 640      * _out_, so as to detect exceptions that should be removed as
 641      * well as those which should be added.
 642      */
 643     if (diff > DIFF_HARD && w <= 3)
 644         diff = DIFF_HARD;
 645
 646     grid = NULL;
 647     clues = snewn(4*w, int);
 648     soln = snewn(a, digit);
 649     soln2 = snewn(a, digit);
 650     order = snewn(max(4*w,a), int);
 651
 652     while (1) {
 653         /*
 654          * Construct a latin square to be the solution.
 655          */
 656         sfree(grid);
 657         grid = latin_generate(w, rs);
 658
 659         /*
 660          * Fill in the clues.
 661          */
 662         for (i = 0; i < 4*w; i++) {
 663             int start, step, j, k, best;
 664             STARTSTEP(start, step, i, w);
 665             k = best = 0;
 666             for (j = 0; j < w; j++) {
 667                 if (grid[start+j*step] > best) {
 668                     best = grid[start+j*step];
 669                     k++;
 670                 }
 671             }
 672             clues[i] = k;
 673         }
 674
 675         /*
 676          * Remove the grid numbers and then the clues, one by one,
 677          * for as long as the game remains soluble at the given
 678          * difficulty.
 679          */
 680         memcpy(soln, grid, a);
 681
 682         if (diff == DIFF_EASY && w <= 5) {
 683             /*
 684              * Special case: for Easy-mode grids that are small
 685              * enough, it's nice to be able to find completely empty
 686              * grids.
 687              */
 688             memset(soln2, 0, a);
 689             ret = solver(w, clues, soln2, diff);
 690             if (ret > diff)
 691                 continue;
 692         }
 693
 694         for (i = 0; i < a; i++)
 695             order[i] = i;
 696         shuffle(order, a, sizeof(*order), rs);
 697         for (i = 0; i < a; i++) {
 698             int j = order[i];
 699
 700             memcpy(soln2, grid, a);
 701             soln2[j] = 0;
 702             ret = solver(w, clues, soln2, diff);
 703             if (ret <= diff)
 704                 grid[j] = 0;
 705         }
 706
 707         if (diff > DIFF_EASY) {        /* leave all clues on Easy mode */
 708             for (i = 0; i < 4*w; i++)
 709                 order[i] = i;
 710             shuffle(order, 4*w, sizeof(*order), rs);
 711             for (i = 0; i < 4*w; i++) {
 712                 int j = order[i];
 713                 int clue = clues[j];
 714
 715                 memcpy(soln2, grid, a);
 716                 clues[j] = 0;
 717                 ret = solver(w, clues, soln2, diff);
 718                 if (ret > diff)
 719                     clues[j] = clue;
 720             }
 721         }
 722
 723         /*
 724          * See if the game can be solved at the specified difficulty
 725          * level, but not at the one below.
 726          */
 727         memcpy(soln2, grid, a);
 728         ret = solver(w, clues, soln2, diff);
 729         if (ret != diff)
 730             continue;                  /* go round again */
 731
 732         /*
 733          * We've got a usable puzzle!
 734          */
 735         break;
 736     }
 737
 738     /*
 739      * Encode the puzzle description.
 740      */
 741     desc = snewn(40*a, char);
 742     p = desc;
 743     for (i = 0; i < 4*w; i++) {
 744         p += sprintf(p, "%s%.0d", i?"/":"", clues[i]);
 745     }
 746     for (i = 0; i < a; i++)
 747         if (grid[i])
 748             break;
 749     if (i < a) {
 750         int run = 0;
 751
 752         *p++ = ',';
 753
 754         for (i = 0; i <= a; i++) {
 755             int n = (i < a ? grid[i] : -1);
 756
 757             if (!n)
 758                 run++;
 759             else {
 760                 if (run) {
 761                     while (run > 0) {
 762                         int thisrun = min(run, 26);
 763                         *p++ = thisrun - 1 + 'a';
 764                         run -= thisrun;
 765                     }
 766                 } else {
 767                     /*
 768                      * If there's a number in the very top left or
 769                      * bottom right, there's no point putting an
 770                      * unnecessary _ before or after it.
 771                      */
 772                     if (i > 0 && n > 0)
 773                         *p++ = '_';
 774                 }
 775                 if (n > 0)
 776                     p += sprintf(p, "%d", n);
 777                 run = 0;
 778             }
 779         }
 780     }
 781     *p++ = '\0';
 782     desc = sresize(desc, p - desc, char);
 783
 784     /*
 785      * Encode the solution.
 786      */
 787     *aux = snewn(a+2, char);
 788     (*aux)[0] = 'S';
 789     for (i = 0; i < a; i++)
 790         (*aux)[i+1] = '0' + soln[i];
 791     (*aux)[a+1] = '\0';
 792
 793     sfree(grid);
 794     sfree(clues);
 795     sfree(soln);
 796     sfree(soln2);
 797     sfree(order);
 798
 799     return desc;
 800 }
 801
 802 /* ----------------------------------------------------------------------
 803  * Gameplay.
 804  */
 805
 806 static char *validate_desc(game_params *params, char *desc)
 807 {
 808     int w = params->w, a = w*w;
 809     const char *p = desc;
 810     int i, clue;
 811
 812     /*
 813      * Verify that the right number of clues are given, and that
 814      * they're in range.
 815      */
 816     for (i = 0; i < 4*w; i++) {
 817         if (!*p)
 818             return "Too few clues for grid size";
 819
 820         if (i > 0) {
 821             if (*p != '/')
 822                 return "Expected commas between clues";
 823             p++;
 824         }
 825
 826         if (isdigit((unsigned char)*p)) {
 827             clue = atoi(p);
 828             while (*p && isdigit((unsigned char)*p)) p++;
 829
 830             if (clue <= 0 || clue > w)
 831                 return "Clue number out of range";
 832         }
 833     }
 834     if (*p == '/')
 835         return "Too many clues for grid size";
 836
 837     if (*p == ',') {
 838         /*
 839          * Verify that the right amount of grid data is given, and
 840          * that any grid elements provided are in range.
 841          */
 842         int squares = 0;
 843
 844         p++;
 845         while (*p) {
 846             int c = *p++;
 847             if (c >= 'a' && c <= 'z') {
 848                 squares += c - 'a' + 1;
 849             } else if (c == '_') {
 850                 /* do nothing */;
 851             } else if (c > '0' && c <= '9') {
 852                 int val = atoi(p-1);
 853                 if (val < 1 || val > w)
 854                     return "Out-of-range number in grid description";
 855                 squares++;
 856                 while (*p && isdigit((unsigned char)*p)) p++;
 857             } else
 858                 return "Invalid character in game description";
 859         }
 860
 861         if (squares < a)
 862             return "Not enough data to fill grid";
 863
 864         if (squares > a)
 865             return "Too much data to fit in grid";
 866     }
 867
 868     return NULL;
 869 }
 870
 871 static game_state *new_game(midend *me, game_params *params, char *desc)
 872 {
 873     int w = params->w, a = w*w;
 874     game_state *state = snew(game_state);
 875     const char *p = desc;
 876     int i;
 877
 878     state->par = *params;              /* structure copy */
 879     state->clues = snew(struct clues);
 880     state->clues->refcount = 1;
 881     state->clues->w = w;
 882     state->clues->clues = snewn(4*w, int);
 883     state->clues->immutable = snewn(a, digit);
 884     state->grid = snewn(a, digit);
 885     state->pencil = snewn(a, int);
 886
 887     for (i = 0; i < a; i++) {
 888         state->grid[i] = 0;
 889         state->pencil[i] = 0;
 890     }
 891
 892     memset(state->clues->immutable, 0, a);
 893
 894     for (i = 0; i < 4*w; i++) {
 895         if (i > 0) {
 896             assert(*p == '/');
 897             p++;
 898         }
 899         if (*p && isdigit((unsigned char)*p)) {
 900             state->clues->clues[i] = atoi(p);
 901             while (*p && isdigit((unsigned char)*p)) p++;
 902         } else
 903             state->clues->clues[i] = 0;
 904     }
 905
 906     if (*p == ',') {
 907         int pos = 0;
 908         p++;
 909         while (*p) {
 910             int c = *p++;
 911             if (c >= 'a' && c <= 'z') {
 912                 pos += c - 'a' + 1;
 913             } else if (c == '_') {
 914                 /* do nothing */;
 915             } else if (c > '0' && c <= '9') {
 916                 int val = atoi(p-1);
 917                 assert(val >= 1 && val <= w);
 918                 assert(pos < a);
 919                 state->grid[pos] = state->clues->immutable[pos] = val;
 920                 pos++;
 921                 while (*p && isdigit((unsigned char)*p)) p++;
 922             } else
 923                 assert(!"Corrupt game description");
 924         }
 925         assert(pos == a);
 926     }
 927     assert(!*p);
 928
 929     state->completed = state->cheated = FALSE;
 930
 931     return state;
 932 }
 933
 934 static game_state *dup_game(game_state *state)
 935 {
 936     int w = state->par.w, a = w*w;
 937     game_state *ret = snew(game_state);
 938
 939     ret->par = state->par;             /* structure copy */
 940
 941     ret->clues = state->clues;
 942     ret->clues->refcount++;
 943
 944     ret->grid = snewn(a, digit);
 945     ret->pencil = snewn(a, int);
 946     memcpy(ret->grid, state->grid, a*sizeof(digit));
 947     memcpy(ret->pencil, state->pencil, a*sizeof(int));
 948
 949     ret->completed = state->completed;
 950     ret->cheated = state->cheated;
 951
 952     return ret;
 953 }
 954
 955 static void free_game(game_state *state)
 956 {
 957     sfree(state->grid);
 958     sfree(state->pencil);
 959     if (--state->clues->refcount <= 0) {
 960         sfree(state->clues->immutable);
 961         sfree(state->clues->clues);
 962         sfree(state->clues);
 963     }
 964     sfree(state);
 965 }
 966
 967 static char *solve_game(game_state *state, game_state *currstate,
 968                         char *aux, char **error)
 969 {
 970     int w = state->par.w, a = w*w;
 971     int i, ret;
 972     digit *soln;
 973     char *out;
 974
 975     if (aux)
 976         return dupstr(aux);
 977
 978     soln = snewn(a, digit);
 979     memcpy(soln, state->clues->immutable, a);
 980
 981     ret = solver(w, state->clues->clues, soln, DIFFCOUNT-1);
 982
 983     if (ret == diff_impossible) {
 984         *error = "No solution exists for this puzzle";
 985         out = NULL;
 986     } else if (ret == diff_ambiguous) {
 987         *error = "Multiple solutions exist for this puzzle";
 988         out = NULL;
 989     } else {
 990         out = snewn(a+2, char);
 991         out[0] = 'S';
 992         for (i = 0; i < a; i++)
 993             out[i+1] = '0' + soln[i];
 994         out[a+1] = '\0';
 995     }
 996
 997     sfree(soln);
 998     return out;
 999 }
1000
1001 static int game_can_format_as_text_now(game_params *params)
1002 {
1003     return TRUE;
1004 }
1005
1006 static char *game_text_format(game_state *state)
1007 {
1008     int w = state->par.w /* , a = w*w */;
1009     char *ret;
1010     char *p;
1011     int x, y;
1012     int total;
1013
1014     /*
1015      * We have:
1016      *  - a top clue row, consisting of three spaces, then w clue
1017      *    digits with spaces between (total 2*w+3 chars including
1018      *    newline)
1019      *  - a blank line (one newline)
1020      *  - w main rows, consisting of a left clue digit, two spaces,
1021      *    w grid digits with spaces between, two spaces and a right
1022      *    clue digit (total 2*w+6 chars each including newline)
1023      *  - a blank line (one newline)
1024      *  - a bottom clue row (same as top clue row)
1025      *  - terminating NUL.
1026      *
1027      * Total size is therefore 2*(2*w+3) + 2 + w*(2*w+6) + 1
1028      * = 2w^2+10w+9.
1029      */
1030     total = 2*w*w + 10*w + 9;
1031     ret = snewn(total, char);
1032     p = ret;
1033
1034     /* Top clue row. */
1035     *p++ = ' '; *p++ = ' ';
1036     for (x = 0; x < w; x++) {
1037         *p++ = ' ';
1038         *p++ = (state->clues->clues[x] ? '0' + state->clues->clues[x] : ' ');
1039     }
1040     *p++ = '\n';
1041
1042     /* Blank line. */
1043     *p++ = '\n';
1044
1045     /* Main grid. */
1046     for (y = 0; y < w; y++) {
1047         *p++ = (state->clues->clues[y+2*w] ? '0' + state->clues->clues[y+2*w] :
1048                 ' ');
1049         *p++ = ' ';
1050         for (x = 0; x < w; x++) {
1051             *p++ = ' ';
1052             *p++ = (state->grid[y*w+x] ? '0' + state->grid[y*w+x] : ' ');
1053         }
1054         *p++ = ' '; *p++ = ' ';
1055         *p++ = (state->clues->clues[y+3*w] ? '0' + state->clues->clues[y+3*w] :
1056                 ' ');
1057         *p++ = '\n';
1058     }
1059
1060     /* Blank line. */
1061     *p++ = '\n';
1062
1063     /* Bottom clue row. */
1064     *p++ = ' '; *p++ = ' ';
1065     for (x = 0; x < w; x++) {
1066         *p++ = ' ';
1067         *p++ = (state->clues->clues[x+w] ? '0' + state->clues->clues[x+w] :
1068                 ' ');
1069     }
1070     *p++ = '\n';
1071
1072     *p++ = '\0';
1073     assert(p == ret + total);
1074
1075     return ret;
1076 }
1077
1078 struct game_ui {
1079     /*
1080      * These are the coordinates of the currently highlighted
1081      * square on the grid, if hshow = 1.
1082      */
1083     int hx, hy;
1084     /*
1085      * This indicates whether the current highlight is a
1086      * pencil-mark one or a real one.
1087      */
1088     int hpencil;
1089     /*
1090      * This indicates whether or not we're showing the highlight
1091      * (used to be hx = hy = -1); important so that when we're
1092      * using the cursor keys it doesn't keep coming back at a
1093      * fixed position. When hshow = 1, pressing a valid number
1094      * or letter key or Space will enter that number or letter in the grid.
1095      */
1096     int hshow;
1097     /*
1098      * This indicates whether we're using the highlight as a cursor;
1099      * it means that it doesn't vanish on a keypress, and that it is
1100      * allowed on immutable squares.
1101      */
1102     int hcursor;
1103 };
1104
1105 static game_ui *new_ui(game_state *state)
1106 {
1107     game_ui *ui = snew(game_ui);
1108
1109     ui->hx = ui->hy = 0;
1110     ui->hpencil = ui->hshow = ui->hcursor = 0;
1111
1112     return ui;
1113 }
1114
1115 static void free_ui(game_ui *ui)
1116 {
1117     sfree(ui);
1118 }
1119
1120 static char *encode_ui(game_ui *ui)
1121 {
1122     return NULL;
1123 }
1124
1125 static void decode_ui(game_ui *ui, char *encoding)
1126 {
1127 }
1128
1129 static void game_changed_state(game_ui *ui, game_state *oldstate,
1130                                game_state *newstate)
1131 {
1132     int w = newstate->par.w;
1133     /*
1134      * We prevent pencil-mode highlighting of a filled square, unless
1135      * we're using the cursor keys. So if the user has just filled in
1136      * a square which we had a pencil-mode highlight in (by Undo, or
1137      * by Redo, or by Solve), then we cancel the highlight.
1138      */
1139     if (ui->hshow && ui->hpencil && !ui->hcursor &&
1140         newstate->grid[ui->hy * w + ui->hx] != 0) {
1141         ui->hshow = 0;
1142     }
1143 }
1144
1145 #define PREFERRED_TILESIZE 48
1146 #define TILESIZE (ds->tilesize)
1147 #define BORDER (TILESIZE * 9 / 8)
1148 #define COORD(x) ((x)*TILESIZE + BORDER)
1149 #define FROMCOORD(x) (((x)+(TILESIZE-BORDER)) / TILESIZE - 1)
1150
1151 /* These always return positive values, though y offsets are actually -ve */
1152 #define X_3D_DISP(height, w) ((height) * TILESIZE / (8 * (w)))
1153 #define Y_3D_DISP(height, w) ((height) * TILESIZE / (4 * (w)))
1154
1155 #define FLASH_TIME 0.4F
1156
1157 #define DF_PENCIL_SHIFT 16
1158 #define DF_ERROR 0x8000
1159 #define DF_HIGHLIGHT 0x4000
1160 #define DF_HIGHLIGHT_PENCIL 0x2000
1161 #define DF_IMMUTABLE 0x1000
1162 #define DF_PLAYAREA 0x0800
1163 #define DF_DIGIT_MASK 0x00FF
1164
1165 struct game_drawstate {
1166     int tilesize;
1167     int three_d;                /* default 3D graphics are user-disableable */
1168     int started;
1169     long *tiles;                       /* (w+2)*(w+2) temp space */
1170     long *drawn;                       /* (w+2)*(w+2)*4: current drawn data */
1171     int *errtmp;
1172 };
1173
1174 static int check_errors(game_state *state, int *errors)
1175 {
1176     int w = state->par.w /*, a = w*w */;
1177     int W = w+2, A = W*W;              /* the errors array is (w+2) square */
1178     int *clues = state->clues->clues;
1179     digit *grid = state->grid;
1180     int i, x, y, errs = FALSE;
1181     int tmp[32];
1182
1183     assert(w < lenof(tmp));
1184
1185     if (errors)
1186         for (i = 0; i < A; i++)
1187             errors[i] = 0;
1188
1189     for (y = 0; y < w; y++) {
1190         unsigned long mask = 0, errmask = 0;
1191         for (x = 0; x < w; x++) {
1192             unsigned long bit = 1UL << grid[y*w+x];
1193             errmask |= (mask & bit);
1194             mask |= bit;
1195         }
1196
1197         if (mask != (1L << (w+1)) - (1L << 1)) {
1198             errs = TRUE;
1199             errmask &= ~1UL;
1200             if (errors) {
1201                 for (x = 0; x < w; x++)
1202                     if (errmask & (1UL << grid[y*w+x]))
1203                         errors[(y+1)*W+(x+1)] = TRUE;
1204             }
1205         }
1206     }
1207
1208     for (x = 0; x < w; x++) {
1209         unsigned long mask = 0, errmask = 0;
1210         for (y = 0; y < w; y++) {
1211             unsigned long bit = 1UL << grid[y*w+x];
1212             errmask |= (mask & bit);
1213             mask |= bit;
1214         }
1215
1216         if (mask != (1 << (w+1)) - (1 << 1)) {
1217             errs = TRUE;
1218             errmask &= ~1UL;
1219             if (errors) {
1220                 for (y = 0; y < w; y++)
1221                     if (errmask & (1UL << grid[y*w+x]))
1222                         errors[(y+1)*W+(x+1)] = TRUE;
1223             }
1224         }
1225     }
1226
1227     for (i = 0; i < 4*w; i++) {
1228         int start, step, j, n, best;
1229         STARTSTEP(start, step, i, w);
1230
1231         if (!clues[i])
1232             continue;
1233
1234         best = n = 0;
1235         for (j = 0; j < w; j++) {
1236             int number = grid[start+j*step];
1237             if (!number)
1238                 break;                 /* can't tell what happens next */
1239             if (number > best) {
1240                 best = number;
1241                 n++;
1242             }
1243         }
1244
1245         if (n > clues[i] || (j == w && n < clues[i])) {
1246             if (errors) {
1247                 int x, y;
1248                 CLUEPOS(x, y, i, w);
1249                 errors[(y+1)*W+(x+1)] = TRUE;
1250             }
1251             errs = TRUE;
1252         }
1253     }
1254
1255     return errs;
1256 }
1257
1258 static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
1259                             int x, int y, int button)
1260 {
1261     int w = state->par.w;
1262     int tx, ty;
1263     char buf[80];
1264
1265     button &= ~MOD_MASK;
1266
1267     tx = FROMCOORD(x);
1268     ty = FROMCOORD(y);
1269
1270     if (ds->three_d) {
1271         /*
1272          * In 3D mode, just locating the mouse click in the natural
1273          * square grid may not be sufficient to tell which tower the
1274          * user clicked on. Investigate the _tops_ of the nearby
1275          * towers to see if a click on one grid square was actually
1276          * a click on a tower protruding into that region from
1277          * another.
1278          */
1279         int dx, dy;
1280         for (dy = 0; dy <= 1; dy++)
1281             for (dx = 0; dx >= -1; dx--) {
1282                 int cx = tx + dx, cy = ty + dy;
1283                 if (cx >= 0 && cx < w && cy >= 0 && cy < w) {
1284                     int height = state->grid[cy*w+cx];
1285                     int bx = COORD(cx), by = COORD(cy);
1286                     int ox = bx + X_3D_DISP(height, w);
1287                     int oy = by - Y_3D_DISP(height, w);
1288                     if (/* on top face? */
1289                         (x - ox >= 0 && x - ox < TILESIZE &&
1290                          y - oy >= 0 && y - oy < TILESIZE) ||
1291                         /* in triangle between top-left corners? */
1292                         (ox > bx && x >= bx && x <= ox && y <= by &&
1293                          (by-y) * (ox-bx) <= (by-oy) * (x-bx)) ||
1294                         /* in triangle between bottom-right corners? */
1295                         (ox > bx && x >= bx+TILESIZE && x <= ox+TILESIZE &&
1296                          y >= oy+TILESIZE &&
1297                          (by-y+TILESIZE)*(ox-bx) >= (by-oy)*(x-bx-TILESIZE))) {
1298                         tx = cx;
1299                         ty = cy;
1300                     }
1301                 }
1302             }
1303     }
1304
1305     if (tx >= 0 && tx < w && ty >= 0 && ty < w) {
1306         if (button == LEFT_BUTTON) {
1307             if (tx == ui->hx && ty == ui->hy &&
1308                 ui->hshow && ui->hpencil == 0) {
1309                 ui->hshow = 0;
1310             } else {
1311                 ui->hx = tx;
1312                 ui->hy = ty;
1313                 ui->hshow = !state->clues->immutable[ty*w+tx];
1314                 ui->hpencil = 0;
1315             }
1316             ui->hcursor = 0;
1317             return "";                 /* UI activity occurred */
1318         }
1319         if (button == RIGHT_BUTTON) {
1320             /*
1321              * Pencil-mode highlighting for non filled squares.
1322              */
1323             if (state->grid[ty*w+tx] == 0) {
1324                 if (tx == ui->hx && ty == ui->hy &&
1325                     ui->hshow && ui->hpencil) {
1326                     ui->hshow = 0;
1327                 } else {
1328                     ui->hpencil = 1;
1329                     ui->hx = tx;
1330                     ui->hy = ty;
1331                     ui->hshow = 1;
1332                 }
1333             } else {
1334                 ui->hshow = 0;
1335             }
1336             ui->hcursor = 0;
1337             return "";                 /* UI activity occurred */
1338         }
1339     }
1340     if (IS_CURSOR_MOVE(button)) {
1341         move_cursor(button, &ui->hx, &ui->hy, w, w, 0);
1342         ui->hshow = ui->hcursor = 1;
1343         return "";
1344     }
1345     if (ui->hshow &&
1346         (button == CURSOR_SELECT)) {
1347         ui->hpencil = 1 - ui->hpencil;
1348         ui->hcursor = 1;
1349         return "";
1350     }
1351
1352     if (ui->hshow &&
1353         ((button >= '0' && button <= '9' && button - '0' <= w) ||
1354          button == CURSOR_SELECT2 || button == '\b')) {
1355         int n = button - '0';
1356         if (button == CURSOR_SELECT2 || button == '\b')
1357             n = 0;
1358
1359         /*
1360          * Can't make pencil marks in a filled square. This can only
1361          * become highlighted if we're using cursor keys.
1362          */
1363         if (ui->hpencil && state->grid[ui->hy*w+ui->hx])
1364             return NULL;
1365
1366         /*
1367          * Can't do anything to an immutable square.
1368          */
1369         if (state->clues->immutable[ui->hy*w+ui->hx])
1370             return NULL;
1371
1372         sprintf(buf, "%c%d,%d,%d",
1373                 (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n);
1374
1375         if (!ui->hcursor) ui->hshow = 0;
1376
1377         return dupstr(buf);
1378     }
1379
1380     if (button == 'M' || button == 'm')
1381         return dupstr("M");
1382
1383     return NULL;
1384 }
1385
1386 static game_state *execute_move(game_state *from, char *move)
1387 {
1388     int w = from->par.w, a = w*w;
1389     game_state *ret;
1390     int x, y, i, n;
1391
1392     if (move[0] == 'S') {
1393         ret = dup_game(from);
1394         ret->completed = ret->cheated = TRUE;
1395
1396         for (i = 0; i < a; i++) {
1397             if (move[i+1] < '1' || move[i+1] > '0'+w) {
1398                 free_game(ret);
1399                 return NULL;
1400             }
1401             ret->grid[i] = move[i+1] - '0';
1402             ret->pencil[i] = 0;
1403         }
1404
1405         if (move[a+1] != '\0') {
1406             free_game(ret);
1407             return NULL;
1408         }
1409
1410         return ret;
1411     } else if ((move[0] == 'P' || move[0] == 'R') &&
1412         sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
1413         x >= 0 && x < w && y >= 0 && y < w && n >= 0 && n <= w) {
1414         if (from->clues->immutable[y*w+x])
1415             return NULL;
1416
1417         ret = dup_game(from);
1418         if (move[0] == 'P' && n > 0) {
1419             ret->pencil[y*w+x] ^= 1L << n;
1420         } else {
1421             ret->grid[y*w+x] = n;
1422             ret->pencil[y*w+x] = 0;
1423
1424             if (!ret->completed && !check_errors(ret, NULL))
1425                 ret->completed = TRUE;
1426         }
1427         return ret;
1428     } else if (move[0] == 'M') {
1429         /*
1430          * Fill in absolutely all pencil marks everywhere. (I
1431          * wouldn't use this for actual play, but it's a handy
1432          * starting point when following through a set of
1433          * diagnostics output by the standalone solver.)
1434          */
1435         ret = dup_game(from);
1436         for (i = 0; i < a; i++) {
1437             if (!ret->grid[i])
1438                 ret->pencil[i] = (1L << (w+1)) - (1L << 1);
1439         }
1440         return ret;
1441     } else
1442         return NULL;                   /* couldn't parse move string */
1443 }
1444
1445 /* ----------------------------------------------------------------------
1446  * Drawing routines.
1447  */
1448
1449 #define SIZE(w) ((w) * TILESIZE + 2*BORDER)
1450
1451 static void game_compute_size(game_params *params, int tilesize,
1452                               int *x, int *y)
1453 {
1454     /* Ick: fake up `ds->tilesize' for macro expansion purposes */
1455     struct { int tilesize; } ads, *ds = &ads;
1456     ads.tilesize = tilesize;
1457
1458     *x = *y = SIZE(params->w);
1459 }
1460
1461 static void game_set_size(drawing *dr, game_drawstate *ds,
1462                           game_params *params, int tilesize)
1463 {
1464     ds->tilesize = tilesize;
1465 }
1466
1467 static float *game_colours(frontend *fe, int *ncolours)
1468 {
1469     float *ret = snewn(3 * NCOLOURS, float);
1470
1471     frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
1472
1473     ret[COL_GRID * 3 + 0] = 0.0F;
1474     ret[COL_GRID * 3 + 1] = 0.0F;
1475     ret[COL_GRID * 3 + 2] = 0.0F;
1476
1477     ret[COL_USER * 3 + 0] = 0.0F;
1478     ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
1479     ret[COL_USER * 3 + 2] = 0.0F;
1480
1481     ret[COL_HIGHLIGHT * 3 + 0] = 0.78F * ret[COL_BACKGROUND * 3 + 0];
1482     ret[COL_HIGHLIGHT * 3 + 1] = 0.78F * ret[COL_BACKGROUND * 3 + 1];
1483     ret[COL_HIGHLIGHT * 3 + 2] = 0.78F * ret[COL_BACKGROUND * 3 + 2];
1484
1485     ret[COL_ERROR * 3 + 0] = 1.0F;
1486     ret[COL_ERROR * 3 + 1] = 0.0F;
1487     ret[COL_ERROR * 3 + 2] = 0.0F;
1488
1489     ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
1490     ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
1491     ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
1492
1493     *ncolours = NCOLOURS;
1494     return ret;
1495 }
1496
1497 static game_drawstate *game_new_drawstate(drawing *dr, game_state *state)
1498 {
1499     int w = state->par.w /*, a = w*w */;
1500     struct game_drawstate *ds = snew(struct game_drawstate);
1501     int i;
1502
1503     ds->tilesize = 0;
1504     ds->three_d = !getenv("TOWERS_2D");
1505     ds->started = FALSE;
1506     ds->tiles = snewn((w+2)*(w+2), long);
1507     ds->drawn = snewn((w+2)*(w+2)*4, long);
1508     for (i = 0; i < (w+2)*(w+2)*4; i++)
1509         ds->drawn[i] = -1;
1510     ds->errtmp = snewn((w+2)*(w+2), int);
1511
1512     return ds;
1513 }
1514
1515 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
1516 {
1517     sfree(ds->errtmp);
1518     sfree(ds->tiles);
1519     sfree(ds->drawn);
1520     sfree(ds);
1521 }
1522
1523 static void draw_tile(drawing *dr, game_drawstate *ds, struct clues *clues,
1524                       int x, int y, long tile)
1525 {
1526     int w = clues->w /* , a = w*w */;
1527     int tx, ty, bg;
1528     char str[64];
1529
1530     tx = COORD(x);
1531     ty = COORD(y);
1532
1533     bg = (tile & DF_HIGHLIGHT) ? COL_HIGHLIGHT : COL_BACKGROUND;
1534
1535     /* draw tower */
1536     if (ds->three_d && (tile & DF_PLAYAREA) && (tile & DF_DIGIT_MASK)) {
1537         int coords[8];
1538         int xoff = X_3D_DISP(tile & DF_DIGIT_MASK, w);
1539         int yoff = Y_3D_DISP(tile & DF_DIGIT_MASK, w);
1540
1541         /* left face of tower */
1542         coords[0] = tx;
1543         coords[1] = ty - 1;
1544         coords[2] = tx;
1545         coords[3] = ty + TILESIZE - 1;
1546         coords[4] = coords[2] + xoff;
1547         coords[5] = coords[3] - yoff;
1548         coords[6] = coords[0] + xoff;
1549         coords[7] = coords[1] - yoff;
1550         draw_polygon(dr, coords, 4, bg, COL_GRID);
1551
1552         /* bottom face of tower */
1553         coords[0] = tx + TILESIZE;
1554         coords[1] = ty + TILESIZE - 1;
1555         coords[2] = tx;
1556         coords[3] = ty + TILESIZE - 1;
1557         coords[4] = coords[2] + xoff;
1558         coords[5] = coords[3] - yoff;
1559         coords[6] = coords[0] + xoff;
1560         coords[7] = coords[1] - yoff;
1561         draw_polygon(dr, coords, 4, bg, COL_GRID);
1562
1563         /* now offset all subsequent drawing to the top of the tower */
1564         tx += xoff;
1565         ty -= yoff;
1566     }
1567
1568     /* erase background */
1569     draw_rect(dr, tx, ty, TILESIZE, TILESIZE, bg);
1570
1571     /* pencil-mode highlight */
1572     if (tile & DF_HIGHLIGHT_PENCIL) {
1573         int coords[6];
1574         coords[0] = tx;
1575         coords[1] = ty;
1576         coords[2] = tx+TILESIZE/2;
1577         coords[3] = ty;
1578         coords[4] = tx;
1579         coords[5] = ty+TILESIZE/2;
1580         draw_polygon(dr, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
1581     }
1582
1583     /* draw box outline */
1584     if (tile & DF_PLAYAREA) {
1585         int coords[8];
1586         coords[0] = tx;
1587         coords[1] = ty - 1;
1588         coords[2] = tx + TILESIZE;
1589         coords[3] = ty - 1;
1590         coords[4] = tx + TILESIZE;
1591         coords[5] = ty + TILESIZE - 1;
1592         coords[6] = tx;
1593         coords[7] = ty + TILESIZE - 1;
1594         draw_polygon(dr, coords, 4, -1, COL_GRID);
1595     }
1596
1597     /* new number needs drawing? */
1598     if (tile & DF_DIGIT_MASK) {
1599         str[1] = '\0';
1600         str[0] = (tile & DF_DIGIT_MASK) + '0';
1601         draw_text(dr, tx + TILESIZE/2, ty + TILESIZE/2, FONT_VARIABLE,
1602                   (tile & DF_PLAYAREA ? TILESIZE/2 : TILESIZE*2/5),
1603                   ALIGN_VCENTRE | ALIGN_HCENTRE,
1604                   (tile & DF_ERROR) ? COL_ERROR :
1605                   (x < 0 || y < 0 || x >= w || y >= w) ? COL_GRID :
1606                   (tile & DF_IMMUTABLE) ? COL_GRID : COL_USER, str);
1607     } else {
1608         int i, j, npencil;
1609         int pl, pr, pt, pb;
1610         float bestsize;
1611         int pw, ph, minph, pbest, fontsize;
1612
1613         /* Count the pencil marks required. */
1614         for (i = 1, npencil = 0; i <= w; i++)
1615             if (tile & (1L << (i + DF_PENCIL_SHIFT)))
1616                 npencil++;
1617         if (npencil) {
1618
1619             minph = 2;
1620
1621             /*
1622              * Determine the bounding rectangle within which we're going
1623              * to put the pencil marks.
1624              */
1625             /* Start with the whole square, minus space for impinging towers */
1626             pl = tx + (ds->three_d ? X_3D_DISP(w,w) : 0);
1627             pr = tx + TILESIZE;
1628             pt = ty;
1629             pb = ty + TILESIZE - (ds->three_d ? Y_3D_DISP(w,w) : 0);
1630
1631             /*
1632              * We arrange our pencil marks in a grid layout, with
1633              * the number of rows and columns adjusted to allow the
1634              * maximum font size.
1635              *
1636              * So now we work out what the grid size ought to be.
1637              */
1638             bestsize = 0.0;
1639             pbest = 0;
1640             /* Minimum */
1641             for (pw = 3; pw < max(npencil,4); pw++) {
1642                 float fw, fh, fs;
1643
1644                 ph = (npencil + pw - 1) / pw;
1645                 ph = max(ph, minph);
1646                 fw = (pr - pl) / (float)pw;
1647                 fh = (pb - pt) / (float)ph;
1648                 fs = min(fw, fh);
1649                 if (fs > bestsize) {
1650                     bestsize = fs;
1651                     pbest = pw;
1652                 }
1653             }
1654             assert(pbest > 0);
1655             pw = pbest;
1656             ph = (npencil + pw - 1) / pw;
1657             ph = max(ph, minph);
1658
1659             /*
1660              * Now we've got our grid dimensions, work out the pixel
1661              * size of a grid element, and round it to the nearest
1662              * pixel. (We don't want rounding errors to make the
1663              * grid look uneven at low pixel sizes.)
1664              */
1665             fontsize = min((pr - pl) / pw, (pb - pt) / ph);
1666
1667             /*
1668              * Centre the resulting figure in the square.
1669              */
1670             pl = pl + (pr - pl - fontsize * pw) / 2;
1671             pt = pt + (pb - pt - fontsize * ph) / 2;
1672
1673             /*
1674              * Now actually draw the pencil marks.
1675              */
1676             for (i = 1, j = 0; i <= w; i++)
1677                 if (tile & (1L << (i + DF_PENCIL_SHIFT))) {
1678                     int dx = j % pw, dy = j / pw;
1679
1680                     str[1] = '\0';
1681                     str[0] = i + '0';
1682                     draw_text(dr, pl + fontsize * (2*dx+1) / 2,
1683                               pt + fontsize * (2*dy+1) / 2,
1684                               FONT_VARIABLE, fontsize,
1685                               ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
1686                     j++;
1687                 }
1688         }
1689     }
1690 }
1691
1692 static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
1693                         game_state *state, int dir, game_ui *ui,
1694                         float animtime, float flashtime)
1695 {
1696     int w = state->par.w /*, a = w*w */;
1697     int i, x, y;
1698
1699     if (!ds->started) {
1700         /*
1701          * The initial contents of the window are not guaranteed and
1702          * can vary with front ends. To be on the safe side, all
1703          * games should start by drawing a big background-colour
1704          * rectangle covering the whole window.
1705          */
1706         draw_rect(dr, 0, 0, SIZE(w), SIZE(w), COL_BACKGROUND);
1707
1708         draw_update(dr, 0, 0, SIZE(w), SIZE(w));
1709
1710         ds->started = TRUE;
1711     }
1712
1713     check_errors(state, ds->errtmp);
1714
1715     /*
1716      * Work out what data each tile should contain.
1717      */
1718     for (i = 0; i < (w+2)*(w+2); i++)
1719         ds->tiles[i] = 0;              /* completely blank square */
1720     /* The clue squares... */
1721     for (i = 0; i < 4*w; i++) {
1722         long tile = state->clues->clues[i];
1723
1724         CLUEPOS(x, y, i, w);
1725
1726         if (ds->errtmp[(y+1)*(w+2)+(x+1)])
1727             tile |= DF_ERROR;
1728
1729         ds->tiles[(y+1)*(w+2)+(x+1)] = tile;
1730     }
1731     /* ... and the main grid. */
1732     for (y = 0; y < w; y++) {
1733         for (x = 0; x < w; x++) {
1734             long tile = DF_PLAYAREA;
1735
1736             if (state->grid[y*w+x])
1737                 tile |= state->grid[y*w+x];
1738             else
1739                 tile |= (long)state->pencil[y*w+x] << DF_PENCIL_SHIFT;
1740
1741             if (ui->hshow && ui->hx == x && ui->hy == y)
1742                 tile |= (ui->hpencil ? DF_HIGHLIGHT_PENCIL : DF_HIGHLIGHT);
1743
1744             if (state->clues->immutable[y*w+x])
1745                 tile |= DF_IMMUTABLE;
1746
1747             if (flashtime > 0 &&
1748                 (flashtime <= FLASH_TIME/3 ||
1749                  flashtime >= FLASH_TIME*2/3))
1750                 tile |= DF_HIGHLIGHT;  /* completion flash */
1751
1752             if (ds->errtmp[(y+1)*(w+2)+(x+1)])
1753                 tile |= DF_ERROR;
1754
1755             ds->tiles[(y+1)*(w+2)+(x+1)] = tile;
1756         }
1757     }
1758
1759     /*
1760      * Now actually draw anything that needs to be changed.
1761      */
1762     for (y = 0; y < w+2; y++) {
1763         for (x = 0; x < w+2; x++) {
1764             long tl, tr, bl, br;
1765             int i = y*(w+2)+x;
1766
1767             tr = ds->tiles[y*(w+2)+x];
1768             tl = (x == 0 ? 0 : ds->tiles[y*(w+2)+(x-1)]);
1769             br = (y == w+1 ? 0 : ds->tiles[(y+1)*(w+2)+x]);
1770             bl = (x == 0 || y == w+1 ? 0 : ds->tiles[(y+1)*(w+2)+(x-1)]);
1771
1772             if (ds->drawn[i*4] != tl || ds->drawn[i*4+1] != tr ||
1773                 ds->drawn[i*4+2] != bl || ds->drawn[i*4+3] != br) {
1774                 clip(dr, COORD(x-1), COORD(y-1), TILESIZE, TILESIZE);
1775
1776                 draw_tile(dr, ds, state->clues, x-1, y-1, tr);
1777                 if (x > 0)
1778                     draw_tile(dr, ds, state->clues, x-2, y-1, tl);
1779                 if (y <= w)
1780                     draw_tile(dr, ds, state->clues, x-1, y, br);
1781                 if (x > 0 && y <= w)
1782                     draw_tile(dr, ds, state->clues, x-2, y, bl);
1783
1784                 unclip(dr);
1785                 draw_update(dr, COORD(x-1), COORD(y-1), TILESIZE, TILESIZE);
1786
1787                 ds->drawn[i*4] = tl;
1788                 ds->drawn[i*4+1] = tr;
1789                 ds->drawn[i*4+2] = bl;
1790                 ds->drawn[i*4+3] = br;
1791             }
1792         }
1793     }
1794 }
1795
1796 static float game_anim_length(game_state *oldstate, game_state *newstate,
1797                               int dir, game_ui *ui)
1798 {
1799     return 0.0F;
1800 }
1801
1802 static float game_flash_length(game_state *oldstate, game_state *newstate,
1803                                int dir, game_ui *ui)
1804 {
1805     if (!oldstate->completed && newstate->completed &&
1806         !oldstate->cheated && !newstate->cheated)
1807         return FLASH_TIME;
1808     return 0.0F;
1809 }
1810
1811 static int game_status(game_state *state)
1812 {
1813     return state->completed ? +1 : 0;
1814 }
1815
1816 static int game_timing_state(game_state *state, game_ui *ui)
1817 {
1818     if (state->completed)
1819         return FALSE;
1820     return TRUE;
1821 }
1822
1823 static void game_print_size(game_params *params, float *x, float *y)
1824 {
1825     int pw, ph;
1826
1827     /*
1828      * We use 9mm squares by default, like Solo.
1829      */
1830     game_compute_size(params, 900, &pw, &ph);
1831     *x = pw / 100.0F;
1832     *y = ph / 100.0F;
1833 }
1834
1835 static void game_print(drawing *dr, game_state *state, int tilesize)
1836 {
1837     int w = state->par.w;
1838     int ink = print_mono_colour(dr, 0);
1839     int i, x, y;
1840
1841     /* Ick: fake up `ds->tilesize' for macro expansion purposes */
1842     game_drawstate ads, *ds = &ads;
1843     game_set_size(dr, ds, NULL, tilesize);
1844
1845     /*
1846      * Border.
1847      */
1848     print_line_width(dr, 3 * TILESIZE / 40);
1849     draw_rect_outline(dr, BORDER, BORDER, w*TILESIZE, w*TILESIZE, ink);
1850
1851     /*
1852      * Main grid.
1853      */
1854     for (x = 1; x < w; x++) {
1855         print_line_width(dr, TILESIZE / 40);
1856         draw_line(dr, BORDER+x*TILESIZE, BORDER,
1857                   BORDER+x*TILESIZE, BORDER+w*TILESIZE, ink);
1858     }
1859     for (y = 1; y < w; y++) {
1860         print_line_width(dr, TILESIZE / 40);
1861         draw_line(dr, BORDER, BORDER+y*TILESIZE,
1862                   BORDER+w*TILESIZE, BORDER+y*TILESIZE, ink);
1863     }
1864
1865     /*
1866      * Clues.
1867      */
1868     for (i = 0; i < 4*w; i++) {
1869         char str[128];
1870
1871         if (!state->clues->clues[i])
1872             continue;
1873
1874         CLUEPOS(x, y, i, w);
1875
1876         sprintf (str, "%d", state->clues->clues[i]);
1877
1878         draw_text(dr, BORDER + x*TILESIZE + TILESIZE/2,
1879                   BORDER + y*TILESIZE + TILESIZE/2,
1880                   FONT_VARIABLE, TILESIZE/2,
1881                   ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
1882     }
1883
1884     /*
1885      * Numbers for the solution, if any.
1886      */
1887     for (y = 0; y < w; y++)
1888         for (x = 0; x < w; x++)
1889             if (state->grid[y*w+x]) {
1890                 char str[2];
1891                 str[1] = '\0';
1892                 str[0] = state->grid[y*w+x] + '0';
1893                 draw_text(dr, BORDER + x*TILESIZE + TILESIZE/2,
1894                           BORDER + y*TILESIZE + TILESIZE/2,
1895                           FONT_VARIABLE, TILESIZE/2,
1896                           ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
1897             }
1898 }
1899
1900 #ifdef COMBINED
1901 #define thegame towers
1902 #endif
1903
1904 const struct game thegame = {
1905     "Towers", "games.towers", "towers",
1906     default_params,
1907     game_fetch_preset,
1908     decode_params,
1909     encode_params,
1910     free_params,
1911     dup_params,
1912     TRUE, game_configure, custom_params,
1913     validate_params,
1914     new_game_desc,
1915     validate_desc,
1916     new_game,
1917     dup_game,
1918     free_game,
1919     TRUE, solve_game,
1920     TRUE, game_can_format_as_text_now, game_text_format,
1921     new_ui,
1922     free_ui,
1923     encode_ui,
1924     decode_ui,
1925     game_changed_state,
1926     interpret_move,
1927     execute_move,
1928     PREFERRED_TILESIZE, game_compute_size, game_set_size,
1929     game_colours,
1930     game_new_drawstate,
1931     game_free_drawstate,
1932     game_redraw,
1933     game_anim_length,
1934     game_flash_length,
1935     game_status,
1936     TRUE, FALSE, game_print_size, game_print,
1937     FALSE,                             /* wants_statusbar */
1938     FALSE, game_timing_state,
1939     REQUIRE_RBUTTON | REQUIRE_NUMPAD,  /* flags */
1940 };
1941
1942 #ifdef STANDALONE_SOLVER
1943
1944 #include <stdarg.h>
1945
1946 int main(int argc, char **argv)
1947 {
1948     game_params *p;
1949     game_state *s;
1950     char *id = NULL, *desc, *err;
1951     int grade = FALSE;
1952     int ret, diff, really_show_working = FALSE;
1953
1954     while (--argc > 0) {
1955         char *p = *++argv;
1956         if (!strcmp(p, "-v")) {
1957             really_show_working = TRUE;
1958         } else if (!strcmp(p, "-g")) {
1959             grade = TRUE;
1960         } else if (*p == '-') {
1961             fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
1962             return 1;
1963         } else {
1964             id = p;
1965         }
1966     }
1967
1968     if (!id) {
1969         fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
1970         return 1;
1971     }
1972
1973     desc = strchr(id, ':');
1974     if (!desc) {
1975         fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
1976         return 1;
1977     }
1978     *desc++ = '\0';
1979
1980     p = default_params();
1981     decode_params(p, id);
1982     err = validate_desc(p, desc);
1983     if (err) {
1984         fprintf(stderr, "%s: %s\n", argv[0], err);
1985         return 1;
1986     }
1987     s = new_game(NULL, p, desc);
1988
1989     /*
1990      * When solving an Easy puzzle, we don't want to bother the
1991      * user with Hard-level deductions. For this reason, we grade
1992      * the puzzle internally before doing anything else.
1993      */
1994     ret = -1;                          /* placate optimiser */
1995     solver_show_working = FALSE;
1996     for (diff = 0; diff < DIFFCOUNT; diff++) {
1997         memcpy(s->grid, s->clues->immutable, p->w * p->w);
1998         ret = solver(p->w, s->clues->clues, s->grid, diff);
1999         if (ret <= diff)
2000             break;
2001     }
2002
2003     if (diff == DIFFCOUNT) {
2004         if (grade)
2005             printf("Difficulty rating: ambiguous\n");
2006         else
2007             printf("Unable to find a unique solution\n");
2008     } else {
2009         if (grade) {
2010             if (ret == diff_impossible)
2011                 printf("Difficulty rating: impossible (no solution exists)\n");
2012             else
2013                 printf("Difficulty rating: %s\n", towers_diffnames[ret]);
2014         } else {
2015             solver_show_working = really_show_working;
2016             memcpy(s->grid, s->clues->immutable, p->w * p->w);
2017             ret = solver(p->w, s->clues->clues, s->grid, diff);
2018             if (ret != diff)
2019                 printf("Puzzle is inconsistent\n");
2020             else
2021                 fputs(game_text_format(s), stdout);
2022         }
2023     }
2024
2025     return 0;
2026 }
2027
2028 #endif
2029
2030 /* vim: set shiftwidth=4 tabstop=8: */