ref: 27160f7ad291b486efb108502722a7e8999c42c8
parent: 87eaeb51fe1577e8c2acb1314d889d7ee2a6903d
author: Simon Tatham <anakin@pobox.com>
date: Mon Mar 6 15:03:27 EST 2006
Introduce a new deductive mode in Slant's Hard level, which is the generalisation of the previous deduction involving two 3s or two 1s either adjacent or separated by a row of contiguous 2s. I always said that was an ugly loop and really ought to arise naturally as a special case of something more believable, and here it is. The practical upshot is that Hard mode has just become slightly harder: some grids generated by the new Slant will be unsolvable by the old one's solver. I don't think it's become _excessively_ more hard; I think I'm happy with the new difficulty level. (In particular, I don't think the new level is sufficiently harder than the old to make it worth preserving the old one as Medium or anything like that.) [originally from svn r6591]
--- a/slant.c
+++ b/slant.c
@@ -24,6 +24,7 @@
#include <stdio.h>
#include <stdlib.h>
+#include <stdarg.h>
#include <string.h>
#include <assert.h>
#include <ctype.h>
@@ -273,6 +274,27 @@
signed char *slashval;
/*
+ * Stores possible v-shapes. This array is w by h in size, but
+ * not every bit of every entry is meaningful. The bits mean:
+ *
+ * - bit 0 for a square means that that square and the one to
+ * its right might form a v-shape between them
+ * - bit 1 for a square means that that square and the one to
+ * its right might form a ^-shape between them
+ * - bit 2 for a square means that that square and the one
+ * below it might form a >-shape between them
+ * - bit 3 for a square means that that square and the one
+ * below it might form a <-shape between them
+ *
+ * Any starting 1 or 3 clue rules out four bits in this array
+ * immediately; we can rule out further bits during play using
+ * partially filled 2 clues; whenever a pair of squares is
+ * known not to be _either_ kind of v-shape, we can mark them
+ * as equivalent.
+ */
+ unsigned char *vbitmap;
+
+ /*
* Useful to have this information automatically passed to
* solver subroutines. (This pointer is not dynamically
* allocated by new_scratch and free_scratch.)
@@ -289,11 +311,13 @@
ret->border = snewn(W*H, unsigned char);
ret->equiv = snewn(w*h, int);
ret->slashval = snewn(w*h, signed char);
+ ret->vbitmap = snewn(w*h, unsigned char);
return ret;
}
static void free_scratch(struct solver_scratch *sc)
{+ sfree(sc->vbitmap);
sfree(sc->slashval);
sfree(sc->equiv);
sfree(sc->border);
@@ -388,6 +412,36 @@
}
}
+static int vbitmap_clear(int w, int h, struct solver_scratch *sc,
+ int x, int y, int vbits, char *reason, ...)
+{+ int done_something = FALSE;
+ int vbit;
+
+ for (vbit = 1; vbit <= 8; vbit <<= 1)
+ if (vbits & sc->vbitmap[y*w+x] & vbit) {+ done_something = TRUE;
+#ifdef SOLVER_DIAGNOSTICS
+ if (verbose) {+ va_list ap;
+
+ printf("ruling out %c shape at (%d,%d)-(%d,%d) (",+ "!v^!>!!!<"[vbit], x, y,
+ x+((vbit&0x3)!=0), y+((vbit&0xC)!=0));
+
+ va_start(ap, reason);
+ vprintf(reason, ap);
+ va_end(ap);
+
+ printf(")\n");+ }
+#endif
+ sc->vbitmap[y*w+x] &= ~vbit;
+ }
+
+ return done_something;
+}
+
/*
* Solver. Returns 0 for impossibility, 1 for success, 2 for
* ambiguity or failure to converge.
@@ -427,6 +481,11 @@
memset(sc->slashval, 0, w*h);
/*
+ * Set up the vbitmap array. Initially all types of v are possible.
+ */
+ memset(sc->vbitmap, 0xF, w*h);
+
+ /*
* Initialise the `exits' and `border' arrays. Theses is used
* to do second-order loop avoidance: the dual of the no loops
* constraint is that every point must be somehow connected to
@@ -454,69 +513,6 @@
}
/*
- * Make a one-off preliminary pass over the grid looking for
- * starting-point arrangements. The ones we need to spot are:
- *
- * - two adjacent 1s in the centre of the grid imply that each
- * one's single line points towards the other. (If either 1
- * were connected on the far side, the two squares shared
- * between the 1s would both link to the other 1 as a
- * consequence of neither linking to the first.) Thus, we
- * can fill in the four squares around them.
- *
- * - dually, two adjacent 3s imply that each one's _non_-line
- * points towards the other.
- *
- * - if the pair of 1s and 3s is not _adjacent_ but is
- * separated by one or more 2s, the reasoning still applies.
- *
- * This is more advanced than just spotting obvious starting
- * squares such as central 4s and edge 2s, so we disable it on
- * DIFF_EASY.
- *
- * (I don't like this loop; it feels grubby to me. My
- * mathematical intuition feels there ought to be some more
- * general deductive form which contains this loop as a special
- * case, but I can't bring it to mind right now.)
- */
- if (difficulty > DIFF_EASY) {- for (y = 1; y+1 < H; y++)
- for (x = 1; x+1 < W; x++) {- int v = clues[y*W+x], s, x2, y2, dx, dy;
- if (v != 1 && v != 3)
- continue;
- /* Slash value of the square up and left of (x,y). */
- s = (v == 1 ? +1 : -1);
-
- /* Look in each direction once. */
- for (dy = 0; dy < 2; dy++) {- dx = 1 - dy;
- x2 = x+dx;
- y2 = y+dy;
- if (x2+1 >= W || y2+1 >= H)
- continue; /* too close to the border */
- while (x2+dx+1 < W && y2+dy+1 < H && clues[y2*W+x2] == 2)
- x2 += dx, y2 += dy;
- if (clues[y2*W+x2] == v) {-#ifdef SOLVER_DIAGNOSTICS
- if (verbose)
- printf("found adjacent %ds at %d,%d and %d,%d\n",- v, x, y, x2, y2);
-#endif
- fill_square(w, h, x-1, y-1, s, soln,
- sc->connected, sc);
- fill_square(w, h, x-1+dy, y-1+dx, -s, soln,
- sc->connected, sc);
- fill_square(w, h, x2, y2, s, soln,
- sc->connected, sc);
- fill_square(w, h, x2-dy, y2-dx, -s, soln,
- sc->connected, sc);
- }
- }
- }
- }
-
- /*
* Repeatedly try to deduce something until we can't.
*/
do {@@ -836,6 +832,147 @@
done_something = TRUE;
}
}
+
+ if (done_something)
+ continue;
+
+ /*
+ * Now see what we can do with the vbitmap array. All
+ * vbitmap deductions are disabled at Easy level.
+ */
+ if (difficulty <= DIFF_EASY)
+ continue;
+
+ for (y = 0; y < h; y++)
+ for (x = 0; x < w; x++) {+ int s, c;
+
+ /*
+ * Any line already placed in a square must rule
+ * out any type of v which contradicts it.
+ */
+ if ((s = soln[y*w+x]) != 0) {+ if (x > 0)
+ done_something |=
+ vbitmap_clear(w, h, sc, x-1, y, (s < 0 ? 0x1 : 0x2),
+ "contradicts known edge at (%d,%d)",x,y);
+ if (x+1 < w)
+ done_something |=
+ vbitmap_clear(w, h, sc, x, y, (s < 0 ? 0x2 : 0x1),
+ "contradicts known edge at (%d,%d)",x,y);
+ if (y > 0)
+ done_something |=
+ vbitmap_clear(w, h, sc, x, y-1, (s < 0 ? 0x4 : 0x8),
+ "contradicts known edge at (%d,%d)",x,y);
+ if (y+1 < h)
+ done_something |=
+ vbitmap_clear(w, h, sc, x, y, (s < 0 ? 0x8 : 0x4),
+ "contradicts known edge at (%d,%d)",x,y);
+ }
+
+ /*
+ * If both types of v are ruled out for a pair of
+ * adjacent squares, mark them as equivalent.
+ */
+ if (x+1 < w && !(sc->vbitmap[y*w+x] & 0x3)) {+ int n1 = y*w+x, n2 = y*w+(x+1);
+ if (dsf_canonify(sc->equiv, n1) !=
+ dsf_canonify(sc->equiv, n2)) {+ dsf_merge(sc->equiv, n1, n2);
+ done_something = TRUE;
+#ifdef SOLVER_DIAGNOSTICS
+ if (verbose)
+ printf("(%d,%d) and (%d,%d) must be equivalent"+ " because both v-shapes are ruled out\n",
+ x, y, x+1, y);
+#endif
+ }
+ }
+ if (y+1 < h && !(sc->vbitmap[y*w+x] & 0xC)) {+ int n1 = y*w+x, n2 = (y+1)*w+x;
+ if (dsf_canonify(sc->equiv, n1) !=
+ dsf_canonify(sc->equiv, n2)) {+ dsf_merge(sc->equiv, n1, n2);
+ done_something = TRUE;
+#ifdef SOLVER_DIAGNOSTICS
+ if (verbose)
+ printf("(%d,%d) and (%d,%d) must be equivalent"+ " because both v-shapes are ruled out\n",
+ x, y, x, y+1);
+#endif
+ }
+ }
+
+ /*
+ * The remaining work in this loop only works
+ * around non-edge clue points.
+ */
+ if (y == 0 || x == 0)
+ continue;
+ if ((c = clues[y*W+x]) < 0)
+ continue;
+
+ /*
+ * x,y marks a clue point not on the grid edge. See
+ * if this clue point allows us to rule out any v
+ * shapes.
+ */
+
+ if (c == 1) {+ /*
+ * A 1 clue can never have any v shape pointing
+ * at it.
+ */
+ done_something |=
+ vbitmap_clear(w, h, sc, x-1, y-1, 0x5,
+ "points at 1 clue at (%d,%d)", x, y);
+ done_something |=
+ vbitmap_clear(w, h, sc, x-1, y, 0x2,
+ "points at 1 clue at (%d,%d)", x, y);
+ done_something |=
+ vbitmap_clear(w, h, sc, x, y-1, 0x8,
+ "points at 1 clue at (%d,%d)", x, y);
+ } else if (c == 3) {+ /*
+ * A 3 clue can never have any v shape pointing
+ * away from it.
+ */
+ done_something |=
+ vbitmap_clear(w, h, sc, x-1, y-1, 0xA,
+ "points away from 3 clue at (%d,%d)", x, y);
+ done_something |=
+ vbitmap_clear(w, h, sc, x-1, y, 0x1,
+ "points away from 3 clue at (%d,%d)", x, y);
+ done_something |=
+ vbitmap_clear(w, h, sc, x, y-1, 0x4,
+ "points away from 3 clue at (%d,%d)", x, y);
+ } else if (c == 2) {+ /*
+ * If a 2 clue has any kind of v ruled out on
+ * one side of it, the same v is ruled out on
+ * the other side.
+ */
+ done_something |=
+ vbitmap_clear(w, h, sc, x-1, y-1,
+ (sc->vbitmap[(y )*w+(x-1)] & 0x3) ^ 0x3,
+ "propagated by 2 clue at (%d,%d)", x, y);
+ done_something |=
+ vbitmap_clear(w, h, sc, x-1, y-1,
+ (sc->vbitmap[(y-1)*w+(x )] & 0xC) ^ 0xC,
+ "propagated by 2 clue at (%d,%d)", x, y);
+ done_something |=
+ vbitmap_clear(w, h, sc, x-1, y,
+ (sc->vbitmap[(y-1)*w+(x-1)] & 0x3) ^ 0x3,
+ "propagated by 2 clue at (%d,%d)", x, y);
+ done_something |=
+ vbitmap_clear(w, h, sc, x, y-1,
+ (sc->vbitmap[(y-1)*w+(x-1)] & 0xC) ^ 0xC,
+ "propagated by 2 clue at (%d,%d)", x, y);
+ }
+
+#undef CLEARBITS
+
+ }
} while (done_something);