X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?p=matchsticks-search.git;a=blobdiff_plain;f=main.c;h=d923704f3962c805984567e957e1b02bbcfb2a7d;hp=8aaebad359679275a74ebd524460c6f67d0356f6;hb=9ec76da798715053418c6cac1baf7e0632cfc145;hpb=cbcccfb5ca0495bda408bf11dd118c1cf894c83f

diff --git a/main.c b/main.c
index 8aaebad..d923704 100644
--- a/main.c
+++ b/main.c
@@ -5,7 +5,13 @@
  *
  * 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>
  */
 
 /*
@@ -34,6 +40,7 @@
 #include <unistd.h>
 #include <stdbool.h>
 #include <inttypes.h>
+#include <math.h>
 #include <sys/types.h>
 #include <sys/wait.h>
 #include <sys/uio.h>
@@ -41,6 +48,10 @@
 
 #include <glpk.h>
 
+#ifndef VERSION
+#define VERSION "(unknown-version)"
+#endif
+
 /*
  * Algorithm.
  *
@@ -53,7 +64,8 @@
  *
  * 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:
  *
@@ -71,11 +83,18 @@
  * 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
@@ -86,6 +105,8 @@
 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;
@@ -94,6 +115,9 @@ static double best;
 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 void iterate(void);
@@ -107,6 +131,26 @@ static void progress_eol(void) {
   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;
+  n_max_frags = ceil(n / near_best) - 1;
+  m_max_frags = ceil(m / near_best) - 1;
+}
+
 /*----- multicore support -----*/
 
 /*
@@ -146,10 +190,11 @@ typedef struct {
   pid_t pid;
 } Worker;
 static Worker *mc_us;
+static bool mc_am_generator;
 
 static void multicore_check_for_new_best(void);
 
-#define MAX_NIOVS 3
+#define MAX_NIOVS 4
 static AdjWord mc_iter_min;
 static int mc_niovs;
 static size_t mc_iovlen;
@@ -170,6 +215,7 @@ static void mc_rwvsetup_outer(void) {
   IOV(maxhamweight, 1);
   IOV(mc_iter_min, 1);
   IOV(*adjmatrix, multicore_iteration_boundary);
+  IOV(*weight, m);
 }
 
 static void mc_rwvsetup_full(void) {
@@ -202,6 +248,8 @@ static void mc_awaitpid(int wnum, pid_t pid) {
 }
 
 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();
@@ -209,14 +257,30 @@ static void multicore_outer_iteration(int i, AdjWord min) {
   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;
@@ -224,8 +288,8 @@ static void mc_iterate_worker(void) {
     iterate_recurse(mc_org_it_bound, mc_iter_min);
     multicore_iteration_boundary = mc_org_it_bound;
   }
-  LPRINTF("worker %2d reporting",mc_us->w);
   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);
@@ -268,6 +332,7 @@ static void multicore(void) {
 
   genpid = fork();  assert(genpid >= 0);
   if (!genpid) {
+    mc_am_generator = 1;
     LPRINTF("generator running");
     iterate();
     exit(0);
@@ -283,13 +348,15 @@ static void multicore(void) {
     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;
@@ -297,13 +364,14 @@ static void multicore_check_for_new_best(void) {
     if (!got) break;
     assert(got == sizeof(msg));
     if (msg > best)
-      best = msg;
+      set_best(msg);
     mc_bus_read += sizeof(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));
@@ -321,16 +389,20 @@ static void prep(void) {
   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;
 }
 
@@ -339,8 +411,7 @@ static int count_set_adj_bits(AdjWord w) {
 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) {
@@ -351,14 +422,13 @@ 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
@@ -378,6 +448,7 @@ 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
@@ -463,8 +534,8 @@ static void optimise(bool doprint) {
   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 */
@@ -543,7 +614,7 @@ static void optimise(bool doprint) {
 
   HAVE_PRINTED;
 
-  best = got;
+  set_best(got);
   multicore_found_new_best();
 
   if (best_prob) glp_delete_prob(best_prob);
@@ -565,7 +636,14 @@ static void optimise(bool doprint) {
 }
 
 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;
@@ -582,8 +660,20 @@ static void iterate_recurse(int i, AdjWord min) {
     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;
@@ -601,6 +691,14 @@ static void iterate(void) {
 
 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];
@@ -615,7 +713,7 @@ static void report(void) {
         continue;
       a[x][y] = min + glp_get_col_prim(best_prob, i);
     }
-    printf("%d into %d: min fragment %g\n", n, m, min);
+    printf("min fragment %g", min);
     for (i = 0; i < n; i++) {
       for (j = 0; j < m; j++) {
         if (a[i][j])
@@ -625,15 +723,19 @@ static void report(void) {
       }
       printf("\n");
     }
+  } else {
+    printf(" none better than %9.3f ", best);
   }
+  printf("   [%s]\n", 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) {
+  while ((opt = getopt(argc,argv,"j:b:")) >= 0) {
     switch (opt) {
     case 'j': ncpus = atoi(optarg); break;
+    case 'b': set_best(atof(optarg)); break;
     case '+': assert(!"bad option");
     default: abort();
     }
@@ -643,6 +745,7 @@ int main(int argc, char **argv) {
   assert(argc==3);
   n = atoi(argv[1]);
   m = atoi(argv[2]);
+  assert(n > m);
 
   prep();