+/*
+ * Searches for "good" ways to divide n matchsticks up and reassemble them
+ * into m matchsticks. "Good" means the smallest fragment is as big
+ * as possible.
+ *
+ * Invoke as ./main n m
+ *
+ * The arguments must be ordered so that n > m:
+ * n is the number of (more, shorter) input matches of length m
+ * m is the number of (fewer, longer) output matches of length n
+ *
+ * Options:
+ * -j<jobs> run in parallel on <jobs> cores
+ * -b<best> search only for better than <best>
+ */
+
+/*
+ * matchsticks/main.c Copyright 2014 Ian Jackson
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ */
+
+#define _GNU_SOURCE
+
+#include <publib.h>
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
+#include <string.h>
#include <assert.h>
+#include <unistd.h>
+#include <stdbool.h>
#include <inttypes.h>
+#include <math.h>
+#include <sys/types.h>
+#include <sys/wait.h>
+#include <sys/uio.h>
+#include <sys/fcntl.h>
-#include <publib.h>
#include <glpk.h>
+#ifndef VERSION
+#define VERSION "(unknown-version)"
+#endif
+
+/*
+ * Algorithm.
+ *
+ * Each input match contributes, or does not contribute, to each
+ * output match; we do not need to consider multiple fragments
+ * relating to the same input/output pair this gives an n*m adjacency
+ * matrix (bitmap). Given such an adjacency matrix, the problem of
+ * finding the best sizes for the fragments can be expressed as a
+ * linear programming problem.
+ *
+ * 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: one word per input stick, with one bit per output
+ * stick.
+ *
+ * However, there are a couple of wrinkles:
+ *
+ * To best represent the problem as a standard LP problem, we separate
+ * out the size of each fragment into a common minimum size variable,
+ * plus a fragment-specific extra size variable. This reduces the LP
+ * problem size at the cost of making the problem construction, and
+ * interpretation of the results, a bit fiddly.
+ *
+ * Many of the adjacency matrices are equivalent. In particular,
+ * permutations of the columns, or of the rows, do not change the
+ * meaning. It is only necessasry to consider any one permutation.
+ * We make use of this by considering only adjacency matrices whose
+ * bitmap array contains bitmap words whose numerical values are
+ * nondecreasing in array order.
+ *
+ * Once we have a solution, we also avoid considering any candidate
+ * 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 by ensuring
+ * that it is not set in too few: each output stick must consist
+ * of at least two fragments since the output sticks are longer than
+ * the input ones.
+ *
+ * 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
+ * early allows us to eliminate a lot of candidates without doing the
+ * full LP.
+ */
+
typedef uint32_t AdjWord;
#define PRADJ "08"PRIx32
-static int n, m;
+#define FOR_BITS(j,m) for (j=0, j##bit=1; j < (m); j++, j##bit<<=1)
+
+static int n, m, maxhamweight;
static AdjWord *adjmatrix;
static AdjWord adjall;
static double best;
+static glp_prob *best_prob;
+static AdjWord *best_adjmatrix;
+
+static int n_max_frags=INT_MAX, m_max_frags=INT_MAX;
+static int *weight;
+
+static unsigned printcounter;
+
+static void iterate(void);
+static void iterate_recurse(int i, AdjWord min);
+static bool preconsider_ok(int nwords, bool doprint);
+static bool maxhamweight_ok(void);
+static void optimise(bool doprint);
+
+static void progress_eol(void) {
+ fprintf(stderr," \r");
+ fflush(stderr);
+}
+
+static void set_best(double new_best) {
+ best = new_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
+ *
+ * But best values from glpk are slightly approximate, so we
+ * subtract a fudge factor from our target.
+ */
+ double near_best = best * 0.98 - 0.02;
+ if (near_best > 0) {
+ n_max_frags = ceil(n / near_best) - 1;
+ m_max_frags = ceil(m / near_best) - 1;
+ }
+}
+
+/*----- multicore support -----*/
+
+/*
+ * Multicore protocol
+ *
+ * We fork into:
+ * - master (parent)
+ * - generator
+ * - ncpu workers
+ *
+ * ipc facilities:
+ * - one pipe ("work") from generator to workers
+ * - ever-extending file ("bus") containing new "best" values
+ * - one file for each worker giving maxhamweight and adjmatrix for best
+ *
+ * generator runs iterate_recurse to a certain depth and writes the
+ * candidates to a pipe
+ *
+ * workers read candidates from the pipe and resume iterate_recurse
+ * halfway through the recursion
+ *
+ * whenever a worker does a doprint, it checks the bus for new best
+ * value; actual best values are appended
+ *
+ * master waits for generator and all workers to finish and then
+ * runs optimise() for each worker's best, then prints
+ */
+
+static int ncpus = 0, multicore_iteration_boundary = INT_MAX;
+
+static int mc_bus, mc_work[2];
+static off_t mc_bus_read;
+
+typedef struct {
+ int w;
+ FILE *results;
+ pid_t pid;
+} Worker;
+static Worker *mc_us;
+static bool mc_am_generator;
+
+static void multicore_check_for_new_best(void);
+
+#define MAX_NIOVS 4
+static AdjWord mc_iter_min;
+static int mc_niovs;
+static size_t mc_iovlen;
+static struct iovec mc_iov[MAX_NIOVS];
+
+#define IOV0 (mc_niovs = mc_iovlen = 0)
+
+#define IOV(obj, count) ({ \
+ assert(mc_niovs < MAX_NIOVS); \
+ mc_iov[mc_niovs].iov_base = &(obj); \
+ mc_iov[mc_niovs].iov_len = sizeof(obj) * (count); \
+ mc_iovlen += mc_iov[mc_niovs].iov_len; \
+ mc_niovs++; \
+ })
+
+static void mc_rwvsetup_outer(void) {
+ IOV0;
+ IOV(maxhamweight, 1);
+ IOV(mc_iter_min, 1);
+ IOV(*adjmatrix, multicore_iteration_boundary);
+ IOV(*weight, m);
+}
+
+static void mc_rwvsetup_full(void) {
+ IOV0;
+ IOV(*adjmatrix, n);
+}
+
+static void vlprintf(const char *fmt, va_list al) {
+ vfprintf(stderr,fmt,al);
+ progress_eol();
+}
+
+static void LPRINTF(const char *fmt, ...) {
+ va_list al;
+ va_start(al,fmt);
+ vlprintf(fmt,al);
+ va_end(al);
+}
+
+static void mc_awaitpid(int wnum, pid_t pid) {
+ LPRINTF("master awaiting %2d [%ld]",wnum,(long)pid);
+ int status;
+ pid_t got = waitpid(pid, &status, 0);
+ assert(got == pid);
+ if (status) {
+ fprintf(stderr,"\nFAILED SUBPROC %2d [%ld] %d\n",
+ wnum, (long)pid, status);
+ exit(-1);
+ }
+}
+
+static void multicore_outer_iteration(int i, AdjWord min) {
+ static unsigned check_counter;
+
+ assert(i == multicore_iteration_boundary);
+ mc_iter_min = min;
+ mc_rwvsetup_outer();
+ ssize_t r = writev(mc_work[1], mc_iov, mc_niovs);
+ assert(r == mc_iovlen);
+ /* effectively, this writev arranges to transfers control
+ * to some worker's instance of iterate_recurse via mc_iterate_worker */
+
+ if (!(check_counter++ & 0xff))
+ multicore_check_for_new_best();
+}
+
+static void mc_iterate_worker(void) {
+ static time_t lastprint;
+
+ for (;;) {
+ mc_rwvsetup_outer();
+ ssize_t r = readv(mc_work[0], mc_iov, mc_niovs);
+ if (r == 0) break;
+ assert(r == mc_iovlen);
+
+ bool ok = maxhamweight_ok();
+ if (!ok) continue;
+
+ time_t now = time(0);
+ bool doprint = now != lastprint;
+ lastprint = now;
+
+ ok = preconsider_ok(multicore_iteration_boundary, doprint);
+ if (doprint) progress_eol();
+ if (!ok) continue;
+
+ /* stop iterate_recurse from trying to run multicore_outer_iteration */
+ int mc_org_it_bound = multicore_iteration_boundary;
+ multicore_iteration_boundary = INT_MAX;
+ iterate_recurse(mc_org_it_bound, mc_iter_min);
+ multicore_iteration_boundary = mc_org_it_bound;
+ }
+ if (best_adjmatrix) {
+ LPRINTF("worker %2d reporting",mc_us->w);
+ adjmatrix = best_adjmatrix;
+ mc_rwvsetup_full();
+ ssize_t r = writev(fileno(mc_us->results), mc_iov, mc_niovs);
+ assert(r == mc_iovlen);
+ }
+ LPRINTF("worker %2d ending",mc_us->w);
+ exit(0);
+}
+
+static void multicore(void) {
+ Worker *mc_workers;
+ int w;
+ pid_t genpid;
+
+ multicore_iteration_boundary = n / 2;
+
+ FILE *busf = tmpfile(); assert(busf);
+ mc_bus = fileno(busf);
+ int r = fcntl(mc_bus, F_GETFL); assert(r >= 0);
+ r |= O_APPEND;
+ r = fcntl(mc_bus, F_SETFL, r); assert(r >= 0);
+
+ r = pipe(mc_work); assert(!r);
+
+ mc_workers = xmalloc(sizeof(*mc_workers) * ncpus);
+ for (w=0; w<ncpus; w++) {
+ mc_workers[w].w = w;
+ mc_workers[w].results = tmpfile(); assert(mc_workers[w].results);
+ mc_workers[w].pid = fork(); assert(mc_workers[w].pid >= 0);
+ if (!mc_workers[w].pid) {
+ mc_us = &mc_workers[w];
+ close(mc_work[1]);
+ LPRINTF("worker %2d running", w);
+ mc_iterate_worker();
+ exit(0);
+ }
+ }
+
+ close(mc_work[0]);
+
+ genpid = fork(); assert(genpid >= 0);
+ if (!genpid) {
+ mc_am_generator = 1;
+ LPRINTF("generator running");
+ iterate();
+ exit(0);
+ }
+
+ close(mc_work[1]);
+ mc_awaitpid(-1, genpid);
+ for (w=0; w<ncpus; w++)
+ mc_awaitpid(w, mc_workers[w].pid);
+
+ for (w=0; w<ncpus; w++) {
+ mc_rwvsetup_full();
+ LPRINTF("reading report from %2d",w);
+ ssize_t sr = preadv(fileno(mc_workers[w].results), mc_iov, mc_niovs, 0);
+ if (!sr) continue;
+ LPRINTF("got report from %2d",w);
+ maxhamweight = 0;
+ optimise(1);
+ }
+}
+
+static void multicore_check_for_new_best(void) {
+ if (!(mc_us || mc_am_generator))
+ return;
+
+ for (;;) {
+ double msg;
+ ssize_t got = pread(mc_bus, &msg, sizeof(msg), mc_bus_read);
+ if (!got) break;
+ assert(got == sizeof(msg));
+ if (msg > best)
+ set_best(msg);
+ mc_bus_read += sizeof(msg);
+ }
+}
+
+static void multicore_found_new_best(void) {
+ if (!mc_us)
+ return;
+
+ if (mc_us /* might be master */) fprintf(stderr," w%-2d ",mc_us->w);
+ ssize_t wrote = write(mc_bus, &best, sizeof(best));
+ assert(wrote == sizeof(best));
+}
+
+/*----- end of multicore support -----*/
+
+static AdjWord *xalloc_adjmatrix(void) {
+ return xmalloc(sizeof(*adjmatrix)*n);
+}
static void prep(void) {
adjall = ~((~(AdjWord)0) << m);
- adjmatrix = xmalloc(sizeof(*adjmatrix)*n);
+ adjmatrix = xalloc_adjmatrix();
+ glp_term_out(GLP_OFF);
+ setlinebuf(stderr);
+ weight = calloc(sizeof(*weight), m); assert(weight);
}
+#if 0
static AdjWord one_adj_bit(int bitnum) {
return (AdjWord)1 << bitnum;
}
+#endif
static int count_set_adj_bits(AdjWord w) {
- int j, total;
- for (j=0, total=0; j<m; j++)
- total += !!(w & one_adj_bit(j));
+ int j, total = 0;
+ AdjWord jbit;
+ FOR_BITS(j,m)
+ total += !!(w & jbit);
return total;
}
-static void optimise(void) {
- int i, j, totalfrags;
+#define PRINTF(...) if (!doprint) ; else fprintf(stderr, __VA_ARGS__)
+
+static int totalfrags;
+
+static bool maxhamweight_ok(void) {
+ return maxhamweight <= m_max_frags;
+}
+
+static bool preconsider_ok(int nwords, bool doprint) {
+ int i;
+
+ PRINTF("%2d ", maxhamweight);
- for (i=0, totalfrags=0; i<n; i++) {
+ bool had_max = 0;
+ for (i=0, totalfrags=0; i<nwords; 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\n");
- return;
+ PRINTF("%"PRADJ" ", adjmatrix[i]);
+ if (frags > m_max_frags) {
+ PRINTF(" too fine");
+ goto out;
}
+ had_max += (frags >= maxhamweight);
+ totalfrags += frags;
+ }
+ if (!had_max) {
+ /* Skip this candidate as its max hamming weight is lower than
+ * we're currently looking for (which means we must have done it
+ * already). (The recursive iteration ensures that none of the
+ * words have more than the max hamming weight.) */
+ PRINTF(" nomaxham");
+ goto out;
}
+ return 1;
+
+ out:
+ return 0;
+}
+
+static void optimise(bool doprint) {
+ /* Consider the best answer (if any) for a given adjacency matrix */
+ glp_prob *prob = 0;
+ int i, j;
+ AdjWord jbit;
+
+ /*
+ * Up to a certain point, optimise() can be restarted. We use this
+ * to go back and print the debugging output if it turns out that we
+ * have an interesting case. The HAVE_PRINTED macro does this: its
+ * semantics are to go back in time and make sure that we have
+ * printed the description of the search case.
+ */
+#define HAVE_PRINTED ({ \
+ if (!doprint) { doprint = 1; goto retry_with_print; } \
+ })
+ retry_with_print:
+ if (prob) {
+ glp_delete_prob(prob);
+ prob = 0;
+ }
+
+ bool ok = preconsider_ok(n, doprint);
+ if (!ok)
+ goto out;
/*
* We formulate our problem as an LP problem as follows.
* which we build up as we go.
*/
- glp_prob *prob = glp_create_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; \
+ 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_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 */
+ /* \forall_i x_total_i = m */
+ /* \forall_i x_total_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; j++) {
- for (j=0; j<m; j++) {
- if (!(adjmatrix[i] & one_adj_bit(j)))
+ for (i=0; i<n; i++) {
+ FOR_BITS(j,m) {
+ if (!(adjmatrix[i] & jbit))
continue;
/* x_total_i += x_minimum */
/* x_total_j += x_minimum */
/* 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 */
assert(next_matrix_entry == matrix_entries_size);
- glp_load_matrix(prob, next_matrix_entry,
+ glp_load_matrix(prob, matrix_entries_size-1,
matrix_entries_XY[1], matrix_entries_XY[0],
matrix_entries);
- printf("nyi\n");
+ 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;
+
+ set_best(got);
+ multicore_found_new_best();
+
+ 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) progress_eol();
+ if (doprint) multicore_check_for_new_best();
}
static void iterate_recurse(int i, AdjWord min) {
+ int j;
+ AdjWord jbit;
+
if (i >= n) {
- optimise();
+ for (j=0; j<m; j++)
+ if (weight[j] < 2)
+ return;
+
+ printcounter++;
+ optimise(!(printcounter & 0xfff));
+ return;
+ }
+ if (i >= multicore_iteration_boundary) {
+ multicore_outer_iteration(i, min);
return;
}
for (adjmatrix[i] = min;
;
adjmatrix[i]++) {
+ if (count_set_adj_bits(adjmatrix[i]) > maxhamweight)
+ goto again;
+ if (i == 0 && (adjmatrix[i] & (1+adjmatrix[i])))
+ goto again;
+
+ FOR_BITS(j,m)
+ if (adjmatrix[i] & jbit)
+ weight[j]++;
+ for (int j = 0; j < m; j++)
+ if (weight[j] > n_max_frags)
+ goto takeout;
+
iterate_recurse(i+1, adjmatrix[i]);
+
+ takeout:
+ FOR_BITS(j,m)
+ if (adjmatrix[i] & jbit)
+ weight[j]--;
+
+ again:
if (adjmatrix[i] == adjall)
return;
}
}
static void iterate(void) {
- iterate_recurse(0, 1);
+ for (maxhamweight=1; maxhamweight<=m; maxhamweight++) {
+ if (!maxhamweight_ok())
+ continue;
+
+ iterate_recurse(0, 1);
+ }
}
+static int gcd(int a, int b)
+{
+ assert(a>0);
+ assert(b>0);
+ while (b) {
+ int t = a % b;
+ a = b;
+ b = t;
+ }
+ return a;
+}
+
+static void print_rational(int n, int d)
+{
+ int g = gcd(n, d);
+ n /= g;
+ d /= g;
+ printf("%d", n);
+ if (d > 1)
+ printf("/%d", d);
+}
+
+#define MAKE_INT_VECTOR_COMPARATOR(thing) \
+ static int compare_ints_##thing(const void *av, const void *bv) \
+ { \
+ const int *a = (const int *)av; \
+ const int *b = (const int *)bv; \
+ int i; \
+ for (i = 0; i < (thing); i++) \
+ if (a[i] != b[i]) \
+ return a[i] > b[i] ? -1 : +1; \
+ return 0; \
+ }
+/* Good grief, if only qsort let me pass a context parameter */
+MAKE_INT_VECTOR_COMPARATOR(1)
+MAKE_INT_VECTOR_COMPARATOR(m)
+MAKE_INT_VECTOR_COMPARATOR(n)
+
+static void report(void) {
+ fprintf(stderr, "\n");
+ if (best_adjmatrix) {
+ int i;
+ fprintf(stderr," ");
+ for (i=0; i<n; i++) fprintf(stderr, " %"PRADJ, best_adjmatrix[i]);
+ }
+ fprintf(stderr, " best=%-12.8f nf<=%d mf<=%d\n",
+ best, n_max_frags, m_max_frags);
+ printf("%d into %d: ", n, m);
+ if (best_prob) {
+ double min = glp_get_obj_val(best_prob);
+ double a[n][m];
+ int ai[n][m];
+ int i, j, k, d, cols, imin;
+ for (i = 0; i < n; i++)
+ for (j = 0; j < m; j++)
+ a[i][j] = 0;
+ cols = glp_get_num_cols(best_prob);
+ for (i = 1; i <= cols; i++) {
+ int x, y;
+ if (2 != sscanf(glp_get_col_name(best_prob, i), "mf %d,%d", &x, &y))
+ continue;
+ a[x][y] = min + glp_get_col_prim(best_prob, i);
+ }
+
+ /*
+ * Try to find a denominator over which all these numbers turn
+ * sensibly into rationals.
+ */
+ for (d = 1;; d++) {
+ /*
+ * Round everything to the nearest multiple of d.
+ */
+ for (i = 0; i < n; i++)
+ for (j = 0; j < m; j++)
+ ai[i][j] = a[i][j] * d + 0.5;
+
+ /*
+ * Ensure the rows and columns add up correctly.
+ */
+ for (i = 0; i < n; i++) {
+ int total = 0;
+ for (j = 0; j < m; j++)
+ total += ai[i][j];
+ if (total != d*m)
+ goto next_d;
+ }
+ for (j = 0; j < m; j++) {
+ int total = 0;
+ for (i = 0; i < n; i++)
+ total += ai[i][j];
+ if (total != d*n)
+ goto next_d;
+ }
+
+ /*
+ * Ensure we haven't rounded a good solution to a worse one, by
+ * finding the new minimum fragment and making sure it's at
+ * least the one we previously had.
+ */
+ imin = d*n;
+ for (i = 0; i < n; i++)
+ for (j = 0; j < m; j++)
+ if (ai[i][j] > 0 && ai[i][j] < imin)
+ imin = ai[i][j];
+
+ if (abs((double)imin / d - min) > 1e-10)
+ goto next_d;
+
+ /*
+ * Got it! We've found a rational-valued dissection.
+ */
+ printf("min fragment ");
+ print_rational(imin, d);
+ printf(" [%s]\n", VERSION);
+
+ /*
+ * We don't really want to output the matrix, so instead let's
+ * output the ways in which the sticks are cut up.
+ */
+ {
+ int ai2[m][n];
+ for (i = 0; i < n; i++) {
+ for (j = 0; j < m; j++)
+ ai2[j][i] = ai[i][j];
+ }
+ for (i = 0; i < n; i++)
+ qsort(ai+i, m, sizeof(int), compare_ints_1);
+ qsort(ai, n, m*sizeof(int), compare_ints_m);
+ printf(" Cut up %d sticks of length %d like this:\n", n, m);
+ for (i = 0; i < n ;) {
+ for (j = 1; i+j < n && compare_ints_m(ai+i, ai+i+j) == 0; j++);
+ printf(" %d x (", j);
+ for (k = 0; k < m && ai[i][k] > 0; k++) {
+ if (k > 0) printf(" + ");
+ print_rational(ai[i][k], d);
+ }
+ printf(")\n");
+ i += j;
+ }
+
+ for (j = 0; j < m; j++)
+ qsort(ai2+j, n, sizeof(int), compare_ints_1);
+ qsort(ai2, m, n*sizeof(int), compare_ints_n);
+ printf(" Reassemble as %d sticks of length %d like this:\n", m, n);
+ for (j = 0; j < m ;) {
+ for (i = 1; i+j < m && compare_ints_n(ai2+j, ai2+j+i) == 0; i++);
+ printf(" %d x (", i);
+ for (k = 0; k < n && ai2[j][k] > 0; k++) {
+ if (k > 0) printf(" + ");
+ print_rational(ai2[j][k], d);
+ }
+ printf(")\n");
+ j += i;
+ }
+ }
+ return;
+
+ next_d:;
+ }
+ } else {
+ printf(" none better than %9.3f [%s]\n", best, VERSION);
+ }
+ if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
+}
+
int main(int argc, char **argv) {
+ int opt;
+ double best_to_set = -1.0; /* means 'don't' */
+ while ((opt = getopt(argc,argv,"j:b:")) >= 0) {
+ switch (opt) {
+ case 'j': ncpus = atoi(optarg); break;
+ case 'b': best_to_set = atof(optarg); break;
+ case '+': assert(!"bad option");
+ default: abort();
+ }
+ }
+ argc -= optind-1;
+ argv += optind-1;
+ assert(argc==3);
n = atoi(argv[1]);
m = atoi(argv[2]);
+ assert(n > m);
+ if (best_to_set > 0) set_best(best_to_set);
+
prep();
- iterate();
- if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
+
+ if (ncpus) multicore();
+ else iterate();
+
+ report();
return 0;
}
~ianmdlvl / matchsticks-search.git / blobdiff