fudge the {n,m}_max_frags to deal with rounding errors in glpk results

[matchsticks-search.git] / main.c

diff --git a/main.c b/main.c
index de880e9c356936fa2e847cce8d166ffa9941f6eb..f0bb84f497f12d91f9a1f4416643d80aee002c09 100644 (file)
--- a/main.c
+++ b/main.c
@@ -5,7 +5,9 @@
  *
  * 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
  */
 
 /*
@@ -58,7 +60,8 @@
  *
  * 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 +79,18 @@
  * 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
@@ -119,8 +129,22 @@ static void progress_eol(void) {
 
 static void set_best(double new_best) {
   best = new_best;
-  n_max_frags = floor(n / best);
-  m_max_frags = floor(m / 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 -----*/
@@ -502,7 +526,7 @@ 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 +632,10 @@ 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;
@@ -697,6 +725,7 @@ int main(int argc, char **argv) {
   assert(argc==3);
   n = atoi(argv[1]);
   m = atoi(argv[2]);
+  assert(n > m);
 
   prep();