ref: 12fabc4add608622da87096bb3bed586efee10d9
parent: 5ddb011a57be24f4d3474c497e57e7c22f979106
author: Jonas Kölker <jonaskoelker@yahoo.com>
date: Thu Oct 8 08:20:15 EDT 2015
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.)
--- a/fifteen.c
+++ b/fifteen.c
@@ -473,6 +473,217 @@
return 0;
}
+static void next_move_3x2(int ax, int ay, int bx, int by,
+ int gx, int gy, int *dx, int *dy)
+{+ /* When w = 3 and h = 2 and the tile going in the top left corner
+ * is at (ax, ay) and the tile going in the bottom left corner is
+ * at (bx, by) and the blank tile is at (gx, gy), how do you move? */
+
+ /* Hard-coded shortest solutions. Sorry. */
+ static const unsigned char move[120] = {+ 1,2,0,1,2,2,
+ 2,0,0,2,0,0,
+ 0,0,2,0,2,0,
+ 0,0,0,2,0,2,
+ 2,0,0,0,2,0,
+
+ 0,3,0,1,1,1,
+ 3,0,3,2,1,2,
+ 2,1,1,0,1,0,
+ 2,1,2,1,0,1,
+ 1,2,0,2,1,2,
+
+ 0,1,3,1,3,0,
+ 1,3,1,3,0,3,
+ 0,0,3,3,0,0,
+ 0,0,0,1,2,1,
+ 3,0,0,1,1,1,
+
+ 3,1,1,1,3,0,
+ 1,1,1,1,1,1,
+ 1,3,1,1,3,0,
+ 1,1,3,3,1,3,
+ 1,3,0,0,0,0
+ };
+ static const struct { int dx, dy; } d[4] = {{+1,0},{-1,0},{0,+1},{0,-1}};+
+ int ea = 3*ay + ax, eb = 3*by + bx, eg = 3*gy + gx, v;
+ if (eb > ea) --eb;
+ if (eg > ea) --eg;
+ if (eg > eb) --eg;
+ v = move[ea + eb*6 + eg*5*6];
+ *dx = d[v].dx;
+ *dy = d[v].dy;
+}
+
+static void next_move(int nx, int ny, int ox, int oy, int gx, int gy,
+ int tx, int ty, int w, int *dx, int *dy)
+{+ const int to_tile_x = (gx < nx ? +1 : -1);
+ const int to_goal_x = (gx < tx ? +1 : -1);
+ const int gap_x_on_goal_side = ((nx-tx) * (nx-gx) > 0);
+
+ assert (nx != tx || ny != ty); /* not already in place */
+ assert (nx != gx || ny != gy); /* not placing the gap */
+ assert (ty <= ny); /* because we're greedy (and flipping) */
+ assert (ty <= gy); /* because we're greedy (and flipping) */
+
+ /* TODO: define a termination function. Idea: 0 if solved, or
+ * the number of moves to solve the next piece plus the number of
+ * further unsolved pieces times an upper bound on the number of
+ * moves required to solve any piece. If such a function can be
+ * found, we have (termination && (termination => correctness)).
+ * The catch is our temporary disturbance of 2x3 corners. */
+
+ /* handles end-of-row, when 3 and 4 are in the top right 2x3 box */
+ if (tx == w - 2 &&
+ ny <= ty + 2 && (nx == tx || nx == tx + 1) &&
+ oy <= ty + 2 && (ox == tx || ox == tx + 1) &&
+ gy <= ty + 2 && (gx == tx || gx == tx + 1))
+ {+ next_move_3x2(oy - ty, tx + 1 - ox,
+ ny - ty, tx + 1 - nx,
+ gy - ty, tx + 1 - gx, dy, dx);
+ *dx *= -1;
+ return;
+ }
+
+ if (tx == w - 1) {+ if (ny <= ty + 2 && (nx == tx || nx == tx - 1) &&
+ gy <= ty + 2 && (gx == tx || gx == tx - 1)) {+ next_move_3x2(ny - ty, tx - nx, 0, 1, gy - ty, tx - gx, dy, dx);
+ *dx *= -1;
+ } else if (gy == ty)
+ *dy = +1;
+ else if (nx != tx || ny != ty + 1) {+ next_move((w - 1) - nx, ny, -1, -1, (w - 1) - gx, gy,
+ 0, ty + 1, -1, dx, dy);
+ *dx *= -1;
+ } else if (gx == nx)
+ *dy = -1;
+ else
+ *dx = +1;
+ return;
+ }
+
+ /* note that *dy = -1 is unsafe when gy = ty + 1 and gx < tx */
+ if (gy < ny)
+ if (nx == gx || (gy == ty && gx == tx))
+ *dy = +1;
+ else if (!gap_x_on_goal_side)
+ *dx = to_tile_x;
+ else if (ny - ty > abs(nx - tx))
+ *dx = to_tile_x;
+ else *dy = +1;
+
+ else if (gy == ny)
+ if (nx == tx) /* then we know ny > ty */
+ if (gx > nx || ny > ty + 1)
+ *dy = -1; /* ... so this is safe */
+ else
+ *dy = +1;
+ else if (gap_x_on_goal_side)
+ *dx = to_tile_x;
+ else if (gy == ty || (gy == ty + 1 && gx < tx))
+ *dy = +1;
+ else
+ *dy = -1;
+
+ else if (nx == tx) /* gy > ny */
+ if (gx > nx)
+ *dy = -1;
+ else
+ *dx = +1;
+ else if (gx == nx)
+ *dx = to_goal_x;
+ else if (gap_x_on_goal_side)
+ if (gy == ty + 1 && gx < tx)
+ *dx = to_tile_x;
+ else
+ *dy = -1;
+
+ else if (ny - ty > abs(nx - tx))
+ *dy = -1;
+ else
+ *dx = to_tile_x;
+}
+
+static int compute_hint(const game_state *state, int *out_x, int *out_y)
+{+ /* The overall solving process is this:
+ * 1. Find the next piece to be put in its place
+ * 2. Move it diagonally towards its place
+ * 3. Move it horizontally or vertically towards its place
+ * (Modulo the last two tiles at the end of each row/column)
+ */
+
+ int gx = X(state, state->gap_pos);
+ int gy = Y(state, state->gap_pos);
+
+ int tx, ty, nx, ny, ox, oy, /* {target,next,next2}_{x,y} */ i;+ int dx = 0, dy = 0;
+
+ /* 1. Find the next piece
+ * if (there are no more unfinished columns than rows) {+ * fill the top-most row, left to right
+ * } else { fill the left-most column, top to bottom }+ */
+ const int w = state->w, h = state->h, n = w*h;
+ int next_piece = 0, next_piece_2 = 0, solr = 0, solc = 0;
+ int unsolved_rows = h, unsolved_cols = w;
+
+ assert(out_x);
+ assert(out_y);
+
+ while (solr < h && solc < w) {+ int start, step, stop;
+ if (unsolved_cols <= unsolved_rows)
+ start = solr*w + solc, step = 1, stop = unsolved_cols;
+ else
+ start = solr*w + solc, step = w, stop = unsolved_rows;
+ for (i = 0; i < stop; ++i) {+ const int j = start + i*step;
+ if (state->tiles[j] != j + 1) {+ next_piece = j + 1;
+ next_piece_2 = next_piece + step;
+ break;
+ }
+ }
+ if (i < stop) break;
+
+ (unsolved_cols <= unsolved_rows)
+ ? (++solr, --unsolved_rows)
+ : (++solc, --unsolved_cols);
+ }
+
+ if (next_piece == n)
+ return FALSE;
+
+ /* 2, 3. Move the next piece towards its place */
+
+ /* gx, gy already set */
+ tx = X(state, next_piece - 1); /* where we're going */
+ ty = Y(state, next_piece - 1);
+ for (i = 0; i < n && state->tiles[i] != next_piece; ++i);
+ nx = X(state, i); /* where we're at */
+ ny = Y(state, i);
+ for (i = 0; i < n && state->tiles[i] != next_piece_2; ++i);
+ ox = X(state, i);
+ oy = Y(state, i);
+
+ if (unsolved_cols <= unsolved_rows)
+ next_move(nx, ny, ox, oy, gx, gy, tx, ty, w, &dx, &dy);
+ else
+ next_move(ny, nx, oy, ox, gy, gx, ty, tx, h, &dy, &dx);
+
+ assert (dx || dy);
+
+ *out_x = gx + dx;
+ *out_y = gy + dy;
+ return TRUE;
+}
+
static char *interpret_move(const game_state *state, game_ui *ui,
const game_drawstate *ds,
int x, int y, int button)
@@ -498,6 +709,9 @@
if (invert_cursor)
button = flip_cursor(button); /* undoes the first flip */
move_cursor(button, &nx, &ny, state->w, state->h, FALSE);
+ } else if ((button == 'h' || button == 'H') && !state->completed) {+ if (!compute_hint(state, &nx, &ny))
+ return NULL; /* shouldn't happen, since ^^we^^checked^^ */
} else
return NULL; /* no move */
--- a/puzzles.but
+++ b/puzzles.but
@@ -617,6 +617,10 @@
The arrow keys will move a tile adjacent to the space in the direction
indicated (moving the space in the \e{opposite} direction).+Pressing \q{h} will make a suggested move. Pressing \q{h} enough+times will solve the game, but it may scramble your progress while
+doing so.
+
(All the actions described in \k{common-actions} are also available.) \H{fifteen-params} \I{parameters, for Fifteen}Fifteen parameters