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