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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;

    /*
     * Before anything else, deal with the special case in which
     * all the gems are already collected.
     */
    for (i = 0; i < wh; i++)
      if (currstate->grid[i] == GEM)
          break;
    if (i == wh) {
      *error = "Game is already solved";
      return NULL;
    }

    /*
     * 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;
      int dir;

      for (dir = +1; dir >= -1; dir -= 2) {

          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 = (dir > 0 ? 0 : circuitlen-1);
             i < circuitlen && i >= 0;
             i += dir) {
            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 p, q, k, dest, ni, ti, thisdist;

                /*
                 * Set up the upper and lower bounds of the
                 * reduced section.
                 */
                p = min(i, j);
                q = max(i, j);

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

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

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

                while (head < tail && dist[circuit[q]] < 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[q]];
                assert(thisdist >= 0 && thisdist <= q-p);

                memmove(circuit+p+thisdist, circuit+q,
                      (circuitlen - q) * sizeof(int));
                circuitlen -= q-p;
                q = p + thisdist;
                circuitlen += q-p;

                if (dir > 0)
                  i = q;             /* resume loop from the right place */

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

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

                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 (++p < q) {
                  int xy = nodes[circuit[p]] / DP1;
                  if (currstate->grid[xy] == GEM)
                      unvisited[xy]++;
                }

                j = i;

#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 in each
       * direction 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, 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_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,
    TRUE,                      /* wants_statusbar */
    FALSE, game_timing_state,
    0,                               /* flags */
};

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