wip lp, problem setup compiles

[matchsticks-search.git] / main.c

diff --git a/main.c b/main.c
index 0c694c8f122aa653a07e64774649068145cc7be8..22fa3437bfd7b7b7d3e43a2a25d69ea33a6ef26b 100644 (file)
--- a/main.c
+++ b/main.c
@@ -1,39 +1,146 @@
 
+#include <stdio.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <assert.h>
+#include <inttypes.h>
+
+#include <publib.h>
+#include <glpk.h>
+
 typedef uint32_t AdjWord;
-#define PRADJ PRIx32
+#define PRADJ "08"PRIx32
 
 static int n, m;
-static AdjWord adjmatrix[n];
+static AdjWord *adjmatrix;
 static AdjWord adjall;
 
 static double best;
-static AdjWord adjmatrix_best[n];
 
 static void prep(void) {
   adjall = ~((~(AdjWord)0) << m);
+  adjmatrix = xmalloc(sizeof(*adjmatrix)*n);
+}
+
+static AdjWord one_adj_bit(int bitnum) {
+  return (AdjWord)1 << bitnum;
 }
 
 static int count_set_adj_bits(AdjWord w) {
-  for (int j=0, total=0; j<m; j++)
-    total += !!(w & ((AdjWord)1 << j));
+  int j, total;
+  for (j=0, total=0; j<m; j++)
+    total += !!(w & one_adj_bit(j));
   return total;
 }
 
 static void optimise(void) {
-  for (i=0; i<n; i++) {
+  int i, j, totalfrags;
+
+  for (i=0, totalfrags=0; i<n; i++) {
+    int frags = count_set_adj_bits(adjmatrix[i]);
+    totalfrags += frags;
     printf("%"PRADJ" ", adjmatrix[i]);
-    double maxminsize = (double)m / count_set_adj_bits(adjmatrix[i]);
+    double maxminsize = (double)m / frags;
     if (maxminsize < best) {
       printf(" too fine\n");
       return;
     }
   }
 
+  /*
+   * We formulate our problem as an LP problem as follows.
+   * In this file "n" and "m" are the matchstick numbers.
+   *
+   * Each set bit in the adjacency matrix corresponds to taking a
+   * fragment from old match i and making it part of new match j.
+   *
+   * The structural variables (columns) are:
+   *   x_minimum        minimum size of any fragment (bounded below by 0)
+   *   x_morefrag_i_j   the amount by which the size of the fragment
+   *                     i,j exceeds the minimum size (bounded below by 0)
+   *
+   * The auxiliary variables (rows) are:
+   *   x_total_i       total length for each input match (fixed variable)
+   *   x_total_j       total length for each output match (fixed variable)
+   *
+   * The objective function is simply
+   *   maximise x_minimum
+   *
+   * We use X_ and Y_ to refer to GLPK's (1-based) column and row indices.
+   * ME_ refers to entries in the list of constraint matrix elements
+   * which we build up as we go.
+   */
+
+  glp_prob *prob = glp_create_prob();
+
+  int Y_totals_i = glp_add_rows(prob, n);
+  int Y_totals_j = glp_add_rows(prob, m);
+  int X_minimum = glp_add_cols(prob, 1);
+
+  int next_matrix_entry = 1; /* wtf GLPK! */
+  int matrix_entries_size = next_matrix_entry + n + m + totalfrags*2;
+  double matrix_entries[matrix_entries_size];
+  int matrix_entries_XY[2][matrix_entries_size];
+
+#define ADD_MATRIX_ENTRY(Y,X) ({                       \
+      assert(matrix_entries_size < next_matrix_entry); \
+      matrix_entries_XY[0][next_matrix_entry] = X;     \
+      matrix_entries_XY[1][next_matrix_entry] = Y;     \
+      matrix_entries[next_matrix_entry] = 0;           \
+      next_matrix_entry++;                             \
+    })
+
+  int ME_totals_i__minimum = next_matrix_entry;
+  for (i=0; i<n; i++) ADD_MATRIX_ENTRY(Y_totals_i+i, X_minimum);
+
+  int ME_totals_j__minimum = next_matrix_entry;
+  for (j=0; j<m; j++) ADD_MATRIX_ENTRY(Y_totals_j+j, X_minimum);
+
+  /* \forall_i x_totals_i = m */
+  /* \forall_i x_totals_j = n */
+  for (i=0; i<n; i++) glp_set_row_bnds(prob, Y_totals_i+i, GLP_FX, m,m);
+  for (j=0; j<m; j++) glp_set_row_bnds(prob, Y_totals_j+j, GLP_FX, n,n);
+
+  /* x_minimum >= 0 */
+  glp_set_col_bnds(prob, X_minimum, GLP_LO, 0, 0);
+
+  /* objective is maximising x_minimum */
+  glp_set_obj_dir(prob, GLP_MAX);
+  glp_set_obj_coef(prob, X_minimum, 1);
+
+  for (i=0; i<n; j++) {
+    for (j=0; j<m; j++) {
+      if (!(adjmatrix[i] & one_adj_bit(j)))
+       continue;
+      /* x_total_i += x_minimum */
+      /* x_total_j += x_minimum */
+      matrix_entries[ ME_totals_i__minimum + i ] ++;
+      matrix_entries[ ME_totals_j__minimum + j ] ++;
+
+      /* x_morefrag_i_j >= 0 */
+      int X_morefrag_i_j = glp_add_cols(prob, 1);
+      glp_set_col_bnds(prob, X_morefrag_i_j, GLP_LO, 0, 0);
+
+      /* x_total_i += x_morefrag_i_j */
+      /* x_total_j += x_morefrag_i_j */
+      int ME_totals_i__mf_i_j = ADD_MATRIX_ENTRY(Y_totals_i+i, X_morefrag_i_j);
+      int ME_totals_j__mf_i_j = ADD_MATRIX_ENTRY(Y_totals_j+j, X_morefrag_i_j);
+      matrix_entries[ME_totals_i__mf_i_j] = 1;
+      matrix_entries[ME_totals_j__mf_i_j] = 1;
+    }
+  }
+
+  assert(next_matrix_entry == matrix_entries_size);
+
+  glp_load_matrix(prob, next_matrix_entry,
+                 matrix_entries_XY[1], matrix_entries_XY[0],
+                 matrix_entries);
+
   printf("nyi\n");
 }
 
 static void iterate_recurse(int i, AdjWord min) {
-  if (i > n) {
+  if (i >= n) {
     optimise();
     return;
   }
@@ -41,6 +148,8 @@ static void iterate_recurse(int i, AdjWord min) {
        ;
        adjmatrix[i]++) {
     iterate_recurse(i+1, adjmatrix[i]);
+    if (adjmatrix[i] == adjall)
+      return;
   }
 }