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puzzles/loopgen.c
Simon Tatham 3b9cafa09f Fall back to <math.h> if <tgmath.h> doesn't work. 
This fixes a build failure introduced by commit 2e48ce132e011e8
yesterday.

When I saw that commit I expected the most likely problem would be in
the NestedVM build, which is currently the thing with the most most
out-of-date C implementation. And indeed the NestedVM toolchain
doesn't have <tgmath.h> - but much more surprisingly, our _Windows_
builds failed too, with a compile error inside <tgmath.h> itself!

I haven't looked closely into the problem yet. Our Windows builds are
done with clang, which comes with its own <tgmath.h> superseding the
standard Windows one. So you'd _hope_ that clang could make sense of
its own header! But perhaps the problem is that this is an unusual
compile mode and hasn't been tested.

My fix is to simply add a cmake check for <tgmath.h> - which doesn't
just check the file's existence, it actually tries compiling a file
that #includes it, so it will detect 'file exists but is mysteriously
broken' just as easily as 'not there at all'. So this makes the builds
start working again, precisely on Ben's theory of opportunistically
using <tgmath.h> where possible and falling back to <math.h>
otherwise.

It looks ugly, though! I'm half tempted to make a new header file
whose job is to include a standard set of system headers, just so that
that nasty #ifdef doesn't have to sit at the top of almost all the
source files. But for the moment this at least gets the build working
again.
2023-04-06 07:08:04 +01:00

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/*
* 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>
#ifdef NO_TGMATH_H
# include <math.h>
#else
# include <tgmath.h>
#endif
#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);
}
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