*
* Invoke as ./main n m
*
- * The algorithm is faster if the arguments are ordered so that n > m.
+ * The arguments must be ordered so that n > m:
+ * n is the number of (more, shorter) input matches of length m
+ * m is the number of (fewer, longer) output matches of length n
+ *
+ * Options:
+ * -j<jobs> run in parallel on <jobs> cores
+ * -b<best> search only for better than <best>
*/
/*
* GNU General Public License for more details.
*/
+#define _GNU_SOURCE
+
+#include <publib.h>
+
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <unistd.h>
#include <stdbool.h>
#include <inttypes.h>
+#include <math.h>
+#include <sys/types.h>
+#include <sys/wait.h>
+#include <sys/uio.h>
+#include <sys/fcntl.h>
-#include <publib.h>
#include <glpk.h>
+#ifndef VERSION
+#define VERSION "(unknown-version)"
+#endif
+
/*
* Algorithm.
*
*
* 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 by ensuring
+ * that it is not set in too few: each output stick must consist
+ * of at least two fragments since the output sticks are longer than
+ * the input ones.
+ *
* 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_max_frags=INT_MAX, m_max_frags=INT_MAX;
+static int *weight;
+
static unsigned printcounter;
-static int ncpus = 1;
+static void iterate(void);
+static void iterate_recurse(int i, AdjWord min);
+static bool preconsider_ok(int nwords, bool doprint);
+static bool maxhamweight_ok(void);
+static void optimise(bool doprint);
+
+static void progress_eol(void) {
+ fprintf(stderr," \r");
+ fflush(stderr);
+}
+
+static void set_best(double new_best) {
+ best = new_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
+ *
+ * But best values from glpk are slightly approximate, so we
+ * subtract a fudge factor from our target.
+ */
+ double near_best = best * 0.98 - 0.02;
+ if (near_best > 0) {
+ n_max_frags = ceil(n / near_best) - 1;
+ m_max_frags = ceil(m / near_best) - 1;
+ }
+}
+
+/*----- multicore support -----*/
+
+/*
+ * Multicore protocol
+ *
+ * We fork into:
+ * - master (parent)
+ * - generator
+ * - ncpu workers
+ *
+ * ipc facilities:
+ * - one pipe ("work") from generator to workers
+ * - ever-extending file ("bus") containing new "best" values
+ * - one file for each worker giving maxhamweight and adjmatrix for best
+ *
+ * generator runs iterate_recurse to a certain depth and writes the
+ * candidates to a pipe
+ *
+ * workers read candidates from the pipe and resume iterate_recurse
+ * halfway through the recursion
+ *
+ * whenever a worker does a doprint, it checks the bus for new best
+ * value; actual best values are appended
+ *
+ * master waits for generator and all workers to finish and then
+ * runs optimise() for each worker's best, then prints
+ */
+
+static int ncpus = 0, multicore_iteration_boundary = INT_MAX;
+
+static int mc_bus, mc_work[2];
+static off_t mc_bus_read;
+
+typedef struct {
+ int w;
+ FILE *results;
+ pid_t pid;
+} Worker;
+static Worker *mc_us;
+static bool mc_am_generator;
+
+static void multicore_check_for_new_best(void);
+
+#define MAX_NIOVS 4
+static AdjWord mc_iter_min;
+static int mc_niovs;
+static size_t mc_iovlen;
+static struct iovec mc_iov[MAX_NIOVS];
+
+#define IOV0 (mc_niovs = mc_iovlen = 0)
+
+#define IOV(obj, count) ({ \
+ assert(mc_niovs < MAX_NIOVS); \
+ mc_iov[mc_niovs].iov_base = &(obj); \
+ mc_iov[mc_niovs].iov_len = sizeof(obj) * (count); \
+ mc_iovlen += mc_iov[mc_niovs].iov_len; \
+ mc_niovs++; \
+ })
+
+static void mc_rwvsetup_outer(void) {
+ IOV0;
+ IOV(maxhamweight, 1);
+ IOV(mc_iter_min, 1);
+ IOV(*adjmatrix, multicore_iteration_boundary);
+ IOV(*weight, m);
+}
+
+static void mc_rwvsetup_full(void) {
+ IOV0;
+ IOV(*adjmatrix, n);
+}
+
+static void vlprintf(const char *fmt, va_list al) {
+ vfprintf(stderr,fmt,al);
+ progress_eol();
+}
+
+static void LPRINTF(const char *fmt, ...) {
+ va_list al;
+ va_start(al,fmt);
+ vlprintf(fmt,al);
+ va_end(al);
+}
+
+static void mc_awaitpid(int wnum, pid_t pid) {
+ LPRINTF("master awaiting %2d [%ld]",wnum,(long)pid);
+ int status;
+ pid_t got = waitpid(pid, &status, 0);
+ assert(got == pid);
+ if (status) {
+ fprintf(stderr,"\nFAILED SUBPROC %2d [%ld] %d\n",
+ wnum, (long)pid, status);
+ exit(-1);
+ }
+}
+
+static void multicore_outer_iteration(int i, AdjWord min) {
+ static unsigned check_counter;
+
+ assert(i == multicore_iteration_boundary);
+ mc_iter_min = min;
+ mc_rwvsetup_outer();
+ ssize_t r = writev(mc_work[1], mc_iov, mc_niovs);
+ assert(r == mc_iovlen);
+ /* effectively, this writev arranges to transfers control
+ * to some worker's instance of iterate_recurse via mc_iterate_worker */
+
+ if (!(check_counter++ & 0xff))
+ multicore_check_for_new_best();
+}
+
+static void mc_iterate_worker(void) {
+ static time_t lastprint;
+
+ for (;;) {
+ mc_rwvsetup_outer();
+ ssize_t r = readv(mc_work[0], mc_iov, mc_niovs);
+ if (r == 0) break;
+ assert(r == mc_iovlen);
+
+ bool ok = maxhamweight_ok();
+ if (!ok) continue;
+
+ time_t now = time(0);
+ bool doprint = now != lastprint;
+ lastprint = now;
+
+ ok = preconsider_ok(multicore_iteration_boundary, doprint);
+ if (doprint) progress_eol();
+ if (!ok) continue;
+
+ /* stop iterate_recurse from trying to run multicore_outer_iteration */
+ int mc_org_it_bound = multicore_iteration_boundary;
+ multicore_iteration_boundary = INT_MAX;
+ iterate_recurse(mc_org_it_bound, mc_iter_min);
+ multicore_iteration_boundary = mc_org_it_bound;
+ }
+ if (best_adjmatrix) {
+ LPRINTF("worker %2d reporting",mc_us->w);
+ adjmatrix = best_adjmatrix;
+ mc_rwvsetup_full();
+ ssize_t r = writev(fileno(mc_us->results), mc_iov, mc_niovs);
+ assert(r == mc_iovlen);
+ }
+ LPRINTF("worker %2d ending",mc_us->w);
+ exit(0);
+}
+
+static void multicore(void) {
+ Worker *mc_workers;
+ int w;
+ pid_t genpid;
+
+ multicore_iteration_boundary = n / 2;
+
+ FILE *busf = tmpfile(); assert(busf);
+ mc_bus = fileno(busf);
+ int r = fcntl(mc_bus, F_GETFL); assert(r >= 0);
+ r |= O_APPEND;
+ r = fcntl(mc_bus, F_SETFL, r); assert(r >= 0);
+
+ r = pipe(mc_work); assert(!r);
+
+ mc_workers = xmalloc(sizeof(*mc_workers) * ncpus);
+ for (w=0; w<ncpus; w++) {
+ mc_workers[w].w = w;
+ mc_workers[w].results = tmpfile(); assert(mc_workers[w].results);
+ mc_workers[w].pid = fork(); assert(mc_workers[w].pid >= 0);
+ if (!mc_workers[w].pid) {
+ mc_us = &mc_workers[w];
+ close(mc_work[1]);
+ LPRINTF("worker %2d running", w);
+ mc_iterate_worker();
+ exit(0);
+ }
+ }
+
+ close(mc_work[0]);
+
+ genpid = fork(); assert(genpid >= 0);
+ if (!genpid) {
+ mc_am_generator = 1;
+ LPRINTF("generator running");
+ iterate();
+ exit(0);
+ }
+
+ close(mc_work[1]);
+ mc_awaitpid(-1, genpid);
+ for (w=0; w<ncpus; w++)
+ mc_awaitpid(w, mc_workers[w].pid);
+
+ for (w=0; w<ncpus; w++) {
+ mc_rwvsetup_full();
+ 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 (!(mc_us || mc_am_generator))
+ return;
+
+ for (;;) {
+ double msg;
+ ssize_t got = pread(mc_bus, &msg, sizeof(msg), mc_bus_read);
+ if (!got) break;
+ assert(got == sizeof(msg));
+ if (msg > best)
+ set_best(msg);
+ mc_bus_read += sizeof(msg);
+ }
+}
+
+static void multicore_found_new_best(void) {
+ 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));
+ assert(wrote == sizeof(best));
+}
+
+/*----- end of multicore support -----*/
static AdjWord *xalloc_adjmatrix(void) {
return xmalloc(sizeof(*adjmatrix)*n);
adjall = ~((~(AdjWord)0) << m);
adjmatrix = xalloc_adjmatrix();
glp_term_out(GLP_OFF);
+ setlinebuf(stderr);
+ weight = calloc(sizeof(*weight), m); assert(weight);
}
+#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 void optimise(int doprint) {
- /* Consider the best answer (if any) for a given adjacency matrix */
- glp_prob *prob = 0;
- int i, j, totalfrags;
+#define PRINTF(...) if (!doprint) ; else fprintf(stderr, __VA_ARGS__)
- /*
- * Up to a certain point, optimise() can be restarted. We use this
- * to go back and print the debugging output if it turns out that we
- * have an interesting case. The HAVE_PRINTED macro does this: its
- * semantics are to go back in time and make sure that we have
- * printed the description of the search case.
- */
-#define HAVE_PRINTED ({ \
- if (!doprint) { doprint = 1; goto retry_with_print; } \
- })
- retry_with_print:
- if (prob) {
- glp_delete_prob(prob);
- prob = 0;
- }
+static int totalfrags;
-#define PRINTF(...) if (!doprint) ; else fprintf(stderr, __VA_ARGS__)
+static bool maxhamweight_ok(void) {
+ return maxhamweight <= m_max_frags;
+}
+
+static bool preconsider_ok(int nwords, bool doprint) {
+ int i;
PRINTF("%2d ", maxhamweight);
bool had_max = 0;
- for (i=0, totalfrags=0; i<n; i++) {
+ 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
PRINTF(" nomaxham");
goto out;
}
+ return 1;
+
+ out:
+ return 0;
+}
+
+static void optimise(bool doprint) {
+ /* 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
+ * to go back and print the debugging output if it turns out that we
+ * have an interesting case. The HAVE_PRINTED macro does this: its
+ * semantics are to go back in time and make sure that we have
+ * printed the description of the search case.
+ */
+#define HAVE_PRINTED ({ \
+ if (!doprint) { doprint = 1; goto retry_with_print; } \
+ })
+ retry_with_print:
+ if (prob) {
+ glp_delete_prob(prob);
+ prob = 0;
+ }
+
+ bool ok = preconsider_ok(n, doprint);
+ if (!ok)
+ goto out;
/*
* We formulate our problem as an LP problem as follows.
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 */
HAVE_PRINTED;
- best = got;
+ set_best(got);
+ multicore_found_new_best();
if (best_prob) glp_delete_prob(best_prob);
best_prob = prob;
out:
if (prob)
glp_delete_prob(prob);
- if (doprint) { PRINTF(" \r"); fflush(stdout); }
+ if (doprint) progress_eol();
+ if (doprint) multicore_check_for_new_best();
}
static void iterate_recurse(int i, AdjWord min) {
+ int j;
+ AdjWord jbit;
+
if (i >= n) {
+ for (j=0; j<m; j++)
+ if (weight[j] < 2)
+ return;
+
printcounter++;
optimise(!(printcounter & 0xfff));
return;
}
+ if (i >= multicore_iteration_boundary) {
+ multicore_outer_iteration(i, min);
+ return;
+ }
for (adjmatrix[i] = min;
;
adjmatrix[i]++) {
if (i == 0 && (adjmatrix[i] & (1+adjmatrix[i])))
goto again;
+ FOR_BITS(j,m)
+ if (adjmatrix[i] & jbit)
+ weight[j]++;
+ for (int j = 0; j < m; j++)
+ if (weight[j] > n_max_frags)
+ goto takeout;
+
iterate_recurse(i+1, adjmatrix[i]);
+ takeout:
+ FOR_BITS(j,m)
+ if (adjmatrix[i] & jbit)
+ weight[j]--;
+
again:
if (adjmatrix[i] == adjall)
return;
static void iterate(void) {
for (maxhamweight=1; maxhamweight<=m; maxhamweight++) {
- double maxminsize = (double)m / maxhamweight;
- if (maxminsize <= best)
+ if (!maxhamweight_ok())
continue;
iterate_recurse(0, 1);
}
}
+static int gcd(int a, int b)
+{
+ assert(a>0);
+ assert(b>0);
+ while (b) {
+ int t = a % b;
+ a = b;
+ b = t;
+ }
+ return a;
+}
+
+static void print_rational(int n, int d)
+{
+ int g = gcd(n, d);
+ n /= g;
+ d /= g;
+ printf("%d", n);
+ if (d > 1)
+ printf("/%d", d);
+}
+
+#define MAKE_INT_VECTOR_COMPARATOR(thing) \
+ static int compare_ints_##thing(const void *av, const void *bv) \
+ { \
+ const int *a = (const int *)av; \
+ const int *b = (const int *)bv; \
+ int i; \
+ for (i = 0; i < (thing); i++) \
+ if (a[i] != b[i]) \
+ return a[i] > b[i] ? -1 : +1; \
+ return 0; \
+ }
+/* Good grief, if only qsort let me pass a context parameter */
+MAKE_INT_VECTOR_COMPARATOR(1)
+MAKE_INT_VECTOR_COMPARATOR(m)
+MAKE_INT_VECTOR_COMPARATOR(n)
+
static void report(void) {
fprintf(stderr, "\n");
+ if (best_adjmatrix) {
+ int i;
+ fprintf(stderr," ");
+ for (i=0; i<n; i++) fprintf(stderr, " %"PRADJ, best_adjmatrix[i]);
+ }
+ fprintf(stderr, " best=%-12.8f nf<=%d mf<=%d\n",
+ best, n_max_frags, m_max_frags);
+ printf("%d into %d: ", n, m);
if (best_prob) {
double min = glp_get_obj_val(best_prob);
double a[n][m];
- int i, j, cols;
+ int ai[n][m];
+ int i, j, k, d, cols, imin;
for (i = 0; i < n; i++)
for (j = 0; j < m; j++)
a[i][j] = 0;
continue;
a[x][y] = min + glp_get_col_prim(best_prob, i);
}
- printf("%d into %d: min fragment %g\n", n, m, min);
- for (i = 0; i < n; i++) {
+
+ /*
+ * Try to find a denominator over which all these numbers turn
+ * sensibly into rationals.
+ */
+ for (d = 1;; d++) {
+ /*
+ * Round everything to the nearest multiple of d.
+ */
+ for (i = 0; i < n; i++)
+ for (j = 0; j < m; j++)
+ ai[i][j] = a[i][j] * d + 0.5;
+
+ /*
+ * Ensure the rows and columns add up correctly.
+ */
+ for (i = 0; i < n; i++) {
+ int total = 0;
+ for (j = 0; j < m; j++)
+ total += ai[i][j];
+ if (total != d*m)
+ goto next_d;
+ }
for (j = 0; j < m; j++) {
- if (a[i][j])
- printf(" %9.3f", a[i][j]);
- else
- printf(" ");
+ int total = 0;
+ for (i = 0; i < n; i++)
+ total += ai[i][j];
+ if (total != d*n)
+ goto next_d;
+ }
+
+ /*
+ * Ensure we haven't rounded a good solution to a worse one, by
+ * finding the new minimum fragment and making sure it's at
+ * least the one we previously had.
+ */
+ imin = d*n;
+ for (i = 0; i < n; i++)
+ for (j = 0; j < m; j++)
+ if (ai[i][j] > 0 && ai[i][j] < imin)
+ imin = ai[i][j];
+
+ if (abs((double)imin / d - min) > 1e-10)
+ goto next_d;
+
+ /*
+ * Got it! We've found a rational-valued dissection.
+ */
+ printf("min fragment ");
+ print_rational(imin, d);
+ printf(" [%s]\n", VERSION);
+
+ /*
+ * We don't really want to output the matrix, so instead let's
+ * output the ways in which the sticks are cut up.
+ */
+ {
+ int ai2[m][n];
+ for (i = 0; i < n; i++) {
+ for (j = 0; j < m; j++)
+ ai2[j][i] = ai[i][j];
+ }
+ for (i = 0; i < n; i++)
+ qsort(ai+i, m, sizeof(int), compare_ints_1);
+ qsort(ai, n, m*sizeof(int), compare_ints_m);
+ printf(" Cut up %d sticks of length %d like this:\n", n, m);
+ for (i = 0; i < n ;) {
+ for (j = 1; i+j < n && compare_ints_m(ai+i, ai+i+j) == 0; j++);
+ printf(" %d x (", j);
+ for (k = 0; k < m && ai[i][k] > 0; k++) {
+ if (k > 0) printf(" + ");
+ print_rational(ai[i][k], d);
+ }
+ printf(")\n");
+ i += j;
+ }
+
+ for (j = 0; j < m; j++)
+ qsort(ai2+j, n, sizeof(int), compare_ints_1);
+ qsort(ai2, m, n*sizeof(int), compare_ints_n);
+ printf(" Reassemble as %d sticks of length %d like this:\n", m, n);
+ for (j = 0; j < m ;) {
+ for (i = 1; i+j < m && compare_ints_n(ai2+j, ai2+j+i) == 0; i++);
+ printf(" %d x (", i);
+ for (k = 0; k < n && ai2[j][k] > 0; k++) {
+ if (k > 0) printf(" + ");
+ print_rational(ai2[j][k], d);
+ }
+ printf(")\n");
+ j += i;
+ }
}
- printf("\n");
+ return;
+
+ next_d:;
}
+ } else {
+ printf(" none better than %9.3f [%s]\n", best, VERSION);
}
if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
}
int main(int argc, char **argv) {
int opt;
- while ((opt = getopt(argc,argv,"j:")) >= 0) {
+ double best_to_set = -1.0; /* means 'don't' */
+ while ((opt = getopt(argc,argv,"j:b:")) >= 0) {
switch (opt) {
case 'j': ncpus = atoi(optarg); break;
+ case 'b': best_to_set = atof(optarg); break;
case '+': assert(!"bad option");
default: abort();
}
assert(argc==3);
n = atoi(argv[1]);
m = atoi(argv[2]);
+ assert(n > m);
+ if (best_to_set > 0) set_best(best_to_set);
prep();
- iterate();
+
+ if (ncpus) multicore();
+ else iterate();
+
report();
return 0;
}
~ianmdlvl / matchsticks-search.git / blobdiff