puzzles: refactor and resync with upstream

This brings puzzles up-to-date with upstream revision
2d333750272c3967cfd5cd3677572cddeaad5932, though certain changes made
by me, including cursor-only Untangle and some compilation fixes
remain. Upstream code has been moved to its separate subdirectory and
future syncs can be done by simply copying over the new sources.

Change-Id: Ia6506ca5f78c3627165ea6791d38db414ace0804

1 files changed, 2104 insertions, 0 deletions

diff --git a/apps/plugins/puzzles/src/towers.c b/apps/plugins/puzzles/src/towers.c
new file mode 100644
index 0000000000..a3a7e55a45
--- /dev/null
+++ b/apps/plugins/puzzles/src/towers.c
@@ -0,0 +1,2104 @@
+/*
+ * towers.c: the puzzle also known as 'Skyscrapers'.
+ *
+ * Possible future work:
+ *
+ *  - Relax the upper bound on grid size at 9?
+ *     + I'd need TOCHAR and FROMCHAR macros a bit like group's, to
+ *       be used wherever this code has +'0' or -'0'
+ *     + the pencil marks in the drawstate would need a separate
+ *       word to live in
+ *     + the clues outside the grid would have to cope with being
+ *       multi-digit, meaning in particular that the text formatting
+ *       would become more unpleasant
+ *     + most importantly, though, the solver just isn't fast
+ *       enough. Even at size 9 it can't really do the solver_hard
+ *       factorial-time enumeration at a sensible rate. Easy puzzles
+ *       higher than that would be possible, but more latin-squarey
+ *       than skyscrapery, as it were.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+#include <ctype.h>
+#include <math.h>
+
+#include "puzzles.h"
+#include "latin.h"
+
+/*
+ * Difficulty levels. I do some macro ickery here to ensure that my
+ * enum and the various forms of my name list always match up.
+ */
+#define DIFFLIST(A) \
+    A(EASY,Easy,solver_easy,e) \
+    A(HARD,Hard,solver_hard,h) \
+    A(EXTREME,Extreme,NULL,x) \
+    A(UNREASONABLE,Unreasonable,NULL,u)
+#define ENUM(upper,title,func,lower) DIFF_ ## upper,
+#define TITLE(upper,title,func,lower) #title,
+#define ENCODE(upper,title,func,lower) #lower
+#define CONFIG(upper,title,func,lower) ":" #title
+enum { DIFFLIST(ENUM) DIFFCOUNT };
+static char const *const towers_diffnames[] = { DIFFLIST(TITLE) };
+static char const towers_diffchars[] = DIFFLIST(ENCODE);
+#define DIFFCONFIG DIFFLIST(CONFIG)
+
+enum {
+    COL_BACKGROUND,
+    COL_GRID,
+    COL_USER,
+    COL_HIGHLIGHT,
+    COL_ERROR,
+    COL_PENCIL,
+    COL_DONE,
+    NCOLOURS
+};
+
+struct game_params {
+    int w, diff;
+};
+
+struct clues {
+    int refcount;
+    int w;
+    /*
+     * An array of 4w integers, of which:
+     *  - the first w run across the top
+     *  - the next w across the bottom
+     *  - the third w down the left
+     *  - the last w down the right.
+     */
+    int *clues;
+
+    /*
+     * An array of w*w digits.
+     */
+    digit *immutable;
+};
+
+/*
+ * Macros to compute clue indices and coordinates.
+ */
+#define STARTSTEP(start, step, index, w) do { \
+    if (index < w) \
+        start = index, step = w; \
+    else if (index < 2*w) \
+        start = (w-1)*w+(index-w), step = -w; \
+    else if (index < 3*w) \
+        start = w*(index-2*w), step = 1; \
+    else \
+        start = w*(index-3*w)+(w-1), step = -1; \
+} while (0)
+#define CSTARTSTEP(start, step, index, w) \
+    STARTSTEP(start, step, (((index)+2*w)%(4*w)), w)
+#define CLUEPOS(x, y, index, w) do { \
+    if (index < w) \
+        x = index, y = -1; \
+    else if (index < 2*w) \
+        x = index-w, y = w; \
+    else if (index < 3*w) \
+        x = -1, y = index-2*w; \
+    else \
+        x = w, y = index-3*w; \
+} while (0)
+
+#ifdef STANDALONE_SOLVER
+static const char *const cluepos[] = {
+    "above column", "below column", "left of row", "right of row"
+};
+#endif
+
+struct game_state {
+    game_params par;
+    struct clues *clues;
+    unsigned char *clues_done;
+    digit *grid;
+    int *pencil;                       /* bitmaps using bits 1<<1..1<<n */
+    int completed, cheated;
+};
+
+static game_params *default_params(void)
+{
+    game_params *ret = snew(game_params);
+
+    ret->w = 5;
+    ret->diff = DIFF_EASY;
+
+    return ret;
+}
+
+const static struct game_params towers_presets[] = {
+    {  4, DIFF_EASY         },
+    {  5, DIFF_EASY         },
+    {  5, DIFF_HARD         },
+    {  6, DIFF_EASY         },
+    {  6, DIFF_HARD         },
+    {  6, DIFF_EXTREME      },
+    {  6, DIFF_UNREASONABLE },
+};
+
+static int game_fetch_preset(int i, char **name, game_params **params)
+{
+    game_params *ret;
+    char buf[80];
+
+    if (i < 0 || i >= lenof(towers_presets))
+        return FALSE;
+
+    ret = snew(game_params);
+    *ret = towers_presets[i]; /* structure copy */
+
+    sprintf(buf, "%dx%d %s", ret->w, ret->w, towers_diffnames[ret->diff]);
+
+    *name = dupstr(buf);
+    *params = ret;
+    return TRUE;
+}
+
+static void free_params(game_params *params)
+{
+    sfree(params);
+}
+
+static game_params *dup_params(const game_params *params)
+{
+    game_params *ret = snew(game_params);
+    *ret = *params;                    /* structure copy */
+    return ret;
+}
+
+static void decode_params(game_params *params, char const *string)
+{
+    char const *p = string;
+
+    params->w = atoi(p);
+    while (*p && isdigit((unsigned char)*p)) p++;
+
+    if (*p == 'd') {
+        int i;
+        p++;
+        params->diff = DIFFCOUNT+1; /* ...which is invalid */
+        if (*p) {
+            for (i = 0; i < DIFFCOUNT; i++) {
+                if (*p == towers_diffchars[i])
+                    params->diff = i;
+            }
+            p++;
+        }
+    }
+}
+
+static char *encode_params(const game_params *params, int full)
+{
+    char ret[80];
+
+    sprintf(ret, "%d", params->w);
+    if (full)
+        sprintf(ret + strlen(ret), "d%c", towers_diffchars[params->diff]);
+
+    return dupstr(ret);
+}
+
+static config_item *game_configure(const game_params *params)
+{
+    config_item *ret;
+    char buf[80];
+
+    ret = snewn(3, config_item);
+
+    ret[0].name = "Grid size";
+    ret[0].type = C_STRING;
+    sprintf(buf, "%d", params->w);
+    ret[0].sval = dupstr(buf);
+    ret[0].ival = 0;
+
+    ret[1].name = "Difficulty";
+    ret[1].type = C_CHOICES;
+    ret[1].sval = DIFFCONFIG;
+    ret[1].ival = params->diff;
+
+    ret[2].name = NULL;
+    ret[2].type = C_END;
+    ret[2].sval = NULL;
+    ret[2].ival = 0;
+
+    return ret;
+}
+
+static game_params *custom_params(const config_item *cfg)
+{
+    game_params *ret = snew(game_params);
+
+    ret->w = atoi(cfg[0].sval);
+    ret->diff = cfg[1].ival;
+
+    return ret;
+}
+
+static char *validate_params(const game_params *params, int full)
+{
+    if (params->w < 3 || params->w > 9)
+        return "Grid size must be between 3 and 9";
+    if (params->diff >= DIFFCOUNT)
+        return "Unknown difficulty rating";
+    return NULL;
+}
+
+/* ----------------------------------------------------------------------
+ * Solver.
+ */
+
+struct solver_ctx {
+    int w, diff;
+    int started;
+    int *clues;
+    long *iscratch;
+    int *dscratch;
+};
+
+static int solver_easy(struct latin_solver *solver, void *vctx)
+{
+    struct solver_ctx *ctx = (struct solver_ctx *)vctx;
+    int w = ctx->w;
+    int c, i, j, n, m, furthest;
+    int start, step, cstart, cstep, clue, pos, cpos;
+    int ret = 0;
+#ifdef STANDALONE_SOLVER
+    char prefix[256];
+#endif
+
+    if (!ctx->started) {
+        ctx->started = TRUE;
+        /*
+         * One-off loop to help get started: when a pair of facing
+         * clues sum to w+1, it must mean that the row consists of
+         * two increasing sequences back to back, so we can
+         * immediately place the highest digit by knowing the
+         * lengths of those two sequences.
+         */
+        for (c = 0; c < 3*w; c = (c == w-1 ? 2*w : c+1)) {
+            int c2 = c + w;
+
+            if (ctx->clues[c] && ctx->clues[c2] &&
+                ctx->clues[c] + ctx->clues[c2] == w+1) {
+                STARTSTEP(start, step, c, w);
+                CSTARTSTEP(cstart, cstep, c, w);
+                pos = start + (ctx->clues[c]-1)*step;
+                cpos = cstart + (ctx->clues[c]-1)*cstep;
+                if (solver->cube[cpos*w+w-1]) {
+#ifdef STANDALONE_SOLVER
+                    if (solver_show_working) {
+                        printf("%*sfacing clues on %s %d are maximal:\n",
+                               solver_recurse_depth*4, "",
+                               c>=2*w ? "row" : "column", c % w + 1);
+                        printf("%*s  placing %d at (%d,%d)\n",
+                               solver_recurse_depth*4, "",
+                               w, pos%w+1, pos/w+1);
+                    }
+#endif
+                    latin_solver_place(solver, pos%w, pos/w, w);
+                    ret = 1;
+                } else {
+                    ret = -1;
+                }
+            }
+        }
+
+        if (ret)
+            return ret;
+    }
+
+    /*
+     * Go over every clue doing reasonably simple heuristic
+     * deductions.
+     */
+    for (c = 0; c < 4*w; c++) {
+        clue = ctx->clues[c];
+        if (!clue)
+            continue;
+        STARTSTEP(start, step, c, w);
+        CSTARTSTEP(cstart, cstep, c, w);
+
+        /* Find the location of each number in the row. */
+        for (i = 0; i < w; i++)
+            ctx->dscratch[i] = w;
+        for (i = 0; i < w; i++)
+            if (solver->grid[start+i*step])
+                ctx->dscratch[solver->grid[start+i*step]-1] = i;
+
+        n = m = 0;
+        furthest = w;
+        for (i = w; i >= 1; i--) {
+            if (ctx->dscratch[i-1] == w) {
+                break;
+            } else if (ctx->dscratch[i-1] < furthest) {
+                furthest = ctx->dscratch[i-1];
+                m = i;
+                n++;
+            }
+        }
+        if (clue == n+1 && furthest > 1) {
+#ifdef STANDALONE_SOLVER
+            if (solver_show_working)
+                sprintf(prefix, "%*sclue %s %d is nearly filled:\n",
+                        solver_recurse_depth*4, "",
+                        cluepos[c/w], c%w+1);
+            else
+                prefix[0] = '\0';              /* placate optimiser */
+#endif
+            /*
+             * We can already see an increasing sequence of the very
+             * highest numbers, of length one less than that
+             * specified in the clue. All of those numbers _must_ be
+             * part of the clue sequence, so the number right next
+             * to the clue must be the final one - i.e. it must be
+             * bigger than any of the numbers between it and m. This
+             * allows us to rule out small numbers in that square.
+             *
+             * (This is a generalisation of the obvious deduction
+             * that when you see a clue saying 1, it must be right
+             * next to the largest possible number; and similarly,
+             * when you see a clue saying 2 opposite that, it must
+             * be right next to the second-largest.)
+             */
+            j = furthest-1;  /* number of small numbers we can rule out */
+            for (i = 1; i <= w && j > 0; i++) {
+                if (ctx->dscratch[i-1] < w && ctx->dscratch[i-1] >= furthest)
+                    continue;          /* skip this number, it's elsewhere */
+                j--;
+                if (solver->cube[cstart*w+i-1]) {
+#ifdef STANDALONE_SOLVER
+                    if (solver_show_working) {
+                        printf("%s%*s  ruling out %d at (%d,%d)\n",
+                               prefix, solver_recurse_depth*4, "",
+                               i, start%w+1, start/w+1);
+                        prefix[0] = '\0';
+                    }
+#endif
+                    solver->cube[cstart*w+i-1] = 0;
+                    ret = 1;
+                }
+            }
+        }
+
+        if (ret)
+            return ret;
+
+#ifdef STANDALONE_SOLVER
+            if (solver_show_working)
+                sprintf(prefix, "%*slower bounds for clue %s %d:\n",
+                        solver_recurse_depth*4, "",
+                        cluepos[c/w], c%w+1);
+            else
+                prefix[0] = '\0';              /* placate optimiser */
+#endif
+
+        i = 0;
+        for (n = w; n > 0; n--) {
+            /*
+             * The largest number cannot occur in the first (clue-1)
+             * squares of the row, or else there wouldn't be space
+             * for a sufficiently long increasing sequence which it
+             * terminated. The second-largest number (not counting
+             * any that are known to be on the far side of a larger
+             * number and hence excluded from this sequence) cannot
+             * occur in the first (clue-2) squares, similarly, and
+             * so on.
+             */
+
+            if (ctx->dscratch[n-1] < w) {
+                for (m = n+1; m < w; m++)
+                    if (ctx->dscratch[m] < ctx->dscratch[n-1])
+                        break;
+                if (m < w)
+                    continue;          /* this number doesn't count */
+            }
+
+            for (j = 0; j < clue - i - 1; j++)
+                if (solver->cube[(cstart + j*cstep)*w+n-1]) {
+#ifdef STANDALONE_SOLVER
+                    if (solver_show_working) {
+                        int pos = start+j*step;
+                        printf("%s%*s  ruling out %d at (%d,%d)\n",
+                               prefix, solver_recurse_depth*4, "",
+                               n, pos%w+1, pos/w+1);
+                        prefix[0] = '\0';
+                    }
+#endif
+                    solver->cube[(cstart + j*cstep)*w+n-1] = 0;
+                    ret = 1;
+                }
+            i++;
+        }
+    }
+
+    if (ret)
+        return ret;
+
+    return 0;
+}
+
+static int solver_hard(struct latin_solver *solver, void *vctx)
+{
+    struct solver_ctx *ctx = (struct solver_ctx *)vctx;
+    int w = ctx->w;
+    int c, i, j, n, best, clue, start, step, ret;
+    long bitmap;
+#ifdef STANDALONE_SOLVER
+    char prefix[256];
+#endif
+
+    /*
+     * Go over every clue analysing all possibilities.
+     */
+    for (c = 0; c < 4*w; c++) {
+        clue = ctx->clues[c];
+        if (!clue)
+            continue;
+        CSTARTSTEP(start, step, c, w);
+
+        for (i = 0; i < w; i++)
+            ctx->iscratch[i] = 0;
+
+        /*
+         * Instead of a tedious physical recursion, I iterate in the
+         * scratch array through all possibilities. At any given
+         * moment, i indexes the element of the box that will next
+         * be incremented.
+         */
+        i = 0;
+        ctx->dscratch[i] = 0;
+        best = n = 0;
+        bitmap = 0;
+
+        while (1) {
+            if (i < w) {
+                /*
+                 * Find the next valid value for cell i.
+                 */
+                int limit = (n == clue ? best : w);
+                int pos = start + step * i;
+                for (j = ctx->dscratch[i] + 1; j <= limit; j++) {
+                    if (bitmap & (1L << j))
+                        continue;      /* used this one already */
+                    if (!solver->cube[pos*w+j-1])
+                        continue;      /* ruled out already */
+
+                    /* Found one. */
+                    break;
+                }
+
+                if (j > limit) {
+                    /* No valid values left; drop back. */
+                    i--;
+                    if (i < 0)
+                        break;         /* overall iteration is finished */
+                    bitmap &= ~(1L << ctx->dscratch[i]);
+                    if (ctx->dscratch[i] == best) {
+                        n--;
+                        best = 0;
+                        for (j = 0; j < i; j++)
+                            if (best < ctx->dscratch[j])
+                                best = ctx->dscratch[j];
+                    }
+                } else {
+                    /* Got a valid value; store it and move on. */
+                    bitmap |= 1L << j;
+                    ctx->dscratch[i++] = j;
+                    if (j > best) {
+                        best = j;
+                        n++;
+                    }
+                    ctx->dscratch[i] = 0;
+                }
+            } else {
+                if (n == clue) {
+                    for (j = 0; j < w; j++)
+                        ctx->iscratch[j] |= 1L << ctx->dscratch[j];
+                }
+                i--;
+                bitmap &= ~(1L << ctx->dscratch[i]);
+                if (ctx->dscratch[i] == best) {
+                    n--;
+                    best = 0;
+                    for (j = 0; j < i; j++)
+                        if (best < ctx->dscratch[j])
+                            best = ctx->dscratch[j];
+                }
+            }
+        }
+
+#ifdef STANDALONE_SOLVER
+        if (solver_show_working)
+            sprintf(prefix, "%*sexhaustive analysis of clue %s %d:\n",
+                    solver_recurse_depth*4, "",
+                    cluepos[c/w], c%w+1);
+        else
+            prefix[0] = '\0';          /* placate optimiser */
+#endif
+
+        ret = 0;
+
+        for (i = 0; i < w; i++) {
+            int pos = start + step * i;
+            for (j = 1; j <= w; j++) {
+                if (solver->cube[pos*w+j-1] &&
+                    !(ctx->iscratch[i] & (1L << j))) {
+#ifdef STANDALONE_SOLVER
+                    if (solver_show_working) {
+                        printf("%s%*s  ruling out %d at (%d,%d)\n",
+                               prefix, solver_recurse_depth*4, "",
+                               j, pos/w+1, pos%w+1);
+                        prefix[0] = '\0';
+                    }
+#endif
+                    solver->cube[pos*w+j-1] = 0;
+                    ret = 1;
+                }
+            }
+
+            /*
+             * Once we find one clue we can do something with in
+             * this way, revert to trying easier deductions, so as
+             * not to generate solver diagnostics that make the
+             * problem look harder than it is.
+             */
+            if (ret)
+                return ret;
+        }
+    }
+
+    return 0;
+}
+
+#define SOLVER(upper,title,func,lower) func,
+static usersolver_t const towers_solvers[] = { DIFFLIST(SOLVER) };
+
+static int solver(int w, int *clues, digit *soln, int maxdiff)
+{
+    int ret;
+    struct solver_ctx ctx;
+
+    ctx.w = w;
+    ctx.diff = maxdiff;
+    ctx.clues = clues;
+    ctx.started = FALSE;
+    ctx.iscratch = snewn(w, long);
+    ctx.dscratch = snewn(w+1, int);
+
+    ret = latin_solver(soln, w, maxdiff,
+                       DIFF_EASY, DIFF_HARD, DIFF_EXTREME,
+                       DIFF_EXTREME, DIFF_UNREASONABLE,
+                       towers_solvers, &ctx, NULL, NULL);
+
+    sfree(ctx.iscratch);
+    sfree(ctx.dscratch);
+
+    return ret;
+}
+
+/* ----------------------------------------------------------------------
+ * Grid generation.
+ */
+
+static char *new_game_desc(const game_params *params, random_state *rs,
+                           char **aux, int interactive)
+{
+    int w = params->w, a = w*w;
+    digit *grid, *soln, *soln2;
+    int *clues, *order;
+    int i, ret;
+    int diff = params->diff;
+    char *desc, *p;
+
+    /*
+     * Difficulty exceptions: some combinations of size and
+     * difficulty cannot be satisfied, because all puzzles of at
+     * most that difficulty are actually even easier.
+     *
+     * Remember to re-test this whenever a change is made to the
+     * solver logic!
+     *
+     * I tested it using the following shell command:
+
+for d in e h x u; do
+  for i in {3..9}; do
+    echo -n "./towers --generate 1 ${i}d${d}: "
+    perl -e 'alarm 30; exec @ARGV' ./towers --generate 1 ${i}d${d} >/dev/null \
+      && echo ok
+  done
+done
+
+     * Of course, it's better to do that after taking the exceptions
+     * _out_, so as to detect exceptions that should be removed as
+     * well as those which should be added.
+     */
+    if (diff > DIFF_HARD && w <= 3)
+        diff = DIFF_HARD;
+
+    grid = NULL;
+    clues = snewn(4*w, int);
+    soln = snewn(a, digit);
+    soln2 = snewn(a, digit);
+    order = snewn(max(4*w,a), int);
+
+    while (1) {
+        /*
+         * Construct a latin square to be the solution.
+         */
+        sfree(grid);
+        grid = latin_generate(w, rs);
+
+        /*
+         * Fill in the clues.
+         */
+        for (i = 0; i < 4*w; i++) {
+            int start, step, j, k, best;
+            STARTSTEP(start, step, i, w);
+            k = best = 0;
+            for (j = 0; j < w; j++) {
+                if (grid[start+j*step] > best) {
+                    best = grid[start+j*step];
+                    k++;
+                }
+            }
+            clues[i] = k;
+        }
+
+        /*
+         * Remove the grid numbers and then the clues, one by one,
+         * for as long as the game remains soluble at the given
+         * difficulty.
+         */
+        memcpy(soln, grid, a);
+
+        if (diff == DIFF_EASY && w <= 5) {
+            /*
+             * Special case: for Easy-mode grids that are small
+             * enough, it's nice to be able to find completely empty
+             * grids.
+             */
+            memset(soln2, 0, a);
+            ret = solver(w, clues, soln2, diff);
+            if (ret > diff)
+                continue;
+        }
+
+        for (i = 0; i < a; i++)
+            order[i] = i;
+        shuffle(order, a, sizeof(*order), rs);
+        for (i = 0; i < a; i++) {
+            int j = order[i];
+
+            memcpy(soln2, grid, a);
+            soln2[j] = 0;
+            ret = solver(w, clues, soln2, diff);
+            if (ret <= diff)
+                grid[j] = 0;
+        }
+
+        if (diff > DIFF_EASY) {        /* leave all clues on Easy mode */
+            for (i = 0; i < 4*w; i++)
+                order[i] = i;
+            shuffle(order, 4*w, sizeof(*order), rs);
+            for (i = 0; i < 4*w; i++) {
+                int j = order[i];
+                int clue = clues[j];
+
+                memcpy(soln2, grid, a);
+                clues[j] = 0;
+                ret = solver(w, clues, soln2, diff);
+                if (ret > diff)
+                    clues[j] = clue;
+            }
+        }
+
+        /*
+         * See if the game can be solved at the specified difficulty
+         * level, but not at the one below.
+         */
+        memcpy(soln2, grid, a);
+        ret = solver(w, clues, soln2, diff);
+        if (ret != diff)
+            continue;                  /* go round again */
+
+        /*
+         * We've got a usable puzzle!
+         */
+        break;
+    }
+
+    /*
+     * Encode the puzzle description.
+     */
+    desc = snewn(40*a, char);
+    p = desc;
+    for (i = 0; i < 4*w; i++) {
+        if (i)
+            *p++ = '/';
+        if (clues[i])
+            p += sprintf(p, "%d", clues[i]);
+    }
+    for (i = 0; i < a; i++)
+        if (grid[i])
+            break;
+    if (i < a) {
+        int run = 0;
+
+        *p++ = ',';
+
+        for (i = 0; i <= a; i++) {
+            int n = (i < a ? grid[i] : -1);
+
+            if (!n)
+                run++;
+            else {
+                if (run) {
+                    while (run > 0) {
+                        int thisrun = min(run, 26);
+                        *p++ = thisrun - 1 + 'a';
+                        run -= thisrun;
+                    }
+                } else {
+                    /*
+                     * If there's a number in the very top left or
+                     * bottom right, there's no point putting an
+                     * unnecessary _ before or after it.
+                     */
+                    if (i > 0 && n > 0)
+                        *p++ = '_';
+                }
+                if (n > 0)
+                    p += sprintf(p, "%d", n);
+                run = 0;
+            }
+        }
+    }
+    *p++ = '\0';
+    desc = sresize(desc, p - desc, char);
+
+    /*
+     * Encode the solution.
+     */
+    *aux = snewn(a+2, char);
+    (*aux)[0] = 'S';
+    for (i = 0; i < a; i++)
+        (*aux)[i+1] = '0' + soln[i];
+    (*aux)[a+1] = '\0';
+
+    sfree(grid);
+    sfree(clues);
+    sfree(soln);
+    sfree(soln2);
+    sfree(order);
+
+    return desc;
+}
+
+/* ----------------------------------------------------------------------
+ * Gameplay.
+ */
+
+static char *validate_desc(const game_params *params, const char *desc)
+{
+    int w = params->w, a = w*w;
+    const char *p = desc;
+    int i, clue;
+
+    /*
+     * Verify that the right number of clues are given, and that
+     * they're in range.
+     */
+    for (i = 0; i < 4*w; i++) {
+        if (!*p)
+            return "Too few clues for grid size";
+
+        if (i > 0) {
+            if (*p != '/')
+                return "Expected commas between clues";
+            p++;
+        }
+
+        if (isdigit((unsigned char)*p)) {
+            clue = atoi(p);
+            while (*p && isdigit((unsigned char)*p)) p++;
+
+            if (clue <= 0 || clue > w)
+                return "Clue number out of range";
+        }
+    }
+    if (*p == '/')
+        return "Too many clues for grid size";
+
+    if (*p == ',') {
+        /*
+         * Verify that the right amount of grid data is given, and
+         * that any grid elements provided are in range.
+         */
+        int squares = 0;
+
+        p++;
+        while (*p) {
+            int c = *p++;
+            if (c >= 'a' && c <= 'z') {
+                squares += c - 'a' + 1;
+            } else if (c == '_') {
+                /* do nothing */;
+            } else if (c > '0' && c <= '9') {
+                int val = atoi(p-1);
+                if (val < 1 || val > w)
+                    return "Out-of-range number in grid description";
+                squares++;
+                while (*p && isdigit((unsigned char)*p)) p++;
+            } else
+                return "Invalid character in game description";
+        }
+
+        if (squares < a)
+            return "Not enough data to fill grid";
+
+        if (squares > a)
+            return "Too much data to fit in grid";
+    }
+
+    return NULL;
+}
+
+static game_state *new_game(midend *me, const game_params *params,
+                            const char *desc)
+{
+    int w = params->w, a = w*w;
+    game_state *state = snew(game_state);
+    const char *p = desc;
+    int i;
+
+    state->par = *params;              /* structure copy */
+    state->clues = snew(struct clues);
+    state->clues->refcount = 1;
+    state->clues->w = w;
+    state->clues->clues = snewn(4*w, int);
+    state->clues->immutable = snewn(a, digit);
+    state->grid = snewn(a, digit);
+    state->clues_done = snewn(4*w, unsigned char);
+    state->pencil = snewn(a, int);
+
+    for (i = 0; i < a; i++) {
+        state->grid[i] = 0;
+        state->pencil[i] = 0;
+    }
+
+    memset(state->clues->immutable, 0, a);
+    memset(state->clues_done, 0, 4*w*sizeof(unsigned char));
+
+    for (i = 0; i < 4*w; i++) {
+        if (i > 0) {
+            assert(*p == '/');
+            p++;
+        }
+        if (*p && isdigit((unsigned char)*p)) {
+            state->clues->clues[i] = atoi(p);
+            while (*p && isdigit((unsigned char)*p)) p++;
+        } else
+            state->clues->clues[i] = 0;
+    }
+
+    if (*p == ',') {
+        int pos = 0;
+        p++;
+        while (*p) {
+            int c = *p++;
+            if (c >= 'a' && c <= 'z') {
+                pos += c - 'a' + 1;
+            } else if (c == '_') {
+                /* do nothing */;
+            } else if (c > '0' && c <= '9') {
+                int val = atoi(p-1);
+                assert(val >= 1 && val <= w);
+                assert(pos < a);
+                state->grid[pos] = state->clues->immutable[pos] = val;
+                pos++;
+                while (*p && isdigit((unsigned char)*p)) p++;
+            } else
+                assert(!"Corrupt game description");
+        }
+        assert(pos == a);
+    }
+    assert(!*p);
+
+    state->completed = state->cheated = FALSE;
+
+    return state;
+}
+
+static game_state *dup_game(const game_state *state)
+{
+    int w = state->par.w, a = w*w;
+    game_state *ret = snew(game_state);
+
+    ret->par = state->par;             /* structure copy */
+
+    ret->clues = state->clues;
+    ret->clues->refcount++;
+
+    ret->grid = snewn(a, digit);
+    ret->pencil = snewn(a, int);
+    ret->clues_done = snewn(4*w, unsigned char);
+    memcpy(ret->grid, state->grid, a*sizeof(digit));
+    memcpy(ret->pencil, state->pencil, a*sizeof(int));
+    memcpy(ret->clues_done, state->clues_done, 4*w*sizeof(unsigned char));
+
+    ret->completed = state->completed;
+    ret->cheated = state->cheated;
+
+    return ret;
+}
+
+static void free_game(game_state *state)
+{
+    sfree(state->grid);
+    sfree(state->pencil);
+    sfree(state->clues_done);
+    if (--state->clues->refcount <= 0) {
+        sfree(state->clues->immutable);
+        sfree(state->clues->clues);
+        sfree(state->clues);
+    }
+    sfree(state);
+}
+
+static char *solve_game(const game_state *state, const game_state *currstate,
+                        const char *aux, char **error)
+{
+    int w = state->par.w, a = w*w;
+    int i, ret;
+    digit *soln;
+    char *out;
+
+    if (aux)
+        return dupstr(aux);
+
+    soln = snewn(a, digit);
+    memcpy(soln, state->clues->immutable, a);
+
+    ret = solver(w, state->clues->clues, soln, DIFFCOUNT-1);
+
+    if (ret == diff_impossible) {
+        *error = "No solution exists for this puzzle";
+        out = NULL;
+    } else if (ret == diff_ambiguous) {
+        *error = "Multiple solutions exist for this puzzle";
+        out = NULL;
+    } else {
+        out = snewn(a+2, char);
+        out[0] = 'S';
+        for (i = 0; i < a; i++)
+            out[i+1] = '0' + soln[i];
+        out[a+1] = '\0';
+    }
+
+    sfree(soln);
+    return out;
+}
+
+static int game_can_format_as_text_now(const game_params *params)
+{
+    return TRUE;
+}
+
+static char *game_text_format(const game_state *state)
+{
+    int w = state->par.w /* , a = w*w */;
+    char *ret;
+    char *p;
+    int x, y;
+    int total;
+
+    /*
+     * We have:
+     *  - a top clue row, consisting of three spaces, then w clue
+     *    digits with spaces between (total 2*w+3 chars including
+     *    newline)
+     *  - a blank line (one newline)
+     *  - w main rows, consisting of a left clue digit, two spaces,
+     *    w grid digits with spaces between, two spaces and a right
+     *    clue digit (total 2*w+6 chars each including newline)
+     *  - a blank line (one newline)
+     *  - a bottom clue row (same as top clue row)
+     *  - terminating NUL.
+     *
+     * Total size is therefore 2*(2*w+3) + 2 + w*(2*w+6) + 1
+     * = 2w^2+10w+9.
+     */
+    total = 2*w*w + 10*w + 9;
+    ret = snewn(total, char);
+    p = ret;
+
+    /* Top clue row. */
+    *p++ = ' '; *p++ = ' ';
+    for (x = 0; x < w; x++) {
+        *p++ = ' ';
+        *p++ = (state->clues->clues[x] ? '0' + state->clues->clues[x] : ' ');
+    }
+    *p++ = '\n';
+
+    /* Blank line. */
+    *p++ = '\n';
+
+    /* Main grid. */
+    for (y = 0; y < w; y++) {
+        *p++ = (state->clues->clues[y+2*w] ? '0' + state->clues->clues[y+2*w] :
+                ' ');
+        *p++ = ' ';
+        for (x = 0; x < w; x++) {
+            *p++ = ' ';
+            *p++ = (state->grid[y*w+x] ? '0' + state->grid[y*w+x] : ' ');
+        }
+        *p++ = ' '; *p++ = ' ';
+        *p++ = (state->clues->clues[y+3*w] ? '0' + state->clues->clues[y+3*w] :
+                ' ');
+        *p++ = '\n';
+    }
+
+    /* Blank line. */
+    *p++ = '\n';
+
+    /* Bottom clue row. */
+    *p++ = ' '; *p++ = ' ';
+    for (x = 0; x < w; x++) {
+        *p++ = ' ';
+        *p++ = (state->clues->clues[x+w] ? '0' + state->clues->clues[x+w] :
+                ' ');
+    }
+    *p++ = '\n';
+
+    *p++ = '\0';
+    assert(p == ret + total);
+
+    return ret;
+}
+
+struct game_ui {
+    /*
+     * These are the coordinates of the currently highlighted
+     * square on the grid, if hshow = 1.
+     */
+    int hx, hy;
+    /*
+     * This indicates whether the current highlight is a
+     * pencil-mark one or a real one.
+     */
+    int hpencil;
+    /*
+     * This indicates whether or not we're showing the highlight
+     * (used to be hx = hy = -1); important so that when we're
+     * using the cursor keys it doesn't keep coming back at a
+     * fixed position. When hshow = 1, pressing a valid number
+     * or letter key or Space will enter that number or letter in the grid.
+     */
+    int hshow;
+    /*
+     * This indicates whether we're using the highlight as a cursor;
+     * it means that it doesn't vanish on a keypress, and that it is
+     * allowed on immutable squares.
+     */
+    int hcursor;
+};
+
+static game_ui *new_ui(const game_state *state)
+{
+    game_ui *ui = snew(game_ui);
+
+    ui->hx = ui->hy = 0;
+    ui->hpencil = ui->hshow = ui->hcursor = 0;
+
+    return ui;
+}
+
+static void free_ui(game_ui *ui)
+{
+    sfree(ui);
+}
+
+static char *encode_ui(const game_ui *ui)
+{
+    return NULL;
+}
+
+static void decode_ui(game_ui *ui, const char *encoding)
+{
+}
+
+static void game_changed_state(game_ui *ui, const game_state *oldstate,
+                               const game_state *newstate)
+{
+    int w = newstate->par.w;
+    /*
+     * We prevent pencil-mode highlighting of a filled square, unless
+     * we're using the cursor keys. So if the user has just filled in
+     * a square which we had a pencil-mode highlight in (by Undo, or
+     * by Redo, or by Solve), then we cancel the highlight.
+     */
+    if (ui->hshow && ui->hpencil && !ui->hcursor &&
+        newstate->grid[ui->hy * w + ui->hx] != 0) {
+        ui->hshow = 0;
+    }
+}
+
+#define PREFERRED_TILESIZE 48
+#define TILESIZE (ds->tilesize)
+#define BORDER (TILESIZE * 9 / 8)
+#define COORD(x) ((x)*TILESIZE + BORDER)
+#define FROMCOORD(x) (((x)+(TILESIZE-BORDER)) / TILESIZE - 1)
+
+/* These always return positive values, though y offsets are actually -ve */
+#define X_3D_DISP(height, w) ((height) * TILESIZE / (8 * (w)))
+#define Y_3D_DISP(height, w) ((height) * TILESIZE / (4 * (w)))
+
+#define FLASH_TIME 0.4F
+
+#define DF_PENCIL_SHIFT 16
+#define DF_CLUE_DONE 0x10000
+#define DF_ERROR 0x8000
+#define DF_HIGHLIGHT 0x4000
+#define DF_HIGHLIGHT_PENCIL 0x2000
+#define DF_IMMUTABLE 0x1000
+#define DF_PLAYAREA 0x0800
+#define DF_DIGIT_MASK 0x00FF
+
+struct game_drawstate {
+    int tilesize;
+    int three_d;                /* default 3D graphics are user-disableable */
+    int started;
+    long *tiles;                       /* (w+2)*(w+2) temp space */
+    long *drawn;                       /* (w+2)*(w+2)*4: current drawn data */
+    int *errtmp;
+};
+
+static int check_errors(const game_state *state, int *errors)
+{
+    int w = state->par.w /*, a = w*w */;
+    int W = w+2, A = W*W;              /* the errors array is (w+2) square */
+    int *clues = state->clues->clues;
+    digit *grid = state->grid;
+    int i, x, y, errs = FALSE;
+    int tmp[32];
+
+    assert(w < lenof(tmp));
+
+    if (errors)
+        for (i = 0; i < A; i++)
+            errors[i] = 0;
+
+    for (y = 0; y < w; y++) {
+        unsigned long mask = 0, errmask = 0;
+        for (x = 0; x < w; x++) {
+            unsigned long bit = 1UL << grid[y*w+x];
+            errmask |= (mask & bit);
+            mask |= bit;
+        }
+
+        if (mask != (1L << (w+1)) - (1L << 1)) {
+            errs = TRUE;
+            errmask &= ~1UL;
+            if (errors) {
+                for (x = 0; x < w; x++)
+                    if (errmask & (1UL << grid[y*w+x]))
+                        errors[(y+1)*W+(x+1)] = TRUE;
+            }
+        }
+    }
+
+    for (x = 0; x < w; x++) {
+        unsigned long mask = 0, errmask = 0;
+        for (y = 0; y < w; y++) {
+            unsigned long bit = 1UL << grid[y*w+x];
+            errmask |= (mask & bit);
+            mask |= bit;
+        }
+
+        if (mask != (1 << (w+1)) - (1 << 1)) {
+            errs = TRUE;
+            errmask &= ~1UL;
+            if (errors) {
+                for (y = 0; y < w; y++)
+                    if (errmask & (1UL << grid[y*w+x]))
+                        errors[(y+1)*W+(x+1)] = TRUE;
+            }
+        }
+    }
+
+    for (i = 0; i < 4*w; i++) {
+        int start, step, j, n, best;
+        STARTSTEP(start, step, i, w);
+
+        if (!clues[i])
+            continue;
+
+        best = n = 0;
+        for (j = 0; j < w; j++) {
+            int number = grid[start+j*step];
+            if (!number)
+                break;                 /* can't tell what happens next */
+            if (number > best) {
+                best = number;
+                n++;
+            }
+        }
+
+        if (n > clues[i] || (best == w && n < clues[i]) ||
+            (best < w && n == clues[i])) {
+            if (errors) {
+                int x, y;
+                CLUEPOS(x, y, i, w);
+                errors[(y+1)*W+(x+1)] = TRUE;
+            }
+            errs = TRUE;
+        }
+    }
+
+    return errs;
+}
+
+static int clue_index(const game_state *state, int x, int y)
+{
+    int w = state->par.w;
+
+    if (x == -1 || x == w)
+        return w * (x == -1 ? 2 : 3) + y;
+    else if (y == -1 || y == w)
+        return (y == -1 ? 0 : w) + x;
+
+    return -1;
+}
+
+static int is_clue(const game_state *state, int x, int y)
+{
+    int w = state->par.w;
+
+    if (((x == -1 || x == w) && y >= 0 && y < w) ||
+        ((y == -1 || y == w) && x >= 0 && x < w))
+    {
+        if (state->clues->clues[clue_index(state, x, y)] & DF_DIGIT_MASK)
+            return TRUE;
+    }
+
+    return FALSE;
+}
+
+static char *interpret_move(const game_state *state, game_ui *ui,
+                            const game_drawstate *ds,
+                            int x, int y, int button)
+{
+    int w = state->par.w;
+    int shift_or_control = button & (MOD_SHFT | MOD_CTRL);
+    int tx, ty;
+    char buf[80];
+
+    button &= ~MOD_MASK;
+
+    tx = FROMCOORD(x);
+    ty = FROMCOORD(y);
+
+    if (ds->three_d) {
+        /*
+         * In 3D mode, just locating the mouse click in the natural
+         * square grid may not be sufficient to tell which tower the
+         * user clicked on. Investigate the _tops_ of the nearby
+         * towers to see if a click on one grid square was actually
+         * a click on a tower protruding into that region from
+         * another.
+         */
+        int dx, dy;
+        for (dy = 0; dy <= 1; dy++)
+            for (dx = 0; dx >= -1; dx--) {
+                int cx = tx + dx, cy = ty + dy;
+                if (cx >= 0 && cx < w && cy >= 0 && cy < w) {
+                    int height = state->grid[cy*w+cx];
+                    int bx = COORD(cx), by = COORD(cy);
+                    int ox = bx + X_3D_DISP(height, w);
+                    int oy = by - Y_3D_DISP(height, w);
+                    if (/* on top face? */
+                        (x - ox >= 0 && x - ox < TILESIZE &&
+                         y - oy >= 0 && y - oy < TILESIZE) ||
+                        /* in triangle between top-left corners? */
+                        (ox > bx && x >= bx && x <= ox && y <= by &&
+                         (by-y) * (ox-bx) <= (by-oy) * (x-bx)) ||
+                        /* in triangle between bottom-right corners? */
+                        (ox > bx && x >= bx+TILESIZE && x <= ox+TILESIZE &&
+                         y >= oy+TILESIZE &&
+                         (by-y+TILESIZE)*(ox-bx) >= (by-oy)*(x-bx-TILESIZE))) {
+                        tx = cx;
+                        ty = cy;
+                    }
+                }
+            }
+    }
+
+    if (tx >= 0 && tx < w && ty >= 0 && ty < w) {
+        if (button == LEFT_BUTTON) {
+            if (tx == ui->hx && ty == ui->hy &&
+                ui->hshow && ui->hpencil == 0) {
+                ui->hshow = 0;
+            } else {
+                ui->hx = tx;
+                ui->hy = ty;
+                ui->hshow = !state->clues->immutable[ty*w+tx];
+                ui->hpencil = 0;
+            }
+            ui->hcursor = 0;
+            return "";                 /* UI activity occurred */
+        }
+        if (button == RIGHT_BUTTON) {
+            /*
+             * Pencil-mode highlighting for non filled squares.
+             */
+            if (state->grid[ty*w+tx] == 0) {
+                if (tx == ui->hx && ty == ui->hy &&
+                    ui->hshow && ui->hpencil) {
+                    ui->hshow = 0;
+                } else {
+                    ui->hpencil = 1;
+                    ui->hx = tx;
+                    ui->hy = ty;
+                    ui->hshow = 1;
+                }
+            } else {
+                ui->hshow = 0;
+            }
+            ui->hcursor = 0;
+            return "";                 /* UI activity occurred */
+        }
+    } else if (button == LEFT_BUTTON) {
+        if (is_clue(state, tx, ty)) {
+            sprintf(buf, "%c%d,%d", 'D', tx, ty);
+            return dupstr(buf);
+        }
+    }
+    if (IS_CURSOR_MOVE(button)) {
+        if (shift_or_control) {
+            int x = ui->hx, y = ui->hy;
+            switch (button) {
+            case CURSOR_LEFT:   x = -1; break;
+            case CURSOR_RIGHT:  x =  w; break;
+            case CURSOR_UP:     y = -1; break;
+            case CURSOR_DOWN:   y =  w; break;
+            }
+            if (is_clue(state, x, y)) {
+                sprintf(buf, "%c%d,%d", 'D', x, y);
+                return dupstr(buf);
+            }
+            return NULL;
+        }
+        move_cursor(button, &ui->hx, &ui->hy, w, w, 0);
+        ui->hshow = ui->hcursor = 1;
+        return "";
+    }
+    if (ui->hshow &&
+        (button == CURSOR_SELECT)) {
+        ui->hpencil = 1 - ui->hpencil;
+        ui->hcursor = 1;
+        return "";
+    }
+
+    if (ui->hshow &&
+        ((button >= '0' && button <= '9' && button - '0' <= w) ||
+         button == CURSOR_SELECT2 || button == '\b')) {
+        int n = button - '0';
+        if (button == CURSOR_SELECT2 || button == '\b')
+            n = 0;
+
+        /*
+         * Can't make pencil marks in a filled square. This can only
+         * become highlighted if we're using cursor keys.
+         */
+        if (ui->hpencil && state->grid[ui->hy*w+ui->hx])
+            return NULL;
+
+        /*
+         * Can't do anything to an immutable square.
+         */
+        if (state->clues->immutable[ui->hy*w+ui->hx])
+            return NULL;
+
+        sprintf(buf, "%c%d,%d,%d",
+                (char)(ui->hpencil && n > 0 ? 'P' : 'R'), ui->hx, ui->hy, n);
+
+        if (!ui->hcursor) ui->hshow = 0;
+
+        return dupstr(buf);
+    }
+
+    if (button == 'M' || button == 'm')
+        return dupstr("M");
+
+    return NULL;
+}
+
+static game_state *execute_move(const game_state *from, const char *move)
+{
+    int w = from->par.w, a = w*w;
+    game_state *ret = dup_game(from);
+    int x, y, i, n;
+
+    if (move[0] == 'S') {
+        ret->completed = ret->cheated = TRUE;
+
+        for (i = 0; i < a; i++) {
+            if (move[i+1] < '1' || move[i+1] > '0'+w)
+                goto badmove;
+            ret->grid[i] = move[i+1] - '0';
+            ret->pencil[i] = 0;
+        }
+
+        if (move[a+1] != '\0')
+            goto badmove;
+
+        return ret;
+    } else if ((move[0] == 'P' || move[0] == 'R') &&
+        sscanf(move+1, "%d,%d,%d", &x, &y, &n) == 3 &&
+        x >= 0 && x < w && y >= 0 && y < w && n >= 0 && n <= w) {
+        if (from->clues->immutable[y*w+x])
+            goto badmove;
+
+        if (move[0] == 'P' && n > 0) {
+            ret->pencil[y*w+x] ^= 1L << n;
+        } else {
+            ret->grid[y*w+x] = n;
+            ret->pencil[y*w+x] = 0;
+
+            if (!ret->completed && !check_errors(ret, NULL))
+                ret->completed = TRUE;
+        }
+        return ret;
+    } else if (move[0] == 'M') {
+        /*
+         * Fill in absolutely all pencil marks everywhere. (I
+         * wouldn't use this for actual play, but it's a handy
+         * starting point when following through a set of
+         * diagnostics output by the standalone solver.)
+         */
+        for (i = 0; i < a; i++) {
+            if (!ret->grid[i])
+                ret->pencil[i] = (1L << (w+1)) - (1L << 1);
+        }
+        return ret;
+    } else if (move[0] == 'D' && sscanf(move+1, "%d,%d", &x, &y) == 2 &&
+               is_clue(from, x, y)) {
+        int index = clue_index(from, x, y);
+        ret->clues_done[index] = !ret->clues_done[index];
+        return ret;
+    }
+
+  badmove:
+    /* couldn't parse move string */
+    free_game(ret);
+    return NULL;
+}
+
+/* ----------------------------------------------------------------------
+ * Drawing routines.
+ */
+
+#define SIZE(w) ((w) * TILESIZE + 2*BORDER)
+
+static void game_compute_size(const game_params *params, int tilesize,
+                              int *x, int *y)
+{
+    /* Ick: fake up `ds->tilesize' for macro expansion purposes */
+    struct { int tilesize; } ads, *ds = &ads;
+    ads.tilesize = tilesize;
+
+    *x = *y = SIZE(params->w);
+}
+
+static void game_set_size(drawing *dr, game_drawstate *ds,
+                          const game_params *params, int tilesize)
+{
+    ds->tilesize = tilesize;
+}
+
+static float *game_colours(frontend *fe, int *ncolours)
+{
+    float *ret = snewn(3 * NCOLOURS, float);
+
+    frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
+
+    ret[COL_GRID * 3 + 0] = 0.0F;
+    ret[COL_GRID * 3 + 1] = 0.0F;
+    ret[COL_GRID * 3 + 2] = 0.0F;
+
+    ret[COL_USER * 3 + 0] = 0.0F;
+    ret[COL_USER * 3 + 1] = 0.6F * ret[COL_BACKGROUND * 3 + 1];
+    ret[COL_USER * 3 + 2] = 0.0F;
+
+    ret[COL_HIGHLIGHT * 3 + 0] = 0.78F * ret[COL_BACKGROUND * 3 + 0];
+    ret[COL_HIGHLIGHT * 3 + 1] = 0.78F * ret[COL_BACKGROUND * 3 + 1];
+    ret[COL_HIGHLIGHT * 3 + 2] = 0.78F * ret[COL_BACKGROUND * 3 + 2];
+
+    ret[COL_ERROR * 3 + 0] = 1.0F;
+    ret[COL_ERROR * 3 + 1] = 0.0F;
+    ret[COL_ERROR * 3 + 2] = 0.0F;
+
+    ret[COL_PENCIL * 3 + 0] = 0.5F * ret[COL_BACKGROUND * 3 + 0];
+    ret[COL_PENCIL * 3 + 1] = 0.5F * ret[COL_BACKGROUND * 3 + 1];
+    ret[COL_PENCIL * 3 + 2] = ret[COL_BACKGROUND * 3 + 2];
+
+    ret[COL_DONE * 3 + 0] = ret[COL_BACKGROUND * 3 + 0] / 1.5F;
+    ret[COL_DONE * 3 + 1] = ret[COL_BACKGROUND * 3 + 1] / 1.5F;
+    ret[COL_DONE * 3 + 2] = ret[COL_BACKGROUND * 3 + 2] / 1.5F;
+
+    *ncolours = NCOLOURS;
+    return ret;
+}
+
+static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
+{
+    int w = state->par.w /*, a = w*w */;
+    struct game_drawstate *ds = snew(struct game_drawstate);
+    int i;
+
+    ds->tilesize = 0;
+    ds->three_d = !getenv("TOWERS_2D");
+    ds->started = FALSE;
+    ds->tiles = snewn((w+2)*(w+2), long);
+    ds->drawn = snewn((w+2)*(w+2)*4, long);
+    for (i = 0; i < (w+2)*(w+2)*4; i++)
+        ds->drawn[i] = -1;
+    ds->errtmp = snewn((w+2)*(w+2), int);
+
+    return ds;
+}
+
+static void game_free_drawstate(drawing *dr, game_drawstate *ds)
+{
+    sfree(ds->errtmp);
+    sfree(ds->tiles);
+    sfree(ds->drawn);
+    sfree(ds);
+}
+
+static void draw_tile(drawing *dr, game_drawstate *ds, struct clues *clues,
+                      int x, int y, long tile)
+{
+    int w = clues->w /* , a = w*w */;
+    int tx, ty, bg;
+    char str[64];
+
+    tx = COORD(x);
+    ty = COORD(y);
+
+    bg = (tile & DF_HIGHLIGHT) ? COL_HIGHLIGHT : COL_BACKGROUND;
+
+    /* draw tower */
+    if (ds->three_d && (tile & DF_PLAYAREA) && (tile & DF_DIGIT_MASK)) {
+        int coords[8];
+        int xoff = X_3D_DISP(tile & DF_DIGIT_MASK, w);
+        int yoff = Y_3D_DISP(tile & DF_DIGIT_MASK, w);
+
+        /* left face of tower */
+        coords[0] = tx;
+        coords[1] = ty - 1;
+        coords[2] = tx;
+        coords[3] = ty + TILESIZE - 1;
+        coords[4] = coords[2] + xoff;
+        coords[5] = coords[3] - yoff;
+        coords[6] = coords[0] + xoff;
+        coords[7] = coords[1] - yoff;
+        draw_polygon(dr, coords, 4, bg, COL_GRID);
+
+        /* bottom face of tower */
+        coords[0] = tx + TILESIZE;
+        coords[1] = ty + TILESIZE - 1;
+        coords[2] = tx;
+        coords[3] = ty + TILESIZE - 1;
+        coords[4] = coords[2] + xoff;
+        coords[5] = coords[3] - yoff;
+        coords[6] = coords[0] + xoff;
+        coords[7] = coords[1] - yoff;
+        draw_polygon(dr, coords, 4, bg, COL_GRID);
+
+        /* now offset all subsequent drawing to the top of the tower */
+        tx += xoff;
+        ty -= yoff;
+    }
+
+    /* erase background */
+    draw_rect(dr, tx, ty, TILESIZE, TILESIZE, bg);
+
+    /* pencil-mode highlight */
+    if (tile & DF_HIGHLIGHT_PENCIL) {
+        int coords[6];
+        coords[0] = tx;
+        coords[1] = ty;
+        coords[2] = tx+TILESIZE/2;
+        coords[3] = ty;
+        coords[4] = tx;
+        coords[5] = ty+TILESIZE/2;
+        draw_polygon(dr, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);
+    }
+
+    /* draw box outline */
+    if (tile & DF_PLAYAREA) {
+        int coords[8];
+        coords[0] = tx;
+        coords[1] = ty - 1;
+        coords[2] = tx + TILESIZE;
+        coords[3] = ty - 1;
+        coords[4] = tx + TILESIZE;
+        coords[5] = ty + TILESIZE - 1;
+        coords[6] = tx;
+        coords[7] = ty + TILESIZE - 1;
+        draw_polygon(dr, coords, 4, -1, COL_GRID);
+    }
+
+    /* new number needs drawing? */
+    if (tile & DF_DIGIT_MASK) {
+        int color;
+
+        str[1] = '\0';
+        str[0] = (tile & DF_DIGIT_MASK) + '0';
+
+        if (tile & DF_ERROR)
+            color = COL_ERROR;
+        else if (tile & DF_CLUE_DONE)
+            color = COL_DONE;
+        else if (x < 0 || y < 0 || x >= w || y >= w)
+            color = COL_GRID;
+        else if (tile & DF_IMMUTABLE)
+            color = COL_GRID;
+        else
+            color = COL_USER;
+
+        draw_text(dr, tx + TILESIZE/2, ty + TILESIZE/2, FONT_VARIABLE,
+                  (tile & DF_PLAYAREA ? TILESIZE/2 : TILESIZE*2/5),
+                  ALIGN_VCENTRE | ALIGN_HCENTRE, color, str);
+    } else {
+        int i, j, npencil;
+        int pl, pr, pt, pb;
+        float bestsize;
+        int pw, ph, minph, pbest, fontsize;
+
+        /* Count the pencil marks required. */
+        for (i = 1, npencil = 0; i <= w; i++)
+            if (tile & (1L << (i + DF_PENCIL_SHIFT)))
+                npencil++;
+        if (npencil) {
+
+            minph = 2;
+
+            /*
+             * Determine the bounding rectangle within which we're going
+             * to put the pencil marks.
+             */
+            /* Start with the whole square, minus space for impinging towers */
+            pl = tx + (ds->three_d ? X_3D_DISP(w,w) : 0);
+            pr = tx + TILESIZE;
+            pt = ty;
+            pb = ty + TILESIZE - (ds->three_d ? Y_3D_DISP(w,w) : 0);
+
+            /*
+             * We arrange our pencil marks in a grid layout, with
+             * the number of rows and columns adjusted to allow the
+             * maximum font size.
+             *
+             * So now we work out what the grid size ought to be.
+             */
+            bestsize = 0.0;
+            pbest = 0;
+            /* Minimum */
+            for (pw = 3; pw < max(npencil,4); pw++) {
+                float fw, fh, fs;
+
+                ph = (npencil + pw - 1) / pw;
+                ph = max(ph, minph);
+                fw = (pr - pl) / (float)pw;
+                fh = (pb - pt) / (float)ph;
+                fs = min(fw, fh);
+                if (fs > bestsize) {
+                    bestsize = fs;
+                    pbest = pw;
+                }
+            }
+            assert(pbest > 0);
+            pw = pbest;
+            ph = (npencil + pw - 1) / pw;
+            ph = max(ph, minph);
+
+            /*
+             * Now we've got our grid dimensions, work out the pixel
+             * size of a grid element, and round it to the nearest
+             * pixel. (We don't want rounding errors to make the
+             * grid look uneven at low pixel sizes.)
+             */
+            fontsize = min((pr - pl) / pw, (pb - pt) / ph);
+
+            /*
+             * Centre the resulting figure in the square.
+             */
+            pl = pl + (pr - pl - fontsize * pw) / 2;
+            pt = pt + (pb - pt - fontsize * ph) / 2;
+
+            /*
+             * Now actually draw the pencil marks.
+             */
+            for (i = 1, j = 0; i <= w; i++)
+                if (tile & (1L << (i + DF_PENCIL_SHIFT))) {
+                    int dx = j % pw, dy = j / pw;
+
+                    str[1] = '\0';
+                    str[0] = i + '0';
+                    draw_text(dr, pl + fontsize * (2*dx+1) / 2,
+                              pt + fontsize * (2*dy+1) / 2,
+                              FONT_VARIABLE, fontsize,
+                              ALIGN_VCENTRE | ALIGN_HCENTRE, COL_PENCIL, str);
+                    j++;
+                }
+        }
+    }
+}
+
+static void game_redraw(drawing *dr, game_drawstate *ds,
+                        const game_state *oldstate, const game_state *state,
+                        int dir, const game_ui *ui,
+                        float animtime, float flashtime)
+{
+    int w = state->par.w /*, a = w*w */;
+    int i, x, y;
+
+    if (!ds->started) {
+        /*
+         * The initial contents of the window are not guaranteed and
+         * can vary with front ends. To be on the safe side, all
+         * games should start by drawing a big background-colour
+         * rectangle covering the whole window.
+         */
+        draw_rect(dr, 0, 0, SIZE(w), SIZE(w), COL_BACKGROUND);
+
+        draw_update(dr, 0, 0, SIZE(w), SIZE(w));
+
+        ds->started = TRUE;
+    }
+
+    check_errors(state, ds->errtmp);
+
+    /*
+     * Work out what data each tile should contain.
+     */
+    for (i = 0; i < (w+2)*(w+2); i++)
+        ds->tiles[i] = 0;              /* completely blank square */
+    /* The clue squares... */
+    for (i = 0; i < 4*w; i++) {
+        long tile = state->clues->clues[i];
+
+        CLUEPOS(x, y, i, w);
+
+        if (ds->errtmp[(y+1)*(w+2)+(x+1)])
+            tile |= DF_ERROR;
+        else if (state->clues_done[i])
+            tile |= DF_CLUE_DONE;
+
+        ds->tiles[(y+1)*(w+2)+(x+1)] = tile;
+    }
+    /* ... and the main grid. */
+    for (y = 0; y < w; y++) {
+        for (x = 0; x < w; x++) {
+            long tile = DF_PLAYAREA;
+
+            if (state->grid[y*w+x])
+                tile |= state->grid[y*w+x];
+            else
+                tile |= (long)state->pencil[y*w+x] << DF_PENCIL_SHIFT;
+
+            if (ui->hshow && ui->hx == x && ui->hy == y)
+                tile |= (ui->hpencil ? DF_HIGHLIGHT_PENCIL : DF_HIGHLIGHT);
+
+            if (state->clues->immutable[y*w+x])
+                tile |= DF_IMMUTABLE;
+
+            if (flashtime > 0 &&
+                (flashtime <= FLASH_TIME/3 ||
+                 flashtime >= FLASH_TIME*2/3))
+                tile |= DF_HIGHLIGHT;  /* completion flash */
+
+            if (ds->errtmp[(y+1)*(w+2)+(x+1)])
+                tile |= DF_ERROR;
+
+            ds->tiles[(y+1)*(w+2)+(x+1)] = tile;
+        }
+    }
+
+    /*
+     * Now actually draw anything that needs to be changed.
+     */
+    for (y = 0; y < w+2; y++) {
+        for (x = 0; x < w+2; x++) {
+            long tl, tr, bl, br;
+            int i = y*(w+2)+x;
+
+            tr = ds->tiles[y*(w+2)+x];
+            tl = (x == 0 ? 0 : ds->tiles[y*(w+2)+(x-1)]);
+            br = (y == w+1 ? 0 : ds->tiles[(y+1)*(w+2)+x]);
+            bl = (x == 0 || y == w+1 ? 0 : ds->tiles[(y+1)*(w+2)+(x-1)]);
+
+            if (ds->drawn[i*4] != tl || ds->drawn[i*4+1] != tr ||
+                ds->drawn[i*4+2] != bl || ds->drawn[i*4+3] != br) {
+                clip(dr, COORD(x-1), COORD(y-1), TILESIZE, TILESIZE);
+
+                draw_tile(dr, ds, state->clues, x-1, y-1, tr);
+                if (x > 0)
+                    draw_tile(dr, ds, state->clues, x-2, y-1, tl);
+                if (y <= w)
+                    draw_tile(dr, ds, state->clues, x-1, y, br);
+                if (x > 0 && y <= w)
+                    draw_tile(dr, ds, state->clues, x-2, y, bl);
+
+                unclip(dr);
+                draw_update(dr, COORD(x-1), COORD(y-1), TILESIZE, TILESIZE);
+
+                ds->drawn[i*4] = tl;
+                ds->drawn[i*4+1] = tr;
+                ds->drawn[i*4+2] = bl;
+                ds->drawn[i*4+3] = br;
+            }
+        }
+    }
+}
+
+static float game_anim_length(const game_state *oldstate,
+                              const game_state *newstate, int dir, game_ui *ui)
+{
+    return 0.0F;
+}
+
+static float game_flash_length(const game_state *oldstate,
+                               const game_state *newstate, int dir, game_ui *ui)
+{
+    if (!oldstate->completed && newstate->completed &&
+        !oldstate->cheated && !newstate->cheated)
+        return FLASH_TIME;
+    return 0.0F;
+}
+
+static int game_status(const game_state *state)
+{
+    return state->completed ? +1 : 0;
+}
+
+static int game_timing_state(const game_state *state, game_ui *ui)
+{
+    if (state->completed)
+        return FALSE;
+    return TRUE;
+}
+
+static void game_print_size(const game_params *params, float *x, float *y)
+{
+    int pw, ph;
+
+    /*
+     * We use 9mm squares by default, like Solo.
+     */
+    game_compute_size(params, 900, &pw, &ph);
+    *x = pw / 100.0F;
+    *y = ph / 100.0F;
+}
+
+static void game_print(drawing *dr, const game_state *state, int tilesize)
+{
+    int w = state->par.w;
+    int ink = print_mono_colour(dr, 0);
+    int i, x, y;
+
+    /* Ick: fake up `ds->tilesize' for macro expansion purposes */
+    game_drawstate ads, *ds = &ads;
+    game_set_size(dr, ds, NULL, tilesize);
+
+    /*
+     * Border.
+     */
+    print_line_width(dr, 3 * TILESIZE / 40);
+    draw_rect_outline(dr, BORDER, BORDER, w*TILESIZE, w*TILESIZE, ink);
+
+    /*
+     * Main grid.
+     */
+    for (x = 1; x < w; x++) {
+        print_line_width(dr, TILESIZE / 40);
+        draw_line(dr, BORDER+x*TILESIZE, BORDER,
+                  BORDER+x*TILESIZE, BORDER+w*TILESIZE, ink);
+    }
+    for (y = 1; y < w; y++) {
+        print_line_width(dr, TILESIZE / 40);
+        draw_line(dr, BORDER, BORDER+y*TILESIZE,
+                  BORDER+w*TILESIZE, BORDER+y*TILESIZE, ink);
+    }
+
+    /*
+     * Clues.
+     */
+    for (i = 0; i < 4*w; i++) {
+        char str[128];
+
+        if (!state->clues->clues[i])
+            continue;
+
+        CLUEPOS(x, y, i, w);
+
+        sprintf (str, "%d", state->clues->clues[i]);
+
+        draw_text(dr, BORDER + x*TILESIZE + TILESIZE/2,
+                  BORDER + y*TILESIZE + TILESIZE/2,
+                  FONT_VARIABLE, TILESIZE/2,
+                  ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
+    }
+
+    /*
+     * Numbers for the solution, if any.
+     */
+    for (y = 0; y < w; y++)
+        for (x = 0; x < w; x++)
+            if (state->grid[y*w+x]) {
+                char str[2];
+                str[1] = '\0';
+                str[0] = state->grid[y*w+x] + '0';
+                draw_text(dr, BORDER + x*TILESIZE + TILESIZE/2,
+                          BORDER + y*TILESIZE + TILESIZE/2,
+                          FONT_VARIABLE, TILESIZE/2,
+                          ALIGN_VCENTRE | ALIGN_HCENTRE, ink, str);
+            }
+}
+
+#ifdef COMBINED
+#define thegame towers
+#endif
+
+const struct game thegame = {
+    "Towers", "games.towers", "towers",
+    default_params,
+    game_fetch_preset, NULL,
+    decode_params,
+    encode_params,
+    free_params,
+    dup_params,
+    TRUE, game_configure, custom_params,
+    validate_params,
+    new_game_desc,
+    validate_desc,
+    new_game,
+    dup_game,
+    free_game,
+    TRUE, solve_game,
+    TRUE, game_can_format_as_text_now, game_text_format,
+    new_ui,
+    free_ui,
+    encode_ui,
+    decode_ui,
+    game_changed_state,
+    interpret_move,
+    execute_move,
+    PREFERRED_TILESIZE, game_compute_size, game_set_size,
+    game_colours,
+    game_new_drawstate,
+    game_free_drawstate,
+    game_redraw,
+    game_anim_length,
+    game_flash_length,
+    game_status,
+    TRUE, FALSE, game_print_size, game_print,
+    FALSE,                             /* wants_statusbar */
+    FALSE, game_timing_state,
+    REQUIRE_RBUTTON | REQUIRE_NUMPAD,  /* flags */
+};
+
+#ifdef STANDALONE_SOLVER
+
+#include <stdarg.h>
+
+int main(int argc, char **argv)
+{
+    game_params *p;
+    game_state *s;
+    char *id = NULL, *desc, *err;
+    int grade = FALSE;
+    int ret, diff, really_show_working = FALSE;
+
+    while (--argc > 0) {
+        char *p = *++argv;
+        if (!strcmp(p, "-v")) {
+            really_show_working = TRUE;
+        } else if (!strcmp(p, "-g")) {
+            grade = TRUE;
+        } else if (*p == '-') {
+            fprintf(stderr, "%s: unrecognised option `%s'\n", argv[0], p);
+            return 1;
+        } else {
+            id = p;
+        }
+    }
+
+    if (!id) {
+        fprintf(stderr, "usage: %s [-g | -v] <game_id>\n", argv[0]);
+        return 1;
+    }
+
+    desc = strchr(id, ':');
+    if (!desc) {
+        fprintf(stderr, "%s: game id expects a colon in it\n", argv[0]);
+        return 1;
+    }
+    *desc++ = '\0';
+
+    p = default_params();
+    decode_params(p, id);
+    err = validate_desc(p, desc);
+    if (err) {
+        fprintf(stderr, "%s: %s\n", argv[0], err);
+        return 1;
+    }
+    s = new_game(NULL, p, desc);
+
+    /*
+     * When solving an Easy puzzle, we don't want to bother the
+     * user with Hard-level deductions. For this reason, we grade
+     * the puzzle internally before doing anything else.
+     */
+    ret = -1;                          /* placate optimiser */
+    solver_show_working = FALSE;
+    for (diff = 0; diff < DIFFCOUNT; diff++) {
+        memcpy(s->grid, s->clues->immutable, p->w * p->w);
+        ret = solver(p->w, s->clues->clues, s->grid, diff);
+        if (ret <= diff)
+            break;
+    }
+
+    if (diff == DIFFCOUNT) {
+        if (grade)
+            printf("Difficulty rating: ambiguous\n");
+        else
+            printf("Unable to find a unique solution\n");
+    } else {
+        if (grade) {
+            if (ret == diff_impossible)
+                printf("Difficulty rating: impossible (no solution exists)\n");
+            else
+                printf("Difficulty rating: %s\n", towers_diffnames[ret]);
+        } else {
+            solver_show_working = really_show_working;
+            memcpy(s->grid, s->clues->immutable, p->w * p->w);
+            ret = solver(p->w, s->clues->clues, s->grid, diff);
+            if (ret != diff)
+                printf("Puzzle is inconsistent\n");
+            else
+                fputs(game_text_format(s), stdout);
+        }
+    }
+
+    return 0;
+}
+
+#endif
+
+/* vim: set shiftwidth=4 tabstop=8: */