Python code to compute upper bounds on the solution.

[matchsticks-search.git] / main.c

diff --git a/main.c b/main.c
index b7aae53e43007901eb4a547a2d52a188eb61efc2..3ee58c59760729eba27ae8b88123caa59d9062b0 100644 (file)
--- 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_max_frags, m_max_frags;
+static int n_max_frags=INT_MAX, m_max_frags=INT_MAX;
 static int *weight;
 
 static unsigned printcounter;
@@ -128,9 +142,15 @@ static void set_best(double new_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.
    */
-  n_max_frags = ceil(n / best) - 1;
-  m_max_frags = ceil(m / best) - 1;
+  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 -----*/
@@ -245,6 +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);
@@ -254,8 +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 */
@@ -366,8 +392,6 @@ static void prep(void) {
   glp_term_out(GLP_OFF);
   setlinebuf(stderr);
   weight = calloc(sizeof(*weight), m);  assert(weight);
-  n_max_frags = INT_MAX;
-  m_max_frags = INT_MAX;
 }
 
 #if 0
@@ -618,6 +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;
@@ -638,7 +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_max_frags)
+      if (weight[j] > n_max_frags)
         goto takeout;
 
     iterate_recurse(i+1, adjmatrix[i]);
@@ -665,6 +693,14 @@ 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];
@@ -679,7 +715,7 @@ 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);
+    printf("min fragment %g   [%s]\n", min, VERSION);
     for (i = 0; i < n; i++) {
       for (j = 0; j < m; j++) {
         if (a[i][j])
@@ -689,15 +725,19 @@ static void report(void) {
       }
       printf("\n");
     }
+  } 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();
     }
@@ -707,6 +747,8 @@ 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();