#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
#include <inttypes.h>
#include <publib.h>
+#include <glpk.h>
typedef uint32_t AdjWord;
#define PRADJ "08"PRIx32
static int n, m;
+static AdjWord *adjmatrix_counters;
+static AdjWord *adjmatrix_offsets;
static AdjWord *adjmatrix;
static AdjWord adjall;
static double best;
+static glp_prob *best_prob;
+static AdjWord *best_adjmatrix;
+
+static unsigned printcounter;
+
+static AdjWord *xalloc_adjmatrix(void) {
+ return xmalloc(sizeof(*adjmatrix)*n);
+}
static void prep(void) {
+ int i;
adjall = ~((~(AdjWord)0) << m);
- adjmatrix = xmalloc(sizeof(*adjmatrix)*n);
+ adjmatrix = xalloc_adjmatrix();
+ adjmatrix_counters = xalloc_adjmatrix();
+ adjmatrix_offsets = xalloc_adjmatrix();
+ glp_term_out(GLP_OFF);
+ for (i=0; i<n; i++)
+ adjmatrix_offsets[i] = ((i+1)*(AdjWord)0x12345678) & adjall;
+}
+
+static AdjWord one_adj_bit(int bitnum) {
+ return (AdjWord)1 << bitnum;
}
static int count_set_adj_bits(AdjWord w) {
int j, total;
for (j=0, total=0; j<m; j++)
- total += !!(w & ((AdjWord)1 << j));
+ total += !!(w & one_adj_bit(j));
return total;
}
-static void optimise(void) {
- int i;
- for (i=0; i<n; i++) {
- printf("%"PRADJ" ", adjmatrix[i]);
- double maxminsize = (double)m / count_set_adj_bits(adjmatrix[i]);
- if (maxminsize < best) {
- printf(" too fine\n");
- return;
+static void optimise(int doprint) {
+ glp_prob *prob = 0;
+ int i, j, totalfrags;
+
+#define HAVE_PRINTED ({ \
+ if (!doprint) { doprint = 1; goto retry_with_print; } \
+ })
+ retry_with_print:
+#define PRINTF if (!doprint) ; else printf /* bodgy */
+
+ 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 / frags;
+ if (maxminsize <= best) {
+ PRINTF(" too fine");
+ goto out;
}
}
* fragment from old match i and making it part of new match j.
*
* The structural variables (columns) are:
- * x_fragsz_i_j the size of that fragment
- * x_minimum minimum size of any fragment
+ * 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, constraints) are:
+ * 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)
- * x_fragmin_i_j amount by which fragment is > minimum (lower bound 0)
*
- * The objective function is simply to maximise x_minimum
+ * 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.
*/
- printf("nyi\n");
+ 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(next_matrix_entry < matrix_entries_size); \
+ 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);
+ glp_set_col_name(prob, X_minimum, "minimum");
+
+ /* 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; i++) {
+ 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);
+ if (doprint) {
+ char buf[255];
+ snprintf(buf,sizeof(buf),"mf %d,%d",i,j);
+ glp_set_col_name(prob, X_morefrag_i_j, buf);
+ }
+
+ /* 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, matrix_entries_size-1,
+ matrix_entries_XY[1], matrix_entries_XY[0],
+ matrix_entries);
+
+ int r = glp_simplex(prob, NULL);
+ PRINTF(" glp=%d", r);
+
+#define OKERR(e) \
+ case e: PRINTF(" " #e ); goto out;
+#define BADERR(e) \
+ case e: HAVE_PRINTED; printf(" " #e " CRASHING\n"); exit(-1);
+#define DEFAULT \
+ default: HAVE_PRINTED; printf(" ! CRASHING\n"); exit(-1);
+
+ switch (r) {
+ OKERR(GLP_ESING);
+ OKERR(GLP_ECOND);
+ OKERR(GLP_EBOUND);
+ OKERR(GLP_EFAIL);
+ OKERR(GLP_ENOPFS);
+ OKERR(GLP_ENODFS);
+ BADERR(GLP_EBADB);
+ BADERR(GLP_EOBJLL);
+ BADERR(GLP_EOBJUL);
+ BADERR(GLP_EITLIM);
+ BADERR(GLP_ETMLIM);
+ BADERR(GLP_EINSTAB);
+ BADERR(GLP_ENOCVG);
+ case 0: break;
+ DEFAULT;
+ }
+
+ r = glp_get_status(prob);
+ PRINTF(" status=%d", r);
+
+ switch (r) {
+ OKERR(GLP_NOFEAS);
+ OKERR(GLP_UNDEF);
+ BADERR(GLP_FEAS);
+ BADERR(GLP_INFEAS);
+ BADERR(GLP_UNBND);
+ case GLP_OPT: break;
+ DEFAULT;
+ }
+
+ double got = glp_get_obj_val(prob);
+ PRINTF(" %g", got);
+ if (got <= best)
+ goto out;
+
+ HAVE_PRINTED;
+
+ best = got;
+
+ if (best_prob) glp_delete_prob(best_prob);
+ best_prob = prob;
+
+ free(best_adjmatrix);
+ best_adjmatrix = xalloc_adjmatrix();
+ memcpy(best_adjmatrix, adjmatrix, sizeof(*adjmatrix)*n);
+
+ printf(" BEST \n");
+ return;
+
+ }
+ out:
+ if (prob)
+ glp_delete_prob(prob);
+ if (doprint) { printf(" \r"); fflush(stdout); }
}
static void iterate_recurse(int i, AdjWord min) {
if (i >= n) {
- optimise();
+ int ii;
+ for (ii=0; ii<n; ii++) {
+ adjmatrix[ii] = adjmatrix_counters[ii] ^ adjmatrix_offsets[ii];
+ if (!adjmatrix[ii]) return;
+ }
+ printcounter++;
+ optimise(!(printcounter & 0xfff));
return;
}
- for (adjmatrix[i] = min;
+ for (adjmatrix_counters[i] = min;
;
- adjmatrix[i]++) {
- iterate_recurse(i+1, adjmatrix[i]);
- if (adjmatrix[i] == adjall)
+ adjmatrix_counters[i]++) {
+ iterate_recurse(i+1, adjmatrix_counters[i]);
+ if (adjmatrix_counters[i] == adjall)
return;
}
}
static void iterate(void) {
- iterate_recurse(0, 1);
+ iterate_recurse(0, 0);
}
int main(int argc, char **argv) {
m = atoi(argv[2]);
prep();
iterate();
+ printf("\n");
+ if (best_prob)
+ glp_print_sol(best_prob,"/dev/stdout");
if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
return 0;
}
~ianmdlvl / matchsticks-search.git / blobdiff