X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?a=blobdiff_plain;f=main.c;h=57a979654f705bd01912fe773cd01668a92ddb07;hb=7f7db5029057d9d6cfd74de0f464e1913cb80cff;hp=69f56d1a30e8bba421e9e7a7231019a45f08b09d;hpb=41013cb05383473c8ffdcf9afc89dde04760a847;p=matchsticks-search.git

diff --git a/main.c b/main.c
index 69f56d1..57a9796 100644
--- a/main.c
+++ b/main.c
@@ -58,7 +58,8 @@
  *
  * 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 +77,15 @@
  * 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, 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 +106,7 @@ static double best;
 static glp_prob *best_prob;
 static AdjWord *best_adjmatrix;
 
-static int n_over_best, m_over_best;
+static int n_max_frags, m_max_frags;
 static int *weight;
 
 static unsigned printcounter;
@@ -119,8 +124,18 @@ static void progress_eol(void) {
 
 static void set_best(double new_best) {
   best = new_best;
-  n_over_best = floor(n / best);
-  m_over_best = 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
+   */
+  n_max_frags = ceil(n / best) - 1;
+  m_max_frags = ceil(m / best) - 1;
 }
 
 /*----- multicore support -----*/
@@ -356,8 +371,8 @@ static void prep(void) {
   glp_term_out(GLP_OFF);
   setlinebuf(stderr);
   weight = calloc(sizeof(*weight), m);  assert(weight);
-  n_over_best = INT_MAX;
-  m_over_best = INT_MAX;
+  n_max_frags = INT_MAX;
+  m_max_frags = INT_MAX;
 }
 
 #if 0
@@ -379,7 +394,7 @@ static int count_set_adj_bits(AdjWord w) {
 static int totalfrags;
 
 static bool maxhamweight_ok(void) {
-  return maxhamweight <= m_over_best;
+  return maxhamweight <= m_max_frags;
 }
 
 static bool preconsider_ok(int nwords, bool doprint) {
@@ -391,7 +406,7 @@ static bool preconsider_ok(int nwords, bool doprint) {
   for (i=0, totalfrags=0; i<nwords; i++) {
     int frags = count_set_adj_bits(adjmatrix[i]);
     PRINTF("%"PRADJ" ", adjmatrix[i]);
-    if (frags > m_over_best) {
+    if (frags > m_max_frags) {
       PRINTF(" too fine");
       goto out;
     }
@@ -502,7 +517,7 @@ 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 */
@@ -628,7 +643,7 @@ 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]);