ref: 20bd61bf4931396cc74265046a0f1bb4a3c57fd4
dir: /untangle.c/
/*
* untangle.c: Game about planar graphs. You are given a graph
* represented by points and straight lines, with some lines
* crossing; your task is to drag the points into a configuration
* where none of the lines cross.
*
* Cloned from a Flash game called `Planarity', by John Tantalo.
* <http://home.cwru.edu/~jnt5/Planarity> at the time of writing
* this. The Flash game had a fixed set of levels; my added value,
* as usual, is automatic generation of random games to order.
*/
/*
* TODO:
*
* - This puzzle, perhaps uniquely among the collection, could use
* support for non-aspect-ratio-preserving resizes. This would
* require some sort of fairly large redesign, unfortunately (since
* it would invalidate the basic assumption that puzzles' size
* requirements are adequately expressed by a single scalar tile
* size), and probably complicate the rest of the puzzles' API as a
* result. So I'm not sure I really want to do it.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <ctype.h>
#include <limits.h>
#ifdef NO_TGMATH_H
# include <math.h>
#else
# include <tgmath.h>
#endif
#if HAVE_STDINT_H
# include <stdint.h>
#endif
#include "puzzles.h"
#include "tree234.h"
#define CIRCLE_RADIUS 6
#define DRAG_THRESHOLD (CIRCLE_RADIUS * 2)
#define PREFERRED_TILESIZE 64
#define FLASH_TIME 0.30F
#define ANIM_TIME 0.13F
#define SOLVEANIM_TIME 0.50F
enum {
COL_SYSBACKGROUND,
COL_BACKGROUND,
COL_LINE,
#ifdef SHOW_CROSSINGS
COL_CROSSEDLINE,
#endif
COL_OUTLINE,
COL_POINT,
COL_DRAGPOINT,
COL_NEIGHBOUR,
COL_FLASH1,
COL_FLASH2,
NCOLOURS
};
typedef struct point {
/*
* Points are stored using rational coordinates, with the same
* denominator for both coordinates.
*/
long x, y, d;
} point;
typedef struct edge {
/*
* This structure is implicitly associated with a particular
* point set, so all it has to do is to store two point
* indices. It is required to store them in the order (lower,
* higher), i.e. a < b always.
*/
int a, b;
} edge;
struct game_params {
int n; /* number of points */
};
struct graph {
int refcount; /* for deallocation */
tree234 *edges; /* stores `edge' structures */
};
struct game_state {
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;
bool completed, cheated, just_solved;
};
static int edgecmpC(const void *av, const void *bv)
{
const edge *a = (const edge *)av;
const edge *b = (const edge *)bv;
if (a->a < b->a)
return -1;
else if (a->a > b->a)
return +1;
else if (a->b < b->b)
return -1;
else if (a->b > b->b)
return +1;
return 0;
}
static int edgecmp(void *av, void *bv) { return edgecmpC(av, bv); }
static game_params *default_params(void)
{
game_params *ret = snew(game_params);
ret->n = 10;
return ret;
}
static bool game_fetch_preset(int i, char **name, game_params **params)
{
game_params *ret;
int n;
char buf[80];
switch (i) {
case 0: n = 6; break;
case 1: n = 10; break;
case 2: n = 15; break;
case 3: n = 20; break;
case 4: n = 25; break;
default: return false;
}
sprintf(buf, "%d points", n);
*name = dupstr(buf);
*params = ret = snew(game_params);
ret->n = n;
return true;
}
static void free_params(game_params *params)
{
sfree(params);
}
static game_params *dup_params(const game_params *params)
{
game_params *ret = snew(game_params);
*ret = *params; /* structure copy */
return ret;
}
static void decode_params(game_params *params, char const *string)
{
params->n = atoi(string);
}
static char *encode_params(const game_params *params, bool full)
{
char buf[80];
sprintf(buf, "%d", params->n);
return dupstr(buf);
}
static config_item *game_configure(const game_params *params)
{
config_item *ret;
char buf[80];
ret = snewn(3, config_item);
ret[0].name = "Number of points";
ret[0].type = C_STRING;
sprintf(buf, "%d", params->n);
ret[0].u.string.sval = dupstr(buf);
ret[1].name = NULL;
ret[1].type = C_END;
return ret;
}
static game_params *custom_params(const config_item *cfg)
{
game_params *ret = snew(game_params);
ret->n = atoi(cfg[0].u.string.sval);
return ret;
}
static const char *validate_params(const game_params *params, bool full)
{
if (params->n < 4)
return "Number of points must be at least four";
if (params->n > INT_MAX / 3)
return "Number of points must not be unreasonably large";
return NULL;
}
/* ----------------------------------------------------------------------
* Small number of 64-bit integer arithmetic operations, to prevent
* integer overflow at the very core of cross().
*/
#if !HAVE_STDINT_H
/* For prehistoric C implementations, do this the hard way */
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;
}
#else /* HAVE_STDINT_H */
typedef int64_t int64;
#define greater64(i,j) ((i) > (j))
#define sign64(i) ((i) < 0 ? -1 : (i)==0 ? 0 : +1)
#define mulu32to64(x,y) ((int64_t)(unsigned long)(x) * (unsigned long)(y))
#define mul32to64(x,y) ((int64_t)(long)(x) * (long)(y))
static int64 dotprod64(long a, long b, long p, long q)
{
return (int64)a * b + (int64)p * q;
}
#endif /* HAVE_STDINT_H */
/*
* Determine whether the line segments between a1 and a2, and
* between b1 and b2, intersect. We count it as an intersection if
* any of the endpoints lies _on_ the other line.
*/
static bool cross(point a1, point a2, point b1, point b2)
{
long b1x, b1y, b2x, b2y, px, py;
int64 d1, d2, d3;
/*
* The condition for crossing is that b1 and b2 are on opposite
* sides of the line a1-a2, and vice versa. We determine this
* by taking the dot product of b1-a1 with a vector
* perpendicular to a2-a1, and similarly with b2-a1, and seeing
* if they have different signs.
*/
/*
* Construct the vector b1-a1. We don't have to worry too much
* about the denominator, because we're only going to check the
* sign of this vector; we just need to get the numerator
* right.
*/
b1x = b1.x * a1.d - a1.x * b1.d;
b1y = b1.y * a1.d - a1.y * b1.d;
/* Now construct b2-a1, and a vector perpendicular to a2-a1,
* in the same way. */
b2x = b2.x * a1.d - a1.x * b2.d;
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. 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 ((sign64(d1) > 0 && sign64(d2) > 0) ||
(sign64(d1) < 0 && sign64(d2) < 0))
return false;
/*
* If the dot products are both exactly zero, then the two line
* segments are collinear. At this point the intersection
* condition becomes whether or not they overlap within their
* line.
*/
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 = dotprod64(b1x, px, b1y, py);
d2 = dotprod64(b2x, px, b2y, py);
/* If they're both strictly negative, the lines do not cross. */
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 = dotprod64(px, px, py, py);
if (greater64(d1, d3) && greater64(d2, d3))
return false;
}
/*
* We've eliminated the only important special case, and we
* have determined that b1 and b2 are on opposite sides of the
* line a1-a2. Now do the same thing the other way round and
* we're done.
*/
b1x = a1.x * b1.d - b1.x * a1.d;
b1y = a1.y * b1.d - b1.y * a1.d;
b2x = a2.x * b1.d - b1.x * a2.d;
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 = 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;
/*
* The lines must cross.
*/
return true;
}
static unsigned long squarert(unsigned long n) {
unsigned long d, a, b, di;
d = n;
a = 0;
b = 1L << 30; /* largest available power of 4 */
do {
a >>= 1;
di = 2*a + b;
if (di <= d) {
d -= di;
a += b;
}
b >>= 2;
} while (b);
return a;
}
/*
* Our solutions are arranged on a square grid big enough that n
* points occupy about 1/POINTDENSITY of the grid.
*/
#define POINTDENSITY 3
#define MAXDEGREE 4
#define COORDLIMIT(n) squarert((n) * POINTDENSITY)
static void addedge(tree234 *edges, int a, int b)
{
edge *e = snew(edge);
assert(a != b);
e->a = min(a, b);
e->b = max(a, b);
if (add234(edges, e) != e)
/* Duplicate edge. */
sfree(e);
}
static bool isedge(tree234 *edges, int a, int b)
{
edge e;
assert(a != b);
e.a = min(a, b);
e.b = max(a, b);
return find234(edges, &e, NULL) != NULL;
}
typedef struct vertex {
int param;
int vindex;
} vertex;
static int vertcmpC(const void *av, const void *bv)
{
const vertex *a = (const vertex *)av;
const vertex *b = (const vertex *)bv;
if (a->param < b->param)
return -1;
else if (a->param > b->param)
return +1;
else if (a->vindex < b->vindex)
return -1;
else if (a->vindex > b->vindex)
return +1;
return 0;
}
static int vertcmp(void *av, void *bv) { return vertcmpC(av, bv); }
/*
* Construct point coordinates for n points arranged in a circle,
* within the bounding box (0,0) to (w,w).
*/
static void make_circle(point *pts, int n, int w)
{
long d, r, c, i;
/*
* First, decide on a denominator. Although in principle it
* would be nice to set this really high so as to finely
* distinguish all the points on the circle, I'm going to set
* it at a fixed size to prevent integer overflow problems.
*/
d = PREFERRED_TILESIZE;
/*
* Leave a little space outside the circle.
*/
c = d * w / 2;
r = d * w * 3 / 7;
/*
* Place the points.
*/
for (i = 0; i < n; i++) {
double angle = i * 2 * PI / n;
double x = r * sin(angle), y = - r * cos(angle);
pts[i].x = (long)(c + x + 0.5);
pts[i].y = (long)(c + y + 0.5);
pts[i].d = d;
}
}
static char *new_game_desc(const game_params *params, random_state *rs,
char **aux, bool interactive)
{
int n = params->n, i;
long w, h, j, k, m;
point *pts, *pts2;
long *tmp;
tree234 *edges, *vertices;
edge *e, *e2;
vertex *v, *vs, *vlist;
char *ret;
w = h = COORDLIMIT(n);
/*
* Choose n points from this grid.
*/
pts = snewn(n, point);
tmp = snewn(w*h, long);
for (i = 0; i < w*h; i++)
tmp[i] = i;
shuffle(tmp, w*h, sizeof(*tmp), rs);
for (i = 0; i < n; i++) {
pts[i].x = tmp[i] % w;
pts[i].y = tmp[i] / w;
pts[i].d = 1;
}
sfree(tmp);
/*
* Now start adding edges between the points.
*
* At all times, we attempt to add an edge to the lowest-degree
* vertex we currently have, and we try the other vertices as
* candidate second endpoints in order of distance from this
* one. We stop as soon as we find an edge which
*
* (a) does not increase any vertex's degree beyond MAXDEGREE
* (b) does not cross any existing edges
* (c) does not intersect any actual point.
*/
vs = snewn(n, vertex);
vertices = newtree234(vertcmp);
for (i = 0; i < n; i++) {
v = vs + i;
v->param = 0; /* in this tree, param is the degree */
v->vindex = i;
add234(vertices, v);
}
edges = newtree234(edgecmp);
vlist = snewn(n, vertex);
while (1) {
bool added = false;
for (i = 0; i < n; i++) {
v = index234(vertices, i);
j = v->vindex;
if (v->param >= MAXDEGREE)
break; /* nothing left to add! */
/*
* Sort the other vertices into order of their distance
* from this one. Don't bother looking below i, because
* we've already tried those edges the other way round.
* Also here we rule out target vertices with too high
* a degree, and (of course) ones to which we already
* have an edge.
*/
m = 0;
for (k = i+1; k < n; k++) {
vertex *kv = index234(vertices, k);
int ki = kv->vindex;
int dx, dy;
if (kv->param >= MAXDEGREE || isedge(edges, ki, j))
continue;
vlist[m].vindex = ki;
dx = pts[ki].x - pts[j].x;
dy = pts[ki].y - pts[j].y;
vlist[m].param = dx*dx + dy*dy;
m++;
}
qsort(vlist, m, sizeof(*vlist), vertcmpC);
for (k = 0; k < m; k++) {
int p;
int ki = vlist[k].vindex;
/*
* Check to see whether this edge intersects any
* existing edge or point.
*/
for (p = 0; p < n; p++)
if (p != ki && p != j && cross(pts[ki], pts[j],
pts[p], pts[p]))
break;
if (p < n)
continue;
for (p = 0; (e = index234(edges, p)) != NULL; p++)
if (e->a != ki && e->a != j &&
e->b != ki && e->b != j &&
cross(pts[ki], pts[j], pts[e->a], pts[e->b]))
break;
if (e)
continue;
/*
* We're done! Add this edge, modify the degrees of
* the two vertices involved, and break.
*/
addedge(edges, j, ki);
added = true;
del234(vertices, vs+j);
vs[j].param++;
add234(vertices, vs+j);
del234(vertices, vs+ki);
vs[ki].param++;
add234(vertices, vs+ki);
break;
}
if (k < m)
break;
}
if (!added)
break; /* we're done. */
}
/*
* That's our graph. Now shuffle the points, making sure that
* they come out with at least one crossed line when arranged
* in a circle (so that the puzzle isn't immediately solved!).
*/
tmp = snewn(n, long);
for (i = 0; i < n; i++)
tmp[i] = i;
pts2 = snewn(n, point);
make_circle(pts2, n, w);
while (1) {
shuffle(tmp, n, sizeof(*tmp), rs);
for (i = 0; (e = index234(edges, i)) != NULL; i++) {
for (j = i+1; (e2 = index234(edges, j)) != NULL; j++) {
if (e2->a == e->a || e2->a == e->b ||
e2->b == e->a || e2->b == e->b)
continue;
if (cross(pts2[tmp[e2->a]], pts2[tmp[e2->b]],
pts2[tmp[e->a]], pts2[tmp[e->b]]))
break;
}
if (e2)
break;
}
if (e)
break; /* we've found a crossing */
}
/*
* We're done. Now encode the graph in a string format. Let's
* use a comma-separated list of dash-separated vertex number
* pairs, numbered from zero. We'll sort the list to prevent
* side channels.
*/
ret = NULL;
{
const char *sep;
char buf[80];
int retlen;
edge *ea;
retlen = 0;
m = count234(edges);
ea = snewn(m, edge);
for (i = 0; (e = index234(edges, i)) != NULL; i++) {
assert(i < m);
ea[i].a = min(tmp[e->a], tmp[e->b]);
ea[i].b = max(tmp[e->a], tmp[e->b]);
retlen += 1 + sprintf(buf, "%d-%d", ea[i].a, ea[i].b);
}
assert(i == m);
qsort(ea, m, sizeof(*ea), edgecmpC);
ret = snewn(retlen, char);
sep = "";
k = 0;
for (i = 0; i < m; i++) {
k += sprintf(ret + k, "%s%d-%d", sep, ea[i].a, ea[i].b);
sep = ",";
}
assert(k < retlen);
sfree(ea);
}
/*
* Encode the solution we started with as an aux_info string.
*/
{
char buf[80];
char *auxstr;
int auxlen;
auxlen = 2; /* leading 'S' and trailing '\0' */
for (i = 0; i < n; i++) {
j = tmp[i];
pts2[j] = pts[i];
if (pts2[j].d & 1) {
pts2[j].x *= 2;
pts2[j].y *= 2;
pts2[j].d *= 2;
}
pts2[j].x += pts2[j].d / 2;
pts2[j].y += pts2[j].d / 2;
auxlen += sprintf(buf, ";P%d:%ld,%ld/%ld", i,
pts2[j].x, pts2[j].y, pts2[j].d);
}
k = 0;
auxstr = snewn(auxlen, char);
auxstr[k++] = 'S';
for (i = 0; i < n; i++)
k += sprintf(auxstr+k, ";P%d:%ld,%ld/%ld", i,
pts2[i].x, pts2[i].y, pts2[i].d);
assert(k < auxlen);
*aux = auxstr;
}
sfree(pts2);
sfree(tmp);
sfree(vlist);
freetree234(vertices);
sfree(vs);
while ((e = delpos234(edges, 0)) != NULL)
sfree(e);
freetree234(edges);
sfree(pts);
return ret;
}
static const char *validate_desc(const game_params *params, const char *desc)
{
int a, b;
while (*desc) {
a = atoi(desc);
if (a < 0 || a >= params->n)
return "Number out of range in game description";
while (*desc && isdigit((unsigned char)*desc)) desc++;
if (*desc != '-')
return "Expected '-' after number in game description";
desc++; /* eat dash */
b = atoi(desc);
if (b < 0 || b >= params->n)
return "Number out of range in game description";
while (*desc && isdigit((unsigned char)*desc)) desc++;
if (*desc) {
if (*desc != ',')
return "Expected ',' after number in game description";
desc++; /* eat comma */
}
if (a == b)
return "Node linked to itself in game description";
}
return NULL;
}
static void mark_crossings(game_state *state)
{
bool 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 *me, const game_params *params,
const char *desc)
{
int n = params->n;
game_state *state = snew(game_state);
int a, b;
state->params = *params;
state->w = state->h = COORDLIMIT(n);
state->pts = snewn(n, point);
make_circle(state->pts, n, state->w);
state->graph = snew(struct graph);
state->graph->refcount = 1;
state->graph->edges = newtree234(edgecmp);
state->completed = state->cheated = state->just_solved = false;
while (*desc) {
a = atoi(desc);
assert(a >= 0 && a < params->n);
while (*desc && isdigit((unsigned char)*desc)) desc++;
assert(*desc == '-');
desc++; /* eat dash */
b = atoi(desc);
assert(b >= 0 && b < params->n);
while (*desc && isdigit((unsigned char)*desc)) desc++;
if (*desc) {
assert(*desc == ',');
desc++; /* eat comma */
}
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;
}
static game_state *dup_game(const game_state *state)
{
int n = state->params.n;
game_state *ret = snew(game_state);
ret->params = state->params;
ret->w = state->w;
ret->h = state->h;
ret->pts = snewn(n, point);
memcpy(ret->pts, state->pts, n * sizeof(point));
ret->graph = state->graph;
ret->graph->refcount++;
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 void free_game(game_state *state)
{
if (--state->graph->refcount <= 0) {
edge *e;
while ((e = delpos234(state->graph->edges, 0)) != NULL)
sfree(e);
freetree234(state->graph->edges);
sfree(state->graph);
}
sfree(state->pts);
sfree(state);
}
static char *solve_game(const game_state *state, const game_state *currstate,
const char *aux, const 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;
}
/*
* 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 = (long)(ox + 0.5F);
pts[i].y = (long)(oy + 0.5F);
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;
}
struct game_ui {
int dragpoint; /* point being dragged; -1 if none */
point newpoint; /* where it's been dragged to so far */
bool just_dragged; /* reset in game_changed_state */
bool just_moved; /* _set_ in game_changed_state */
float anim_length;
/*
* User preference option to snap dragged points to a coarse-ish
* grid. Requested by a user who otherwise found themself spending
* too much time struggling to get lines nicely horizontal or
* vertical.
*/
bool snap_to_grid;
};
static game_ui *new_ui(const game_state *state)
{
game_ui *ui = snew(game_ui);
ui->dragpoint = -1;
ui->just_moved = ui->just_dragged = false;
ui->snap_to_grid = false;
return ui;
}
static config_item *get_prefs(game_ui *ui)
{
config_item *cfg;
cfg = snewn(2, config_item);
cfg[0].name = "Snap points to a grid";
cfg[0].kw = "snap-to-grid";
cfg[0].type = C_BOOLEAN;
cfg[0].u.boolean.bval = ui->snap_to_grid;
cfg[1].name = NULL;
cfg[1].type = C_END;
return cfg;
}
static void set_prefs(game_ui *ui, const config_item *cfg)
{
ui->snap_to_grid = cfg[0].u.boolean.bval;
}
static void free_ui(game_ui *ui)
{
sfree(ui);
}
static void game_changed_state(game_ui *ui, const game_state *oldstate,
const game_state *newstate)
{
ui->dragpoint = -1;
ui->just_moved = ui->just_dragged;
ui->just_dragged = false;
}
struct game_drawstate {
long tilesize;
int bg, dragpoint;
long *x, *y;
};
static void place_dragged_point(const game_state *state, game_ui *ui,
const game_drawstate *ds, int x, int y)
{
if (ui->snap_to_grid) {
/*
* We snap points to a grid that has n-1 vertices on each
* side. This should be large enough to permit a straight-
* line drawing of any n-vertex planar graph, and moreover,
* any specific planar embedding of that graph.
*
* Source: David Eppstein's book 'Forbidden Configurations in
* Discrete Geometry' mentions (section 16.3, page 182) that
* the point configuration he describes as GRID(n-1,n-1) -
* that is, the vertices of a square grid with n-1 vertices on
* each side - is universal for n-vertex planar graphs. In
* other words (from definitions earlier in the chapter), if a
* graph G admits any drawing in the plane at all, then it can
* be drawn with straight lines, and with all vertices being
* vertices of that grid.
*
* That fact by itself only says that _some_ planar embedding
* of G can be drawn in this grid. We'd prefer that _all_
* embeddings of G can be so drawn, because 'snap to grid' is
* supposed to be a UI affordance, not an extra puzzle
* challenge, so we don't want to constrain the player's
* choice of planar embedding.
*
* But it doesn't make a difference. Proof: given a specific
* planar embedding of G, triangulate it, by adding extra
* edges to every face of degree > 3. When this process
* terminates with every face a triangle, we have a new graph
* G' such that no edge can be added without it ceasing to be
* planar. Standard theorems say that a maximal planar graph
* is 3-connected, and that a 3-connected planar graph has a
* _unique_ embedding. So any drawing of G' in the plane can
* be converted into a drawing of G in the desired embedding,
* by simply removing all the extra edges that we added to
* turn G into G'. And G' is still an n-vertex planar graph,
* hence it can be drawn in GRID(n-1,n-1). []
*/
int d = state->params.n - 1;
x = d * x / (state->w * ds->tilesize);
x *= (state->w * ds->tilesize) / d;
x += (state->w * ds->tilesize) / (2*d);
y = d * y / (state->h * ds->tilesize);
y *= (state->h * ds->tilesize) / d;
y += (state->h * ds->tilesize) / (2*d);
}
ui->newpoint.x = x;
ui->newpoint.y = y;
ui->newpoint.d = ds->tilesize;
}
static char *interpret_move(const game_state *state, game_ui *ui,
const game_drawstate *ds,
int x, int y, int button)
{
int n = state->params.n;
if (IS_MOUSE_DOWN(button)) {
int i, best;
long bestd;
/*
* Begin drag. We drag the vertex _nearest_ to the pointer,
* just in case one is nearly on top of another and we want
* to drag the latter. However, we drag nothing at all if
* the nearest vertex is outside DRAG_THRESHOLD.
*/
best = -1;
bestd = 0;
for (i = 0; i < n; i++) {
long px = state->pts[i].x * ds->tilesize / state->pts[i].d;
long py = state->pts[i].y * ds->tilesize / state->pts[i].d;
long dx = px - x;
long dy = py - y;
long d = dx*dx + dy*dy;
if (best == -1 || bestd > d) {
best = i;
bestd = d;
}
}
if (bestd <= DRAG_THRESHOLD * DRAG_THRESHOLD) {
ui->dragpoint = best;
place_dragged_point(state, ui, ds, x, y);
return MOVE_UI_UPDATE;
}
return MOVE_NO_EFFECT;
} else if (IS_MOUSE_DRAG(button) && ui->dragpoint >= 0) {
place_dragged_point(state, ui, ds, x, y);
return MOVE_UI_UPDATE;
} else if (IS_MOUSE_RELEASE(button) && ui->dragpoint >= 0) {
int p = ui->dragpoint;
char buf[80];
ui->dragpoint = -1; /* terminate drag, no matter what */
/*
* First, see if we're within range. The user can cancel a
* drag by dragging the point right off the window.
*/
if (ui->newpoint.x < 0 ||
ui->newpoint.x >= (long)state->w*ui->newpoint.d ||
ui->newpoint.y < 0 ||
ui->newpoint.y >= (long)state->h*ui->newpoint.d)
return MOVE_UI_UPDATE;
/*
* We aren't cancelling the drag. Construct a move string
* indicating where this point is going to.
*/
sprintf(buf, "P%d:%ld,%ld/%ld", p,
ui->newpoint.x, ui->newpoint.y, ui->newpoint.d);
ui->just_dragged = true;
return dupstr(buf);
} else if (IS_MOUSE_DRAG(button) || IS_MOUSE_RELEASE(button))
return MOVE_NO_EFFECT;
return MOVE_UNUSED;
}
static game_state *execute_move(const game_state *state, const char *move)
{
int n = state->params.n;
int p, k;
long x, y, d;
game_state *ret = dup_game(state);
ret->just_solved = false;
while (*move) {
if (*move == 'S') {
move++;
if (*move == ';') move++;
ret->cheated = ret->just_solved = true;
}
if (*move == 'P' &&
sscanf(move+1, "%d:%ld,%ld/%ld%n", &p, &x, &y, &d, &k) == 4 &&
p >= 0 && p < n && d > 0) {
ret->pts[p].x = x;
ret->pts[p].y = y;
ret->pts[p].d = d;
move += k+1;
if (*move == ';') move++;
} else {
free_game(ret);
return NULL;
}
}
mark_crossings(ret);
return ret;
}
/* ----------------------------------------------------------------------
* Drawing routines.
*/
static void game_compute_size(const game_params *params, int tilesize,
const game_ui *ui, int *x, int *y)
{
*x = *y = COORDLIMIT(params->n) * tilesize;
}
static void game_set_size(drawing *dr, game_drawstate *ds,
const game_params *params, int tilesize)
{
ds->tilesize = tilesize;
}
static float *game_colours(frontend *fe, int *ncolours)
{
float *ret = snewn(3 * NCOLOURS, float);
/*
* COL_BACKGROUND is what we use as the normal background colour.
* Unusually, though, it isn't colour #0: COL_SYSBACKGROUND, a bit
* darker, takes that place. This means that if the user resizes
* an Untangle window so as to change its aspect ratio, the
* still-square playable area will be distinguished from the dead
* space around it.
*/
game_mkhighlight(fe, ret, COL_BACKGROUND, -1, COL_SYSBACKGROUND);
ret[COL_LINE * 3 + 0] = 0.0F;
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;
ret[COL_POINT * 3 + 0] = 0.0F;
ret[COL_POINT * 3 + 1] = 0.0F;
ret[COL_POINT * 3 + 2] = 1.0F;
ret[COL_DRAGPOINT * 3 + 0] = 1.0F;
ret[COL_DRAGPOINT * 3 + 1] = 1.0F;
ret[COL_DRAGPOINT * 3 + 2] = 1.0F;
ret[COL_NEIGHBOUR * 3 + 0] = 1.0F;
ret[COL_NEIGHBOUR * 3 + 1] = 0.0F;
ret[COL_NEIGHBOUR * 3 + 2] = 0.0F;
ret[COL_FLASH1 * 3 + 0] = 0.5F;
ret[COL_FLASH1 * 3 + 1] = 0.5F;
ret[COL_FLASH1 * 3 + 2] = 0.5F;
ret[COL_FLASH2 * 3 + 0] = 1.0F;
ret[COL_FLASH2 * 3 + 1] = 1.0F;
ret[COL_FLASH2 * 3 + 2] = 1.0F;
*ncolours = NCOLOURS;
return ret;
}
static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
{
struct game_drawstate *ds = snew(struct game_drawstate);
int i;
ds->tilesize = 0;
ds->x = snewn(state->params.n, long);
ds->y = snewn(state->params.n, long);
for (i = 0; i < state->params.n; i++)
ds->x[i] = ds->y[i] = -1;
ds->bg = -1;
ds->dragpoint = -1;
return ds;
}
static void game_free_drawstate(drawing *dr, game_drawstate *ds)
{
sfree(ds->y);
sfree(ds->x);
sfree(ds);
}
static point mix(point a, point b, float distance)
{
point ret;
ret.d = a.d * b.d;
ret.x = (long)(a.x * b.d + distance * (b.x * a.d - a.x * b.d));
ret.y = (long)(a.y * b.d + distance * (b.y * a.d - a.y * b.d));
return ret;
}
static void game_redraw(drawing *dr, game_drawstate *ds,
const game_state *oldstate, const game_state *state,
int dir, const game_ui *ui,
float animtime, float flashtime)
{
int w, h;
edge *e;
int i, j;
int bg;
bool points_moved;
/*
* There's no terribly sensible way to do partial redraws of
* this game, so I'm going to have to resort to redrawing the
* whole thing every time.
*/
if (flashtime == 0)
bg = COL_BACKGROUND;
else if ((int)(flashtime * 4 / FLASH_TIME) % 2 == 0)
bg = COL_FLASH1;
else
bg = COL_FLASH2;
/*
* To prevent excessive spinning on redraw during a completion
* flash, we first check to see if _either_ the flash
* background colour has changed _or_ at least one point has
* moved _or_ a drag has begun or ended, and abandon the redraw
* if neither is the case.
*
* Also in this loop we work out the coordinates of all the
* points for this redraw.
*/
points_moved = false;
for (i = 0; i < state->params.n; i++) {
point p = state->pts[i];
long x, y;
if (ui->dragpoint == i)
p = ui->newpoint;
if (oldstate)
p = mix(oldstate->pts[i], p, animtime / ui->anim_length);
x = p.x * ds->tilesize / p.d;
y = p.y * ds->tilesize / p.d;
if (ds->x[i] != x || ds->y[i] != y)
points_moved = true;
ds->x[i] = x;
ds->y[i] = y;
}
if (ds->bg == bg && ds->dragpoint == ui->dragpoint && !points_moved)
return; /* nothing to do */
ds->dragpoint = ui->dragpoint;
ds->bg = bg;
game_compute_size(&state->params, ds->tilesize, ui, &w, &h);
draw_rect(dr, 0, 0, w, h, bg);
/*
* Draw the edges.
*/
for (i = 0; (e = index234(state->graph->edges, i)) != NULL; i++) {
draw_line(dr, ds->x[e->a], ds->y[e->a], ds->x[e->b], ds->y[e->b],
#ifdef SHOW_CROSSINGS
(oldstate?oldstate:state)->crosses[i] ?
COL_CROSSEDLINE :
#endif
COL_LINE);
}
/*
* Draw the points.
*
* When dragging, we should not only vary the colours, but
* leave the point being dragged until last.
*/
for (j = 0; j < 3; j++) {
int thisc = (j == 0 ? COL_POINT :
j == 1 ? COL_NEIGHBOUR : COL_DRAGPOINT);
for (i = 0; i < state->params.n; i++) {
int c;
if (ui->dragpoint == i) {
c = COL_DRAGPOINT;
} else if (ui->dragpoint >= 0 &&
isedge(state->graph->edges, ui->dragpoint, i)) {
c = COL_NEIGHBOUR;
} else {
c = COL_POINT;
}
if (c == thisc) {
#ifdef VERTEX_NUMBERS
draw_circle(dr, ds->x[i], ds->y[i], DRAG_THRESHOLD, bg, bg);
{
char buf[80];
sprintf(buf, "%d", i);
draw_text(dr, ds->x[i], ds->y[i], FONT_VARIABLE,
DRAG_THRESHOLD*3/2,
ALIGN_VCENTRE|ALIGN_HCENTRE, c, buf);
}
#else
draw_circle(dr, ds->x[i], ds->y[i], CIRCLE_RADIUS,
c, COL_OUTLINE);
#endif
}
}
}
draw_update(dr, 0, 0, w, h);
}
static float game_anim_length(const game_state *oldstate,
const game_state *newstate, int dir, game_ui *ui)
{
if (ui->just_moved)
return 0.0F;
if ((dir < 0 ? oldstate : newstate)->just_solved)
ui->anim_length = SOLVEANIM_TIME;
else
ui->anim_length = ANIM_TIME;
return ui->anim_length;
}
static float game_flash_length(const game_state *oldstate,
const game_state *newstate, int dir, game_ui *ui)
{
if (!oldstate->completed && newstate->completed &&
!oldstate->cheated && !newstate->cheated)
return FLASH_TIME;
return 0.0F;
}
static void game_get_cursor_location(const game_ui *ui,
const game_drawstate *ds,
const game_state *state,
const game_params *params,
int *x, int *y, int *w, int *h)
{
}
static int game_status(const game_state *state)
{
return state->completed ? +1 : 0;
}
#ifdef COMBINED
#define thegame untangle
#endif
const struct game thegame = {
"Untangle", "games.untangle", "untangle",
default_params,
game_fetch_preset, NULL,
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, NULL, NULL, /* can_format_as_text_now, text_format */
get_prefs, set_prefs,
new_ui,
free_ui,
NULL, /* encode_ui */
NULL, /* decode_ui */
NULL, /* game_request_keys */
game_changed_state,
NULL, /* current_key_label */
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,
game_get_cursor_location,
game_status,
false, false, NULL, NULL, /* print_size, print */
false, /* wants_statusbar */
false, NULL, /* timing_state */
SOLVE_ANIMATES, /* flags */
};