X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?p=matchsticks-search.git;a=blobdiff_plain;f=main.c;h=8d006d9ca40e6cb35ea4428590ba4cc3d9b1e03e;hp=e246752ef153b4272fb333f13e511fd05aa38252;hb=ebbb693300bda9dcba0caf74f12cded3d6c1786f;hpb=34b443b35453ef92904c2ec6d22a998d6078d028

diff --git a/main.c b/main.c
index e246752..8d006d9 100644
--- a/main.c
+++ b/main.c
@@ -1,27 +1,329 @@
+/*
+ * 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 algorithm is faster if the arguments are ordered so that n > m.
+ */
+
+/*
+ * 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 <sys/types.h>
+#include <sys/wait.h>
+#include <sys/uio.h>
+#include <sys/fcntl.h>
 
-#include <publib.h>
+#include <glpk.h>
+
+/*
+ * 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.
+ *
+ * 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 output 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.
+ *
+ * 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;
+static int n, m, maxhamweight;
 static AdjWord *adjmatrix;
 static AdjWord adjall;
 
 static double best;
+static glp_prob *best_prob;
+static AdjWord *best_adjmatrix;
+
+static unsigned printcounter;
+
+static void iterate(void);
+static void iterate_recurse(int i, AdjWord min);
+static bool preconsider_ok(int nwords, bool doprint);
+static void optimise(bool doprint);
+
+static void progress_eol(void) {
+  fprintf(stderr,"        \r");
+  fflush(stderr);
+}
+
+/*----- 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 void multicore_check_for_new_best(void);
+
+#define MAX_NIOVS 3
+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);
+}
+
+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) {
+  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 */
+}
+
+static void mc_iterate_worker(void) {
+  for (;;) {
+    mc_rwvsetup_outer();
+    ssize_t r = readv(mc_work[0], mc_iov, mc_niovs);
+    if (r == 0) break;
+    assert(r == mc_iovlen);
+
+    /* 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;
+  }
+  LPRINTF("worker %2d reporting",mc_us->w);
+  if (best_adjmatrix) {
+    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) {
+    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;
+    maxhamweight = 0;
+    optimise(1);
+  }
+}
+
+static void multicore_check_for_new_best(void) {
+  if (!ncpus) 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)
+      best = msg;
+    mc_bus_read += sizeof(msg);
+  }
+}
+
+static void multicore_found_new_best(void) {
+  if (!ncpus) 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);
 }
 
 static AdjWord one_adj_bit(int bitnum) {
-  return (AdjWord)1 << j;
+  return (AdjWord)1 << bitnum;
 }
 
 static int count_set_adj_bits(AdjWord w) {
@@ -31,18 +333,65 @@ static int count_set_adj_bits(AdjWord w) {
   return total;
 }
 
-static void optimise(void) {
-  int i, totalfrags;
-  for (i=0, totalfrags=0; i<n; i++) {
+#define PRINTF(...) if (!doprint) ; else fprintf(stderr, __VA_ARGS__)
+
+static int totalfrags;
+
+static bool preconsider_ok(int nwords, bool doprint) {
+  int i;
+
+  PRINTF("%2d ", maxhamweight);
+
+  bool had_max = 0;
+  for (i=0, totalfrags=0; i<nwords; i++) {
     int frags = count_set_adj_bits(adjmatrix[i]);
+    had_max += (frags >= maxhamweight);
     totalfrags += frags;
-    printf("%"PRADJ" ", adjmatrix[i]);
+    PRINTF("%"PRADJ" ", adjmatrix[i]);
     double maxminsize = (double)m / frags;
-    if (maxminsize < best) {
-      printf(" too fine\n");
-      return;
+    if (maxminsize <= best) {
+      PRINTF(" too fine");
+      goto out;
     }
   }
+  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;
+
+  /*
+   * 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.
@@ -68,23 +417,22 @@ static void optimise(void) {
    * 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, i);
-  int Y_totals_j = glp_add_rows(prob, j);
+  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 rows = glp_get_num_rows(prob);
-  int cols = glp_get_num_rows(cols);
 
+  {
   int next_matrix_entry = 1; /* wtf GLPK! */
-  int matrix_entries_size = next_matrix_entry + i + j + totalfrags*2;
+  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++;				\
     })
@@ -95,19 +443,20 @@ static void optimise(void) {
   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_bounds(prob, Y_totals_i+i, GLP_FX, m,m);
-  for (j=0; j<m; j++) glp_set_row_bounds(prob, Y_totals_j+j, GLP_FX, n,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_bounds(prob, X_minimum, GLP_LB, 0, 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 (i=0; i<n; i++) {
     for (j=0; j<m; j++) {
       if (!(adjmatrix[i] & one_adj_bit(j)))
 	continue;
@@ -119,6 +468,11 @@ static void optimise(void) {
       /* 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 */
@@ -131,37 +485,165 @@ static void optimise(void) {
 
   assert(next_matrix_entry == matrix_entries_size);
 
-  for (row=1; row<=rows; row++) {
-    glp_load_matrix(prob, next_matrix_entry,
-		    matrix_entries_XY[1], matrix_entries_XY[0],
-		    matrix_entries);
+  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;
+  multicore_found_new_best();
+
+  if (best_prob) glp_delete_prob(best_prob);
+  best_prob = prob;
 
-  printf("nyi\n");
+  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) {
   if (i >= n) {
-    optimise();
+    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;
+
     iterate_recurse(i+1, adjmatrix[i]);
+
+  again:
     if (adjmatrix[i] == adjall)
       return;
   }
 }
 
 static void iterate(void) {
-  iterate_recurse(0, 1);
+  for (maxhamweight=1; maxhamweight<=m; maxhamweight++) {
+    double maxminsize = (double)m / maxhamweight;
+    if (maxminsize <= best)
+      continue;
+
+    iterate_recurse(0, 1);
+  }
 }
 
+static void report(void) {
+  fprintf(stderr, "\n");
+  if (best_prob) {
+    double min = glp_get_obj_val(best_prob);
+    double a[n][m];
+    int i, j, cols;
+    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);
+    }
+    printf("%d into %d: min fragment %g\n", n, m, min);
+    for (i = 0; i < n; i++) {
+      for (j = 0; j < m; j++) {
+        if (a[i][j])
+          printf(" %9.3f", a[i][j]);
+        else
+          printf("          ");
+      }
+      printf("\n");
+    }
+  }
+  if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
+}
+ 
 int main(int argc, char **argv) {
+  int opt;
+  while ((opt = getopt(argc,argv,"j:")) >= 0) {
+    switch (opt) {
+    case 'j': ncpus = atoi(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]);
+
   prep();
-  iterate();
-  if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
+
+  if (ncpus) multicore();
+  else iterate();
+
+  report();
   return 0;
 }