Solve function for Inertia, using what's essentially an approximate

[sgt/puzzles] / inertia.c

/*
 * inertia.c: Game involving navigating round a grid picking up
 * gems.
 * 
 * Game rules and basic generator design by Ben Olmstead.
 * This re-implementation was written by Simon Tatham.
 */

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <ctype.h>
#include <math.h>

#include "puzzles.h"

/* Used in the game_state */
#define BLANK   'b'
#define GEM     'g'
#define MINE    'm'
#define STOP    's'
#define WALL    'w'

/* Used in the game IDs */
#define START   'S'

/* Used in the game generation */
#define POSSGEM 'G'

/* Used only in the game_drawstate*/
#define UNDRAWN '?'

#define DIRECTIONS 8
#define DP1 (DIRECTIONS+1)
#define DX(dir) ( (dir) & 3 ? (((dir) & 7) > 4 ? -1 : +1) : 0 )
#define DY(dir) ( DX((dir)+6) )

/*
 * Lvalue macro which expects x and y to be in range.
 */
#define LV_AT(w, h, grid, x, y) ( (grid)[(y)*(w)+(x)] )

/*
 * Rvalue macro which can cope with x and y being out of range.
 */
#define AT(w, h, grid, x, y) ( (x)<0 || (x)>=(w) || (y)<0 || (y)>=(h) ? \
                               WALL : LV_AT(w, h, grid, x, y) )

enum {
    COL_BACKGROUND,
    COL_OUTLINE,
    COL_HIGHLIGHT,
    COL_LOWLIGHT,
    COL_PLAYER,
    COL_DEAD_PLAYER,
    COL_MINE,
    COL_GEM,
    COL_WALL,
    COL_HINT,
    NCOLOURS
};

struct game_params {
    int w, h;
};

typedef struct soln {
    int refcount;
    int len;
    unsigned char *list;
} soln;

struct game_state {
    game_params p;
    int px, py;
    int gems;
    char *grid;
    int distance_moved;
    int dead;
    int cheated;
    int solnpos;
    soln *soln;
};

static game_params *default_params(void)
{
    game_params *ret = snew(game_params);

    ret->w = 10;
    ret->h = 8;

    return ret;
}

static void free_params(game_params *params)
{
    sfree(params);
}

static game_params *dup_params(game_params *params)
{
    game_params *ret = snew(game_params);
    *ret = *params;                    /* structure copy */
    return ret;
}

static const struct game_params inertia_presets[] = {
    { 10, 8 },
    { 15, 12 },
    { 20, 16 },
};

static int game_fetch_preset(int i, char **name, game_params **params)
{
    game_params p, *ret;
    char *retname;
    char namebuf[80];

    if (i < 0 || i >= lenof(inertia_presets))
        return FALSE;

    p = inertia_presets[i];
    ret = dup_params(&p);
    sprintf(namebuf, "%dx%d", ret->w, ret->h);
    retname = dupstr(namebuf);

    *params = ret;
    *name = retname;
    return TRUE;
}

static void decode_params(game_params *params, char const *string)
{
    params->w = params->h = atoi(string);
    while (*string && isdigit((unsigned char)*string)) string++;
    if (*string == 'x') {
        string++;
        params->h = atoi(string);
    }
}

static char *encode_params(game_params *params, int full)
{
    char data[256];

    sprintf(data, "%dx%d", params->w, params->h);

    return dupstr(data);
}

static config_item *game_configure(game_params *params)
{
    config_item *ret;
    char buf[80];

    ret = snewn(3, config_item);

    ret[0].name = "Width";
    ret[0].type = C_STRING;
    sprintf(buf, "%d", params->w);
    ret[0].sval = dupstr(buf);
    ret[0].ival = 0;

    ret[1].name = "Height";
    ret[1].type = C_STRING;
    sprintf(buf, "%d", params->h);
    ret[1].sval = dupstr(buf);
    ret[1].ival = 0;

    ret[2].name = NULL;
    ret[2].type = C_END;
    ret[2].sval = NULL;
    ret[2].ival = 0;

    return ret;
}

static game_params *custom_params(config_item *cfg)
{
    game_params *ret = snew(game_params);

    ret->w = atoi(cfg[0].sval);
    ret->h = atoi(cfg[1].sval);

    return ret;
}

static char *validate_params(game_params *params, int full)
{
    /*
     * Avoid completely degenerate cases which only have one
     * row/column. We probably could generate completable puzzles
     * of that shape, but they'd be forced to be extremely boring
     * and at large sizes would take a while to happen upon at
     * random as well.
     */
    if (params->w < 2 || params->h < 2)
        return "Width and height must both be at least two";

    /*
     * The grid construction algorithm creates 1/5 as many gems as
     * grid squares, and must create at least one gem to have an
     * actual puzzle. However, an area-five grid is ruled out by
     * the above constraint, so the practical minimum is six.
     */
    if (params->w * params->h < 6)
        return "Grid area must be at least six squares";

    return NULL;
}

/* ----------------------------------------------------------------------
 * Solver used by grid generator.
 */

struct solver_scratch {
    unsigned char *reachable_from, *reachable_to;
    int *positions;
};

static struct solver_scratch *new_scratch(int w, int h)
{
    struct solver_scratch *sc = snew(struct solver_scratch);

    sc->reachable_from = snewn(w * h * DIRECTIONS, unsigned char);
    sc->reachable_to = snewn(w * h * DIRECTIONS, unsigned char);
    sc->positions = snewn(w * h * DIRECTIONS, int);

    return sc;
}

static void free_scratch(struct solver_scratch *sc)
{
    sfree(sc->reachable_from);
    sfree(sc->reachable_to);
    sfree(sc->positions);
    sfree(sc);
}

static int can_go(int w, int h, char *grid,
                  int x1, int y1, int dir1, int x2, int y2, int dir2)
{
    /*
     * Returns TRUE if we can transition directly from (x1,y1)
     * going in direction dir1, to (x2,y2) going in direction dir2.
     */

    /*
     * If we're actually in the middle of an unoccupyable square,
     * we cannot make any move.
     */
    if (AT(w, h, grid, x1, y1) == WALL ||
        AT(w, h, grid, x1, y1) == MINE)
        return FALSE;

    /*
     * If a move is capable of stopping at x1,y1,dir1, and x2,y2 is
     * the same coordinate as x1,y1, then we can make the
     * transition (by stopping and changing direction).
     * 
     * For this to be the case, we have to either have a wall
     * beyond x1,y1,dir1, or have a stop on x1,y1.
     */
    if (x2 == x1 && y2 == y1 &&
        (AT(w, h, grid, x1, y1) == STOP ||
         AT(w, h, grid, x1, y1) == START ||
         AT(w, h, grid, x1+DX(dir1), y1+DY(dir1)) == WALL))
        return TRUE;

    /*
     * If a move is capable of continuing here, then x1,y1,dir1 can
     * move one space further on.
     */
    if (x2 == x1+DX(dir1) && y2 == y1+DY(dir1) && dir1 == dir2 &&
        (AT(w, h, grid, x2, y2) == BLANK ||
         AT(w, h, grid, x2, y2) == GEM ||
         AT(w, h, grid, x2, y2) == STOP ||
         AT(w, h, grid, x2, y2) == START))
        return TRUE;

    /*
     * That's it.
     */
    return FALSE;
}

static int find_gem_candidates(int w, int h, char *grid,
                               struct solver_scratch *sc)
{
    int wh = w*h;
    int head, tail;
    int sx, sy, gx, gy, gd, pass, possgems;

    /*
     * This function finds all the candidate gem squares, which are
     * precisely those squares which can be picked up on a loop
     * from the starting point back to the starting point. Doing
     * this may involve passing through such a square in the middle
     * of a move; so simple breadth-first search over the _squares_
     * of the grid isn't quite adequate, because it might be that
     * we can only reach a gem from the start by moving over it in
     * one direction, but can only return to the start if we were
     * moving over it in another direction.
     * 
     * Instead, we BFS over a space which mentions each grid square
     * eight times - once for each direction. We also BFS twice:
     * once to find out what square+direction pairs we can reach
     * _from_ the start point, and once to find out what pairs we
     * can reach the start point from. Then a square is reachable
     * if any of the eight directions for that square has both
     * flags set.
     */

    memset(sc->reachable_from, 0, wh * DIRECTIONS);
    memset(sc->reachable_to, 0, wh * DIRECTIONS);

    /*
     * Find the starting square.
     */
    sx = -1;                           /* placate optimiser */
    for (sy = 0; sy < h; sy++) {
        for (sx = 0; sx < w; sx++)
            if (AT(w, h, grid, sx, sy) == START)
                break;
        if (sx < w)
            break;
    }
    assert(sy < h);

    for (pass = 0; pass < 2; pass++) {
        unsigned char *reachable = (pass == 0 ? sc->reachable_from :
                                    sc->reachable_to);
        int sign = (pass == 0 ? +1 : -1);
        int dir;

#ifdef SOLVER_DIAGNOSTICS
        printf("starting pass %d\n", pass);
#endif

        /*
         * `head' and `tail' are indices within sc->positions which
         * track the list of board positions left to process.
         */
        head = tail = 0;
        for (dir = 0; dir < DIRECTIONS; dir++) {
            int index = (sy*w+sx)*DIRECTIONS+dir;
            sc->positions[tail++] = index;
            reachable[index] = TRUE;
#ifdef SOLVER_DIAGNOSTICS
            printf("starting point %d,%d,%d\n", sx, sy, dir);
#endif
        }

        /*
         * Now repeatedly pick an element off the list and process
         * it.
         */
        while (head < tail) {
            int index = sc->positions[head++];
            int dir = index % DIRECTIONS;
            int x = (index / DIRECTIONS) % w;
            int y = index / (w * DIRECTIONS);
            int n, x2, y2, d2, i2;

#ifdef SOLVER_DIAGNOSTICS
            printf("processing point %d,%d,%d\n", x, y, dir);
#endif
            /*
             * The places we attempt to switch to here are:
             *  - each possible direction change (all the other
             *    directions in this square)
             *  - one step further in the direction we're going (or
             *    one step back, if we're in the reachable_to pass).
             */
            for (n = -1; n < DIRECTIONS; n++) {
                if (n < 0) {
                    x2 = x + sign * DX(dir);
                    y2 = y + sign * DY(dir);
                    d2 = dir;
                } else {
                    x2 = x;
                    y2 = y;
                    d2 = n;
                }
                i2 = (y2*w+x2)*DIRECTIONS+d2;
                if (x2 >= 0 && x2 < w &&
                    y2 >= 0 && y2 < h &&
                    !reachable[i2]) {
                    int ok;
#ifdef SOLVER_DIAGNOSTICS
                    printf("  trying point %d,%d,%d", x2, y2, d2);
#endif
                    if (pass == 0)
                        ok = can_go(w, h, grid, x, y, dir, x2, y2, d2);
                    else
                        ok = can_go(w, h, grid, x2, y2, d2, x, y, dir);
#ifdef SOLVER_DIAGNOSTICS
                    printf(" - %sok\n", ok ? "" : "not ");
#endif
                    if (ok) {
                        sc->positions[tail++] = i2;
                        reachable[i2] = TRUE;
                    }
                }
            }
        }
    }

    /*
     * And that should be it. Now all we have to do is find the
     * squares for which there exists _some_ direction such that
     * the square plus that direction form a tuple which is both
     * reachable from the start and reachable to the start.
     */
    possgems = 0;
    for (gy = 0; gy < h; gy++)
        for (gx = 0; gx < w; gx++)
            if (AT(w, h, grid, gx, gy) == BLANK) {
                for (gd = 0; gd < DIRECTIONS; gd++) {
                    int index = (gy*w+gx)*DIRECTIONS+gd;
                    if (sc->reachable_from[index] && sc->reachable_to[index]) {
#ifdef SOLVER_DIAGNOSTICS
                        printf("space at %d,%d is reachable via"
                               " direction %d\n", gx, gy, gd);
#endif
                        LV_AT(w, h, grid, gx, gy) = POSSGEM;
                        possgems++;
                        break;
                    }
                }
            }

    return possgems;
}

/* ----------------------------------------------------------------------
 * Grid generation code.
 */

static char *gengrid(int w, int h, random_state *rs)
{
    int wh = w*h;
    char *grid = snewn(wh+1, char);
    struct solver_scratch *sc = new_scratch(w, h);
    int maxdist_threshold, tries;

    maxdist_threshold = 2;
    tries = 0;

    while (1) {
        int i, j;
        int possgems;
        int *dist, *list, head, tail, maxdist;

        /*
         * We're going to fill the grid with the five basic piece
         * types in about 1/5 proportion. For the moment, though,
         * we leave out the gems, because we'll put those in
         * _after_ we run the solver to tell us where the viable
         * locations are.
         */
        i = 0;
        for (j = 0; j < wh/5; j++)
            grid[i++] = WALL;
        for (j = 0; j < wh/5; j++)
            grid[i++] = STOP;
        for (j = 0; j < wh/5; j++)
            grid[i++] = MINE;
        assert(i < wh);
        grid[i++] = START;
        while (i < wh)
            grid[i++] = BLANK;
        shuffle(grid, wh, sizeof(*grid), rs);

        /*
         * Find the viable gem locations, and immediately give up
         * and try again if there aren't enough of them.
         */
        possgems = find_gem_candidates(w, h, grid, sc);
        if (possgems < wh/5)
            continue;

        /*
         * We _could_ now select wh/5 of the POSSGEMs and set them
         * to GEM, and have a viable level. However, there's a
         * chance that a large chunk of the level will turn out to
         * be unreachable, so first we test for that.
         * 
         * We do this by finding the largest distance from any
         * square to the nearest POSSGEM, by breadth-first search.
         * If this is above a critical threshold, we abort and try
         * again.
         * 
         * (This search is purely geometric, without regard to
         * walls and long ways round.)
         */
        dist = sc->positions;
        list = sc->positions + wh;
        for (i = 0; i < wh; i++)
            dist[i] = -1;
        head = tail = 0;
        for (i = 0; i < wh; i++)
            if (grid[i] == POSSGEM) {
                dist[i] = 0;
                list[tail++] = i;
            }
        maxdist = 0;
        while (head < tail) {
            int pos, x, y, d;

            pos = list[head++];
            if (maxdist < dist[pos])
                maxdist = dist[pos];

            x = pos % w;
            y = pos / w;

            for (d = 0; d < DIRECTIONS; d++) {
                int x2, y2, p2;

                x2 = x + DX(d);
                y2 = y + DY(d);

                if (x2 >= 0 && x2 < w && y2 >= 0 && y2 < h) {
                    p2 = y2*w+x2;
                    if (dist[p2] < 0) {
                        dist[p2] = dist[pos] + 1;
                        list[tail++] = p2;
                    }
                }
            }
        }
        assert(head == wh && tail == wh);

        /*
         * Now abandon this grid and go round again if maxdist is
         * above the required threshold.
         * 
         * We can safely start the threshold as low as 2. As we
         * accumulate failed generation attempts, we gradually
         * raise it as we get more desperate.
         */
        if (maxdist > maxdist_threshold) {
            tries++;
            if (tries == 50) {
                maxdist_threshold++;
                tries = 0;
            }
            continue;
        }

        /*
         * Now our reachable squares are plausibly evenly
         * distributed over the grid. I'm not actually going to
         * _enforce_ that I place the gems in such a way as not to
         * increase that maxdist value; I'm now just going to trust
         * to the RNG to pick a sensible subset of the POSSGEMs.
         */
        j = 0;
        for (i = 0; i < wh; i++)
            if (grid[i] == POSSGEM)
                list[j++] = i;
        shuffle(list, j, sizeof(*list), rs);
        for (i = 0; i < j; i++)
            grid[list[i]] = (i < wh/5 ? GEM : BLANK);
        break;
    }

    free_scratch(sc);

    grid[wh] = '\0';

    return grid;
}

static char *new_game_desc(game_params *params, random_state *rs,
                           char **aux, int interactive)
{
    return gengrid(params->w, params->h, rs);
}

static char *validate_desc(game_params *params, char *desc)
{
    int w = params->w, h = params->h, wh = w*h;
    int starts = 0, gems = 0, i;

    for (i = 0; i < wh; i++) {
        if (!desc[i])
            return "Not enough data to fill grid";
        if (desc[i] != WALL && desc[i] != START && desc[i] != STOP &&
            desc[i] != GEM && desc[i] != MINE && desc[i] != BLANK)
            return "Unrecognised character in game description";
        if (desc[i] == START)
            starts++;
        if (desc[i] == GEM)
            gems++;
    }
    if (desc[i])
        return "Too much data to fill grid";
    if (starts < 1)
        return "No starting square specified";
    if (starts > 1)
        return "More than one starting square specified";
    if (gems < 1)
        return "No gems specified";

    return NULL;
}

static game_state *new_game(midend *me, game_params *params, char *desc)
{
    int w = params->w, h = params->h, wh = w*h;
    int i;
    game_state *state = snew(game_state);

    state->p = *params;                /* structure copy */

    state->grid = snewn(wh, char);
    assert(strlen(desc) == wh);
    memcpy(state->grid, desc, wh);

    state->px = state->py = -1;
    state->gems = 0;
    for (i = 0; i < wh; i++) {
        if (state->grid[i] == START) {
            state->grid[i] = STOP;
            state->px = i % w;
            state->py = i / w;
        } else if (state->grid[i] == GEM) {
            state->gems++;
        }
    }

    assert(state->gems > 0);
    assert(state->px >= 0 && state->py >= 0);

    state->distance_moved = 0;
    state->dead = FALSE;

    state->cheated = FALSE;
    state->solnpos = 0;
    state->soln = NULL;

    return state;
}

static game_state *dup_game(game_state *state)
{
    int w = state->p.w, h = state->p.h, wh = w*h;
    game_state *ret = snew(game_state);

    ret->p = state->p;
    ret->px = state->px;
    ret->py = state->py;
    ret->gems = state->gems;
    ret->grid = snewn(wh, char);
    ret->distance_moved = state->distance_moved;
    ret->dead = FALSE;
    memcpy(ret->grid, state->grid, wh);
    ret->cheated = state->cheated;
    ret->soln = state->soln;
    if (ret->soln)
        ret->soln->refcount++;
    ret->solnpos = state->solnpos;

    return ret;
}

static void free_game(game_state *state)
{
    if (state->soln && --state->soln->refcount == 0) {
        sfree(state->soln->list);
        sfree(state->soln);
    }
    sfree(state->grid);
    sfree(state);
}

/*
 * Internal function used by solver.
 */
static int move_goes_to(int w, int h, char *grid, int x, int y, int d)
{
    int dr;

    /*
     * See where we'd get to if we made this move.
     */
    dr = -1;                           /* placate optimiser */
    while (1) {
        if (AT(w, h, grid, x+DX(d), y+DY(d)) == WALL) {
            dr = DIRECTIONS;           /* hit a wall, so end up stationary */
            break;
        }
        x += DX(d);
        y += DY(d);
        if (AT(w, h, grid, x, y) == STOP) {
            dr = DIRECTIONS;           /* hit a stop, so end up stationary */
            break;
        }
        if (AT(w, h, grid, x, y) == GEM) {
            dr = d;                    /* hit a gem, so we're still moving */
            break;
        }
        if (AT(w, h, grid, x, y) == MINE)
            return -1;                 /* hit a mine, so move is invalid */
    }
    assert(dr >= 0);
    return (y*w+x)*DP1+dr;
}

static int compare_integers(const void *av, const void *bv)
{
    const int *a = (const int *)av;
    const int *b = (const int *)bv;
    if (*a < *b)
        return -1;
    else if (*a > *b)
        return +1;
    else
        return 0;
}

static char *solve_game(game_state *state, game_state *currstate,
                        char *aux, char **error)
{
    int w = state->p.w, h = state->p.h, wh = w*h;
    int *nodes, *nodeindex, *edges, *backedges, *edgei, *backedgei, *circuit;
    int nedges;
    int *dist, *dist2, *list;
    int *unvisited;
    int circuitlen, circuitsize;
    int head, tail, pass, i, j, n, x, y, d, dd;
    char *err, *soln, *p;

    /*
     * Solving Inertia is a question of first building up the graph
     * of where you can get to from where, and secondly finding a
     * tour of the graph which takes in every gem.
     * 
     * This is of course a close cousin of the travelling salesman
     * problem, which is NP-complete; so I rather doubt that any
     * _optimal_ tour can be found in plausible time. Hence I'll
     * restrict myself to merely finding a not-too-bad one.
     * 
     * First construct the graph, by bfsing out move by move from
     * the current player position. Graph vertices will be
     *  - every endpoint of a move (place the ball can be
     *    stationary)
     *  - every gem (place the ball can go through in motion).
     *    Vertices of this type have an associated direction, since
     *    if a gem can be collected by sliding through it in two
     *    different directions it doesn't follow that you can
     *    change direction at it.
     * 
     * I'm going to refer to a non-directional vertex as
     * (y*w+x)*DP1+DIRECTIONS, and a directional one as
     * (y*w+x)*DP1+d.
     */

    /*
     * nodeindex[] maps node codes as shown above to numeric
     * indices in the nodes[] array.
     */
    nodeindex = snewn(DP1*wh, int);
    for (i = 0; i < DP1*wh; i++)
        nodeindex[i] = -1;

    /*
     * Do the bfs to find all the interesting graph nodes.
     */
    nodes = snewn(DP1*wh, int);
    head = tail = 0;

    nodes[tail] = (currstate->py * w + currstate->px) * DP1 + DIRECTIONS;
    nodeindex[nodes[0]] = tail;
    tail++;

    while (head < tail) {
        int nc = nodes[head++], nnc;

        d = nc % DP1;

        /*
         * Plot all possible moves from this node. If the node is
         * directed, there's only one.
         */
        for (dd = 0; dd < DIRECTIONS; dd++) {
            x = nc / DP1;
            y = x / w;
            x %= w;

            if (d < DIRECTIONS && d != dd)
                continue;

            nnc = move_goes_to(w, h, currstate->grid, x, y, dd);
            if (nnc >= 0 && nnc != nc) {
                if (nodeindex[nnc] < 0) {
                    nodes[tail] = nnc;
                    nodeindex[nnc] = tail;
                    tail++;
                }
            }
        }
    }
    n = head;

    /*
     * Now we know how many nodes we have, allocate the edge array
     * and go through setting up the edges.
     */
    edges = snewn(DIRECTIONS*n, int);
    edgei = snewn(n+1, int);
    nedges = 0;

    for (i = 0; i < n; i++) {
        int nc = nodes[i];

        edgei[i] = nedges;

        d = nc % DP1;
        x = nc / DP1;
        y = x / w;
        x %= w;

        for (dd = 0; dd < DIRECTIONS; dd++) {
            int nnc;

            if (d >= DIRECTIONS || d == dd) {
                nnc = move_goes_to(w, h, currstate->grid, x, y, dd);

                if (nnc >= 0 && nnc != nc)
                    edges[nedges++] = nodeindex[nnc];
            }
        }
    }
    edgei[n] = nedges;

    /*
     * Now set up the backedges array.
     */
    backedges = snewn(nedges, int);
    backedgei = snewn(n+1, int);
    for (i = j = 0; i < nedges; i++) {
        while (j+1 < n && i >= edgei[j+1])
            j++;
        backedges[i] = edges[i] * n + j;
    }
    qsort(backedges, nedges, sizeof(int), compare_integers);
    backedgei[0] = 0;
    for (i = j = 0; i < nedges; i++) {
        int k = backedges[i] / n;
        backedges[i] %= n;
        while (j < k)
            backedgei[++j] = i;
    }
    backedgei[n] = nedges;

    /*
     * Set up the initial tour. At all times, our tour is a circuit
     * of graph vertices (which may, and probably will often,
     * repeat vertices). To begin with, it's got exactly one vertex
     * in it, which is the player's current starting point.
     */
    circuitsize = 256;
    circuit = snewn(circuitsize, int);
    circuitlen = 0;
    circuit[circuitlen++] = 0;         /* node index 0 is the starting posn */

    /*
     * Track which gems are as yet unvisited.
     */
    unvisited = snewn(wh, int);
    for (i = 0; i < wh; i++)
        unvisited[i] = FALSE;
    for (i = 0; i < wh; i++)
        if (currstate->grid[i] == GEM)
            unvisited[i] = TRUE;

    /*
     * Allocate space for doing bfses inside the main loop.
     */
    dist = snewn(n, int);
    dist2 = snewn(n, int);
    list = snewn(n, int);

    err = NULL;
    soln = NULL;

    /*
     * Now enter the main loop, in each iteration of which we
     * extend the tour to take in an as yet uncollected gem.
     */
    while (1) {
        int target, n1, n2, bestdist, extralen, targetpos;

#ifdef TSP_DIAGNOSTICS
        printf("circuit is");
        for (i = 0; i < circuitlen; i++) {
            int nc = nodes[circuit[i]];
            printf(" (%d,%d,%d)", nc/DP1%w, nc/(DP1*w), nc%DP1);
        }
        printf("\n");
        printf("moves are ");
        x = nodes[circuit[0]] / DP1 % w;
        y = nodes[circuit[0]] / DP1 / w;
        for (i = 1; i < circuitlen; i++) {
            int x2, y2, dx, dy;
            if (nodes[circuit[i]] % DP1 != DIRECTIONS)
                continue;
            x2 = nodes[circuit[i]] / DP1 % w;
            y2 = nodes[circuit[i]] / DP1 / w;
            dx = (x2 > x ? +1 : x2 < x ? -1 : 0);
            dy = (y2 > y ? +1 : y2 < y ? -1 : 0);
            for (d = 0; d < DIRECTIONS; d++)
                if (DX(d) == dx && DY(d) == dy)
                    printf("%c", "89632147"[d]);
            x = x2;
            y = y2;
        }
        printf("\n");
#endif

        /*
         * First, start a pair of bfses at _every_ vertex currently
         * in the tour, and extend them outwards to find the
         * nearest as yet unreached gem vertex.
         * 
         * This is largely a heuristic: we could pick _any_ doubly
         * reachable node here and still get a valid tour as
         * output. I hope that picking a nearby one will result in
         * generally good tours.
         */
        for (pass = 0; pass < 2; pass++) {
            int *ep = (pass == 0 ? edges : backedges);
            int *ei = (pass == 0 ? edgei : backedgei);
            int *dp = (pass == 0 ? dist : dist2);
            head = tail = 0;
            for (i = 0; i < n; i++)
                dp[i] = -1;
            for (i = 0; i < circuitlen; i++) {
                int ni = circuit[i];
                if (dp[ni] < 0) {
                    dp[ni] = 0;
                    list[tail++] = ni;
                }
            }
            while (head < tail) {
                int ni = list[head++];
                for (i = ei[ni]; i < ei[ni+1]; i++) {
                    int ti = ep[i];
                    if (ti >= 0 && dp[ti] < 0) {
                        dp[ti] = dp[ni] + 1;
                        list[tail++] = ti;
                    }
                }
            }
        }
        /* Now find the nearest unvisited gem. */
        bestdist = -1;
        target = -1;
        for (i = 0; i < n; i++) {
            if (unvisited[nodes[i] / DP1] &&
                dist[i] >= 0 && dist2[i] >= 0) {
                int thisdist = dist[i] + dist2[i];
                if (bestdist < 0 || bestdist > thisdist) {
                    bestdist = thisdist;
                    target = i;
                }
            }
        }

        if (target < 0) {
            /*
             * If we get to here, we haven't found a gem we can get
             * at all, which means we terminate this loop.
             */
            break;
        }

        /*
         * Now we have a graph vertex at list[tail-1] which is an
         * unvisited gem. We want to add that vertex to our tour.
         * So we run two more breadth-first searches: one starting
         * from that vertex and following forward edges, and
         * another starting from the same vertex and following
         * backward edges. This allows us to determine, for each
         * node on the current tour, how quickly we can get both to
         * and from the target vertex from that node.
         */
#ifdef TSP_DIAGNOSTICS
        printf("target node is %d (%d,%d,%d)\n", target, nodes[target]/DP1%w,
               nodes[target]/DP1/w, nodes[target]%DP1);
#endif

        for (pass = 0; pass < 2; pass++) {
            int *ep = (pass == 0 ? edges : backedges);
            int *ei = (pass == 0 ? edgei : backedgei);
            int *dp = (pass == 0 ? dist : dist2);

            for (i = 0; i < n; i++)
                dp[i] = -1;
            head = tail = 0;

            dp[target] = 0;
            list[tail++] = target;

            while (head < tail) {
                int ni = list[head++];
                for (i = ei[ni]; i < ei[ni+1]; i++) {
                    int ti = ep[i];
                    if (ti >= 0 && dp[ti] < 0) {
                        dp[ti] = dp[ni] + 1;
/*printf("pass %d: set dist of vertex %d to %d (via %d)\n", pass, ti, dp[ti], ni);*/
                        list[tail++] = ti;
                    }
                }
            }
        }

        /*
         * Now for every node n, dist[n] gives the length of the
         * shortest path from the target vertex to n, and dist2[n]
         * gives the length of the shortest path from n to the
         * target vertex.
         * 
         * Our next step is to search linearly along the tour to
         * find the optimum place to insert a trip to the target
         * vertex and back. Our two options are either
         *  (a) to find two adjacent vertices A,B in the tour and
         *      replace the edge A->B with the path A->target->B
         *  (b) to find a single vertex X in the tour and replace
         *      it with the complete round trip X->target->X.
         * We do whichever takes the fewest moves.
         */
        n1 = n2 = -1;
        bestdist = -1;
        for (i = 0; i < circuitlen; i++) {
            int thisdist;

            /*
             * Try a round trip from vertex i.
             */
            if (dist[circuit[i]] >= 0 &&
                dist2[circuit[i]] >= 0) {
                thisdist = dist[circuit[i]] + dist2[circuit[i]];
                if (bestdist < 0 || thisdist < bestdist) {
                    bestdist = thisdist;
                    n1 = n2 = i;
                }
            }

            /*
             * Try a trip from vertex i via target to vertex i+1.
             */
            if (i+1 < circuitlen &&
                dist2[circuit[i]] >= 0 &&
                dist[circuit[i+1]] >= 0) {
                thisdist = dist2[circuit[i]] + dist[circuit[i+1]];
                if (bestdist < 0 || thisdist < bestdist) {
                    bestdist = thisdist;
                    n1 = i;
                    n2 = i+1;
                }
            }
        }
        if (bestdist < 0) {
            /*
             * We couldn't find a round trip taking in this gem _at
             * all_. Give up.
             */
            err = "Unable to find a solution from this starting point";
            break;
        }
#ifdef TSP_DIAGNOSTICS
        printf("insertion point: n1=%d, n2=%d, dist=%d\n", n1, n2, bestdist);
#endif

#ifdef TSP_DIAGNOSTICS
        printf("circuit before lengthening is");
        for (i = 0; i < circuitlen; i++) {
            printf(" %d", circuit[i]);
        }
        printf("\n");
#endif

        /*
         * Now actually lengthen the tour to take in this round
         * trip.
         */
        extralen = dist2[circuit[n1]] + dist[circuit[n2]];
        if (n1 != n2)
            extralen--;
        circuitlen += extralen;
        if (circuitlen >= circuitsize) {
            circuitsize = circuitlen + 256;
            circuit = sresize(circuit, circuitsize, int);
        }
        memmove(circuit + n2 + extralen, circuit + n2,
                (circuitlen - n2 - extralen) * sizeof(int));
        n2 += extralen;

#ifdef TSP_DIAGNOSTICS
        printf("circuit in middle of lengthening is");
        for (i = 0; i < circuitlen; i++) {
            printf(" %d", circuit[i]);
        }
        printf("\n");
#endif

        /*
         * Find the shortest-path routes to and from the target,
         * and write them into the circuit.
         */
        targetpos = n1 + dist2[circuit[n1]];
        assert(targetpos - dist2[circuit[n1]] == n1);
        assert(targetpos + dist[circuit[n2]] == n2);
        for (pass = 0; pass < 2; pass++) {
            int dir = (pass == 0 ? -1 : +1);
            int *ep = (pass == 0 ? backedges : edges);
            int *ei = (pass == 0 ? backedgei : edgei);
            int *dp = (pass == 0 ? dist : dist2);
            int nn = (pass == 0 ? n2 : n1);
            int ni = circuit[nn], ti, dest = nn;

            while (1) {
                circuit[dest] = ni;
                if (dp[ni] == 0)
                    break;
                dest += dir;
                ti = -1;
/*printf("pass %d: looking at vertex %d\n", pass, ni);*/
                for (i = ei[ni]; i < ei[ni+1]; i++) {
                    ti = ep[i];
                    if (ti >= 0 && dp[ti] == dp[ni] - 1)
                        break;
                }
                assert(i < ei[ni+1] && ti >= 0);
                ni = ti;
            }
        }

#ifdef TSP_DIAGNOSTICS
        printf("circuit after lengthening is");
        for (i = 0; i < circuitlen; i++) {
            printf(" %d", circuit[i]);
        }
        printf("\n");
#endif

        /*
         * Finally, mark all gems that the new piece of circuit
         * passes through as visited.
         */
        for (i = n1; i <= n2; i++) {
            int pos = nodes[circuit[i]] / DP1;
            assert(pos >= 0 && pos < wh);
            unvisited[pos] = FALSE;
        }
    }

#ifdef TSP_DIAGNOSTICS
    printf("before reduction, moves are ");
    x = nodes[circuit[0]] / DP1 % w;
    y = nodes[circuit[0]] / DP1 / w;
    for (i = 1; i < circuitlen; i++) {
        int x2, y2, dx, dy;
        if (nodes[circuit[i]] % DP1 != DIRECTIONS)
            continue;
        x2 = nodes[circuit[i]] / DP1 % w;
        y2 = nodes[circuit[i]] / DP1 / w;
        dx = (x2 > x ? +1 : x2 < x ? -1 : 0);
        dy = (y2 > y ? +1 : y2 < y ? -1 : 0);
        for (d = 0; d < DIRECTIONS; d++)
            if (DX(d) == dx && DY(d) == dy)
                printf("%c", "89632147"[d]);
        x = x2;
        y = y2;
    }
    printf("\n");
#endif

    /*
     * That's got a basic solution. Now optimise it by removing
     * redundant sections of the circuit: it's entirely possible
     * that a piece of circuit we carefully inserted at one stage
     * to collect a gem has become pointless because the steps
     * required to collect some _later_ gem necessarily passed
     * through the same one.
     * 
     * So first we go through and work out how many times each gem
     * is collected. Then we look for maximal sections of circuit
     * which are redundant in the sense that their removal would
     * not reduce any gem's collection count to zero, and replace
     * each one with a bfs-derived fastest path between their
     * endpoints.
     */
    while (1) {
        int oldlen = circuitlen;

        for (i = 0; i < wh; i++)
            unvisited[i] = 0;
        for (i = 0; i < circuitlen; i++) {
            int xy = nodes[circuit[i]] / DP1;
            if (currstate->grid[xy] == GEM)
                unvisited[xy]++;
        }

        /*
         * If there's any gem we didn't end up visiting at all,
         * give up.
         */
        for (i = 0; i < wh; i++) {
            if (currstate->grid[i] == GEM && unvisited[i] == 0) {
                err = "Unable to find a solution from this starting point";
                break;
            }
        }
        if (i < wh)
            break;

        for (i = j = 0; i < circuitlen; i++) {
            int xy = nodes[circuit[i]] / DP1;
            if (currstate->grid[xy] == GEM && unvisited[xy] > 1) {
                unvisited[xy]--;
            } else if (currstate->grid[xy] == GEM || i == circuitlen-1) {
                /*
                 * circuit[i] collects a gem for the only time, or is
                 * the last node in the circuit. Therefore it cannot be
                 * removed; so we now want to replace the path from
                 * circuit[j] to circuit[i] with a bfs-shortest path.
                 */
                int k, dest, ni, ti, thisdist;

#ifdef TSP_DIAGNOSTICS
                printf("optimising section from %d - %d\n", j, i);
#endif

                for (k = 0; k < n; k++)
                    dist[k] = -1;
                head = tail = 0;

                dist[circuit[j]] = 0;
                list[tail++] = circuit[j];

                while (head < tail && dist[circuit[i]] < 0) {
                    int ni = list[head++];
                    for (k = edgei[ni]; k < edgei[ni+1]; k++) {
                        int ti = edges[k];
                        if (ti >= 0 && dist[ti] < 0) {
                            dist[ti] = dist[ni] + 1;
                            list[tail++] = ti;
                        }
                    }
                }

                thisdist = dist[circuit[i]];
                assert(thisdist >= 0 && thisdist <= i-j);

                memmove(circuit+j+thisdist, circuit+i,
                        (circuitlen - i) * sizeof(int));
                circuitlen -= i-j;
                i = j + thisdist;
                circuitlen += i-j;

#ifdef TSP_DIAGNOSTICS
                printf("new section runs from %d - %d\n", j, i);
#endif

                dest = i;
                assert(dest >= 0);
                ni = circuit[i];

                while (1) {
                    /* printf("dest=%d circuitlen=%d ni=%d dist[ni]=%d\n", dest, circuitlen, ni, dist[ni]); */
                    circuit[dest] = ni;
                    if (dist[ni] == 0)
                        break;
                    dest--;
                    ti = -1;
                    for (k = backedgei[ni]; k < backedgei[ni+1]; k++) {
                        ti = backedges[k];
                        if (ti >= 0 && dist[ti] == dist[ni] - 1)
                            break;
                    }
                    assert(k < backedgei[ni+1] && ti >= 0);
                    ni = ti;
                }

                /*
                 * Now re-increment the visit counts for the new
                 * path.
                 */
                while (++j < i) {
                    int xy = nodes[circuit[j]] / DP1;
                    if (currstate->grid[xy] == GEM)
                        unvisited[xy]++;
                }

#ifdef TSP_DIAGNOSTICS
                printf("during reduction, circuit is");
                for (k = 0; k < circuitlen; k++) {
                    int nc = nodes[circuit[k]];
                    printf(" (%d,%d,%d)", nc/DP1%w, nc/(DP1*w), nc%DP1);
                }
                printf("\n");
                printf("moves are ");
                x = nodes[circuit[0]] / DP1 % w;
                y = nodes[circuit[0]] / DP1 / w;
                for (k = 1; k < circuitlen; k++) {
                    int x2, y2, dx, dy;
                    if (nodes[circuit[k]] % DP1 != DIRECTIONS)
                        continue;
                    x2 = nodes[circuit[k]] / DP1 % w;
                    y2 = nodes[circuit[k]] / DP1 / w;
                    dx = (x2 > x ? +1 : x2 < x ? -1 : 0);
                    dy = (y2 > y ? +1 : y2 < y ? -1 : 0);
                    for (d = 0; d < DIRECTIONS; d++)
                        if (DX(d) == dx && DY(d) == dy)
                            printf("%c", "89632147"[d]);
                    x = x2;
                    y = y2;
                }
                printf("\n");
#endif
            }
        }

#ifdef TSP_DIAGNOSTICS
        printf("after reduction, moves are ");
        x = nodes[circuit[0]] / DP1 % w;
        y = nodes[circuit[0]] / DP1 / w;
        for (i = 1; i < circuitlen; i++) {
            int x2, y2, dx, dy;
            if (nodes[circuit[i]] % DP1 != DIRECTIONS)
                continue;
            x2 = nodes[circuit[i]] / DP1 % w;
            y2 = nodes[circuit[i]] / DP1 / w;
            dx = (x2 > x ? +1 : x2 < x ? -1 : 0);
            dy = (y2 > y ? +1 : y2 < y ? -1 : 0);
            for (d = 0; d < DIRECTIONS; d++)
                if (DX(d) == dx && DY(d) == dy)
                    printf("%c", "89632147"[d]);
            x = x2;
            y = y2;
        }
        printf("\n");
#endif

        /*
         * If we've managed an entire reduction pass and not made
         * the solution any shorter, we're _really_ done.
         */
        if (circuitlen == oldlen)
            break;
    }

    /*
     * Encode the solution as a move string.
     */
    if (!err) {
        soln = snewn(circuitlen+2, char);
        p = soln;
        *p++ = 'S';
        x = nodes[circuit[0]] / DP1 % w;
        y = nodes[circuit[0]] / DP1 / w;
        for (i = 1; i < circuitlen; i++) {
            int x2, y2, dx, dy;
            if (nodes[circuit[i]] % DP1 != DIRECTIONS)
                continue;
            x2 = nodes[circuit[i]] / DP1 % w;
            y2 = nodes[circuit[i]] / DP1 / w;
            dx = (x2 > x ? +1 : x2 < x ? -1 : 0);
            dy = (y2 > y ? +1 : y2 < y ? -1 : 0);
            for (d = 0; d < DIRECTIONS; d++)
                if (DX(d) == dx && DY(d) == dy) {
                    *p++ = '0' + d;
                    break;
                }
            assert(d < DIRECTIONS);
            x = x2;
            y = y2;
        }
        *p++ = '\0';
        assert(p - soln < circuitlen+2);
    }

    sfree(list);
    sfree(dist);
    sfree(dist2);
    sfree(unvisited);
    sfree(circuit);
    sfree(backedgei);
    sfree(backedges);
    sfree(edgei);
    sfree(edges);
    sfree(nodeindex);
    sfree(nodes);

    if (err)
        *error = err;

    return soln;
}

static char *game_text_format(game_state *state)
{
    return NULL;
}

struct game_ui {
    float anim_length;
    int flashtype;
    int deaths;
    int just_made_move;
    int just_died;
};

static game_ui *new_ui(game_state *state)
{
    game_ui *ui = snew(game_ui);
    ui->anim_length = 0.0F;
    ui->flashtype = 0;
    ui->deaths = 0;
    ui->just_made_move = FALSE;
    ui->just_died = FALSE;
    return ui;
}

static void free_ui(game_ui *ui)
{
    sfree(ui);
}

static char *encode_ui(game_ui *ui)
{
    char buf[80];
    /*
     * The deaths counter needs preserving across a serialisation.
     */
    sprintf(buf, "D%d", ui->deaths);
    return dupstr(buf);
}

static void decode_ui(game_ui *ui, char *encoding)
{
    int p = 0;
    sscanf(encoding, "D%d%n", &ui->deaths, &p);
}

static void game_changed_state(game_ui *ui, game_state *oldstate,
                               game_state *newstate)
{
    /*
     * Increment the deaths counter. We only do this if
     * ui->just_made_move is set (redoing a suicide move doesn't
     * kill you _again_), and also we only do it if the game wasn't
     * already completed (once you're finished, you can play).
     */
    if (!oldstate->dead && newstate->dead && ui->just_made_move &&
        oldstate->gems) {
        ui->deaths++;
        ui->just_died = TRUE;
    } else {
        ui->just_died = FALSE;
    }
    ui->just_made_move = FALSE;
}

struct game_drawstate {
    game_params p;
    int tilesize;
    int started;
    unsigned short *grid;
    blitter *player_background;
    int player_bg_saved, pbgx, pbgy;
};

#define PREFERRED_TILESIZE 32
#define TILESIZE (ds->tilesize)
#define BORDER    (TILESIZE)
#define HIGHLIGHT_WIDTH (TILESIZE / 10)
#define COORD(x)  ( (x) * TILESIZE + BORDER )
#define FROMCOORD(x)  ( ((x) - BORDER + TILESIZE) / TILESIZE - 1 )

static char *interpret_move(game_state *state, game_ui *ui, game_drawstate *ds,
                            int x, int y, int button)
{
    int w = state->p.w, h = state->p.h /*, wh = w*h */;
    int dir;
    char buf[80];

    dir = -1;

    if (button == LEFT_BUTTON) {
        /*
         * Mouse-clicking near the target point (or, more
         * accurately, in the appropriate octant) is an alternative
         * way to input moves.
         */

        if (FROMCOORD(x) != state->px || FROMCOORD(y) != state->py) {
            int dx, dy;
            float angle;

            dx = FROMCOORD(x) - state->px;
            dy = FROMCOORD(y) - state->py;
            /* I pass dx,dy rather than dy,dx so that the octants
             * end up the right way round. */
            angle = atan2(dx, -dy);

            angle = (angle + (PI/8)) / (PI/4);
            assert(angle > -16.0F);
            dir = (int)(angle + 16.0F) & 7;
        }
    } else if (button == CURSOR_UP || button == (MOD_NUM_KEYPAD | '8'))
        dir = 0;
    else if (button == CURSOR_DOWN || button == (MOD_NUM_KEYPAD | '2'))
        dir = 4;
    else if (button == CURSOR_LEFT || button == (MOD_NUM_KEYPAD | '4'))
        dir = 6;
    else if (button == CURSOR_RIGHT || button == (MOD_NUM_KEYPAD | '6'))
        dir = 2;
    else if (button == (MOD_NUM_KEYPAD | '7'))
        dir = 7;
    else if (button == (MOD_NUM_KEYPAD | '1'))
        dir = 5;
    else if (button == (MOD_NUM_KEYPAD | '9'))
        dir = 1;
    else if (button == (MOD_NUM_KEYPAD | '3'))
        dir = 3;
    else if (button == ' ' && state->soln && state->solnpos < state->soln->len)
        dir = state->soln->list[state->solnpos];

    if (dir < 0)
        return NULL;

    /*
     * Reject the move if we can't make it at all due to a wall
     * being in the way.
     */
    if (AT(w, h, state->grid, state->px+DX(dir), state->py+DY(dir)) == WALL)
        return NULL;

    /*
     * Reject the move if we're dead!
     */
    if (state->dead)
        return NULL;

    /*
     * Otherwise, we can make the move. All we need to specify is
     * the direction.
     */
    ui->just_made_move = TRUE;
    sprintf(buf, "%d", dir);
    return dupstr(buf);
}

static game_state *execute_move(game_state *state, char *move)
{
    int w = state->p.w, h = state->p.h /*, wh = w*h */;
    int dir;
    game_state *ret;

    if (*move == 'S') {
        int len, i;
        soln *sol;

        /*
         * This is a solve move, so we don't actually _change_ the
         * grid but merely set up a stored solution path.
         */
        move++;
        len = strlen(move);
        sol = snew(soln);
        sol->len = len;
        sol->list = snewn(len, unsigned char);
        for (i = 0; i < len; i++)
            sol->list[i] = move[i] - '0';
        ret = dup_game(state);
        ret->cheated = TRUE;
        ret->soln = sol;
        ret->solnpos = 0;
        sol->refcount = 1;
        return ret;
    }

    dir = atoi(move);
    if (dir < 0 || dir >= DIRECTIONS)
        return NULL;                   /* huh? */

    if (state->dead)
        return NULL;

    if (AT(w, h, state->grid, state->px+DX(dir), state->py+DY(dir)) == WALL)
        return NULL;                   /* wall in the way! */

    /*
     * Now make the move.
     */
    ret = dup_game(state);
    ret->distance_moved = 0;
    while (1) {
        ret->px += DX(dir);
        ret->py += DY(dir);
        ret->distance_moved++;

        if (AT(w, h, ret->grid, ret->px, ret->py) == GEM) {
            LV_AT(w, h, ret->grid, ret->px, ret->py) = BLANK;
            ret->gems--;
        }

        if (AT(w, h, ret->grid, ret->px, ret->py) == MINE) {
            ret->dead = TRUE;
            break;
        }

        if (AT(w, h, ret->grid, ret->px, ret->py) == STOP ||
            AT(w, h, ret->grid, ret->px+DX(dir),
               ret->py+DY(dir)) == WALL)
            break;
    }

    if (ret->soln) {
        /*
         * If this move is the correct next one in the stored
         * solution path, advance solnpos.
         */
        if (ret->soln->list[ret->solnpos] == dir &&
            ret->solnpos+1 < ret->soln->len) {
            ret->solnpos++;
        } else {
            /*
             * Otherwise, the user has strayed from the path, so
             * the path is no longer valid.
             */
            ret->soln->refcount--;
            assert(ret->soln->refcount > 0);/* `state' at least still exists */
            ret->soln = NULL;
            ret->solnpos = 0;
        }
    }

    return ret;
}

/* ----------------------------------------------------------------------
 * Drawing routines.
 */

static void game_compute_size(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 = 2 * BORDER + 1 + params->w * TILESIZE;
    *y = 2 * BORDER + 1 + params->h * TILESIZE;
}

static void game_set_size(drawing *dr, game_drawstate *ds,
                          game_params *params, int tilesize)
{
    ds->tilesize = tilesize;

    assert(!ds->player_background);    /* set_size is never called twice */
    assert(!ds->player_bg_saved);

    ds->player_background = blitter_new(dr, TILESIZE, TILESIZE);
}

static float *game_colours(frontend *fe, game_state *state, int *ncolours)
{
    float *ret = snewn(3 * NCOLOURS, float);
    int i;

    game_mkhighlight(fe, ret, COL_BACKGROUND, COL_HIGHLIGHT, COL_LOWLIGHT);

    ret[COL_OUTLINE * 3 + 0] = 0.0F;
    ret[COL_OUTLINE * 3 + 1] = 0.0F;
    ret[COL_OUTLINE * 3 + 2] = 0.0F;

    ret[COL_PLAYER * 3 + 0] = 0.0F;
    ret[COL_PLAYER * 3 + 1] = 1.0F;
    ret[COL_PLAYER * 3 + 2] = 0.0F;

    ret[COL_DEAD_PLAYER * 3 + 0] = 1.0F;
    ret[COL_DEAD_PLAYER * 3 + 1] = 0.0F;
    ret[COL_DEAD_PLAYER * 3 + 2] = 0.0F;

    ret[COL_MINE * 3 + 0] = 0.0F;
    ret[COL_MINE * 3 + 1] = 0.0F;
    ret[COL_MINE * 3 + 2] = 0.0F;

    ret[COL_GEM * 3 + 0] = 0.6F;
    ret[COL_GEM * 3 + 1] = 1.0F;
    ret[COL_GEM * 3 + 2] = 1.0F;

    for (i = 0; i < 3; i++) {
        ret[COL_WALL * 3 + i] = (3 * ret[COL_BACKGROUND * 3 + i] +
                                 1 * ret[COL_HIGHLIGHT * 3 + i]) / 4;
    }

    ret[COL_HINT * 3 + 0] = 1.0F;
    ret[COL_HINT * 3 + 1] = 1.0F;
    ret[COL_HINT * 3 + 2] = 0.0F;

    *ncolours = NCOLOURS;
    return ret;
}

static game_drawstate *game_new_drawstate(drawing *dr, game_state *state)
{
    int w = state->p.w, h = state->p.h, wh = w*h;
    struct game_drawstate *ds = snew(struct game_drawstate);
    int i;

    ds->tilesize = 0;

    /* We can't allocate the blitter rectangle for the player background
     * until we know what size to make it. */
    ds->player_background = NULL;
    ds->player_bg_saved = FALSE;
    ds->pbgx = ds->pbgy = -1;

    ds->p = state->p;                  /* structure copy */
    ds->started = FALSE;
    ds->grid = snewn(wh, unsigned short);
    for (i = 0; i < wh; i++)
        ds->grid[i] = UNDRAWN;

    return ds;
}

static void game_free_drawstate(drawing *dr, game_drawstate *ds)
{
    if (ds->player_background)
        blitter_free(dr, ds->player_background);
    sfree(ds->grid);
    sfree(ds);
}

static void draw_player(drawing *dr, game_drawstate *ds, int x, int y,
                        int dead, int hintdir)
{
    if (dead) {
        int coords[DIRECTIONS*4];
        int d;

        for (d = 0; d < DIRECTIONS; d++) {
            float x1, y1, x2, y2, x3, y3, len;

            x1 = DX(d);
            y1 = DY(d);
            len = sqrt(x1*x1+y1*y1); x1 /= len; y1 /= len;

            x3 = DX(d+1);
            y3 = DY(d+1);
            len = sqrt(x3*x3+y3*y3); x3 /= len; y3 /= len;

            x2 = (x1+x3) / 4;
            y2 = (y1+y3) / 4;

            coords[d*4+0] = x + TILESIZE/2 + (int)((TILESIZE*3/7) * x1);
            coords[d*4+1] = y + TILESIZE/2 + (int)((TILESIZE*3/7) * y1);
            coords[d*4+2] = x + TILESIZE/2 + (int)((TILESIZE*3/7) * x2);
            coords[d*4+3] = y + TILESIZE/2 + (int)((TILESIZE*3/7) * y2);
        }
        draw_polygon(dr, coords, DIRECTIONS*2, COL_DEAD_PLAYER, COL_OUTLINE);
    } else {
        draw_circle(dr, x + TILESIZE/2, y + TILESIZE/2,
                    TILESIZE/3, COL_PLAYER, COL_OUTLINE);
    }

    if (!dead && hintdir >= 0) {
        float scale = (DX(hintdir) && DY(hintdir) ? 0.8F : 1.0F);
        int ax = (TILESIZE*2/5) * scale * DX(hintdir);
        int ay = (TILESIZE*2/5) * scale * DY(hintdir);
        int px = -ay, py = ax;
        int ox = x + TILESIZE/2, oy = y + TILESIZE/2;
        int coords[14], *c;

        c = coords;
        *c++ = ox + px/9;
        *c++ = oy + py/9;
        *c++ = ox + px/9 + ax*2/3;
        *c++ = oy + py/9 + ay*2/3;
        *c++ = ox + px/3 + ax*2/3;
        *c++ = oy + py/3 + ay*2/3;
        *c++ = ox + ax;
        *c++ = oy + ay;
        *c++ = ox - px/3 + ax*2/3;
        *c++ = oy - py/3 + ay*2/3;
        *c++ = ox - px/9 + ax*2/3;
        *c++ = oy - py/9 + ay*2/3;
        *c++ = ox - px/9;
        *c++ = oy - py/9;
        draw_polygon(dr, coords, 7, COL_HINT, COL_OUTLINE);
    }

    draw_update(dr, x, y, TILESIZE, TILESIZE);
}

#define FLASH_DEAD 0x100
#define FLASH_WIN  0x200
#define FLASH_MASK 0x300

static void draw_tile(drawing *dr, game_drawstate *ds, int x, int y, int v)
{
    int tx = COORD(x), ty = COORD(y);
    int bg = (v & FLASH_DEAD ? COL_DEAD_PLAYER :
              v & FLASH_WIN ? COL_HIGHLIGHT : COL_BACKGROUND);

    v &= ~FLASH_MASK;

    clip(dr, tx+1, ty+1, TILESIZE-1, TILESIZE-1);
    draw_rect(dr, tx+1, ty+1, TILESIZE-1, TILESIZE-1, bg);

    if (v == WALL) {
        int coords[6];

        coords[0] = tx + TILESIZE;
        coords[1] = ty + TILESIZE;
        coords[2] = tx + TILESIZE;
        coords[3] = ty + 1;
        coords[4] = tx + 1;
        coords[5] = ty + TILESIZE;
        draw_polygon(dr, coords, 3, COL_LOWLIGHT, COL_LOWLIGHT);

        coords[0] = tx + 1;
        coords[1] = ty + 1;
        draw_polygon(dr, coords, 3, COL_HIGHLIGHT, COL_HIGHLIGHT);

        draw_rect(dr, tx + 1 + HIGHLIGHT_WIDTH, ty + 1 + HIGHLIGHT_WIDTH,
                  TILESIZE - 2*HIGHLIGHT_WIDTH,
                  TILESIZE - 2*HIGHLIGHT_WIDTH, COL_WALL);
    } else if (v == MINE) {
        int cx = tx + TILESIZE / 2;
        int cy = ty + TILESIZE / 2;
        int r = TILESIZE / 2 - 3;
        int coords[4*5*2];
        int xdx = 1, xdy = 0, ydx = 0, ydy = 1;
        int tdx, tdy, i;

        for (i = 0; i < 4*5*2; i += 5*2) {
            coords[i+2*0+0] = cx - r/6*xdx + r*4/5*ydx;
            coords[i+2*0+1] = cy - r/6*xdy + r*4/5*ydy;
            coords[i+2*1+0] = cx - r/6*xdx + r*ydx;
            coords[i+2*1+1] = cy - r/6*xdy + r*ydy;
            coords[i+2*2+0] = cx + r/6*xdx + r*ydx;
            coords[i+2*2+1] = cy + r/6*xdy + r*ydy;
            coords[i+2*3+0] = cx + r/6*xdx + r*4/5*ydx;
            coords[i+2*3+1] = cy + r/6*xdy + r*4/5*ydy;
            coords[i+2*4+0] = cx + r*3/5*xdx + r*3/5*ydx;
            coords[i+2*4+1] = cy + r*3/5*xdy + r*3/5*ydy;

            tdx = ydx;
            tdy = ydy;
            ydx = xdx;
            ydy = xdy;
            xdx = -tdx;
            xdy = -tdy;
        }

        draw_polygon(dr, coords, 5*4, COL_MINE, COL_MINE);

        draw_rect(dr, cx-r/3, cy-r/3, r/3, r/4, COL_HIGHLIGHT);
    } else if (v == STOP) {
        draw_circle(dr, tx + TILESIZE/2, ty + TILESIZE/2,
                    TILESIZE*3/7, -1, COL_OUTLINE);
        draw_rect(dr, tx + TILESIZE*3/7, ty+1,
                  TILESIZE - 2*(TILESIZE*3/7) + 1, TILESIZE-1, bg);
        draw_rect(dr, tx+1, ty + TILESIZE*3/7,
                  TILESIZE-1, TILESIZE - 2*(TILESIZE*3/7) + 1, bg);
    } else if (v == GEM) {
        int coords[8];

        coords[0] = tx+TILESIZE/2;
        coords[1] = ty+TILESIZE*1/7;
        coords[2] = tx+TILESIZE*1/7;
        coords[3] = ty+TILESIZE/2;
        coords[4] = tx+TILESIZE/2;
        coords[5] = ty+TILESIZE-TILESIZE*1/7;
        coords[6] = tx+TILESIZE-TILESIZE*1/7;
        coords[7] = ty+TILESIZE/2;

        draw_polygon(dr, coords, 4, COL_GEM, COL_OUTLINE);
    }

    unclip(dr);
    draw_update(dr, tx, ty, TILESIZE, TILESIZE);
}

#define BASE_ANIM_LENGTH 0.1F
#define FLASH_LENGTH 0.3F

static void game_redraw(drawing *dr, game_drawstate *ds, game_state *oldstate,
                        game_state *state, int dir, game_ui *ui,
                        float animtime, float flashtime)
{
    int w = state->p.w, h = state->p.h /*, wh = w*h */;
    int x, y;
    float ap;
    int player_dist;
    int flashtype;
    int gems, deaths;
    char status[256];

    if (flashtime &&
        !((int)(flashtime * 3 / FLASH_LENGTH) % 2))
        flashtype = ui->flashtype;
    else
        flashtype = 0;

    /*
     * Erase the player sprite.
     */
    if (ds->player_bg_saved) {
        assert(ds->player_background);
        blitter_load(dr, ds->player_background, ds->pbgx, ds->pbgy);
        draw_update(dr, ds->pbgx, ds->pbgy, TILESIZE, TILESIZE);
        ds->player_bg_saved = FALSE;
    }

    /*
     * Initialise a fresh drawstate.
     */
    if (!ds->started) {
        int wid, ht;

        /*
         * Blank out the window initially.
         */
        game_compute_size(&ds->p, TILESIZE, &wid, &ht);
        draw_rect(dr, 0, 0, wid, ht, COL_BACKGROUND);
        draw_update(dr, 0, 0, wid, ht);

        /*
         * Draw the grid lines.
         */
        for (y = 0; y <= h; y++)
            draw_line(dr, COORD(0), COORD(y), COORD(w), COORD(y),
                      COL_LOWLIGHT);
        for (x = 0; x <= w; x++)
            draw_line(dr, COORD(x), COORD(0), COORD(x), COORD(h),
                      COL_LOWLIGHT);

        ds->started = TRUE;
    }

    /*
     * If we're in the process of animating a move, let's start by
     * working out how far the player has moved from their _older_
     * state.
     */
    if (oldstate) {
        ap = animtime / ui->anim_length;
        player_dist = ap * (dir > 0 ? state : oldstate)->distance_moved;
    } else {
        player_dist = 0;
        ap = 0.0F;
    }

    /*
     * Draw the grid contents.
     * 
     * We count the gems as we go round this loop, for the purposes
     * of the status bar. Of course we have a gems counter in the
     * game_state already, but if we do the counting in this loop
     * then it tracks gems being picked up in a sliding move, and
     * updates one by one.
     */
    gems = 0;
    for (y = 0; y < h; y++)
        for (x = 0; x < w; x++) {
            unsigned short v = (unsigned char)state->grid[y*w+x];

            /*
             * Special case: if the player is in the process of
             * moving over a gem, we draw the gem iff they haven't
             * gone past it yet.
             */
            if (oldstate && oldstate->grid[y*w+x] != state->grid[y*w+x]) {
                /*
                 * Compute the distance from this square to the
                 * original player position.
                 */
                int dist = max(abs(x - oldstate->px), abs(y - oldstate->py));

                /*
                 * If the player has reached here, use the new grid
                 * element. Otherwise use the old one.
                 */
                if (player_dist < dist)
                    v = oldstate->grid[y*w+x];
                else
                    v = state->grid[y*w+x];
            }

            /*
             * Special case: erase the mine the dead player is
             * sitting on. Only at the end of the move.
             */
            if (v == MINE && !oldstate && state->dead &&
                x == state->px && y == state->py)
                v = BLANK;

            if (v == GEM)
                gems++;

            v |= flashtype;

            if (ds->grid[y*w+x] != v) {
                draw_tile(dr, ds, x, y, v);
                ds->grid[y*w+x] = v;
            }
        }

    /*
     * Gem counter in the status bar. We replace it with
     * `COMPLETED!' when it reaches zero ... or rather, when the
     * _current state_'s gem counter is zero. (Thus, `Gems: 0' is
     * shown between the collection of the last gem and the
     * completion of the move animation that did it.)
     */
    if (state->dead && (!oldstate || oldstate->dead)) {
        sprintf(status, "DEAD!");
    } else if (state->gems || (oldstate && oldstate->gems)) {
        if (state->cheated)
            sprintf(status, "Auto-solver used. ");
        else
            *status = '\0';
        sprintf(status + strlen(status), "Gems: %d", gems);
    } else if (state->cheated) {
        sprintf(status, "Auto-solved.");
    } else {
        sprintf(status, "COMPLETED!");
    }
    /* We subtract one from the visible death counter if we're still
     * animating the move at the end of which the death took place. */
    deaths = ui->deaths;
    if (oldstate && ui->just_died) {
        assert(deaths > 0);
        deaths--;
    }
    if (deaths)
        sprintf(status + strlen(status), "   Deaths: %d", deaths);
    status_bar(dr, status);

    /*
     * Draw the player sprite.
     */
    assert(!ds->player_bg_saved);
    assert(ds->player_background);
    {
        int ox, oy, nx, ny;
        nx = COORD(state->px);
        ny = COORD(state->py);
        if (oldstate) {
            ox = COORD(oldstate->px);
            oy = COORD(oldstate->py);
        } else {
            ox = nx;
            oy = ny;
        }
        ds->pbgx = ox + ap * (nx - ox);
        ds->pbgy = oy + ap * (ny - oy);
    }
    blitter_save(dr, ds->player_background, ds->pbgx, ds->pbgy);
    draw_player(dr, ds, ds->pbgx, ds->pbgy,
                (state->dead && !oldstate),
                (!oldstate && state->soln ?
                 state->soln->list[state->solnpos] : -1));
    ds->player_bg_saved = TRUE;
}

static float game_anim_length(game_state *oldstate, game_state *newstate,
                              int dir, game_ui *ui)
{
    int dist;
    if (dir > 0)
        dist = newstate->distance_moved;
    else
        dist = oldstate->distance_moved;
    ui->anim_length = sqrt(dist) * BASE_ANIM_LENGTH;
    return ui->anim_length;
}

static float game_flash_length(game_state *oldstate, game_state *newstate,
                               int dir, game_ui *ui)
{
    if (!oldstate->dead && newstate->dead) {
        ui->flashtype = FLASH_DEAD;
        return FLASH_LENGTH;
    } else if (oldstate->gems && !newstate->gems) {
        ui->flashtype = FLASH_WIN;
        return FLASH_LENGTH;
    }
    return 0.0F;
}

static int game_wants_statusbar(void)
{
    return TRUE;
}

static int game_timing_state(game_state *state, game_ui *ui)
{
    return TRUE;
}

static void game_print_size(game_params *params, float *x, float *y)
{
}

static void game_print(drawing *dr, game_state *state, int tilesize)
{
}

#ifdef COMBINED
#define thegame inertia
#endif

const struct game thegame = {
    "Inertia", "games.inertia",
    default_params,
    game_fetch_preset,
    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,
    FALSE, 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,
    FALSE, FALSE, game_print_size, game_print,
    game_wants_statusbar,
    FALSE, game_timing_state,
    0,                                 /* mouse_priorities */
};