// 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.hpp>

 #include <boost/optional.hpp>

 #include <vector>

 #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 != 0);

     return *smallest_value->value;

   }

   const value_type& top() const

   {

     find_smallest();

     assert(smallest_value->value != 0);

     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 != 0);

       // 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