/*
* TODO:
*
- * - Docs and checklist etc
* - Any way we can speed up redraws on GTK? Uck.
+ *
+ * - It would be nice if we could somehow auto-detect a real `long
+ * long' type on the host platform and use it in place of my
+ * hand-hacked int64s. It'd be faster and more reliable.
*/
#include <stdio.h>
enum {
COL_BACKGROUND,
COL_LINE,
+#ifdef SHOW_CROSSINGS
+ COL_CROSSEDLINE,
+#endif
COL_OUTLINE,
COL_POINT,
COL_DRAGPOINT,
game_params params;
int w, h; /* extent of coordinate system only */
point *pts;
+#ifdef SHOW_CROSSINGS
+ int *crosses; /* mark edges which are crossed */
+#endif
struct graph *graph;
int completed, cheated, just_solved;
};
return NULL;
}
+/* ----------------------------------------------------------------------
+ * Small number of 64-bit integer arithmetic operations, to prevent
+ * integer overflow at the very core of cross().
+ */
+
+typedef struct {
+ long hi;
+ unsigned long lo;
+} int64;
+
+#define greater64(i,j) ( (i).hi>(j).hi || ((i).hi==(j).hi && (i).lo>(j).lo))
+#define sign64(i) ((i).hi < 0 ? -1 : (i).hi==0 && (i).lo==0 ? 0 : +1)
+
+static int64 mulu32to64(unsigned long x, unsigned long y)
+{
+ unsigned long a, b, c, d, t;
+ int64 ret;
+
+ a = (x & 0xFFFF) * (y & 0xFFFF);
+ b = (x & 0xFFFF) * (y >> 16);
+ c = (x >> 16) * (y & 0xFFFF);
+ d = (x >> 16) * (y >> 16);
+
+ ret.lo = a;
+ ret.hi = d + (b >> 16) + (c >> 16);
+ t = (b & 0xFFFF) << 16;
+ ret.lo += t;
+ if (ret.lo < t)
+ ret.hi++;
+ t = (c & 0xFFFF) << 16;
+ ret.lo += t;
+ if (ret.lo < t)
+ ret.hi++;
+
+#ifdef DIAGNOSTIC_VIA_LONGLONG
+ assert(((unsigned long long)ret.hi << 32) + ret.lo ==
+ (unsigned long long)x * y);
+#endif
+
+ return ret;
+}
+
+static int64 mul32to64(long x, long y)
+{
+ int sign = +1;
+ int64 ret;
+#ifdef DIAGNOSTIC_VIA_LONGLONG
+ long long realret = (long long)x * y;
+#endif
+
+ if (x < 0)
+ x = -x, sign = -sign;
+ if (y < 0)
+ y = -y, sign = -sign;
+
+ ret = mulu32to64(x, y);
+
+ if (sign < 0) {
+ ret.hi = -ret.hi;
+ ret.lo = -ret.lo;
+ if (ret.lo)
+ ret.hi--;
+ }
+
+#ifdef DIAGNOSTIC_VIA_LONGLONG
+ assert(((unsigned long long)ret.hi << 32) + ret.lo == realret);
+#endif
+
+ return ret;
+}
+
+static int64 dotprod64(long a, long b, long p, long q)
+{
+ int64 ab, pq;
+
+ ab = mul32to64(a, b);
+ pq = mul32to64(p, q);
+ ab.hi += pq.hi;
+ ab.lo += pq.lo;
+ if (ab.lo < pq.lo)
+ ab.hi++;
+ return ab;
+}
+
/*
* Determine whether the line segments between a1 and a2, and
* between b1 and b2, intersect. We count it as an intersection if
*/
static int cross(point a1, point a2, point b1, point b2)
{
- long b1x, b1y, b2x, b2y, px, py, d1, d2, d3;
+ long b1x, b1y, b2x, b2y, px, py;
+ int64 d1, d2, d3;
/*
* The condition for crossing is that b1 and b2 are on opposite
b2y = b2.y * a1.d - a1.y * b2.d;
px = a1.y * a2.d - a2.y * a1.d;
py = a2.x * a1.d - a1.x * a2.d;
- /* Take the dot products. */
- d1 = b1x * px + b1y * py;
- d2 = b2x * px + b2y * py;
+ /* Take the dot products. Here we resort to 64-bit arithmetic. */
+ d1 = dotprod64(b1x, px, b1y, py);
+ d2 = dotprod64(b2x, px, b2y, py);
/* If they have the same non-zero sign, the lines do not cross. */
- if ((d1 > 0 && d2 > 0) || (d1 < 0 && d2 < 0))
+ if ((sign64(d1) > 0 && sign64(d2) > 0) ||
+ (sign64(d1) < 0 && sign64(d2) < 0))
return FALSE;
/*
* condition becomes whether or not they overlap within their
* line.
*/
- if (d1 == 0 && d2 == 0) {
+ if (sign64(d1) == 0 && sign64(d2) == 0) {
/* Construct the vector a2-a1. */
px = a2.x * a1.d - a1.x * a2.d;
py = a2.y * a1.d - a1.y * a2.d;
/* Determine the dot products of b1-a1 and b2-a1 with this. */
- d1 = b1x * px + b1y * py;
- d2 = b2x * px + b2y * py;
+ d1 = dotprod64(b1x, px, b1y, py);
+ d2 = dotprod64(b2x, px, b2y, py);
/* If they're both strictly negative, the lines do not cross. */
- if (d1 < 0 && d2 < 0)
+ if (sign64(d1) < 0 && sign64(d2) < 0)
return FALSE;
/* Otherwise, take the dot product of a2-a1 with itself. If
* the other two dot products both exceed this, the lines do
* not cross. */
- d3 = px * px + py * py;
- if (d1 > d3 && d2 > d3)
+ d3 = dotprod64(px, px, py, py);
+ if (greater64(d1, d3) && greater64(d2, d3))
return FALSE;
}
b2y = a2.y * b1.d - b1.y * a2.d;
px = b1.y * b2.d - b2.y * b1.d;
py = b2.x * b1.d - b1.x * b2.d;
- d1 = b1x * px + b1y * py;
- d2 = b2x * px + b2y * py;
- if ((d1 > 0 && d2 > 0) || (d1 < 0 && d2 < 0))
+ d1 = dotprod64(b1x, px, b1y, py);
+ d2 = dotprod64(b2x, px, b2y, py);
+ if ((sign64(d1) > 0 && sign64(d2) > 0) ||
+ (sign64(d1) < 0 && sign64(d2) < 0))
return FALSE;
/*
return NULL;
}
+static void mark_crossings(game_state *state)
+{
+ int ok = TRUE;
+ int i, j;
+ edge *e, *e2;
+
+#ifdef SHOW_CROSSINGS
+ for (i = 0; (e = index234(state->graph->edges, i)) != NULL; i++)
+ state->crosses[i] = FALSE;
+#endif
+
+ /*
+ * Check correctness: for every pair of edges, see whether they
+ * cross.
+ */
+ for (i = 0; (e = index234(state->graph->edges, i)) != NULL; i++) {
+ for (j = i+1; (e2 = index234(state->graph->edges, j)) != NULL; j++) {
+ if (e2->a == e->a || e2->a == e->b ||
+ e2->b == e->a || e2->b == e->b)
+ continue;
+ if (cross(state->pts[e2->a], state->pts[e2->b],
+ state->pts[e->a], state->pts[e->b])) {
+ ok = FALSE;
+#ifdef SHOW_CROSSINGS
+ state->crosses[i] = state->crosses[j] = TRUE;
+#else
+ goto done; /* multi-level break - sorry */
+#endif
+ }
+ }
+ }
+
+ /*
+ * e == NULL if we've gone through all the edge pairs
+ * without finding a crossing.
+ */
+#ifndef SHOW_CROSSINGS
+ done:
+#endif
+ if (ok)
+ state->completed = TRUE;
+}
+
static game_state *new_game(midend_data *me, game_params *params, char *desc)
{
int n = params->n;
addedge(state->graph->edges, a, b);
}
+#ifdef SHOW_CROSSINGS
+ state->crosses = snewn(count234(state->graph->edges), int);
+ mark_crossings(state); /* sets up `crosses' and `completed' */
+#endif
+
return state;
}
ret->completed = state->completed;
ret->cheated = state->cheated;
ret->just_solved = state->just_solved;
+#ifdef SHOW_CROSSINGS
+ ret->crosses = snewn(count234(ret->graph->edges), int);
+ memcpy(ret->crosses, state->crosses,
+ count234(ret->graph->edges) * sizeof(int));
+#endif
return ret;
}
static char *solve_game(game_state *state, game_state *currstate,
char *aux, char **error)
{
+ int n = state->params.n;
+ int matrix[4];
+ point *pts;
+ int i, j, besti;
+ float bestd;
+ char buf[80], *ret;
+ int retlen, retsize;
+
if (!aux) {
*error = "Solution not known for this puzzle";
return NULL;
}
- return dupstr(aux);
+ /*
+ * Decode the aux_info to get the original point positions.
+ */
+ pts = snewn(n, point);
+ aux++; /* eat 'S' */
+ for (i = 0; i < n; i++) {
+ int p, k;
+ long x, y, d;
+ int ret = sscanf(aux, ";P%d:%ld,%ld/%ld%n", &p, &x, &y, &d, &k);
+ if (ret != 4 || p != i) {
+ *error = "Internal error: aux_info badly formatted";
+ sfree(pts);
+ return NULL;
+ }
+ pts[i].x = x;
+ pts[i].y = y;
+ pts[i].d = d;
+ aux += k;
+ }
+
+ /*
+ * Now go through eight possible symmetries of the point set.
+ * For each one, work out the sum of the Euclidean distances
+ * between the points' current positions and their new ones.
+ *
+ * We're squaring distances here, which means we're at risk of
+ * integer overflow. Fortunately, there's no real need to be
+ * massively careful about rounding errors, since this is a
+ * non-essential bit of the code; so I'll just work in floats
+ * internally.
+ */
+ besti = -1;
+ bestd = 0.0F;
+
+ for (i = 0; i < 8; i++) {
+ float d;
+
+ matrix[0] = matrix[1] = matrix[2] = matrix[3] = 0;
+ matrix[i & 1] = (i & 2) ? +1 : -1;
+ matrix[3-(i&1)] = (i & 4) ? +1 : -1;
+
+ d = 0.0F;
+ for (j = 0; j < n; j++) {
+ float px = (float)pts[j].x / pts[j].d;
+ float py = (float)pts[j].y / pts[j].d;
+ float sx = (float)currstate->pts[j].x / currstate->pts[j].d;
+ float sy = (float)currstate->pts[j].y / currstate->pts[j].d;
+ float cx = (float)currstate->w / 2;
+ float cy = (float)currstate->h / 2;
+ float ox, oy, dx, dy;
+
+ px -= cx;
+ py -= cy;
+
+ ox = matrix[0] * px + matrix[1] * py;
+ oy = matrix[2] * px + matrix[3] * py;
+
+ ox += cx;
+ oy += cy;
+
+ dx = ox - sx;
+ dy = oy - sy;
+
+ d += dx*dx + dy*dy;
+ }
+
+ if (besti < 0 || bestd > d) {
+ besti = i;
+ bestd = d;
+ }
+ }
+
+ assert(besti >= 0);
+
+ /*
+ * Now we know which symmetry is closest to the points' current
+ * positions. Use it.
+ */
+ matrix[0] = matrix[1] = matrix[2] = matrix[3] = 0;
+ matrix[besti & 1] = (besti & 2) ? +1 : -1;
+ matrix[3-(besti&1)] = (besti & 4) ? +1 : -1;
+
+ retsize = 256;
+ ret = snewn(retsize, char);
+ retlen = 0;
+ ret[retlen++] = 'S';
+ ret[retlen] = '\0';
+
+ for (i = 0; i < n; i++) {
+ float px = (float)pts[i].x / pts[i].d;
+ float py = (float)pts[i].y / pts[i].d;
+ float cx = (float)currstate->w / 2;
+ float cy = (float)currstate->h / 2;
+ float ox, oy;
+ int extra;
+
+ px -= cx;
+ py -= cy;
+
+ ox = matrix[0] * px + matrix[1] * py;
+ oy = matrix[2] * px + matrix[3] * py;
+
+ ox += cx;
+ oy += cy;
+
+ /*
+ * Use a fixed denominator of 2, because we know the
+ * original points were on an integer grid offset by 1/2.
+ */
+ pts[i].d = 2;
+ ox *= pts[i].d;
+ oy *= pts[i].d;
+ pts[i].x = ox + 0.5;
+ pts[i].y = oy + 0.5;
+
+ extra = sprintf(buf, ";P%d:%ld,%ld/%ld", i,
+ pts[i].x, pts[i].y, pts[i].d);
+ if (retlen + extra >= retsize) {
+ retsize = retlen + extra + 256;
+ ret = sresize(ret, retsize, char);
+ }
+ strcpy(ret + retlen, buf);
+ retlen += extra;
+ }
+
+ sfree(pts);
+
+ return ret;
}
static char *game_text_format(game_state *state)
}
}
- /*
- * Check correctness: for every pair of edges, see whether they
- * cross.
- */
- if (!ret->completed) {
- int i, j;
- edge *e, *e2;
-
- for (i = 0; (e = index234(ret->graph->edges, i)) != NULL; i++) {
- for (j = i+1; (e2 = index234(ret->graph->edges, j)) != NULL; j++) {
- if (e2->a == e->a || e2->a == e->b ||
- e2->b == e->a || e2->b == e->b)
- continue;
- if (cross(ret->pts[e2->a], ret->pts[e2->b],
- ret->pts[e->a], ret->pts[e->b]))
- break;
- }
- if (e2)
- break;
- }
-
- /*
- * e == NULL if we've gone through all the edge pairs
- * without finding a crossing.
- */
- ret->completed = (e == NULL);
- }
+ mark_crossings(ret);
return ret;
}
ret[COL_LINE * 3 + 1] = 0.0F;
ret[COL_LINE * 3 + 2] = 0.0F;
+#ifdef SHOW_CROSSINGS
+ ret[COL_CROSSEDLINE * 3 + 0] = 1.0F;
+ ret[COL_CROSSEDLINE * 3 + 1] = 0.0F;
+ ret[COL_CROSSEDLINE * 3 + 2] = 0.0F;
+#endif
+
ret[COL_OUTLINE * 3 + 0] = 0.0F;
ret[COL_OUTLINE * 3 + 1] = 0.0F;
ret[COL_OUTLINE * 3 + 2] = 0.0F;
x2 = p2.x * ds->tilesize / p2.d;
y2 = p2.y * ds->tilesize / p2.d;
- draw_line(fe, x1, y1, x2, y2, COL_LINE);
+ draw_line(fe, x1, y1, x2, y2,
+#ifdef SHOW_CROSSINGS
+ (oldstate?oldstate:state)->crosses[i] ?
+ COL_CROSSEDLINE :
+#endif
+ COL_LINE);
}
/*
~mdw / sgt / puzzles / blobdiff