12 typedef uint32_t AdjWord;
13 #define PRADJ "08"PRIx32
16 static AdjWord *adjmatrix;
17 static AdjWord adjall;
20 static glp_prob *best_prob;
21 static AdjWord *best_adjmatrix;
23 static AdjWord *xalloc_adjmatrix(void) {
24 return xmalloc(sizeof(*adjmatrix)*n);
27 static void prep(void) {
28 adjall = ~((~(AdjWord)0) << m);
29 adjmatrix = xalloc_adjmatrix();
32 static AdjWord one_adj_bit(int bitnum) {
33 return (AdjWord)1 << bitnum;
36 static int count_set_adj_bits(AdjWord w) {
38 for (j=0, total=0; j<m; j++)
39 total += !!(w & one_adj_bit(j));
43 static void optimise(void) {
46 for (i=0, totalfrags=0; i<n; i++) {
47 int frags = count_set_adj_bits(adjmatrix[i]);
49 printf("%"PRADJ" ", adjmatrix[i]);
50 double maxminsize = (double)m / frags;
51 if (maxminsize < best) {
52 printf(" too fine\n");
58 * We formulate our problem as an LP problem as follows.
59 * In this file "n" and "m" are the matchstick numbers.
61 * Each set bit in the adjacency matrix corresponds to taking a
62 * fragment from old match i and making it part of new match j.
64 * The structural variables (columns) are:
65 * x_minimum minimum size of any fragment (bounded below by 0)
66 * x_morefrag_i_j the amount by which the size of the fragment
67 * i,j exceeds the minimum size (bounded below by 0)
69 * The auxiliary variables (rows) are:
70 * x_total_i total length for each input match (fixed variable)
71 * x_total_j total length for each output match (fixed variable)
73 * The objective function is simply
76 * We use X_ and Y_ to refer to GLPK's (1-based) column and row indices.
77 * ME_ refers to entries in the list of constraint matrix elements
78 * which we build up as we go.
81 glp_prob *prob = glp_create_prob();
83 int Y_totals_i = glp_add_rows(prob, n);
84 int Y_totals_j = glp_add_rows(prob, m);
85 int X_minimum = glp_add_cols(prob, 1);
87 int next_matrix_entry = 1; /* wtf GLPK! */
88 int matrix_entries_size = next_matrix_entry + n + m + totalfrags*2;
89 double matrix_entries[matrix_entries_size];
90 int matrix_entries_XY[2][matrix_entries_size];
92 #define ADD_MATRIX_ENTRY(Y,X) ({ \
93 assert(next_matrix_entry < matrix_entries_size); \
94 matrix_entries_XY[0][next_matrix_entry] = (X); \
95 matrix_entries_XY[1][next_matrix_entry] = (Y); \
96 matrix_entries[next_matrix_entry] = 0; \
97 next_matrix_entry++; \
100 int ME_totals_i__minimum = next_matrix_entry;
101 for (i=0; i<n; i++) ADD_MATRIX_ENTRY(Y_totals_i+i, X_minimum);
103 int ME_totals_j__minimum = next_matrix_entry;
104 for (j=0; j<m; j++) ADD_MATRIX_ENTRY(Y_totals_j+j, X_minimum);
106 /* \forall_i x_totals_i = m */
107 /* \forall_i x_totals_j = n */
108 for (i=0; i<n; i++) glp_set_row_bnds(prob, Y_totals_i+i, GLP_FX, m,m);
109 for (j=0; j<m; j++) glp_set_row_bnds(prob, Y_totals_j+j, GLP_FX, n,n);
112 glp_set_col_bnds(prob, X_minimum, GLP_LO, 0, 0);
114 /* objective is maximising x_minimum */
115 glp_set_obj_dir(prob, GLP_MAX);
116 glp_set_obj_coef(prob, X_minimum, 1);
118 for (i=0; i<n; i++) {
119 for (j=0; j<m; j++) {
120 if (!(adjmatrix[i] & one_adj_bit(j)))
122 /* x_total_i += x_minimum */
123 /* x_total_j += x_minimum */
124 matrix_entries[ ME_totals_i__minimum + i ] ++;
125 matrix_entries[ ME_totals_j__minimum + j ] ++;
127 /* x_morefrag_i_j >= 0 */
128 int X_morefrag_i_j = glp_add_cols(prob, 1);
129 glp_set_col_bnds(prob, X_morefrag_i_j, GLP_LO, 0, 0);
131 /* x_total_i += x_morefrag_i_j */
132 /* x_total_j += x_morefrag_i_j */
133 int ME_totals_i__mf_i_j = ADD_MATRIX_ENTRY(Y_totals_i+i, X_morefrag_i_j);
134 int ME_totals_j__mf_i_j = ADD_MATRIX_ENTRY(Y_totals_j+j, X_morefrag_i_j);
135 matrix_entries[ME_totals_i__mf_i_j] = 1;
136 matrix_entries[ME_totals_j__mf_i_j] = 1;
140 assert(next_matrix_entry == matrix_entries_size);
142 glp_load_matrix(prob, matrix_entries_size-1,
143 matrix_entries_XY[1], matrix_entries_XY[0],
146 int r = glp_simplex(prob, NULL);
147 printf(" simplex=%d", r);
150 case e: printf(" " #e "\n"); goto out;
152 case e: printf(" " #e " CRASHING\n"); exit(-1);
154 default: printf(" ! CRASHING\n"); exit(-1);
172 r = glp_get_status(prob);
173 printf(" status=%d", r);
185 double got = glp_get_obj_val(prob);
194 if (best_prob) glp_delete_prob(best_prob);
197 free(best_adjmatrix);
198 best_adjmatrix = xalloc_adjmatrix();
199 memcpy(best_adjmatrix, adjmatrix, sizeof(*adjmatrix)*n);
205 glp_delete_prob(prob);
208 static void iterate_recurse(int i, AdjWord min) {
213 for (adjmatrix[i] = min;
216 iterate_recurse(i+1, adjmatrix[i]);
217 if (adjmatrix[i] == adjall)
222 static void iterate(void) {
223 iterate_recurse(0, 1);
226 int main(int argc, char **argv) {
231 if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }