comparison DEPENDENCIES/generic/include/boost/pending/relaxed_heap.hpp @ 16:2665513ce2d3

Add boost headers

+// Copyright 2004 The Trustees of Indiana University.
+
+// Use, modification and distribution is subject to the Boost Software
+// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+//  Authors: Douglas Gregor
+//           Andrew Lumsdaine
+#ifndef BOOST_RELAXED_HEAP_HEADER
+#define BOOST_RELAXED_HEAP_HEADER
+
+#include <functional>
+#include <boost/property_map/property_map.hpp>
+#include <boost/optional.hpp>
+#include <vector>
+#include <climits> // for CHAR_BIT
+#include <boost/none.hpp>
+
+#ifdef BOOST_RELAXED_HEAP_DEBUG
+#  include <iostream>
+#endif // BOOST_RELAXED_HEAP_DEBUG
+
+#if defined(BOOST_MSVC)
+#  pragma warning(push)
+#  pragma warning(disable:4355) // complaint about using 'this' to
+#endif                          // initialize a member
+
+namespace boost {
+
+template<typename IndexedType,
+         typename Compare = std::less<IndexedType>,
+         typename ID = identity_property_map>
+class relaxed_heap
+{
+  struct group;
+
+  typedef relaxed_heap self_type;
+  typedef std::size_t  rank_type;
+
+public:
+  typedef IndexedType  value_type;
+  typedef rank_type    size_type;
+
+private:
+  /**
+   * The kind of key that a group has. The actual values are discussed
+   * in-depth in the documentation of the @c kind field of the @c group
+   * structure. Note that the order of the enumerators *IS* important
+   * and must not be changed.
+   */
+  enum group_key_kind { smallest_key, stored_key, largest_key };
+
+  struct group {
+    explicit group(group_key_kind kind = largest_key)
+      : kind(kind), parent(this), rank(0) { }
+
+    /** The value associated with this group. This value is only valid
+     *  when @c kind!=largest_key (which indicates a deleted
+     *  element). Note that the use of boost::optional increases the
+     *  memory requirements slightly but does not result in extraneous
+     *  memory allocations or deallocations. The optional could be
+     *  eliminated when @c value_type is a model of
+     *  DefaultConstructible.
+     */
+    ::boost::optional<value_type> value;
+
+    /**
+     * The kind of key stored at this group. This may be @c
+     * smallest_key, which indicates that the key is infinitely small;
+     * @c largest_key, which indicates that the key is infinitely
+     * large; or @c stored_key, which means that the key is unknown,
+     * but its relationship to other keys can be determined via the
+     * comparison function object.
+     */
+    group_key_kind        kind;
+
+    /// The parent of this group. Will only be NULL for the dummy root group
+    group*                parent;
+
+    /// The rank of this group. Equivalent to the number of children in
+    /// the group.
+    rank_type            rank;
+
+    /** The children of this group. For the dummy root group, these are
+     * the roots. This is an array of length log n containing pointers
+     * to the child groups.
+     */
+    group**               children;
+  };
+
+  size_type log_base_2(size_type n) // log2 is a macro on some platforms
+  {
+    size_type leading_zeroes = 0;
+    do {
+      size_type next = n << 1;
+      if (n == (next >> 1)) {
+        ++leading_zeroes;
+        n = next;
+      } else {
+        break;
+      }
+    } while (true);
+    return sizeof(size_type) * CHAR_BIT - leading_zeroes - 1;
+  }
+
+public:
+  relaxed_heap(size_type n, const Compare& compare = Compare(),
+               const ID& id = ID())
+    : compare(compare), id(id), root(smallest_key), groups(n),
+      smallest_value(0)
+  {
+    if (n == 0) {
+      root.children = new group*[1];
+      return;
+    }
+
+    log_n = log_base_2(n);
+    if (log_n == 0) log_n = 1;
+    size_type g = n / log_n;
+    if (n % log_n > 0) ++g;
+    size_type log_g = log_base_2(g);
+    size_type r = log_g;
+
+    // Reserve an appropriate amount of space for data structures, so
+    // that we do not need to expand them.
+    index_to_group.resize(g);
+    A.resize(r + 1, 0);
+    root.rank = r + 1;
+    root.children = new group*[(log_g + 1) * (g + 1)];
+    for (rank_type i = 0; i < r+1; ++i) root.children[i] = 0;
+
+    // Build initial heap
+    size_type idx = 0;
+    while (idx < g) {
+      root.children[r] = &index_to_group[idx];
+      idx = build_tree(root, idx, r, log_g + 1);
+      if (idx != g)
+        r = static_cast<size_type>(log_base_2(g-idx));
+    }
+  }
+
+  ~relaxed_heap() { delete [] root.children; }
+
+  void push(const value_type& x)
+  {
+    groups[get(id, x)] = x;
+    update(x);
+  }
+
+  void update(const value_type& x)
+  {
+    group* a = &index_to_group[get(id, x) / log_n];
+    if (!a->value
+        || *a->value == x
+        || compare(x, *a->value)) {
+      if (a != smallest_value) smallest_value = 0;
+      a->kind = stored_key;
+      a->value = x;
+      promote(a);
+    }
+  }
+
+  void remove(const value_type& x)
+  {
+    group* a = &index_to_group[get(id, x) / log_n];
+    assert(groups[get(id, x)] != 0);
+    a->value = x;
+    a->kind = smallest_key;
+    promote(a);
+    smallest_value = a;
+    pop();
+  }
+
+  value_type& top()
+  {
+    find_smallest();
+    assert(smallest_value->value != none);
+    return *smallest_value->value;
+  }
+
+  const value_type& top() const
+  {
+    find_smallest();
+    assert(smallest_value->value != none);
+    return *smallest_value->value;
+  }
+
+  bool empty() const
+  {
+    find_smallest();
+    return !smallest_value || (smallest_value->kind == largest_key);
+  }
+
+  bool contains(const value_type& x) const { return groups[get(id, x)]; }
+
+  void pop()
+  {
+    // Fill in smallest_value. This is the group x.
+    find_smallest();
+    group* x = smallest_value;
+    smallest_value = 0;
+
+    // Make x a leaf, giving it the smallest value within its group
+    rank_type r = x->rank;
+    group* p = x->parent;
+    {
+      assert(x->value != none);
+
+      // Find x's group
+      size_type start = get(id, *x->value) - get(id, *x->value) % log_n;
+      size_type end = start + log_n;
+      if (end > groups.size()) end = groups.size();
+
+      // Remove the smallest value from the group, and find the new
+      // smallest value.
+      groups[get(id, *x->value)].reset();
+      x->value.reset();
+      x->kind = largest_key;
+      for (size_type i = start; i < end; ++i) {
+        if (groups[i] && (!x->value || compare(*groups[i], *x->value))) {
+          x->kind = stored_key;
+          x->value = groups[i];
+        }
+      }
+    }
+    x->rank = 0;
+
+    // Combine prior children of x with x
+    group* y = x;
+    for (size_type c = 0; c < r; ++c) {
+      group* child = x->children[c];
+      if (A[c] == child) A[c] = 0;
+      y = combine(y, child);
+    }
+
+    // If we got back something other than x, let y take x's place
+    if (y != x) {
+      y->parent = p;
+      p->children[r] = y;
+
+      assert(r == y->rank);
+      if (A[y->rank] == x)
+        A[y->rank] = do_compare(y, p)? y : 0;
+    }
+  }
+
+#ifdef BOOST_RELAXED_HEAP_DEBUG
+  /*************************************************************************
+   * Debugging support                                                     *
+   *************************************************************************/
+  void dump_tree() { dump_tree(std::cout); }
+  void dump_tree(std::ostream& out) { dump_tree(out, &root); }
+
+  void dump_tree(std::ostream& out, group* p, bool in_progress = false)
+  {
+    if (!in_progress) {
+      out << "digraph heap {\n"
+          << "  edge[dir=\"back\"];\n";
+    }
+
+    size_type p_index = 0;
+    if (p != &root) while (&index_to_group[p_index] != p) ++p_index;
+
+    for (size_type i = 0; i < p->rank; ++i) {
+      group* c = p->children[i];
+      if (c) {
+        size_type c_index = 0;
+        if (c != &root) while (&index_to_group[c_index] != c) ++c_index;
+
+        out << "  ";
+        if (p == &root) out << 'p'; else out << p_index;
+        out << " -> ";
+        if (c == &root) out << 'p'; else out << c_index;
+        if (A[c->rank] == c) out << " [style=\"dotted\"]";
+        out << ";\n";
+        dump_tree(out, c, true);
+
+        // Emit node information
+        out << "  ";
+        if (c == &root) out << 'p'; else out << c_index;
+        out << " [label=\"";
+        if (c == &root) out << 'p'; else out << c_index;
+        out << ":";
+        size_type start = c_index * log_n;
+        size_type end = start + log_n;
+        if (end > groups.size()) end = groups.size();
+        while (start != end) {
+          if (groups[start]) {
+            out << " " << get(id, *groups[start]);
+            if (*groups[start] == *c->value) out << "(*)";
+          }
+          ++start;
+        }
+        out << '"';
+
+        if (do_compare(c, p)) {
+          out << "  ";
+          if (c == &root) out << 'p'; else out << c_index;
+          out << ", style=\"filled\", fillcolor=\"gray\"";
+        }
+        out << "];\n";
+      } else {
+        assert(p->parent == p);
+      }
+    }
+    if (!in_progress) out << "}\n";
+  }
+
+  bool valid()
+  {
+    // Check that the ranks in the A array match the ranks of the
+    // groups stored there. Also, the active groups must be the last
+    // child of their parent.
+    for (size_type r = 0; r < A.size(); ++r) {
+      if (A[r] && A[r]->rank != r) return false;
+
+      if (A[r] && A[r]->parent->children[A[r]->parent->rank-1] != A[r])
+        return false;
+    }
+
+    // The root must have no value and a key of -Infinity
+    if (root.kind != smallest_key) return false;
+
+    return valid(&root);
+  }
+
+  bool valid(group* p)
+  {
+    for (size_type i = 0; i < p->rank; ++i) {
+      group* c = p->children[i];
+      if (c) {
+        // Check link structure
+        if (c->parent != p) return false;
+        if (c->rank != i) return false;
+
+        // A bad group must be active
+        if (do_compare(c, p) && A[i] != c) return false;
+
+        // Check recursively
+        if (!valid(c)) return false;
+      } else {
+        // Only the root may
+        if (p != &root) return false;
+      }
+    }
+    return true;
+  }
+
+#endif // BOOST_RELAXED_HEAP_DEBUG
+
+private:
+  size_type
+  build_tree(group& parent, size_type idx, size_type r, size_type max_rank)
+  {
+    group& this_group = index_to_group[idx];
+    this_group.parent = &parent;
+    ++idx;
+
+    this_group.children = root.children + (idx * max_rank);
+    this_group.rank = r;
+    for (size_type i = 0; i < r; ++i) {
+      this_group.children[i] = &index_to_group[idx];
+      idx = build_tree(this_group, idx, i, max_rank);
+    }
+    return idx;
+  }
+
+  void find_smallest() const
+  {
+    group** roots = root.children;
+
+    if (!smallest_value) {
+      std::size_t i;
+      for (i = 0; i < root.rank; ++i) {
+        if (roots[i] &&
+            (!smallest_value || do_compare(roots[i], smallest_value))) {
+          smallest_value = roots[i];
+        }
+      }
+      for (i = 0; i < A.size(); ++i) {
+        if (A[i] && (!smallest_value || do_compare(A[i], smallest_value)))
+          smallest_value = A[i];
+      }
+    }
+  }
+
+  bool do_compare(group* x, group* y) const
+  {
+    return (x->kind < y->kind
+            || (x->kind == y->kind
+                && x->kind == stored_key
+                && compare(*x->value, *y->value)));
+  }
+
+  void promote(group* a)
+  {
+    assert(a != 0);
+    rank_type r = a->rank;
+    group* p = a->parent;
+    assert(p != 0);
+    if (do_compare(a, p)) {
+      // s is the rank + 1 sibling
+      group* s = p->rank > r + 1? p->children[r + 1] : 0;
+
+      // If a is the last child of p
+      if (r == p->rank - 1) {
+        if (!A[r]) A[r] = a;
+        else if (A[r] != a) pair_transform(a);
+      } else {
+        assert(s != 0);
+        if (A[r + 1] == s) active_sibling_transform(a, s);
+        else good_sibling_transform(a, s);
+      }
+    }
+  }
+
+  group* combine(group* a1, group* a2)
+  {
+    assert(a1->rank == a2->rank);
+    if (do_compare(a2, a1)) do_swap(a1, a2);
+    a1->children[a1->rank++] = a2;
+    a2->parent = a1;
+    clean(a1);
+    return a1;
+  }
+
+  void clean(group* q)
+  {
+    if (2 > q->rank) return;
+    group* qp = q->children[q->rank-1];
+    rank_type s = q->rank - 2;
+    group* x = q->children[s];
+    group* xp = qp->children[s];
+    assert(s == x->rank);
+
+    // If x is active, swap x and xp
+    if (A[s] == x) {
+      q->children[s] = xp;
+      xp->parent = q;
+      qp->children[s] = x;
+      x->parent = qp;
+    }
+  }
+
+  void pair_transform(group* a)
+  {
+#if defined(BOOST_RELAXED_HEAP_DEBUG) && BOOST_RELAXED_HEAP_DEBUG > 1
+    std::cerr << "- pair transform\n";
+#endif
+    rank_type r = a->rank;
+
+    // p is a's parent
+    group* p = a->parent;
+    assert(p != 0);
+
+    // g is p's parent (a's grandparent)
+    group* g = p->parent;
+    assert(g != 0);
+
+    // a' <- A(r)
+    assert(A[r] != 0);
+    group* ap = A[r];
+    assert(ap != 0);
+
+    // A(r) <- nil
+    A[r] = 0;
+
+    // let a' have parent p'
+    group* pp = ap->parent;
+    assert(pp != 0);
+
+    // let a' have grandparent g'
+    group* gp = pp->parent;
+    assert(gp != 0);
+
+    // Remove a and a' from their parents
+    assert(ap == pp->children[pp->rank-1]); // Guaranteed because ap is active
+    --pp->rank;
+
+    // Guaranteed by caller
+    assert(a == p->children[p->rank-1]);
+    --p->rank;
+
+    // Note: a, ap, p, pp all have rank r
+    if (do_compare(pp, p)) {
+      do_swap(a, ap);
+      do_swap(p, pp);
+      do_swap(g, gp);
+    }
+
+    // Assuming k(p) <= k(p')
+    // make p' the rank r child of p
+    assert(r == p->rank);
+    p->children[p->rank++] = pp;
+    pp->parent = p;
+
+    // Combine a, ap into a rank r+1 group c
+    group* c = combine(a, ap);
+
+    // make c the rank r+1 child of g'
+    assert(gp->rank > r+1);
+    gp->children[r+1] = c;
+    c->parent = gp;
+
+#if defined(BOOST_RELAXED_HEAP_DEBUG) && BOOST_RELAXED_HEAP_DEBUG > 1
+    std::cerr << "After pair transform...\n";
+    dump_tree();
+#endif
+
+    if (A[r+1] == pp) A[r+1] = c;
+    else promote(c);
+  }
+
+  void active_sibling_transform(group* a, group* s)
+  {
+#if defined(BOOST_RELAXED_HEAP_DEBUG) && BOOST_RELAXED_HEAP_DEBUG > 1
+    std::cerr << "- active sibling transform\n";
+#endif
+    group* p = a->parent;
+    group* g = p->parent;
+
+    // remove a, s from their parents
+    assert(s->parent == p);
+    assert(p->children[p->rank-1] == s);
+    --p->rank;
+    assert(p->children[p->rank-1] == a);
+    --p->rank;
+
+    rank_type r = a->rank;
+    A[r+1] = 0;
+    a = combine(p, a);
+    group* c = combine(a, s);
+
+    // make c the rank r+2 child of g
+    assert(g->children[r+2] == p);
+    g->children[r+2] = c;
+    c->parent = g;
+    if (A[r+2] == p) A[r+2] = c;
+    else promote(c);
+  }
+
+  void good_sibling_transform(group* a, group* s)
+  {
+#if defined(BOOST_RELAXED_HEAP_DEBUG) && BOOST_RELAXED_HEAP_DEBUG > 1
+    std::cerr << "- good sibling transform\n";
+#endif
+    rank_type r = a->rank;
+    group* c = s->children[s->rank-1];
+    assert(c->rank == r);
+    if (A[r] == c) {
+#if defined(BOOST_RELAXED_HEAP_DEBUG) && BOOST_RELAXED_HEAP_DEBUG > 1
+      std::cerr << "- good sibling pair transform\n";
+#endif
+      A[r] = 0;
+      group* p = a->parent;
+
+      // Remove c from its parent
+      --s->rank;
+
+      // Make s the rank r child of p
+      s->parent = p;
+      p->children[r] = s;
+
+      // combine a, c and let the result by the rank r+1 child of p
+      assert(p->rank > r+1);
+      group* x = combine(a, c);
+      x->parent = p;
+      p->children[r+1] = x;
+
+      if (A[r+1] == s) A[r+1] = x;
+      else promote(x);
+
+#if defined(BOOST_RELAXED_HEAP_DEBUG) && BOOST_RELAXED_HEAP_DEBUG > 1
+      dump_tree(std::cerr);
+#endif
+      //      pair_transform(a);
+    } else {
+      // Clean operation
+      group* p = a->parent;
+      s->children[r] = a;
+      a->parent = s;
+      p->children[r] = c;
+      c->parent = p;
+
+      promote(a);
+    }
+  }
+
+  static void do_swap(group*& x, group*& y)
+  {
+    group* tmp = x;
+    x = y;
+    y = tmp;
+  }
+
+  /// Function object that compares two values in the heap
+  Compare compare;
+
+  /// Mapping from values to indices in the range [0, n).
+  ID id;
+
+  /** The root group of the queue. This group is special because it will
+   *  never store a value, but it acts as a parent to all of the
+   *  roots. Thus, its list of children is the list of roots.
+   */
+  group root;
+
+  /** Mapping from the group index of a value to the group associated
+   *  with that value. If a value is not in the queue, then the "value"
+   *  field will be empty.
+   */
+  std::vector<group> index_to_group;
+
+  /** Flat data structure containing the values in each of the
+   *  groups. It will be indexed via the id of the values. The groups
+   *  are each log_n long, with the last group potentially being
+   *  smaller.
+   */
+  std::vector< ::boost::optional<value_type> > groups;
+
+  /** The list of active groups, indexed by rank. When A[r] is null,
+   *  there is no active group of rank r. Otherwise, A[r] is the active
+   *  group of rank r.
+   */
+  std::vector<group*> A;
+
+  /** The group containing the smallest value in the queue, which must
+   *  be either a root or an active group. If this group is null, then we
+   *  will need to search for this group when it is needed.
+   */
+  mutable group* smallest_value;
+
+  /// Cached value log_base_2(n)
+  size_type log_n;
+};
+
+
+} // end namespace boost
+
+#if defined(BOOST_MSVC)
+#  pragma warning(pop)
+#endif
+
+#endif // BOOST_RELAXED_HEAP_HEADER