X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?p=matchsticks-search.git;a=blobdiff_plain;f=main.c;h=96f945cf0efd8f91a425997222536638d75e1ef1;hp=e8915f7c5661dcd93fb75479e22f80ebce7f629a;hb=25b3132348e1f5964f4ec4bc4e1226f21d14bb3f;hpb=966b39b19e31dfe232d74da21c76f2981eae2201

diff --git a/main.c b/main.c
index e8915f7..96f945c 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>
  */
 
 /*
@@ -58,7 +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:
  *
@@ -76,11 +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
@@ -101,7 +115,7 @@ static double best;
 static glp_prob *best_prob;
 static AdjWord *best_adjmatrix;
 
-static int n_over_best;
+static int n_max_frags=INT_MAX, m_max_frags=INT_MAX;
 static int *weight;
 
 static unsigned printcounter;
@@ -119,7 +133,24 @@ static void progress_eol(void) {
 
 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
+   *
+   * 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 -----*/
@@ -234,6 +265,8 @@ static void multicore_outer_iteration(int i, AdjWord min) {
 }
 
 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);
@@ -243,8 +276,12 @@ static void mc_iterate_worker(void) {
     bool ok = maxhamweight_ok();
     if (!ok) continue;
 
-    ok = preconsider_ok(multicore_iteration_boundary, 1);
-    progress_eol();
+    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 */
@@ -355,7 +392,6 @@ static void prep(void) {
   glp_term_out(GLP_OFF);
   setlinebuf(stderr);
   weight = calloc(sizeof(*weight), m);  assert(weight);
-  n_over_best = INT_MAX;
 }
 
 #if 0
@@ -377,8 +413,7 @@ 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) {
@@ -389,14 +424,13 @@ 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
@@ -502,7 +536,7 @@ static void optimise(bool doprint) {
   glp_set_obj_coef(prob, X_minimum, 1);
 
   for (i=0; i<n; i++) {
-    for (j=0, jbit=1; j<m; j++, jbit<<=1) {
+    FOR_BITS(j,m) {
       if (!(adjmatrix[i] & jbit))
 	continue;
       /* x_total_i += x_minimum */
@@ -608,6 +642,10 @@ static void iterate_recurse(int i, AdjWord min) {
   AdjWord jbit;
 
   if (i >= n) {
+    for (j=0; j<m; j++)
+      if (weight[j] < 2)
+	return;
+
     printcounter++;
     optimise(!(printcounter & 0xfff));
     return;
@@ -628,7 +666,7 @@ static void iterate_recurse(int i, AdjWord min) {
       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]);
@@ -653,12 +691,59 @@ static void iterate(void) {
   }
 }
 
+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;
@@ -669,25 +754,115 @@ static void report(void) {
         continue;
       a[x][y] = min + glp_get_col_prim(best_prob, i);
     }
-    printf("%d into %d: min fragment %g   [%s]\n", n, m, min, VERSION);
-    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;
       }
-      printf("\n");
+
+      /*
+       * 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;
+        }
+      }
+      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();
     }
@@ -697,6 +872,8 @@ int main(int argc, char **argv) {
   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();