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 unsigned printcounter;
25 static AdjWord *xalloc_adjmatrix(void) {
26 return xmalloc(sizeof(*adjmatrix)*n);
29 static void prep(void) {
30 adjall = ~((~(AdjWord)0) << m);
31 adjmatrix = xalloc_adjmatrix();
32 glp_term_out(GLP_OFF);
35 static AdjWord one_adj_bit(int bitnum) {
36 return (AdjWord)1 << bitnum;
39 static int count_set_adj_bits(AdjWord w) {
41 for (j=0, total=0; j<m; j++)
42 total += !!(w & one_adj_bit(j));
46 static void optimise(int doprint) {
50 #define HAVE_PRINTED ({ \
51 if (!doprint) { doprint = 1; goto retry_with_print; } \
54 #define PRINTF if (!doprint) ; else printf /* bodgy */
56 for (i=0, totalfrags=0; i<n; i++) {
57 int frags = count_set_adj_bits(adjmatrix[i]);
59 PRINTF("%"PRADJ" ", adjmatrix[i]);
60 double maxminsize = (double)m / frags;
61 if (maxminsize <= best) {
68 * We formulate our problem as an LP problem as follows.
69 * In this file "n" and "m" are the matchstick numbers.
71 * Each set bit in the adjacency matrix corresponds to taking a
72 * fragment from old match i and making it part of new match j.
74 * The structural variables (columns) are:
75 * x_minimum minimum size of any fragment (bounded below by 0)
76 * x_morefrag_i_j the amount by which the size of the fragment
77 * i,j exceeds the minimum size (bounded below by 0)
79 * The auxiliary variables (rows) are:
80 * x_total_i total length for each input match (fixed variable)
81 * x_total_j total length for each output match (fixed variable)
83 * The objective function is simply
86 * We use X_ and Y_ to refer to GLPK's (1-based) column and row indices.
87 * ME_ refers to entries in the list of constraint matrix elements
88 * which we build up as we go.
91 prob = glp_create_prob();
93 int Y_totals_i = glp_add_rows(prob, n);
94 int Y_totals_j = glp_add_rows(prob, m);
95 int X_minimum = glp_add_cols(prob, 1);
98 int next_matrix_entry = 1; /* wtf GLPK! */
99 int matrix_entries_size = next_matrix_entry + n + m + totalfrags*2;
100 double matrix_entries[matrix_entries_size];
101 int matrix_entries_XY[2][matrix_entries_size];
103 #define ADD_MATRIX_ENTRY(Y,X) ({ \
104 assert(next_matrix_entry < matrix_entries_size); \
105 matrix_entries_XY[0][next_matrix_entry] = (X); \
106 matrix_entries_XY[1][next_matrix_entry] = (Y); \
107 matrix_entries[next_matrix_entry] = 0; \
108 next_matrix_entry++; \
111 int ME_totals_i__minimum = next_matrix_entry;
112 for (i=0; i<n; i++) ADD_MATRIX_ENTRY(Y_totals_i+i, X_minimum);
114 int ME_totals_j__minimum = next_matrix_entry;
115 for (j=0; j<m; j++) ADD_MATRIX_ENTRY(Y_totals_j+j, X_minimum);
117 /* \forall_i x_totals_i = m */
118 /* \forall_i x_totals_j = n */
119 for (i=0; i<n; i++) glp_set_row_bnds(prob, Y_totals_i+i, GLP_FX, m,m);
120 for (j=0; j<m; j++) glp_set_row_bnds(prob, Y_totals_j+j, GLP_FX, n,n);
123 glp_set_col_bnds(prob, X_minimum, GLP_LO, 0, 0);
124 glp_set_col_name(prob, X_minimum, "minimum");
126 /* objective is maximising x_minimum */
127 glp_set_obj_dir(prob, GLP_MAX);
128 glp_set_obj_coef(prob, X_minimum, 1);
130 for (i=0; i<n; i++) {
131 for (j=0; j<m; j++) {
132 if (!(adjmatrix[i] & one_adj_bit(j)))
134 /* x_total_i += x_minimum */
135 /* x_total_j += x_minimum */
136 matrix_entries[ ME_totals_i__minimum + i ] ++;
137 matrix_entries[ ME_totals_j__minimum + j ] ++;
139 /* x_morefrag_i_j >= 0 */
140 int X_morefrag_i_j = glp_add_cols(prob, 1);
141 glp_set_col_bnds(prob, X_morefrag_i_j, GLP_LO, 0, 0);
144 snprintf(buf,sizeof(buf),"mf %d,%d",i,j);
145 glp_set_col_name(prob, X_morefrag_i_j, buf);
148 /* x_total_i += x_morefrag_i_j */
149 /* x_total_j += x_morefrag_i_j */
150 int ME_totals_i__mf_i_j = ADD_MATRIX_ENTRY(Y_totals_i+i, X_morefrag_i_j);
151 int ME_totals_j__mf_i_j = ADD_MATRIX_ENTRY(Y_totals_j+j, X_morefrag_i_j);
152 matrix_entries[ME_totals_i__mf_i_j] = 1;
153 matrix_entries[ME_totals_j__mf_i_j] = 1;
157 assert(next_matrix_entry == matrix_entries_size);
159 glp_load_matrix(prob, matrix_entries_size-1,
160 matrix_entries_XY[1], matrix_entries_XY[0],
163 int r = glp_simplex(prob, NULL);
164 PRINTF(" glp=%d", r);
167 case e: PRINTF(" " #e ); goto out;
169 case e: HAVE_PRINTED; printf(" " #e " CRASHING\n"); exit(-1);
171 default: HAVE_PRINTED; printf(" ! CRASHING\n"); exit(-1);
191 r = glp_get_status(prob);
192 PRINTF(" status=%d", r);
204 double got = glp_get_obj_val(prob);
213 if (best_prob) glp_delete_prob(best_prob);
216 free(best_adjmatrix);
217 best_adjmatrix = xalloc_adjmatrix();
218 memcpy(best_adjmatrix, adjmatrix, sizeof(*adjmatrix)*n);
226 glp_delete_prob(prob);
227 if (doprint) { printf(" \r"); fflush(stdout); }
230 static void iterate_recurse(int i, AdjWord min) {
233 optimise(!(printcounter & 0xfff));
236 for (adjmatrix[i] = min;
239 iterate_recurse(i+1, adjmatrix[i]);
240 if (adjmatrix[i] == adjall)
245 static void iterate(void) {
246 iterate_recurse(0, 1);
249 int main(int argc, char **argv) {
256 glp_print_sol(best_prob,"/dev/stdout");
257 if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }