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Add hinting feature to Fifteen (press 'h' for a hint).
This is really an incremental solver. It alternates between solving rows and solving columns. Each row and column is solved one piece at a time. Except for some temporary trickery with the last two pieces in a row or column, once a piece is solved it is never moved again. (On non-square grids it first solves some rows or some columns until the unsolved part is a square, then starts alternating.)
This commit is contained in:
Jonas Kölker
committed by
Simon Tatham
Simon Tatham
parent
5ddb011a57
commit
12fabc4add
214
fifteen.c
214
fifteen.c
@ -473,6 +473,217 @@ static int flip_cursor(int button)
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return 0;
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return 0;
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}
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}
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static void next_move_3x2(int ax, int ay, int bx, int by,
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int gx, int gy, int *dx, int *dy)
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{
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/* When w = 3 and h = 2 and the tile going in the top left corner
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* is at (ax, ay) and the tile going in the bottom left corner is
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* at (bx, by) and the blank tile is at (gx, gy), how do you move? */
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/* Hard-coded shortest solutions. Sorry. */
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static const unsigned char move[120] = {
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1,2,0,1,2,2,
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2,0,0,2,0,0,
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0,0,2,0,2,0,
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0,0,0,2,0,2,
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2,0,0,0,2,0,
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0,3,0,1,1,1,
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3,0,3,2,1,2,
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2,1,1,0,1,0,
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2,1,2,1,0,1,
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1,2,0,2,1,2,
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0,1,3,1,3,0,
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1,3,1,3,0,3,
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0,0,3,3,0,0,
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0,0,0,1,2,1,
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3,0,0,1,1,1,
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3,1,1,1,3,0,
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1,1,1,1,1,1,
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1,3,1,1,3,0,
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1,1,3,3,1,3,
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1,3,0,0,0,0
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};
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static const struct { int dx, dy; } d[4] = {{+1,0},{-1,0},{0,+1},{0,-1}};
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int ea = 3*ay + ax, eb = 3*by + bx, eg = 3*gy + gx, v;
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if (eb > ea) --eb;
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if (eg > ea) --eg;
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if (eg > eb) --eg;
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v = move[ea + eb*6 + eg*5*6];
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*dx = d[v].dx;
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*dy = d[v].dy;
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}
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static void next_move(int nx, int ny, int ox, int oy, int gx, int gy,
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int tx, int ty, int w, int *dx, int *dy)
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{
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const int to_tile_x = (gx < nx ? +1 : -1);
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const int to_goal_x = (gx < tx ? +1 : -1);
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const int gap_x_on_goal_side = ((nx-tx) * (nx-gx) > 0);
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assert (nx != tx || ny != ty); /* not already in place */
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assert (nx != gx || ny != gy); /* not placing the gap */
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assert (ty <= ny); /* because we're greedy (and flipping) */
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assert (ty <= gy); /* because we're greedy (and flipping) */
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/* TODO: define a termination function. Idea: 0 if solved, or
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* the number of moves to solve the next piece plus the number of
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* further unsolved pieces times an upper bound on the number of
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* moves required to solve any piece. If such a function can be
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* found, we have (termination && (termination => correctness)).
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* The catch is our temporary disturbance of 2x3 corners. */
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/* handles end-of-row, when 3 and 4 are in the top right 2x3 box */
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if (tx == w - 2 &&
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ny <= ty + 2 && (nx == tx || nx == tx + 1) &&
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oy <= ty + 2 && (ox == tx || ox == tx + 1) &&
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gy <= ty + 2 && (gx == tx || gx == tx + 1))
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{
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next_move_3x2(oy - ty, tx + 1 - ox,
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ny - ty, tx + 1 - nx,
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gy - ty, tx + 1 - gx, dy, dx);
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*dx *= -1;
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return;
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}
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if (tx == w - 1) {
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if (ny <= ty + 2 && (nx == tx || nx == tx - 1) &&
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gy <= ty + 2 && (gx == tx || gx == tx - 1)) {
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next_move_3x2(ny - ty, tx - nx, 0, 1, gy - ty, tx - gx, dy, dx);
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*dx *= -1;
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} else if (gy == ty)
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*dy = +1;
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else if (nx != tx || ny != ty + 1) {
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next_move((w - 1) - nx, ny, -1, -1, (w - 1) - gx, gy,
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0, ty + 1, -1, dx, dy);
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*dx *= -1;
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} else if (gx == nx)
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*dy = -1;
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else
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*dx = +1;
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return;
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}
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/* note that *dy = -1 is unsafe when gy = ty + 1 and gx < tx */
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if (gy < ny)
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if (nx == gx || (gy == ty && gx == tx))
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*dy = +1;
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else if (!gap_x_on_goal_side)
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*dx = to_tile_x;
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else if (ny - ty > abs(nx - tx))
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*dx = to_tile_x;
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else *dy = +1;
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else if (gy == ny)
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if (nx == tx) /* then we know ny > ty */
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if (gx > nx || ny > ty + 1)
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*dy = -1; /* ... so this is safe */
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else
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*dy = +1;
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else if (gap_x_on_goal_side)
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*dx = to_tile_x;
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else if (gy == ty || (gy == ty + 1 && gx < tx))
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*dy = +1;
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else
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*dy = -1;
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else if (nx == tx) /* gy > ny */
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if (gx > nx)
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*dy = -1;
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else
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*dx = +1;
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else if (gx == nx)
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*dx = to_goal_x;
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else if (gap_x_on_goal_side)
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if (gy == ty + 1 && gx < tx)
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*dx = to_tile_x;
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else
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*dy = -1;
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else if (ny - ty > abs(nx - tx))
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*dy = -1;
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else
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*dx = to_tile_x;
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}
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static int compute_hint(const game_state *state, int *out_x, int *out_y)
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{
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/* The overall solving process is this:
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* 1. Find the next piece to be put in its place
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* 2. Move it diagonally towards its place
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* 3. Move it horizontally or vertically towards its place
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* (Modulo the last two tiles at the end of each row/column)
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*/
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int gx = X(state, state->gap_pos);
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int gy = Y(state, state->gap_pos);
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int tx, ty, nx, ny, ox, oy, /* {target,next,next2}_{x,y} */ i;
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int dx = 0, dy = 0;
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/* 1. Find the next piece
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* if (there are no more unfinished columns than rows) {
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* fill the top-most row, left to right
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* } else { fill the left-most column, top to bottom }
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*/
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const int w = state->w, h = state->h, n = w*h;
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int next_piece = 0, next_piece_2 = 0, solr = 0, solc = 0;
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int unsolved_rows = h, unsolved_cols = w;
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assert(out_x);
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assert(out_y);
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while (solr < h && solc < w) {
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int start, step, stop;
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if (unsolved_cols <= unsolved_rows)
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start = solr*w + solc, step = 1, stop = unsolved_cols;
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else
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start = solr*w + solc, step = w, stop = unsolved_rows;
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for (i = 0; i < stop; ++i) {
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const int j = start + i*step;
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if (state->tiles[j] != j + 1) {
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next_piece = j + 1;
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next_piece_2 = next_piece + step;
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break;
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}
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}
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if (i < stop) break;
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(unsolved_cols <= unsolved_rows)
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? (++solr, --unsolved_rows)
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: (++solc, --unsolved_cols);
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}
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if (next_piece == n)
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return FALSE;
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/* 2, 3. Move the next piece towards its place */
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/* gx, gy already set */
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tx = X(state, next_piece - 1); /* where we're going */
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ty = Y(state, next_piece - 1);
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for (i = 0; i < n && state->tiles[i] != next_piece; ++i);
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nx = X(state, i); /* where we're at */
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ny = Y(state, i);
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for (i = 0; i < n && state->tiles[i] != next_piece_2; ++i);
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ox = X(state, i);
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oy = Y(state, i);
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if (unsolved_cols <= unsolved_rows)
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next_move(nx, ny, ox, oy, gx, gy, tx, ty, w, &dx, &dy);
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else
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next_move(ny, nx, oy, ox, gy, gx, ty, tx, h, &dy, &dx);
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assert (dx || dy);
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*out_x = gx + dx;
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*out_y = gy + dy;
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return TRUE;
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}
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static char *interpret_move(const game_state *state, game_ui *ui,
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static char *interpret_move(const game_state *state, game_ui *ui,
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const game_drawstate *ds,
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const game_drawstate *ds,
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int x, int y, int button)
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int x, int y, int button)
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@ -498,6 +709,9 @@ static char *interpret_move(const game_state *state, game_ui *ui,
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if (invert_cursor)
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if (invert_cursor)
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button = flip_cursor(button); /* undoes the first flip */
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button = flip_cursor(button); /* undoes the first flip */
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move_cursor(button, &nx, &ny, state->w, state->h, FALSE);
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move_cursor(button, &nx, &ny, state->w, state->h, FALSE);
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} else if ((button == 'h' || button == 'H') && !state->completed) {
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if (!compute_hint(state, &nx, &ny))
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return NULL; /* shouldn't happen, since ^^we^^checked^^ */
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} else
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} else
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return NULL; /* no move */
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return NULL; /* no move */
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@ -617,6 +617,10 @@ mouse pointer.
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The arrow keys will move a tile adjacent to the space in the direction
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The arrow keys will move a tile adjacent to the space in the direction
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indicated (moving the space in the \e{opposite} direction).
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indicated (moving the space in the \e{opposite} direction).
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Pressing \q{h} will make a suggested move. Pressing \q{h} enough
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times will solve the game, but it may scramble your progress while
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doing so.
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(All the actions described in \k{common-actions} are also available.)
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(All the actions described in \k{common-actions} are also available.)
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\H{fifteen-params} \I{parameters, for Fifteen}Fifteen parameters
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\H{fifteen-params} \I{parameters, for Fifteen}Fifteen parameters
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