X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?p=matchsticks-search.git;a=blobdiff_plain;f=main.c;h=93dc7ebe5325269db8fda05f5fe954a081489ed3;hp=15b534bd3bc3c9eb0447b059e5bf013de4969b44;hb=a7a2c255e61d14619fce2e4af2eeee1d2ed6d870;hpb=3164b7155efcca47cfedccb778b5a7471629e2f4

diff --git a/main.c b/main.c
index 15b534b..93dc7eb 100644
--- a/main.c
+++ b/main.c
@@ -1,18 +1,99 @@
+/*
+ * 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 <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.
+ *
+ * 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
 
+#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;
@@ -21,8 +102,261 @@ static double best;
 static glp_prob *best_prob;
 static AdjWord *best_adjmatrix;
 
+static int n_max_frags, m_max_frags;
+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
+   */
+  n_max_frags = ceil(n / best) - 1;
+  m_max_frags = ceil(m / 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) {
+  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;
+
+    ok = preconsider_ok(multicore_iteration_boundary, 1);
+    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);
 }
@@ -31,47 +365,89 @@ static void prep(void) {
   adjall = ~((~(AdjWord)0) << m);
   adjmatrix = xalloc_adjmatrix();
   glp_term_out(GLP_OFF);
+  setlinebuf(stderr);
+  weight = calloc(sizeof(*weight), m);  assert(weight);
+  n_max_frags = INT_MAX;
+  m_max_frags = INT_MAX;
 }
 
+#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(int doprint) {
-  glp_prob *prob = 0;
-  int i, j, totalfrags;
+#define PRINTF(...) if (!doprint) ; else fprintf(stderr, __VA_ARGS__)
 
-#define HAVE_PRINTED ({						\
-      if (!doprint) { doprint = 1; goto retry_with_print; }	\
-    })
- retry_with_print:
-#define PRINTF if (!doprint) ; else printf /* bodgy */
+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);
 
   bool had_max = 0;
-  for (i=0, totalfrags=0; i<n; i++) {
+  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]);
-    double maxminsize = (double)m / frags;
-    if (maxminsize <= best) {
+    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.
@@ -123,8 +499,8 @@ static void optimise(int doprint) {
   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);
 
@@ -137,8 +513,8 @@ static void optimise(int doprint) {
   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)))
+    FOR_BITS(j,m) {
+      if (!(adjmatrix[i] & jbit))
 	continue;
       /* x_total_i += x_minimum */
       /* x_total_j += x_minimum */
@@ -217,7 +593,8 @@ static void optimise(int doprint) {
 
   HAVE_PRINTED;
 
-  best = got;
+  set_best(got);
+  multicore_found_new_best();
 
   if (best_prob) glp_delete_prob(best_prob);
   best_prob = prob;
@@ -226,30 +603,52 @@ static void optimise(int doprint) {
   best_adjmatrix = xalloc_adjmatrix();
   memcpy(best_adjmatrix, adjmatrix, sizeof(*adjmatrix)*n);
 
-  printf(" BEST        \n");
+  PRINTF(" BEST        \n");
   return;
 
   }
  out:
   if (prob)
     glp_delete_prob(prob);
-  if (doprint) { printf("        \r"); fflush(stdout); }
+  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) {
     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;
@@ -258,22 +657,63 @@ static void iterate_recurse(int i, AdjWord min) {
 
 static void iterate(void) {
   for (maxhamweight=1; maxhamweight<=m; maxhamweight++) {
-    double maxminsize = (double)m / maxhamweight;
-    if (maxminsize <= best)
+    if (!maxhamweight_ok())
       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   [%s]\n", n, m, min, VERSION);
+    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();
-  printf("\n");
-  if (best_prob)
-    glp_print_sol(best_prob,"/dev/stdout");
-  if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
+
+  if (ncpus) multicore();
+  else iterate();
+
+  report();
   return 0;
 }