*
* We search all possible adjacency matrices, and for each one we run
* GLPK's simplex solver. We represent the adjacency matrix as an
- * array of bitmaps.
+ * array of bitmaps: one word per input stick, with one bit per output
+ * stick.
*
* However, there are a couple of wrinkles:
*
* nondecreasing in array order.
*
* Once we have a solution, we also avoid considering any candidate
- * which involves dividing one of the output sticks into so many
+ * which involves dividing one of the input sticks into so many
* fragment that the smallest fragment would necessarily be no bigger
* than our best solution. That is, we reject candidates where any of
* the hamming weights of the adjacency bitmap words are too large.
*
+ * We further winnow the set of possible adjacency matrices, by
+ * ensuring the same bit is not set in too many entries of adjmatrix
+ * (ie, as above, only considering output sticks).
+ *
* And, we want to do the search in order of increasing maximum
* hamming weight. This is because in practice optimal solutions tend
* to have low hamming weight, and having found a reasonable solution
typedef uint32_t AdjWord;
#define PRADJ "08"PRIx32
+#define FOR_BITS(j,m) for (j=0, j##bit=1; j < (m); j++, j##bit<<=1)
+
static int n, m, maxhamweight;
static AdjWord *adjmatrix;
static AdjWord adjall;
static glp_prob *best_prob;
static AdjWord *best_adjmatrix;
-static int n_over_best;
+static int n_max_frags, m_max_frags;
static int *weight;
static unsigned printcounter;
static void set_best(double new_best) {
best = new_best;
- n_over_best = floor(n / best);
+ /*
+ * When computing n_max_frags, we want to set a value that will skip
+ * anything that won't provide strictly better solutions. So we
+ * want
+ * frags < n / best
+ * _ _
+ * <=> frags < | n / best |
+ * _ _
+ * <=> frags <= | n / best | - 1
+ */
+ n_max_frags = ceil(n / best) - 1;
+ m_max_frags = ceil(m / best) - 1;
}
/*----- multicore support -----*/
pid_t pid;
} Worker;
static Worker *mc_us;
+static bool mc_am_generator;
static void multicore_check_for_new_best(void);
genpid = fork(); assert(genpid >= 0);
if (!genpid) {
+ mc_am_generator = 1;
LPRINTF("generator running");
iterate();
exit(0);
LPRINTF("reading report from %2d",w);
ssize_t sr = preadv(fileno(mc_workers[w].results), mc_iov, mc_niovs, 0);
if (!sr) continue;
+ LPRINTF("got report from %2d",w);
maxhamweight = 0;
optimise(1);
}
}
static void multicore_check_for_new_best(void) {
- if (!ncpus) return;
+ if (!(mc_us || mc_am_generator))
+ return;
for (;;) {
double msg;
}
static void multicore_found_new_best(void) {
- if (!ncpus) return;
+ if (!mc_us)
+ return;
if (mc_us /* might be master */) fprintf(stderr," w%-2d ",mc_us->w);
ssize_t wrote = write(mc_bus, &best, sizeof(best));
glp_term_out(GLP_OFF);
setlinebuf(stderr);
weight = calloc(sizeof(*weight), m); assert(weight);
- n_over_best = INT_MAX;
+ n_max_frags = INT_MAX;
+ m_max_frags = INT_MAX;
}
+#if 0
static AdjWord one_adj_bit(int bitnum) {
return (AdjWord)1 << bitnum;
}
+#endif
static int count_set_adj_bits(AdjWord w) {
- int j, total;
- for (j=0, total=0; j<m; j++)
- total += !!(w & one_adj_bit(j));
+ int j, total = 0;
+ AdjWord jbit;
+ FOR_BITS(j,m)
+ total += !!(w & jbit);
return total;
}
static int totalfrags;
static bool maxhamweight_ok(void) {
- double maxminsize = (double)m / maxhamweight;
- return maxminsize > best;
+ return maxhamweight <= m_max_frags;
}
static bool preconsider_ok(int nwords, bool doprint) {
bool had_max = 0;
for (i=0, totalfrags=0; i<nwords; i++) {
int frags = count_set_adj_bits(adjmatrix[i]);
- had_max += (frags >= maxhamweight);
- totalfrags += frags;
PRINTF("%"PRADJ" ", adjmatrix[i]);
- double maxminsize = (double)m / frags;
- if (maxminsize <= best) {
+ if (frags > m_max_frags) {
PRINTF(" too fine");
goto out;
}
+ had_max += (frags >= maxhamweight);
+ totalfrags += frags;
}
if (!had_max) {
/* Skip this candidate as its max hamming weight is lower than
/* Consider the best answer (if any) for a given adjacency matrix */
glp_prob *prob = 0;
int i, j;
+ AdjWord jbit;
/*
* Up to a certain point, optimise() can be restarted. We use this
glp_set_obj_coef(prob, X_minimum, 1);
for (i=0; i<n; i++) {
- for (j=0; j<m; j++) {
- if (!(adjmatrix[i] & one_adj_bit(j)))
+ FOR_BITS(j,m) {
+ if (!(adjmatrix[i] & jbit))
continue;
/* x_total_i += x_minimum */
/* x_total_j += x_minimum */
}
static void iterate_recurse(int i, AdjWord min) {
+ int j;
+ AdjWord jbit;
+
if (i >= n) {
printcounter++;
optimise(!(printcounter & 0xfff));
if (i == 0 && (adjmatrix[i] & (1+adjmatrix[i])))
goto again;
- for (int j = 0; j < m; j++)
- if (adjmatrix[i] & one_adj_bit(j))
+ FOR_BITS(j,m)
+ if (adjmatrix[i] & jbit)
weight[j]++;
for (int j = 0; j < m; j++)
- if (weight[j] >= n_over_best)
+ if (weight[j] >= n_max_frags)
goto takeout;
iterate_recurse(i+1, adjmatrix[i]);
takeout:
- for (int j = 0; j < m; j++)
- if (adjmatrix[i] & one_adj_bit(j))
+ FOR_BITS(j,m)
+ if (adjmatrix[i] & jbit)
weight[j]--;
again:
~ianmdlvl / matchsticks-search.git / blobdiff