chiark / gitweb /
Until now, Same Game has been the only puzzle in this collection
authorSimon Tatham <anakin@pobox.com>
Thu, 21 Jul 2005 18:06:31 +0000 (18:06 +0000)
committerSimon Tatham <anakin@pobox.com>
Thu, 21 Jul 2005 18:06:31 +0000 (18:06 +0000)
which is unable to guarantee that every grid it generates can be
solved. So I'm eliminating that exception: this checkin contains a
more sophisticated grid generator which does guarantee solubility.
It's a bit slow (most noticeably on the 15x10c3 preset), and the
quality of the generated grids is slightly weird (a tendency toward
small regions rather than large sweeping areas of contiguous
colour); however, I'm willing to see the latter as a feature for
now, since making the game more challenging while simultaneously
guaranteeing it to be possible sounds like an all-round win to me.

From now on I'm raising my standards for contributions to this
collection. I made this fix to Same Game because I heard a user
_automatically assume_ that any puzzle in my collection would not be
so uncouth as to generate an impossible grid; as of this checkin
that's actually true, and I intend to maintain that standard of
quality henceforth.

(Guaranteeing a _unique_ solution is more of an optional extra,
since there are many games for which it isn't a meaningful concept
or isn't particularly desirable. Which is not to say that _some_
games wouldn't be of unacceptably low quality if they failed to
guarantee uniqueness; it depends on the game.)

[originally from svn r6124]

puzzles.but
samegame.c

index e468df55ed81eac448dca1082ab5d5b46f3cde94..cc3ee75ca63df97727c70ad116169a721178eefc 100644 (file)
@@ -959,11 +959,6 @@ Removing a region causes the rest of the grid to shuffle up:
 blocks that are suspended will fall down (first), and then empty
 columns are filled from the right. 
 
-The game generator does not try to guarantee soluble grids;
-it will, however, ensure that there are at least 2 squares of each 
-colour on the grid at the start (and will forbid custom grids for which
-that would be impossible).
-
 Same Game was contributed to this collection by James Harvey.
 
 \H{samegame-controls} \i{Same Game controls}
@@ -1009,6 +1004,23 @@ any points at all. With the alternative \q{(n-1)^2} system, regions of
 two squares score a point each, and larger regions score relatively
 more points.
 
+\dt \e{Ensure solubility}
+
+\dd If this option is ticked (the default state), generated grids
+will be guaranteed to have at least one solution.
+
+\lcont{
+
+If you turn it off, the game generator will not try to guarantee
+soluble grids; it will, however, still ensure that there are at
+least 2 squares of each colour on the grid at the start (since a
+grid with exactly one square of a given colour is \e{definitely}
+insoluble). Grids generated with this option disabled may contain
+more large areas of contiguous colour, leading to opportunities for
+higher scores; they can also take less time to generate.
+
+}
+
 
 \C{flip} \i{Flip}
 
index 4bb535d9c3dca3481488fe6874799aba447d7291..60e0272fef074adafbcb968120e2f3c0b0499525 100644 (file)
@@ -3,6 +3,65 @@
  *                selecting regions of contiguous colours.
  */
 
+/*
+ * TODO on grid generation:
+ * 
+ *  - Generation speed could still be improved.
+ *     * 15x10c3 is the only really difficult one of the existing
+ *       presets. The others are all either small enough, or have
+ *       the great flexibility given by four colours, that they
+ *       don't take long at all.
+ *     * I still suspect many problems arise from separate
+ *      subareas. I wonder if we can also somehow prioritise left-
+ *      or rightmost insertions so as to avoid area splitting at
+ *      all where feasible? It's not easy, though, because the
+ *      current shuffle-then-try-all-options approach to move
+ *      choice doesn't leave room for `soft' probabilistic
+ *      prioritisation: we either try all class A moves before any
+ *      class B ones, or we don't.
+ *
+ *  - The current generation algorithm inserts exactly two squares
+ *    at a time, with a single exception at the beginning of
+ *    generation for grids of odd overall size. An obvious
+ *    extension would be to permit larger inverse moves during
+ *    generation.
+ *     * this might reduce the number of failed generations by
+ *       making the insertion algorithm more flexible
+ *     * on the other hand, it would be significantly more complex
+ *     * if I do this I'll need to take out the odd-subarea
+ *       avoidance
+ *     * a nice feature of the current algorithm is that the
+ *       computer's `intended' solution always receives the minimum
+ *       possible score, so that pretty much the player's entire
+ *       score represents how much better they did than the
+ *       computer.
+ *
+ *  - Is it possible we can _temporarily_ tolerate neighbouring
+ *    squares of the same colour, until we've finished setting up
+ *    our inverse move?
+ *     * or perhaps even not choose the colour of our inserted
+ *       region until we have finished placing it, and _then_ look
+ *       at what colours border on it?
+ *     * I don't think this is currently meaningful unless we're
+ *       placing more than a domino at a time.
+ *
+ *  - possibly write out a full solution so that Solve can somehow
+ *    show it step by step?
+ *     * aux_info would have to encode the click points
+ *     * solve_game() would have to encode not only those click
+ *      points but also give a move string which reconstructed the
+ *      initial state
+ *     * the game_state would include a pointer to a solution move
+ *      list, plus an index into that list
+ *     * game_changed_state would auto-select the next move if
+ *      handed a new state which had a solution move list active
+ *     * execute_move, if passed such a state as input, would check
+ *      to see whether the move being made was the same as the one
+ *      stated by the solution, and if so would advance the move
+ *      index. Failing that it would return a game_state without a
+ *      solution move list active at all.
+ */
+
 #include <stdio.h>
 #include <stdlib.h>
 #include <string.h>
@@ -38,6 +97,7 @@ enum {
 /* scoresub is 1 or 2 (for (n-1)^2 or (n-2)^2) */
 struct game_params {
     int w, h, ncols, scoresub;
+    int soluble;                      /* choose generation algorithm */
 };
 
 /* These flags must be unique across all uses; in the game_state,
@@ -82,15 +142,16 @@ static game_params *default_params(void)
     ret->h = 5;
     ret->ncols = 3;
     ret->scoresub = 2;
+    ret->soluble = TRUE;
     return ret;
 }
 
 static const struct game_params samegame_presets[] = {
-    { 5, 5, 3, 2 },
-    { 10, 5, 3, 2 },
-    { 15, 10, 3, 2 },
-    { 15, 10, 4, 2 },
-    { 20, 15, 4, 2 }
+    { 5, 5, 3, 2, TRUE },
+    { 10, 5, 3, 2, TRUE },
+    { 15, 10, 3, 2, TRUE },
+    { 15, 10, 4, 2, TRUE },
+    { 20, 15, 4, 2, TRUE }
 };
 
 static int game_fetch_preset(int i, char **name, game_params **params)
@@ -136,26 +197,33 @@ static void decode_params(game_params *params, char const *string)
     } else {
        params->h = params->w;
     }
-    if (*p++ == 'c') {
+    if (*p == 'c') {
+       p++;
        params->ncols = atoi(p);
        while (*p && isdigit((unsigned char)*p)) p++;
     } else {
        params->ncols = 3;
     }
-    if (*p++ == 's') {
+    if (*p == 's') {
+       p++;
        params->scoresub = atoi(p);
        while (*p && isdigit((unsigned char)*p)) p++;
     } else {
        params->scoresub = 2;
     }
+    if (*p == 'r') {
+       p++;
+       params->soluble = FALSE;
+    }
 }
 
 static char *encode_params(game_params *params, int full)
 {
     char ret[80];
 
-    sprintf(ret, "%dx%dc%ds%d",
-           params->w, params->h, params->ncols, params->scoresub);
+    sprintf(ret, "%dx%dc%ds%d%s",
+           params->w, params->h, params->ncols, params->scoresub,
+           full && !params->soluble ? "r" : "");
     return dupstr(ret);
 }
 
@@ -164,7 +232,7 @@ static config_item *game_configure(game_params *params)
     config_item *ret;
     char buf[80];
 
-    ret = snewn(5, config_item);
+    ret = snewn(6, config_item);
 
     ret[0].name = "Width";
     ret[0].type = C_STRING;
@@ -189,10 +257,15 @@ static config_item *game_configure(game_params *params)
     ret[3].sval = ":(n-1)^2:(n-2)^2";
     ret[3].ival = params->scoresub-1;
 
-    ret[4].name = NULL;
-    ret[4].type = C_END;
+    ret[4].name = "Ensure solubility";
+    ret[4].type = C_BOOLEAN;
     ret[4].sval = NULL;
-    ret[4].ival = 0;
+    ret[4].ival = params->soluble;
+
+    ret[5].name = NULL;
+    ret[5].type = C_END;
+    ret[5].sval = NULL;
+    ret[5].ival = 0;
 
     return ret;
 }
@@ -205,6 +278,7 @@ static game_params *custom_params(config_item *cfg)
     ret->h = atoi(cfg[1].sval);
     ret->ncols = atoi(cfg[2].sval);
     ret->scoresub = cfg[3].ival + 1;
+    ret->soluble = cfg[4].ival;
 
     return ret;
 }
@@ -213,15 +287,23 @@ static char *validate_params(game_params *params, int full)
 {
     if (params->w < 1 || params->h < 1)
        return "Width and height must both be positive";
-    if (params->ncols < 2)
-       return "It's too easy with only one colour...";
+
     if (params->ncols > 9)
        return "Maximum of 9 colours";
 
-    /* ...and we must make sure we can generate at least 2 squares
-     * of each colour so it's theoretically soluble. */
-    if ((params->w * params->h) < (params->ncols * 2))
-       return "Too many colours makes given grid size impossible";
+    if (params->soluble) {
+       if (params->ncols < 3)
+           return "Number of colours must be at least three";
+       if (params->w * params->h <= 1)
+           return "Grid area must be greater than 1";
+    } else {
+       if (params->ncols < 2)
+           return "Number of colours must be at least three";
+       /* ...and we must make sure we can generate at least 2 squares
+        * of each colour so it's theoretically soluble. */
+       if ((params->w * params->h) < (params->ncols * 2))
+           return "Too many colours makes given grid size impossible";
+    }
 
     if ((params->scoresub < 1) || (params->scoresub > 2))
        return "Scoring system not recognised";
@@ -229,41 +311,622 @@ static char *validate_params(game_params *params, int full)
     return NULL;
 }
 
-/* Currently this is a very very dumb game-generation engine; it
- * just picks randomly from the tile space. I had a look at a few
- * other same game implementations, and none of them attempt to do
- * anything to try and make sure the grid started off with a nice
- * set of large blocks.
- *
- * It does at least make sure that there are >= 2 of each colour
- * present at the start.
+/*
+ * Guaranteed-soluble grid generator.
  */
+static void gen_grid(int w, int h, int nc, int *grid, random_state *rs)
+{
+    int wh = w*h, tc = nc+1;
+    int i, j, k, c, x, y, pos, n;
+    int *list, *grid2;
+    int ok, failures = 0;
 
-static char *new_game_desc(game_params *params, random_state *rs,
-                          char **aux, int interactive)
+    /*
+     * We'll use `list' to track the possible places to put our
+     * next insertion. There are up to h places to insert in each
+     * column: in a column of height n there are n+1 places because
+     * we can insert at the very bottom or the very top, but a
+     * column of height h can't have anything at all inserted in it
+     * so we have up to h in each column. Likewise, with n columns
+     * present there are n+1 places to fit a new one in between but
+     * we can't insert a column if there are already w; so there
+     * are a maximum of w new columns too. Total is wh + w.
+     */
+    list = snewn(wh + w, int);
+    grid2 = snewn(wh, int);
+
+    do {
+        /*
+         * Start with two or three squares - depending on parity of w*h
+         * - of a random colour.
+         */
+        for (i = 0; i < wh; i++)
+            grid[i] = 0;
+        j = 2 + (wh % 2);
+        c = 1 + random_upto(rs, nc);
+       if (j <= w) {
+           for (i = 0; i < j; i++)
+               grid[(h-1)*w+i] = c;
+       } else {
+           assert(j <= h);
+           for (i = 0; i < j; i++)
+               grid[(h-1-i)*w] = c;
+       }
+
+        /*
+         * Now repeatedly insert a two-square blob in the grid, of
+         * whatever colour will go at the position we chose.
+         */
+        while (1) {
+            n = 0;
+
+            /*
+             * Build up a list of insertion points. Each point is
+             * encoded as y*w+x; insertion points between columns are
+             * encoded as h*w+x.
+             */
+
+            if (grid[wh - 1] == 0) {
+                /*
+                 * The final column is empty, so we can insert new
+                 * columns.
+                 */
+                for (i = 0; i < w; i++) {
+                    list[n++] = wh + i;
+                    if (grid[(h-1)*w + i] == 0)
+                        break;
+                }
+            }
+
+            /*
+             * Now look for places to insert within columns.
+             */
+            for (i = 0; i < w; i++) {
+                if (grid[(h-1)*w+i] == 0)
+                    break;                    /* no more columns */
+
+                if (grid[i] != 0)
+                    continue;         /* this column is full */
+
+                for (j = h; j-- > 0 ;) {
+                    list[n++] = j*w+i;
+                    if (grid[j*w+i] == 0)
+                        break;        /* this column is exhausted */
+                }
+            }
+
+            if (n == 0)
+                break;                /* we're done */
+
+            /*
+             * Shuffle the list.
+             */
+            shuffle(list, n, sizeof(*list), rs);
+
+#ifdef GENERATION_DIAGNOSTICS
+            printf("initial grid:\n");
+            {
+                int x,y;
+                for (y = 0; y < h; y++) {
+                    for (x = 0; x < w; x++) {
+                        if (grid[y*w+x] == 0)
+                            printf("-");
+                        else
+                            printf("%d", grid[y*w+x]);
+                    }
+                    printf("\n");
+                }
+            }
+#endif
+
+            /*
+             * Now go through the list one element at a time and
+             * actually attempt to insert something there.
+             */
+            while (n-- > 0) {
+                int dirs[4], ndirs, dir;
+
+                pos = list[n];
+                x = pos % w;
+                y = pos / w;
+
+                memcpy(grid2, grid, wh * sizeof(int));
+
+                if (y == h) {
+                    /*
+                     * Insert a column at position x.
+                     */
+                    for (i = w-1; i > x; i--)
+                        for (j = 0; j < h; j++)
+                            grid2[j*w+i] = grid2[j*w+(i-1)];
+                    /*
+                     * Clear the new column.
+                     */
+                    for (j = 0; j < h; j++)
+                        grid2[j*w+x] = 0;
+                    /*
+                     * Decrement y so that our first square is actually
+                     * inserted _in_ the grid rather than just below it.
+                     */
+                    y--;
+                }
+
+                /*
+                 * Insert a square within column x at position y.
+                 */
+                for (i = 0; i+1 <= y; i++)
+                    grid2[i*w+x] = grid2[(i+1)*w+x];
+
+#ifdef GENERATION_DIAGNOSTICS
+                printf("trying at n=%d (%d,%d)\n", n, x, y);
+                grid2[y*w+x] = tc;
+                {
+                    int x,y;
+                    for (y = 0; y < h; y++) {
+                        for (x = 0; x < w; x++) {
+                            if (grid2[y*w+x] == 0)
+                                printf("-");
+                            else if (grid2[y*w+x] <= nc)
+                                printf("%d", grid2[y*w+x]);
+                            else
+                                printf("*");
+                        }
+                        printf("\n");
+                    }
+                }
+#endif
+
+                /*
+                 * Pick our square colour so that it doesn't match any
+                 * of its neighbours.
+                 */
+                {
+                    int wrongcol[4], nwrong = 0;
+
+                    /*
+                     * List the neighbouring colours.
+                     */
+                    if (x > 0)
+                        wrongcol[nwrong++] = grid2[y*w+(x-1)];
+                    if (x+1 < w)
+                        wrongcol[nwrong++] = grid2[y*w+(x+1)];
+                    if (y > 0)
+                        wrongcol[nwrong++] = grid2[(y-1)*w+x];
+                    if (y+1 < h)
+                        wrongcol[nwrong++] = grid2[(y+1)*w+x];
+
+                    /*
+                     * Eliminate duplicates. We can afford a shoddy
+                     * algorithm here because the problem size is
+                     * bounded.
+                     */
+                    for (i = j = 0 ;; i++) {
+                        int pos = -1, min = 0;
+                        if (j > 0)
+                            min = wrongcol[j-1];
+                        for (k = i; k < nwrong; k++)
+                            if (wrongcol[k] > min &&
+                                (pos == -1 || wrongcol[k] < wrongcol[pos]))
+                                pos = k;
+                        if (pos >= 0) {
+                            int v = wrongcol[pos];
+                            wrongcol[pos] = wrongcol[j];
+                            wrongcol[j++] = v;
+                        } else
+                            break;
+                    }
+                    nwrong = j;
+
+                    /*
+                     * If no colour will go here, stop trying.
+                     */
+                    if (nwrong == nc)
+                        continue;
+
+                    /*
+                     * Otherwise, pick a colour from the remaining
+                     * ones.
+                     */
+                    c = 1 + random_upto(rs, nc - nwrong);
+                    for (i = 0; i < nwrong; i++) {
+                        if (c >= wrongcol[i])
+                            c++;
+                        else
+                            break;
+                    }
+                }
+
+                /*
+                 * Place the new square.
+                 * 
+                 * Although I've _chosen_ the new region's colour
+                 * (so that we can check adjacency), I'm going to
+                 * actually place it as an invalid colour (tc)
+                 * until I'm sure it's viable. This is so that I
+                 * can conveniently check that I really have made a
+                 * _valid_ inverse move later on.
+                 */
+#ifdef GENERATION_DIAGNOSTICS
+                printf("picked colour %d\n", c);
+#endif
+                grid2[y*w+x] = tc;
+
+                /*
+                 * Now attempt to extend it in one of three ways: left,
+                 * right or up.
+                 */
+                ndirs = 0;
+                if (x > 0 &&
+                    grid2[y*w+(x-1)] != c &&
+                    grid2[x-1] == 0 &&
+                    (y+1 >= h || grid2[(y+1)*w+(x-1)] != c) &&
+                    (y+1 >= h || grid2[(y+1)*w+(x-1)] != 0) &&
+                    (x <= 1 || grid2[y*w+(x-2)] != c))
+                    dirs[ndirs++] = -1;    /* left */
+                if (x+1 < w &&
+                    grid2[y*w+(x+1)] != c &&
+                    grid2[x+1] == 0 &&
+                    (y+1 >= h || grid2[(y+1)*w+(x+1)] != c) &&
+                    (y+1 >= h || grid2[(y+1)*w+(x+1)] != 0) &&
+                    (x+2 >= w || grid2[y*w+(x+2)] != c))
+                    dirs[ndirs++] = +1;    /* right */
+                if (y > 0 &&
+                    grid2[x] == 0 &&
+                    (x <= 0 || grid2[(y-1)*w+(x-1)] != c) &&
+                    (x+1 >= w || grid2[(y-1)*w+(x+1)] != c)) {
+                    /*
+                     * We add this possibility _twice_, so that the
+                     * probability of placing a vertical domino is
+                     * about the same as that of a horizontal. This
+                     * should yield less bias in the generated
+                     * grids.
+                     */
+                    dirs[ndirs++] = 0;     /* up */
+                    dirs[ndirs++] = 0;     /* up */
+                }
+
+                if (ndirs == 0)
+                    continue;
+
+                dir = dirs[random_upto(rs, ndirs)];
+
+#ifdef GENERATION_DIAGNOSTICS
+                printf("picked dir %d\n", dir);
+#endif
+
+                /*
+                 * Insert a square within column (x+dir) at position y.
+                 */
+                for (i = 0; i+1 <= y; i++)
+                    grid2[i*w+x+dir] = grid2[(i+1)*w+x+dir];
+                grid2[y*w+x+dir] = tc;
+
+                /*
+                 * See if we've divided the remaining grid squares
+                 * into sub-areas. If so, we need every sub-area to
+                 * have an even area or we won't be able to
+                 * complete generation.
+                 * 
+                 * If the height is odd and not all columns are
+                 * present, we can increase the area of a subarea
+                 * by adding a new column in it, so in that
+                 * situation we don't mind having as many odd
+                 * subareas as there are spare columns.
+                 * 
+                 * If the height is even, we can't fix it at all.
+                 */
+                {
+                    int nerrs = 0, nfix = 0;
+                    k = 0;             /* current subarea size */
+                    for (i = 0; i < w; i++) {
+                        if (grid2[(h-1)*w+i] == 0) {
+                            if (h % 2)
+                                nfix++;
+                            continue;
+                        }
+                        for (j = 0; j < h && grid2[j*w+i] == 0; j++);
+                        assert(j < h);
+                        if (j == 0) {
+                            /*
+                             * End of previous subarea.
+                             */
+                            if (k % 2)
+                                nerrs++;
+                            k = 0;
+                        } else {
+                            k += j;
+                        }
+                    }
+                    if (k % 2)
+                        nerrs++;
+                    if (nerrs > nfix)
+                        continue;      /* try a different placement */
+                }
+
+                /*
+                 * We've made a move. Verify that it is a valid
+                 * move and that if made it would indeed yield the
+                 * previous grid state. The criteria are:
+                 * 
+                 *  (a) removing all the squares of colour tc (and
+                 *      shuffling the columns up etc) from grid2
+                 *      would yield grid
+                 *  (b) no square of colour tc is adjacent to one
+                 *      of colour c
+                 *  (c) all the squares of colour tc form a single
+                 *      connected component
+                 * 
+                 * We verify the latter property at the same time
+                 * as checking that removing all the tc squares
+                 * would yield the previous grid. Then we colour
+                 * the tc squares in colour c by breadth-first
+                 * search, which conveniently permits us to test
+                 * that they're all connected.
+                 */
+                {
+                    int x1, x2, y1, y2;
+                    int ok = TRUE;
+                    int fillstart = -1, ntc = 0;
+
+#ifdef GENERATION_DIAGNOSTICS
+                    {
+                        int x,y;
+                        printf("testing move (new, old):\n");
+                        for (y = 0; y < h; y++) {
+                            for (x = 0; x < w; x++) {
+                                if (grid2[y*w+x] == 0)
+                                    printf("-");
+                                else if (grid2[y*w+x] <= nc)
+                                    printf("%d", grid2[y*w+x]);
+                                else
+                                    printf("*");
+                            }
+                            printf("   ");
+                            for (x = 0; x < w; x++) {
+                                if (grid[y*w+x] == 0)
+                                    printf("-");
+                                else
+                                    printf("%d", grid[y*w+x]);
+                            }
+                            printf("\n");
+                        }
+                    }
+#endif
+
+                    for (x1 = x2 = 0; x2 < w; x2++) {
+                        int usedcol = FALSE;
+
+                        for (y1 = y2 = h-1; y2 >= 0; y2--) {
+                            if (grid2[y2*w+x2] == tc) {
+                                ntc++;
+                                if (fillstart == -1)
+                                    fillstart = y2*w+x2;
+                                if ((y2+1 < h && grid2[(y2+1)*w+x2] == c) ||
+                                    (y2-1 >= 0 && grid2[(y2-1)*w+x2] == c) ||
+                                    (x2+1 < w && grid2[y2*w+x2+1] == c) ||
+                                    (x2-1 >= 0 && grid2[y2*w+x2-1] == c)) {
+#ifdef GENERATION_DIAGNOSTICS
+                                    printf("adjacency failure at %d,%d\n",
+                                           x2, y2);
+#endif
+                                    ok = FALSE;
+                                }
+                                continue;
+                            }
+                            if (grid2[y2*w+x2] == 0)
+                                break;
+                            usedcol = TRUE;
+                            if (grid2[y2*w+x2] != grid[y1*w+x1]) {
+#ifdef GENERATION_DIAGNOSTICS
+                                printf("matching failure at %d,%d vs %d,%d\n",
+                                       x2, y2, x1, y1);
+#endif
+                                ok = FALSE;
+                            }
+                            y1--;
+                        }
+
+                        /*
+                         * If we've reached the top of the column
+                         * in grid2, verify that we've also reached
+                         * the top of the column in `grid'.
+                         */
+                        if (usedcol) {
+                            while (y1 >= 0) {
+                                if (grid[y1*w+x1] != 0) {
+#ifdef GENERATION_DIAGNOSTICS
+                                    printf("junk at column top (%d,%d)\n",
+                                           x1, y1);
+#endif
+                                    ok = FALSE;
+                                }
+                                y1--;
+                            }
+                        }
+
+                        if (!ok)
+                            break;
+
+                        if (usedcol)
+                            x1++;
+                    }
+
+                    if (!ok) {
+                        assert(!"This should never happen");
+
+                        /*
+                         * If this game is compiled NDEBUG so that
+                         * the assertion doesn't bring it to a
+                         * crashing halt, the only thing we can do
+                         * is to give up, loop round again, and
+                         * hope to randomly avoid making whatever
+                         * type of move just caused this failure.
+                         */
+                        continue;
+                    }
+
+                    /*
+                     * Now use bfs to fill in the tc section as
+                     * colour c. We use `list' to store the set of
+                     * squares we have to process.
+                     */
+                    i = j = 0;
+                    assert(fillstart >= 0);
+                    list[i++] = fillstart;
+#ifdef OUTPUT_SOLUTION
+                    printf("M");
+#endif
+                    while (j < i) {
+                        k = list[j];
+                        x = k % w;
+                        y = k / w;
+#ifdef OUTPUT_SOLUTION
+                        printf("%s%d", j ? "," : "", k);
+#endif
+                        j++;
+
+                        assert(grid2[k] == tc);
+                        grid2[k] = c;
+
+                        if (x > 0 && grid2[k-1] == tc)
+                            list[i++] = k-1;
+                        if (x+1 < w && grid2[k+1] == tc)
+                            list[i++] = k+1;
+                        if (y > 0 && grid2[k-w] == tc)
+                            list[i++] = k-w;
+                        if (y+1 < h && grid2[k+w] == tc)
+                            list[i++] = k+w;
+                    }
+#ifdef OUTPUT_SOLUTION
+                    printf("\n");
+#endif
+
+                    /*
+                     * Check that we've filled the same number of
+                     * tc squares as we originally found.
+                     */
+                    assert(j == ntc);
+                }
+
+                memcpy(grid, grid2, wh * sizeof(int));
+
+                break;                /* done it! */
+            }
+
+#ifdef GENERATION_DIAGNOSTICS
+            {
+                int x,y;
+                printf("n=%d\n", n);
+                for (y = 0; y < h; y++) {
+                    for (x = 0; x < w; x++) {
+                        if (grid[y*w+x] == 0)
+                            printf("-");
+                        else
+                            printf("%d", grid[y*w+x]);
+                    }
+                    printf("\n");
+                }
+            }
+#endif
+
+            if (n < 0)
+                break;
+        }
+
+        ok = TRUE;
+        for (i = 0; i < wh; i++)
+            if (grid[i] == 0) {
+                ok = FALSE;
+                failures++;
+#if defined GENERATION_DIAGNOSTICS || defined SHOW_INCOMPLETE
+                {
+                    int x,y;
+                    printf("incomplete grid:\n");
+                    for (y = 0; y < h; y++) {
+                        for (x = 0; x < w; x++) {
+                            if (grid[y*w+x] == 0)
+                                printf("-");
+                            else
+                                printf("%d", grid[y*w+x]);
+                        }
+                        printf("\n");
+                    }
+                }
+#endif
+                break;
+            }
+
+    } while (!ok);
+
+#if defined GENERATION_DIAGNOSTICS || defined COUNT_FAILURES
+    printf("%d failures\n", failures);
+#endif
+#ifdef GENERATION_DIAGNOSTICS
+    {
+        int x,y;
+        printf("final grid:\n");
+        for (y = 0; y < h; y++) {
+            for (x = 0; x < w; x++) {
+                printf("%d", grid[y*w+x]);
+            }
+            printf("\n");
+        }
+    }
+#endif
+
+    sfree(grid2);
+    sfree(list);
+}
+
+/*
+ * Not-guaranteed-soluble grid generator; kept as a legacy, and in
+ * case someone finds the slightly odd quality of the guaranteed-
+ * soluble grids to be aesthetically displeasing or finds its CPU
+ * utilisation to be excessive.
+ */
+static void gen_grid_random(int w, int h, int nc, int *grid, random_state *rs)
 {
-    char *ret;
-    int n, i, j, c, retlen, *tiles;
+    int i, j, c;
+    int n = w * h;
 
-    n = params->w * params->h;
-    tiles = snewn(n, int);
-    memset(tiles, 0, n*sizeof(int));
+    for (i = 0; i < n; i++)
+       grid[i] = 0;
 
-    /* randomly place two of each colour */
-    for (c = 0; c < params->ncols; c++) {
+    /*
+     * Our sole concession to not gratuitously generating insoluble
+     * grids is to ensure we have at least two of every colour.
+     */
+    for (c = 1; c <= nc; c++) {
        for (j = 0; j < 2; j++) {
            do {
                i = (int)random_upto(rs, n);
-           } while (tiles[i] != 0);
-           tiles[i] = c+1;
+           } while (grid[i] != 0);
+           grid[i] = c;
        }
     }
 
-    /* fill in the rest randomly */
+    /*
+     * Fill in the rest of the grid at random.
+     */
     for (i = 0; i < n; i++) {
-       if (tiles[i] == 0)
-           tiles[i] = (int)random_upto(rs, params->ncols)+1;
+       if (grid[i] == 0)
+           grid[i] = (int)random_upto(rs, nc)+1;
     }
+}
+
+static char *new_game_desc(game_params *params, random_state *rs,
+                          char **aux, int interactive)
+{
+    char *ret;
+    int n, i, retlen, *tiles;
+
+    n = params->w * params->h;
+    tiles = snewn(n, int);
+
+    if (params->soluble)
+       gen_grid(params->w, params->h, params->ncols, tiles, rs);
+    else
+       gen_grid_random(params->w, params->h, params->ncols, tiles, rs);
 
     ret = NULL;
     retlen = 0;