ref: b5e02b0b9c1b35b0b907bf6d63e62b9fafd9cb7e
dir: /loopgen.c/
/*
* loopgen.c: loop generation functions for grid.[ch].
*/
#include <stdio.h>
#include <stdlib.h>
#include <stddef.h>
#include <string.h>
#include <assert.h>
#include <ctype.h>
#include <math.h>
#include "puzzles.h"
#include "tree234.h"
#include "grid.h"
#include "loopgen.h"
/* We're going to store lists of current candidate faces for colouring black
* or white.
* Each face gets a 'score', which tells us how adding that face right
* now would affect the curliness of the solution loop. We're trying to
* maximise that quantity so will bias our random selection of faces to
* colour those with high scores */
struct face_score {
int white_score;
int black_score;
unsigned long random;
/* No need to store a grid_face* here. The 'face_scores' array will
* be a list of 'face_score' objects, one for each face of the grid, so
* the position (index) within the 'face_scores' array will determine
* which face corresponds to a particular face_score.
* Having a single 'face_scores' array for all faces simplifies memory
* management, and probably improves performance, because we don't have to
* malloc/free each individual face_score, and we don't have to maintain
* a mapping from grid_face* pointers to face_score* pointers.
*/
};
static int generic_sort_cmpfn(void *v1, void *v2, size_t offset)
{
struct face_score *f1 = v1;
struct face_score *f2 = v2;
int r;
r = *(int *)((char *)f2 + offset) - *(int *)((char *)f1 + offset);
if (r) {
return r;
}
if (f1->random < f2->random)
return -1;
else if (f1->random > f2->random)
return 1;
/*
* It's _just_ possible that two faces might have been given
* the same random value. In that situation, fall back to
* comparing based on the positions within the face_scores list.
* This introduces a tiny directional bias, but not a significant one.
*/
return f1 - f2;
}
static int white_sort_cmpfn(void *v1, void *v2)
{
return generic_sort_cmpfn(v1, v2, offsetof(struct face_score,white_score));
}
static int black_sort_cmpfn(void *v1, void *v2)
{
return generic_sort_cmpfn(v1, v2, offsetof(struct face_score,black_score));
}
/* 'board' is an array of enum face_colour, indicating which faces are
* currently black/white/grey. 'colour' is FACE_WHITE or FACE_BLACK.
* Returns whether it's legal to colour the given face with this colour. */
static bool can_colour_face(grid *g, char* board, int face_index,
enum face_colour colour)
{
int i, j;
grid_face *test_face = g->faces + face_index;
grid_face *starting_face, *current_face;
grid_dot *starting_dot;
int transitions;
bool current_state, s; /* equal or not-equal to 'colour' */
bool found_same_coloured_neighbour = false;
assert(board[face_index] != colour);
/* Can only consider a face for colouring if it's adjacent to a face
* with the same colour. */
for (i = 0; i < test_face->order; i++) {
grid_edge *e = test_face->edges[i];
grid_face *f = (e->face1 == test_face) ? e->face2 : e->face1;
if (FACE_COLOUR(f) == colour) {
found_same_coloured_neighbour = true;
break;
}
}
if (!found_same_coloured_neighbour)
return false;
/* Need to avoid creating a loop of faces of this colour around some
* differently-coloured faces.
* Also need to avoid meeting a same-coloured face at a corner, with
* other-coloured faces in between. Here's a simple test that (I believe)
* takes care of both these conditions:
*
* Take the circular path formed by this face's edges, and inflate it
* slightly outwards. Imagine walking around this path and consider
* the faces that you visit in sequence. This will include all faces
* touching the given face, either along an edge or just at a corner.
* Count the number of 'colour'/not-'colour' transitions you encounter, as
* you walk along the complete loop. This will obviously turn out to be
* an even number.
* If 0, we're either in the middle of an "island" of this colour (should
* be impossible as we're not supposed to create black or white loops),
* or we're about to start a new island - also not allowed.
* If 4 or greater, there are too many separate coloured regions touching
* this face, and colouring it would create a loop or a corner-violation.
* The only allowed case is when the count is exactly 2. */
/* i points to a dot around the test face.
* j points to a face around the i^th dot.
* The current face will always be:
* test_face->dots[i]->faces[j]
* We assume dots go clockwise around the test face,
* and faces go clockwise around dots. */
/*
* The end condition is slightly fiddly. In sufficiently strange
* degenerate grids, our test face may be adjacent to the same
* other face multiple times (typically if it's the exterior
* face). Consider this, in particular:
*
* +--+
* | |
* +--+--+
* | | |
* +--+--+
*
* The bottom left face there is adjacent to the exterior face
* twice, so we can't just terminate our iteration when we reach
* the same _face_ we started at. Furthermore, we can't
* condition on having the same (i,j) pair either, because
* several (i,j) pairs identify the bottom left contiguity with
* the exterior face! We canonicalise the (i,j) pair by taking
* one step around before we set the termination tracking.
*/
i = j = 0;
current_face = test_face->dots[0]->faces[0];
if (current_face == test_face) {
j = 1;
current_face = test_face->dots[0]->faces[1];
}
transitions = 0;
current_state = (FACE_COLOUR(current_face) == colour);
starting_dot = NULL;
starting_face = NULL;
while (true) {
/* Advance to next face.
* Need to loop here because it might take several goes to
* find it. */
while (true) {
j++;
if (j == test_face->dots[i]->order)
j = 0;
if (test_face->dots[i]->faces[j] == test_face) {
/* Advance to next dot round test_face, then
* find current_face around new dot
* and advance to the next face clockwise */
i++;
if (i == test_face->order)
i = 0;
for (j = 0; j < test_face->dots[i]->order; j++) {
if (test_face->dots[i]->faces[j] == current_face)
break;
}
/* Must actually find current_face around new dot,
* or else something's wrong with the grid. */
assert(j != test_face->dots[i]->order);
/* Found, so advance to next face and try again */
} else {
break;
}
}
/* (i,j) are now advanced to next face */
current_face = test_face->dots[i]->faces[j];
s = (FACE_COLOUR(current_face) == colour);
if (!starting_dot) {
starting_dot = test_face->dots[i];
starting_face = current_face;
current_state = s;
} else {
if (s != current_state) {
++transitions;
current_state = s;
if (transitions > 2)
break;
}
if (test_face->dots[i] == starting_dot &&
current_face == starting_face)
break;
}
}
return (transitions == 2) ? true : false;
}
/* Count the number of neighbours of 'face', having colour 'colour' */
static int face_num_neighbours(grid *g, char *board, grid_face *face,
enum face_colour colour)
{
int colour_count = 0;
int i;
grid_face *f;
grid_edge *e;
for (i = 0; i < face->order; i++) {
e = face->edges[i];
f = (e->face1 == face) ? e->face2 : e->face1;
if (FACE_COLOUR(f) == colour)
++colour_count;
}
return colour_count;
}
/* The 'score' of a face reflects its current desirability for selection
* as the next face to colour white or black. We want to encourage moving
* into grey areas and increasing loopiness, so we give scores according to
* how many of the face's neighbours are currently coloured the same as the
* proposed colour. */
static int face_score(grid *g, char *board, grid_face *face,
enum face_colour colour)
{
/* Simple formula: score = 0 - num. same-coloured neighbours,
* so a higher score means fewer same-coloured neighbours. */
return -face_num_neighbours(g, board, face, colour);
}
/*
* Generate a new complete random closed loop for the given grid.
*
* The method is to generate a WHITE/BLACK colouring of all the faces,
* such that the WHITE faces will define the inside of the path, and the
* BLACK faces define the outside.
* To do this, we initially colour all faces GREY. The infinite space outside
* the grid is coloured BLACK, and we choose a random face to colour WHITE.
* Then we gradually grow the BLACK and the WHITE regions, eliminating GREY
* faces, until the grid is filled with BLACK/WHITE. As we grow the regions,
* we avoid creating loops of a single colour, to preserve the topological
* shape of the WHITE and BLACK regions.
* We also try to make the boundary as loopy and twisty as possible, to avoid
* generating paths that are uninteresting.
* The algorithm works by choosing a BLACK/WHITE colour, then choosing a GREY
* face that can be coloured with that colour (without violating the
* topological shape of that region). It's not obvious, but I think this
* algorithm is guaranteed to terminate without leaving any GREY faces behind.
* Indeed, if there are any GREY faces at all, both the WHITE and BLACK
* regions can be grown.
* This is checked using assert()ions, and I haven't seen any failures yet.
*
* Hand-wavy proof: imagine what can go wrong...
*
* Could the white faces get completely cut off by the black faces, and still
* leave some grey faces remaining?
* No, because then the black faces would form a loop around both the white
* faces and the grey faces, which is disallowed because we continually
* maintain the correct topological shape of the black region.
* Similarly, the black faces can never get cut off by the white faces. That
* means both the WHITE and BLACK regions always have some room to grow into
* the GREY regions.
* Could it be that we can't colour some GREY face, because there are too many
* WHITE/BLACK transitions as we walk round the face? (see the
* can_colour_face() function for details)
* No. Imagine otherwise, and we see WHITE/BLACK/WHITE/BLACK as we walk
* around the face. The two WHITE faces would be connected by a WHITE path,
* and the BLACK faces would be connected by a BLACK path. These paths would
* have to cross, which is impossible.
* Another thing that could go wrong: perhaps we can't find any GREY face to
* colour WHITE, because it would create a loop-violation or a corner-violation
* with the other WHITE faces?
* This is a little bit tricky to prove impossible. Imagine you have such a
* GREY face (that is, if you coloured it WHITE, you would create a WHITE loop
* or corner violation).
* That would cut all the non-white area into two blobs. One of those blobs
* must be free of BLACK faces (because the BLACK stuff is a connected blob).
* So we have a connected GREY area, completely surrounded by WHITE
* (including the GREY face we've tentatively coloured WHITE).
* A well-known result in graph theory says that you can always find a GREY
* face whose removal leaves the remaining GREY area connected. And it says
* there are at least two such faces, so we can always choose the one that
* isn't the "tentative" GREY face. Colouring that face WHITE leaves
* everything nice and connected, including that "tentative" GREY face which
* acts as a gateway to the rest of the non-WHITE grid.
*/
void generate_loop(grid *g, char *board, random_state *rs,
loopgen_bias_fn_t bias, void *biasctx)
{
int i, j;
int num_faces = g->num_faces;
struct face_score *face_scores; /* Array of face_score objects */
struct face_score *fs; /* Points somewhere in the above list */
struct grid_face *cur_face;
tree234 *lightable_faces_sorted;
tree234 *darkable_faces_sorted;
int *face_list;
bool do_random_pass;
/* Make a board */
memset(board, FACE_GREY, num_faces);
/* Create and initialise the list of face_scores */
face_scores = snewn(num_faces, struct face_score);
for (i = 0; i < num_faces; i++) {
face_scores[i].random = random_bits(rs, 31);
face_scores[i].black_score = face_scores[i].white_score = 0;
}
/* Colour a random, finite face white. The infinite face is implicitly
* coloured black. Together, they will seed the random growth process
* for the black and white areas. */
i = random_upto(rs, num_faces);
board[i] = FACE_WHITE;
/* We need a way of favouring faces that will increase our loopiness.
* We do this by maintaining a list of all candidate faces sorted by
* their score and choose randomly from that with appropriate skew.
* In order to avoid consistently biasing towards particular faces, we
* need the sort order _within_ each group of scores to be completely
* random. But it would be abusing the hospitality of the tree234 data
* structure if our comparison function were nondeterministic :-). So with
* each face we associate a random number that does not change during a
* particular run of the generator, and use that as a secondary sort key.
* Yes, this means we will be biased towards particular random faces in
* any one run but that doesn't actually matter. */
lightable_faces_sorted = newtree234(white_sort_cmpfn);
darkable_faces_sorted = newtree234(black_sort_cmpfn);
/* Initialise the lists of lightable and darkable faces. This is
* slightly different from the code inside the while-loop, because we need
* to check every face of the board (the grid structure does not keep a
* list of the infinite face's neighbours). */
for (i = 0; i < num_faces; i++) {
grid_face *f = g->faces + i;
struct face_score *fs = face_scores + i;
if (board[i] != FACE_GREY) continue;
/* We need the full colourability check here, it's not enough simply
* to check neighbourhood. On some grids, a neighbour of the infinite
* face is not necessarily darkable. */
if (can_colour_face(g, board, i, FACE_BLACK)) {
fs->black_score = face_score(g, board, f, FACE_BLACK);
add234(darkable_faces_sorted, fs);
}
if (can_colour_face(g, board, i, FACE_WHITE)) {
fs->white_score = face_score(g, board, f, FACE_WHITE);
add234(lightable_faces_sorted, fs);
}
}
/* Colour faces one at a time until no more faces are colourable. */
while (true)
{
enum face_colour colour;
tree234 *faces_to_pick;
int c_lightable = count234(lightable_faces_sorted);
int c_darkable = count234(darkable_faces_sorted);
if (c_lightable == 0 && c_darkable == 0) {
/* No more faces we can use at all. */
break;
}
assert(c_lightable != 0 && c_darkable != 0);
/* Choose a colour, and colour the best available face
* with that colour. */
colour = random_upto(rs, 2) ? FACE_WHITE : FACE_BLACK;
if (colour == FACE_WHITE)
faces_to_pick = lightable_faces_sorted;
else
faces_to_pick = darkable_faces_sorted;
if (bias) {
/*
* Go through all the candidate faces and pick the one the
* bias function likes best, breaking ties using the
* ordering in our tree234 (which is why we replace only
* if score > bestscore, not >=).
*/
int j, k;
struct face_score *best = NULL;
int score, bestscore = 0;
for (j = 0;
(fs = (struct face_score *)index234(faces_to_pick, j))!=NULL;
j++) {
assert(fs);
k = fs - face_scores;
assert(board[k] == FACE_GREY);
board[k] = colour;
score = bias(biasctx, board, k);
board[k] = FACE_GREY;
bias(biasctx, board, k); /* let bias know we put it back */
if (!best || score > bestscore) {
bestscore = score;
best = fs;
}
}
fs = best;
} else {
fs = (struct face_score *)index234(faces_to_pick, 0);
}
assert(fs);
i = fs - face_scores;
assert(board[i] == FACE_GREY);
board[i] = colour;
if (bias)
bias(biasctx, board, i); /* notify bias function of the change */
/* Remove this newly-coloured face from the lists. These lists should
* only contain grey faces. */
del234(lightable_faces_sorted, fs);
del234(darkable_faces_sorted, fs);
/* Remember which face we've just coloured */
cur_face = g->faces + i;
/* The face we've just coloured potentially affects the colourability
* and the scores of any neighbouring faces (touching at a corner or
* edge). So the search needs to be conducted around all faces
* touching the one we've just lit. Iterate over its corners, then
* over each corner's faces. For each such face, we remove it from
* the lists, recalculate any scores, then add it back to the lists
* (depending on whether it is lightable, darkable or both). */
for (i = 0; i < cur_face->order; i++) {
grid_dot *d = cur_face->dots[i];
for (j = 0; j < d->order; j++) {
grid_face *f = d->faces[j];
int fi; /* face index of f */
if (f == NULL)
continue;
if (f == cur_face)
continue;
/* If the face is already coloured, it won't be on our
* lightable/darkable lists anyway, so we can skip it without
* bothering with the removal step. */
if (FACE_COLOUR(f) != FACE_GREY) continue;
/* Find the face index and face_score* corresponding to f */
fi = f - g->faces;
fs = face_scores + fi;
/* Remove from lightable list if it's in there. We do this,
* even if it is still lightable, because the score might
* be different, and we need to remove-then-add to maintain
* correct sort order. */
del234(lightable_faces_sorted, fs);
if (can_colour_face(g, board, fi, FACE_WHITE)) {
fs->white_score = face_score(g, board, f, FACE_WHITE);
add234(lightable_faces_sorted, fs);
}
/* Do the same for darkable list. */
del234(darkable_faces_sorted, fs);
if (can_colour_face(g, board, fi, FACE_BLACK)) {
fs->black_score = face_score(g, board, f, FACE_BLACK);
add234(darkable_faces_sorted, fs);
}
}
}
}
/* Clean up */
freetree234(lightable_faces_sorted);
freetree234(darkable_faces_sorted);
sfree(face_scores);
/* The next step requires a shuffled list of all faces */
face_list = snewn(num_faces, int);
for (i = 0; i < num_faces; ++i) {
face_list[i] = i;
}
shuffle(face_list, num_faces, sizeof(int), rs);
/* The above loop-generation algorithm can often leave large clumps
* of faces of one colour. In extreme cases, the resulting path can be
* degenerate and not very satisfying to solve.
* This next step alleviates this problem:
* Go through the shuffled list, and flip the colour of any face we can
* legally flip, and which is adjacent to only one face of the opposite
* colour - this tends to grow 'tendrils' into any clumps.
* Repeat until we can find no more faces to flip. This will
* eventually terminate, because each flip increases the loop's
* perimeter, which cannot increase for ever.
* The resulting path will have maximal loopiness (in the sense that it
* cannot be improved "locally". Unfortunately, this allows a player to
* make some illicit deductions. To combat this (and make the path more
* interesting), we do one final pass making random flips. */
/* Set to true for final pass */
do_random_pass = false;
while (true) {
/* Remember whether a flip occurred during this pass */
bool flipped = false;
for (i = 0; i < num_faces; ++i) {
int j = face_list[i];
enum face_colour opp =
(board[j] == FACE_WHITE) ? FACE_BLACK : FACE_WHITE;
if (can_colour_face(g, board, j, opp)) {
grid_face *face = g->faces +j;
if (do_random_pass) {
/* final random pass */
if (!random_upto(rs, 10))
board[j] = opp;
} else {
/* normal pass - flip when neighbour count is 1 */
if (face_num_neighbours(g, board, face, opp) == 1) {
board[j] = opp;
flipped = true;
}
}
}
}
if (do_random_pass) break;
if (!flipped) do_random_pass = true;
}
sfree(face_list);
}