From: simon Date: Sat, 21 May 2005 13:23:26 +0000 (+0000) Subject: Solution uniqueness for Net. Can be disabled on request (but is X-Git-Url: https://git.distorted.org.uk/~mdw/sgt/puzzles/commitdiff_plain/c0edd11f62b378695f9fbddbc4da8e0dd18c9ee6 Solution uniqueness for Net. Can be disabled on request (but is enabled by default), since ambiguous sections in grids can present additional interesting challenges. I think uniqueness is a better default, though. git-svn-id: svn://svn.tartarus.org/sgt/puzzles@5816 cda61777-01e9-0310-a592-d414129be87e --- diff --git a/net.c b/net.c index d8caa01..da9e54c 100644 --- a/net.c +++ b/net.c @@ -72,6 +72,7 @@ struct game_params { int width; int height; int wrapping; + int unique; float barrier_probability; }; @@ -88,9 +89,12 @@ struct game_state { unsigned char *barriers; }; +#define OFFSETWH(x2,y2,x1,y1,dir,width,height) \ + ( (x2) = ((x1) + width + X((dir))) % width, \ + (y2) = ((y1) + height + Y((dir))) % height) + #define OFFSET(x2,y2,x1,y1,dir,state) \ - ( (x2) = ((x1) + (state)->width + X((dir))) % (state)->width, \ - (y2) = ((y1) + (state)->height + Y((dir))) % (state)->height) + OFFSETWH(x2,y2,x1,y1,dir,(state)->width,(state)->height) #define index(state, a, x, y) ( a[(y) * (state)->width + (x)] ) #define tile(state, x, y) index(state, (state)->tiles, x, y) @@ -100,9 +104,9 @@ struct xyd { int x, y, direction; }; -static int xyd_cmp(void *av, void *bv) { - struct xyd *a = (struct xyd *)av; - struct xyd *b = (struct xyd *)bv; +static int xyd_cmp(const void *av, const void *bv) { + const struct xyd *a = (const struct xyd *)av; + const struct xyd *b = (const struct xyd *)bv; if (a->x < b->x) return -1; if (a->x > b->x) @@ -118,6 +122,8 @@ static int xyd_cmp(void *av, void *bv) { return 0; }; +static int xyd_cmp_nc(void *av, void *bv) { return xyd_cmp(av, bv); } + static struct xyd *new_xyd(int x, int y, int direction) { struct xyd *xyd = snew(struct xyd); @@ -137,6 +143,7 @@ static game_params *default_params(void) ret->width = 5; ret->height = 5; ret->wrapping = FALSE; + ret->unique = TRUE; ret->barrier_probability = 0.0; return ret; @@ -166,6 +173,7 @@ static int game_fetch_preset(int i, char **name, game_params **params) ret->width = values[i].x; ret->height = values[i].y; ret->wrapping = values[i].wrap; + ret->unique = TRUE; ret->barrier_probability = 0.0; sprintf(str, "%dx%d%s", ret->width, ret->height, @@ -198,13 +206,23 @@ static void decode_params(game_params *ret, char const *string) p++; ret->height = atoi(p); while (*p && isdigit(*p)) p++; - if ( (ret->wrapping = (*p == 'w')) != 0 ) - p++; - if (*p == 'b') - ret->barrier_probability = atof(p+1); } else { ret->height = ret->width; } + + while (*p) { + if (*p == 'w') { + p++; + ret->wrapping = TRUE; + } else if (*p == 'b') { + p++; + ret->barrier_probability = atof(p); + while (*p && isdigit(*p)) p++; + } else if (*p == 'a') { + p++; + ret->unique = FALSE; + } + } } static char *encode_params(game_params *params, int full) @@ -217,6 +235,8 @@ static char *encode_params(game_params *params, int full) ret[len++] = 'w'; if (full && params->barrier_probability) len += sprintf(ret+len, "b%g", params->barrier_probability); + if (!params->unique) + ret[len++] = 'a'; assert(len < lenof(ret)); ret[len] = '\0'; @@ -228,7 +248,7 @@ static config_item *game_configure(game_params *params) config_item *ret; char buf[80]; - ret = snewn(5, config_item); + ret = snewn(6, config_item); ret[0].name = "Width"; ret[0].type = C_STRING; @@ -253,10 +273,15 @@ static config_item *game_configure(game_params *params) ret[3].sval = dupstr(buf); ret[3].ival = 0; - ret[4].name = NULL; - ret[4].type = C_END; + ret[4].name = "Ensure unique solution"; + ret[4].type = C_BOOLEAN; ret[4].sval = NULL; - ret[4].ival = 0; + ret[4].ival = params->unique; + + ret[5].name = NULL; + ret[5].type = C_END; + ret[5].sval = NULL; + ret[5].ival = 0; return ret; } @@ -269,6 +294,7 @@ static game_params *custom_params(config_item *cfg) ret->height = atoi(cfg[1].sval); ret->wrapping = cfg[2].ival; ret->barrier_probability = (float)atof(cfg[3].sval); + ret->unique = cfg[4].ival; return ret; } @@ -291,9 +317,754 @@ static char *validate_params(game_params *params) } /* ---------------------------------------------------------------------- + * Solver used to assure solution uniqueness during generation. + */ + +/* + * Test cases I used while debugging all this were + * + * ./net --generate 1 13x11w#12300 + * which expands under the non-unique grid generation rules to + * 13x11w:5eaade1bd222664436d5e2965c12656b1129dd825219e3274d558d5eb2dab5da18898e571d5a2987be79746bd95726c597447d6da96188c513add829da7681da954db113d3cd244 + * and has two ambiguous areas. + * + * An even better one is + * 13x11w#507896411361192 + * which expands to + * 13x11w:b7125b1aec598eb31bd58d82572bc11494e5dee4e8db2bdd29b88d41a16bdd996d2996ddec8c83741a1e8674e78328ba71737b8894a9271b1cd1399453d1952e43951d9b712822e + * and has an ambiguous area _and_ a situation where loop avoidance + * is a necessary deductive technique. + * + * Then there's + * 48x25w#820543338195187 + * becoming + * 48x25w:255989d14cdd185deaa753a93821a12edc1ab97943ac127e2685d7b8b3c48861b2192416139212b316eddd35de43714ebc7628d753db32e596284d9ec52c5a7dc1b4c811a655117d16dc28921b2b4161352cab1d89d18bc836b8b891d55ea4622a1251861b5bc9a8aa3e5bcd745c95229ca6c3b5e21d5832d397e917325793d7eb442dc351b2db2a52ba8e1651642275842d8871d5534aabc6d5b741aaa2d48ed2a7dbbb3151ddb49d5b9a7ed1ab98ee75d613d656dbba347bc514c84556b43a9bc65a3256ead792488b862a9d2a8a39b4255a4949ed7dbd79443292521265896b4399c95ede89d7c8c797a6a57791a849adea489359a158aa12e5dacce862b8333b7ebea7d344d1a3c53198864b73a9dedde7b663abb1b539e1e8853b1b7edb14a2a17ebaae4dbe63598a2e7e9a2dbdad415bc1d8cb88cbab5a8c82925732cd282e641ea3bd7d2c6e776de9117a26be86deb7c82c89524b122cb9397cd1acd2284e744ea62b9279bae85479ababe315c3ac29c431333395b24e6a1e3c43a2da42d4dce84aadd5b154aea555eaddcbd6e527d228c19388d9b424d94214555a7edbdeebe569d4a56dc51a86bd9963e377bb74752bd5eaa5761ba545e297b62a1bda46ab4aee423ad6c661311783cc18786d4289236563cb4a75ec67d481c14814994464cd1b87396dee63e5ab6e952cc584baa1d4c47cb557ec84dbb63d487c8728118673a166846dd3a4ebc23d6cb9c5827d96b4556e91899db32b517eda815ae271a8911bd745447121dc8d321557bc2a435ebec1bbac35b1a291669451174e6aa2218a4a9c5a6ca31ebc45d84e3a82c121e9ced7d55e9a + * which has a spot (far right) where slightly more complex loop + * avoidance is required. + */ + +static int dsf_canonify(int *dsf, int val) +{ + int v2 = val; + + while (dsf[val] != val) + val = dsf[val]; + + while (v2 != val) { + int tmp = dsf[v2]; + dsf[v2] = val; + v2 = tmp; + } + + return val; +} + +static void dsf_merge(int *dsf, int v1, int v2) +{ + v1 = dsf_canonify(dsf, v1); + v2 = dsf_canonify(dsf, v2); + dsf[v2] = v1; +} + +struct todo { + unsigned char *marked; + int *buffer; + int buflen; + int head, tail; +}; + +static struct todo *todo_new(int maxsize) +{ + struct todo *todo = snew(struct todo); + todo->marked = snewn(maxsize, unsigned char); + memset(todo->marked, 0, maxsize); + todo->buflen = maxsize + 1; + todo->buffer = snewn(todo->buflen, int); + todo->head = todo->tail = 0; + return todo; +} + +static void todo_free(struct todo *todo) +{ + sfree(todo->marked); + sfree(todo->buffer); + sfree(todo); +} + +static void todo_add(struct todo *todo, int index) +{ + if (todo->marked[index]) + return; /* already on the list */ + todo->marked[index] = TRUE; + todo->buffer[todo->tail++] = index; + if (todo->tail == todo->buflen) + todo->tail = 0; +} + +static int todo_get(struct todo *todo) { + int ret; + + if (todo->head == todo->tail) + return -1; /* list is empty */ + ret = todo->buffer[todo->head++]; + if (todo->head == todo->buflen) + todo->head = 0; + todo->marked[ret] = FALSE; + + return ret; +} + +static int net_solver(int w, int h, unsigned char *tiles, int wrapping) +{ + unsigned char *tilestate; + unsigned char *edgestate; + int *deadends; + int *equivalence; + struct todo *todo; + int i, j, x, y; + int area; + int done_something; + + /* + * Set up the solver's data structures. + */ + + /* + * tilestate stores the possible orientations of each tile. + * There are up to four of these, so we'll index the array in + * fours. tilestate[(y * w + x) * 4] and its three successive + * members give the possible orientations, clearing to 255 from + * the end as things are ruled out. + * + * In this loop we also count up the area of the grid (which is + * not _necessarily_ equal to w*h, because there might be one + * or more blank squares present. This will never happen in a + * grid generated _by_ this program, but it's worth keeping the + * solver as general as possible.) + */ + tilestate = snewn(w * h * 4, unsigned char); + area = 0; + for (i = 0; i < w*h; i++) { + tilestate[i * 4] = tiles[i] & 0xF; + for (j = 1; j < 4; j++) { + if (tilestate[i * 4 + j - 1] == 255 || + A(tilestate[i * 4 + j - 1]) == tilestate[i * 4]) + tilestate[i * 4 + j] = 255; + else + tilestate[i * 4 + j] = A(tilestate[i * 4 + j - 1]); + } + if (tiles[i] != 0) + area++; + } + + /* + * edgestate stores the known state of each edge. It is 0 for + * unknown, 1 for open (connected) and 2 for closed (not + * connected). + * + * In principle we need only worry about each edge once each, + * but in fact it's easier to track each edge twice so that we + * can reference it from either side conveniently. Also I'm + * going to allocate _five_ bytes per tile, rather than the + * obvious four, so that I can index edgestate[(y*w+x) * 5 + d] + * where d is 1,2,4,8 and they never overlap. + */ + edgestate = snewn((w * h - 1) * 5 + 9, unsigned char); + memset(edgestate, 0, (w * h - 1) * 5 + 9); + + /* + * deadends tracks which edges have dead ends on them. It is + * indexed by tile and direction: deadends[(y*w+x) * 5 + d] + * tells you whether heading out of tile (x,y) in direction d + * can reach a limited amount of the grid. Values are area+1 + * (no dead end known) or less than that (can reach _at most_ + * this many other tiles by heading this way out of this tile). + */ + deadends = snewn((w * h - 1) * 5 + 9, int); + for (i = 0; i < (w * h - 1) * 5 + 9; i++) + deadends[i] = area+1; + + /* + * equivalence tracks which sets of tiles are known to be + * connected to one another, so we can avoid creating loops by + * linking together tiles which are already linked through + * another route. + * + * This is a disjoint set forest structure: equivalence[i] + * contains the index of another member of the equivalence + * class containing i, or contains i itself for precisely one + * member in each such class. To find a representative member + * of the equivalence class containing i, you keep replacing i + * with equivalence[i] until it stops changing; then you go + * _back_ along the same path and point everything on it + * directly at the representative member so as to speed up + * future searches. Then you test equivalence between tiles by + * finding the representative of each tile and seeing if + * they're the same; and you create new equivalence (merge + * classes) by finding the representative of each tile and + * setting equivalence[one]=the_other. + */ + equivalence = snewn(w * h, int); + for (i = 0; i < w*h; i++) + equivalence[i] = i; /* initially all distinct */ + + /* + * On a non-wrapping grid, we instantly know that all the edges + * round the edge are closed. + */ + if (!wrapping) { + for (i = 0; i < w; i++) { + edgestate[i * 5 + 2] = edgestate[((h-1) * w + i) * 5 + 8] = 2; + } + for (i = 0; i < h; i++) { + edgestate[(i * w + w-1) * 5 + 1] = edgestate[(i * w) * 5 + 4] = 2; + } + } + + /* + * Since most deductions made by this solver are local (the + * exception is loop avoidance, where joining two tiles + * together on one side of the grid can theoretically permit a + * fresh deduction on the other), we can address the scaling + * problem inherent in iterating repeatedly over the entire + * grid by instead working with a to-do list. + */ + todo = todo_new(w * h); + + /* + * Main deductive loop. + */ + done_something = TRUE; /* prevent instant termination! */ + while (1) { + int index; + + /* + * Take a tile index off the todo list and process it. + */ + index = todo_get(todo); + if (index == -1) { + /* + * If we have run out of immediate things to do, we + * have no choice but to scan the whole grid for + * longer-range things we've missed. Hence, I now add + * every square on the grid back on to the to-do list. + * I also set `done_something' to FALSE at this point; + * if we later come back here and find it still FALSE, + * we will know we've scanned the entire grid without + * finding anything new to do, and we can terminate. + */ + if (!done_something) + break; + for (i = 0; i < w*h; i++) + todo_add(todo, i); + done_something = FALSE; + + index = todo_get(todo); + } + + y = index / w; + x = index % w; + { + int d, ourclass = dsf_canonify(equivalence, y*w+x); + int deadendmax[9]; + + deadendmax[1] = deadendmax[2] = deadendmax[4] = deadendmax[8] = 0; + + for (i = j = 0; i < 4 && tilestate[(y*w+x) * 4 + i] != 255; i++) { + int valid; + int nnondeadends, nondeadends[4], deadendtotal; + int nequiv, equiv[5]; + int val = tilestate[(y*w+x) * 4 + i]; + + valid = TRUE; + nnondeadends = deadendtotal = 0; + equiv[0] = ourclass; + nequiv = 1; + for (d = 1; d <= 8; d += d) { + /* + * Immediately rule out this orientation if it + * conflicts with any known edge. + */ + if ((edgestate[(y*w+x) * 5 + d] == 1 && !(val & d)) || + (edgestate[(y*w+x) * 5 + d] == 2 && (val & d))) + valid = FALSE; + + if (val & d) { + /* + * Count up the dead-end statistics. + */ + if (deadends[(y*w+x) * 5 + d] <= area) { + deadendtotal += deadends[(y*w+x) * 5 + d]; + } else { + nondeadends[nnondeadends++] = d; + } + + /* + * Ensure we aren't linking to any tiles, + * through edges not already known to be + * open, which create a loop. + */ + if (edgestate[(y*w+x) * 5 + d] == 0) { + int c, k, x2, y2; + + OFFSETWH(x2, y2, x, y, d, w, h); + c = dsf_canonify(equivalence, y2*w+x2); + for (k = 0; k < nequiv; k++) + if (c == equiv[k]) + break; + if (k == nequiv) + equiv[nequiv++] = c; + else + valid = FALSE; + } + } + } + + if (nnondeadends == 0) { + /* + * If this orientation links together dead-ends + * with a total area of less than the entire + * grid, it is invalid. + * + * (We add 1 to deadendtotal because of the + * tile itself, of course; one tile linking + * dead ends of size 2 and 3 forms a subnetwork + * with a total area of 6, not 5.) + */ + if (deadendtotal+1 < area) + valid = FALSE; + } else if (nnondeadends == 1) { + /* + * If this orientation links together one or + * more dead-ends with precisely one + * non-dead-end, then we may have to mark that + * non-dead-end as a dead end going the other + * way. However, it depends on whether all + * other orientations share the same property. + */ + deadendtotal++; + if (deadendmax[nondeadends[0]] < deadendtotal) + deadendmax[nondeadends[0]] = deadendtotal; + } else { + /* + * If this orientation links together two or + * more non-dead-ends, then we can rule out the + * possibility of putting in new dead-end + * markings in those directions. + */ + int k; + for (k = 0; k < nnondeadends; k++) + deadendmax[nondeadends[k]] = area+1; + } + + if (valid) + tilestate[(y*w+x) * 4 + j++] = val; +#ifdef SOLVER_DIAGNOSTICS + else + printf("ruling out orientation %x at %d,%d\n", val, x, y); +#endif + } + + assert(j > 0); /* we can't lose _all_ possibilities! */ + + if (j < i) { + int a, o; + done_something = TRUE; + + /* + * We have ruled out at least one tile orientation. + * Make sure the rest are blanked. + */ + while (j < 4) + tilestate[(y*w+x) * 4 + j++] = 255; + + /* + * Now go through them again and see if we've + * deduced anything new about any edges. + */ + a = 0xF; o = 0; + for (i = 0; i < 4 && tilestate[(y*w+x) * 4 + i] != 255; i++) { + a &= tilestate[(y*w+x) * 4 + i]; + o |= tilestate[(y*w+x) * 4 + i]; + } + for (d = 1; d <= 8; d += d) + if (edgestate[(y*w+x) * 5 + d] == 0) { + int x2, y2, d2; + OFFSETWH(x2, y2, x, y, d, w, h); + d2 = F(d); + if (a & d) { + /* This edge is open in all orientations. */ +#ifdef SOLVER_DIAGNOSTICS + printf("marking edge %d,%d:%d open\n", x, y, d); +#endif + edgestate[(y*w+x) * 5 + d] = 1; + edgestate[(y2*w+x2) * 5 + d2] = 1; + dsf_merge(equivalence, y*w+x, y2*w+x2); + done_something = TRUE; + todo_add(todo, y2*w+x2); + } else if (!(o & d)) { + /* This edge is closed in all orientations. */ +#ifdef SOLVER_DIAGNOSTICS + printf("marking edge %d,%d:%d closed\n", x, y, d); +#endif + edgestate[(y*w+x) * 5 + d] = 2; + edgestate[(y2*w+x2) * 5 + d2] = 2; + done_something = TRUE; + todo_add(todo, y2*w+x2); + } + } + + } + + /* + * Now check the dead-end markers and see if any of + * them has lowered from the real ones. + */ + for (d = 1; d <= 8; d += d) { + int x2, y2, d2; + OFFSETWH(x2, y2, x, y, d, w, h); + d2 = F(d); + if (deadendmax[d] > 0 && + deadends[(y2*w+x2) * 5 + d2] > deadendmax[d]) { +#ifdef SOLVER_DIAGNOSTICS + printf("setting dead end value %d,%d:%d to %d\n", + x2, y2, d2, deadendmax[d]); +#endif + deadends[(y2*w+x2) * 5 + d2] = deadendmax[d]; + done_something = TRUE; + todo_add(todo, y2*w+x2); + } + } + + } + } + + /* + * Mark all completely determined tiles as locked. + */ + j = TRUE; + for (i = 0; i < w*h; i++) { + if (tilestate[i * 4 + 1] == 255) { + assert(tilestate[i * 4 + 0] != 255); + tiles[i] = tilestate[i * 4] | LOCKED; + } else { + tiles[i] &= ~LOCKED; + j = FALSE; + } + } + + /* + * Free up working space. + */ + todo_free(todo); + sfree(tilestate); + sfree(edgestate); + sfree(deadends); + sfree(equivalence); + + return j; +} + +/* ---------------------------------------------------------------------- * Randomly select a new game description. */ +/* + * Function to randomly perturb an ambiguous section in a grid, to + * attempt to ensure unique solvability. + */ +static void perturb(int w, int h, unsigned char *tiles, int wrapping, + random_state *rs, int startx, int starty, int startd) +{ + struct xyd *perimeter, *perim2, *loop[2], looppos[2]; + int nperim, perimsize, nloop[2], loopsize[2]; + int x, y, d, i; + + /* + * We know that the tile at (startx,starty) is part of an + * ambiguous section, and we also know that its neighbour in + * direction startd is fully specified. We begin by tracing all + * the way round the ambiguous area. + */ + nperim = perimsize = 0; + perimeter = NULL; + x = startx; + y = starty; + d = startd; +#ifdef PERTURB_DIAGNOSTICS + printf("perturb %d,%d:%d\n", x, y, d); +#endif + do { + int x2, y2, d2; + + if (nperim >= perimsize) { + perimsize = perimsize * 3 / 2 + 32; + perimeter = sresize(perimeter, perimsize, struct xyd); + } + perimeter[nperim].x = x; + perimeter[nperim].y = y; + perimeter[nperim].direction = d; + nperim++; +#ifdef PERTURB_DIAGNOSTICS + printf("perimeter: %d,%d:%d\n", x, y, d); +#endif + + /* + * First, see if we can simply turn left from where we are + * and find another locked square. + */ + d2 = A(d); + OFFSETWH(x2, y2, x, y, d2, w, h); + if ((!wrapping && (abs(x2-x) > 1 || abs(y2-y) > 1)) || + (tiles[y2*w+x2] & LOCKED)) { + d = d2; + } else { + /* + * Failing that, step left into the new square and look + * in front of us. + */ + x = x2; + y = y2; + OFFSETWH(x2, y2, x, y, d, w, h); + if ((wrapping || (abs(x2-x) <= 1 && abs(y2-y) <= 1)) && + !(tiles[y2*w+x2] & LOCKED)) { + /* + * And failing _that_, we're going to have to step + * forward into _that_ square and look right at the + * same locked square as we started with. + */ + x = x2; + y = y2; + d = C(d); + } + } + + } while (x != startx || y != starty || d != startd); + + /* + * Our technique for perturbing this ambiguous area is to + * search round its edge for a join we can make: that is, an + * edge on the perimeter which is (a) not currently connected, + * and (b) connecting it would not yield a full cross on either + * side. Then we make that join, search round the network to + * find the loop thus constructed, and sever the loop at a + * randomly selected other point. + */ + perim2 = snewn(nperim, struct xyd); + memcpy(perim2, perimeter, nperim * sizeof(struct xyd)); + /* Shuffle the perimeter, so as to search it without directional bias. */ + for (i = nperim; --i ;) { + int j = random_upto(rs, i+1); + struct xyd t; + + t = perim2[j]; + perim2[j] = perim2[i]; + perim2[i] = t; + } + for (i = 0; i < nperim; i++) { + int x2, y2; + + x = perim2[i].x; + y = perim2[i].y; + d = perim2[i].direction; + + OFFSETWH(x2, y2, x, y, d, w, h); + if (!wrapping && (abs(x2-x) > 1 || abs(y2-y) > 1)) + continue; /* can't link across non-wrapping border */ + if (tiles[y*w+x] & d) + continue; /* already linked in this direction! */ + if (((tiles[y*w+x] | d) & 15) == 15) + continue; /* can't turn this tile into a cross */ + if (((tiles[y2*w+x2] | F(d)) & 15) == 15) + continue; /* can't turn other tile into a cross */ + + /* + * We've found the point at which we're going to make a new + * link. + */ +#ifdef PERTURB_DIAGNOSTICS + printf("linking %d,%d:%d\n", x, y, d); +#endif + tiles[y*w+x] |= d; + tiles[y2*w+x2] |= F(d); + + break; + } + + if (i == nperim) + return; /* nothing we can do! */ + + /* + * Now we've constructed a new link, we need to find the entire + * loop of which it is a part. + * + * In principle, this involves doing a complete search round + * the network. However, I anticipate that in the vast majority + * of cases the loop will be quite small, so what I'm going to + * do is make _two_ searches round the network in parallel, one + * keeping its metaphorical hand on the left-hand wall while + * the other keeps its hand on the right. As soon as one of + * them gets back to its starting point, I abandon the other. + */ + for (i = 0; i < 2; i++) { + loopsize[i] = nloop[i] = 0; + loop[i] = NULL; + looppos[i].x = x; + looppos[i].y = y; + looppos[i].direction = d; + } + while (1) { + for (i = 0; i < 2; i++) { + int x2, y2, j; + + x = looppos[i].x; + y = looppos[i].y; + d = looppos[i].direction; + + OFFSETWH(x2, y2, x, y, d, w, h); + + /* + * Add this path segment to the loop, unless it exactly + * reverses the previous one on the loop in which case + * we take it away again. + */ +#ifdef PERTURB_DIAGNOSTICS + printf("looppos[%d] = %d,%d:%d\n", i, x, y, d); +#endif + if (nloop[i] > 0 && + loop[i][nloop[i]-1].x == x2 && + loop[i][nloop[i]-1].y == y2 && + loop[i][nloop[i]-1].direction == F(d)) { +#ifdef PERTURB_DIAGNOSTICS + printf("removing path segment %d,%d:%d from loop[%d]\n", + x2, y2, F(d), i); +#endif + nloop[i]--; + } else { + if (nloop[i] >= loopsize[i]) { + loopsize[i] = loopsize[i] * 3 / 2 + 32; + loop[i] = sresize(loop[i], loopsize[i], struct xyd); + } +#ifdef PERTURB_DIAGNOSTICS + printf("adding path segment %d,%d:%d to loop[%d]\n", + x, y, d, i); +#endif + loop[i][nloop[i]++] = looppos[i]; + } + +#ifdef PERTURB_DIAGNOSTICS + printf("tile at new location is %x\n", tiles[y2*w+x2] & 0xF); +#endif + d = F(d); + for (j = 0; j < 4; j++) { + if (i == 0) + d = A(d); + else + d = C(d); +#ifdef PERTURB_DIAGNOSTICS + printf("trying dir %d\n", d); +#endif + if (tiles[y2*w+x2] & d) { + looppos[i].x = x2; + looppos[i].y = y2; + looppos[i].direction = d; + break; + } + } + + assert(j < 4); + assert(nloop[i] > 0); + + if (looppos[i].x == loop[i][0].x && + looppos[i].y == loop[i][0].y && + looppos[i].direction == loop[i][0].direction) { +#ifdef PERTURB_DIAGNOSTICS + printf("loop %d finished tracking\n", i); +#endif + + /* + * Having found our loop, we now sever it at a + * randomly chosen point - absolutely any will do - + * which is not the one we joined it at to begin + * with. Conveniently, the one we joined it at is + * loop[i][0], so we just avoid that one. + */ + j = random_upto(rs, nloop[i]-1) + 1; + x = loop[i][j].x; + y = loop[i][j].y; + d = loop[i][j].direction; + OFFSETWH(x2, y2, x, y, d, w, h); + tiles[y*w+x] &= ~d; + tiles[y2*w+x2] &= ~F(d); + + break; + } + } + if (i < 2) + break; + } + sfree(loop[0]); + sfree(loop[1]); + + /* + * Finally, we must mark the entire disputed section as locked, + * to prevent the perturb function being called on it multiple + * times. + * + * To do this, we _sort_ the perimeter of the area. The + * existing xyd_cmp function will arrange things into columns + * for us, in such a way that each column has the edges in + * vertical order. Then we can work down each column and fill + * in all the squares between an up edge and a down edge. + */ + qsort(perimeter, nperim, sizeof(struct xyd), xyd_cmp); + x = y = -1; + for (i = 0; i <= nperim; i++) { + if (i == nperim || perimeter[i].x > x) { + /* + * Fill in everything from the last Up edge to the + * bottom of the grid, if necessary. + */ + if (x != -1) { + while (y < h) { +#ifdef PERTURB_DIAGNOSTICS + printf("resolved: locking tile %d,%d\n", x, y); +#endif + tiles[y * w + x] |= LOCKED; + y++; + } + x = y = -1; + } + + if (i == nperim) + break; + + x = perimeter[i].x; + y = 0; + } + + if (perimeter[i].direction == U) { + x = perimeter[i].x; + y = perimeter[i].y; + } else if (perimeter[i].direction == D) { + /* + * Fill in everything from the last Up edge to here. + */ + assert(x == perimeter[i].x && y <= perimeter[i].y); + while (y <= perimeter[i].y) { +#ifdef PERTURB_DIAGNOSTICS + printf("resolved: locking tile %d,%d\n", x, y); +#endif + tiles[y * w + x] |= LOCKED; + y++; + } + x = y = -1; + } + } + + sfree(perimeter); +} + static char *new_game_desc(game_params *params, random_state *rs, game_aux_info **aux) { @@ -305,13 +1076,16 @@ static char *new_game_desc(game_params *params, random_state *rs, w = params->width; h = params->height; + cx = w / 2; + cy = h / 2; + tiles = snewn(w * h, unsigned char); - memset(tiles, 0, w * h); barriers = snewn(w * h, unsigned char); - memset(barriers, 0, w * h); - cx = w / 2; - cy = h / 2; + begin_generation: + + memset(tiles, 0, w * h); + memset(barriers, 0, w * h); /* * Construct the unshuffled grid. @@ -355,7 +1129,7 @@ static char *new_game_desc(game_params *params, random_state *rs, * containing no unreached squares, no full crosses _and_ no * closed loops. [] */ - possibilities = newtree234(xyd_cmp); + possibilities = newtree234(xyd_cmp_nc); if (cx+1 < w) add234(possibilities, new_xyd(cx, cy, R)); @@ -483,10 +1257,64 @@ static char *new_game_desc(game_params *params, random_state *rs, assert(count234(possibilities) == 0); freetree234(possibilities); + if (params->unique) { + int prevn = -1; + + /* + * Run the solver to check unique solubility. + */ + while (!net_solver(w, h, tiles, params->wrapping)) { + int n = 0; + + /* + * We expect (in most cases) that most of the grid will + * be uniquely specified already, and the remaining + * ambiguous sections will be small and separate. So + * our strategy is to find each individual such + * section, and perform a perturbation on the network + * in that area. + */ + for (y = 0; y < h; y++) for (x = 0; x < w; x++) { + if (x+1 < w && ((tiles[y*w+x] ^ tiles[y*w+x+1]) & LOCKED)) { + n++; + if (tiles[y*w+x] & LOCKED) + perturb(w, h, tiles, params->wrapping, rs, x+1, y, L); + else + perturb(w, h, tiles, params->wrapping, rs, x, y, R); + } + if (y+1 < h && ((tiles[y*w+x] ^ tiles[(y+1)*w+x]) & LOCKED)) { + n++; + if (tiles[y*w+x] & LOCKED) + perturb(w, h, tiles, params->wrapping, rs, x, y+1, U); + else + perturb(w, h, tiles, params->wrapping, rs, x, y, D); + } + } + + /* + * Now n counts the number of ambiguous sections we + * have fiddled with. If we haven't managed to decrease + * it from the last time we ran the solver, give up and + * regenerate the entire grid. + */ + if (prevn != -1 && prevn <= n) + goto begin_generation; /* (sorry) */ + + prevn = n; + } + + /* + * The solver will have left a lot of LOCKED bits lying + * around in the tiles array. Remove them. + */ + for (x = 0; x < w*h; x++) + tiles[x] &= ~LOCKED; + } + /* * Now compute a list of the possible barrier locations. */ - barriertree = newtree234(xyd_cmp); + barriertree = newtree234(xyd_cmp_nc); for (y = 0; y < h; y++) { for (x = 0; x < w; x++) { @@ -807,17 +1635,21 @@ static game_state *solve_game(game_state *state, game_aux_info *aux, game_state *ret; if (!aux) { - *error = "Solution not known for this puzzle"; - return NULL; + /* + * Run the internal solver on the provided grid. This might + * not yield a complete solution. + */ + ret = dup_game(state); + net_solver(ret->width, ret->height, ret->tiles, ret->wrapping); + } else { + assert(aux->width == state->width); + assert(aux->height == state->height); + ret = dup_game(state); + memcpy(ret->tiles, aux->tiles, ret->width * ret->height); + ret->used_solve = ret->just_used_solve = TRUE; + ret->completed = TRUE; } - assert(aux->width == state->width); - assert(aux->height == state->height); - ret = dup_game(state); - memcpy(ret->tiles, aux->tiles, ret->width * ret->height); - ret->used_solve = ret->just_used_solve = TRUE; - ret->completed = TRUE; - return ret; } @@ -850,7 +1682,7 @@ static unsigned char *compute_active(game_state *state) * We only store (x,y) pairs in todo, but it's easier to reuse * xyd_cmp and just store direction 0 every time. */ - todo = newtree234(xyd_cmp); + todo = newtree234(xyd_cmp_nc); index(state, active, state->cx, state->cy) = ACTIVE; add234(todo, new_xyd(state->cx, state->cy, 0)); diff --git a/puzzles.but b/puzzles.but index 44bdb25..bf2601b 100644 --- a/puzzles.but +++ b/puzzles.but @@ -346,6 +346,15 @@ barrier is placed between two tiles to prevent flow between them (a higher number gives more barriers). Since barriers are immovable, they act as constraints on the solution (i.e., hints). +\dt \e{Ensure unique solution} + +\dd Normally, Net will make sure that the puzzles it presents have +only one solution. Puzzles with ambiguous sections can be more +difficult and more subtle, so if you like you can turn off this +feature and risk having ambiguous puzzles. (Also, finding \e{all} +the possible solutions can be an additional challenge for an +advanced player.) + \lcont{ The grid generation in Net has been carefully arranged so that the