// boost heap: binomial heap
//
// Copyright (C) 2010 Tim Blechmann
//
// Distributed under 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)

#ifndef BOOST_HEAP_BINOMIAL_HEAP_HPP
#define BOOST_HEAP_BINOMIAL_HEAP_HPP

#include <algorithm>
#include <utility>
#include <vector>

#include <boost/assert.hpp>

#include <boost/heap/detail/heap_comparison.hpp>
#include <boost/heap/detail/heap_node.hpp>
#include <boost/heap/detail/stable_heap.hpp>
#include <boost/heap/detail/tree_iterator.hpp>
#include <boost/type_traits/integral_constant.hpp>

#ifdef BOOST_HAS_PRAGMA_ONCE
#    pragma once
#endif

#ifndef BOOST_DOXYGEN_INVOKED
#    ifdef BOOST_HEAP_SANITYCHECKS
#        define BOOST_HEAP_ASSERT BOOST_ASSERT
#    else
#        define BOOST_HEAP_ASSERT( expression )
#    endif
#endif

namespace boost { namespace heap {
namespace detail {

typedef parameter::parameters< boost::parameter::optional< tag::allocator >,
                               boost::parameter::optional< tag::compare >,
                               boost::parameter::optional< tag::stable >,
                               boost::parameter::optional< tag::constant_time_size >,
                               boost::parameter::optional< tag::stability_counter_type > >
    binomial_heap_signature;

template < typename T, typename Parspec >
struct make_binomial_heap_base
{
    static const bool constant_time_size
        = parameter::binding< Parspec, tag::constant_time_size, boost::true_type >::type::value;
    typedef typename detail::make_heap_base< T, Parspec, constant_time_size >::type               base_type;
    typedef typename detail::make_heap_base< T, Parspec, constant_time_size >::allocator_argument allocator_argument;
    typedef typename detail::make_heap_base< T, Parspec, constant_time_size >::compare_argument   compare_argument;

    typedef parent_pointing_heap_node< typename base_type::internal_type > node_type;

    typedef typename boost::allocator_rebind< allocator_argument, node_type >::type allocator_type;

    struct type : base_type, allocator_type
    {
        type( compare_argument const& arg ) :
            base_type( arg )
        {}

        type( allocator_type const& alloc ) :
            allocator_type( alloc )
        {}

#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
        type( type const& rhs ) :
            base_type( rhs ),
            allocator_type( rhs )
        {}

        type( type&& rhs ) :
            base_type( std::move( static_cast< base_type& >( rhs ) ) ),
            allocator_type( std::move( static_cast< allocator_type& >( rhs ) ) )
        {}

        type& operator=( type&& rhs )
        {
            base_type::operator=( std::move( static_cast< base_type& >( rhs ) ) );
            allocator_type::operator=( std::move( static_cast< allocator_type& >( rhs ) ) );
            return *this;
        }

        type& operator=( type const& rhs )
        {
            base_type::operator=( static_cast< base_type const& >( rhs ) );
            allocator_type::operator=( static_cast< allocator_type const& >( rhs ) );
            return *this;
        }
#endif
    };
};

} // namespace detail

/**
 * \class binomial_heap
 * \brief binomial heap
 *
 * The template parameter T is the type to be managed by the container.
 * The user can specify additional options and if no options are provided default options are used.
 *
 * The container supports the following options:
 * - \c boost::heap::stable<>, defaults to \c stable<false>
 * - \c boost::heap::compare<>, defaults to \c compare<std::less<T> >
 * - \c boost::heap::allocator<>, defaults to \c allocator<std::allocator<T> >
 * - \c boost::heap::constant_time_size<>, defaults to \c constant_time_size<true>
 * - \c boost::heap::stability_counter_type<>, defaults to \c stability_counter_type<boost::uintmax_t>
 *
 */
#ifdef BOOST_DOXYGEN_INVOKED
template < class T, class... Options >
#else
template < typename T,
           class A0 = boost::parameter::void_,
           class A1 = boost::parameter::void_,
           class A2 = boost::parameter::void_,
           class A3 = boost::parameter::void_ >
#endif
class binomial_heap :
    private detail::make_binomial_heap_base< T, typename detail::binomial_heap_signature::bind< A0, A1, A2, A3 >::type >::type
{
    typedef typename detail::binomial_heap_signature::bind< A0, A1, A2, A3 >::type bound_args;
    typedef detail::make_binomial_heap_base< T, bound_args >                       base_maker;
    typedef typename base_maker::type                                              super_t;

    typedef typename super_t::internal_type          internal_type;
    typedef typename super_t::size_holder_type       size_holder;
    typedef typename super_t::stability_counter_type stability_counter_type;
    typedef typename base_maker::allocator_argument  allocator_argument;

    template < typename Heap1, typename Heap2 >
    friend struct heap_merge_emulate;

public:
    static const bool constant_time_size    = super_t::constant_time_size;
    static const bool has_ordered_iterators = true;
    static const bool is_mergable           = true;
    static const bool is_stable             = detail::extract_stable< bound_args >::value;
    static const bool has_reserve           = false;

private:
#ifndef BOOST_DOXYGEN_INVOKED
    struct implementation_defined : detail::extract_allocator_types< typename base_maker::allocator_argument >
    {
        typedef T value_type;
        typedef typename detail::extract_allocator_types< typename base_maker::allocator_argument >::size_type size_type;
        typedef typename detail::extract_allocator_types< typename base_maker::allocator_argument >::reference reference;

        typedef typename base_maker::compare_argument value_compare;
        typedef typename base_maker::allocator_type   allocator_type;
        typedef typename base_maker::node_type        node;

        typedef typename boost::allocator_pointer< allocator_type >::type       node_pointer;
        typedef typename boost::allocator_const_pointer< allocator_type >::type const_node_pointer;

        typedef detail::node_handle< node_pointer, super_t, reference > handle_type;

        typedef typename base_maker::node_type node_type;

        typedef boost::intrusive::list< detail::heap_node_base< false >, boost::intrusive::constant_time_size< true > >
            node_list_type;

        typedef typename node_list_type::iterator                             node_list_iterator;
        typedef typename node_list_type::const_iterator                       node_list_const_iterator;
        typedef detail::value_extractor< value_type, internal_type, super_t > value_extractor;

        typedef detail::recursive_tree_iterator< node_type,
                                                 node_list_const_iterator,
                                                 const value_type,
                                                 value_extractor,
                                                 detail::list_iterator_converter< node_type, node_list_type > >
                         iterator;
        typedef iterator const_iterator;

        typedef detail::tree_iterator< node_type,
                                       const value_type,
                                       allocator_type,
                                       value_extractor,
                                       detail::list_iterator_converter< node_type, node_list_type >,
                                       true,
                                       true,
                                       value_compare >
            ordered_iterator;
    };
#endif

public:
    typedef T value_type;

    typedef typename implementation_defined::size_type        size_type;
    typedef typename implementation_defined::difference_type  difference_type;
    typedef typename implementation_defined::value_compare    value_compare;
    typedef typename implementation_defined::allocator_type   allocator_type;
    typedef typename implementation_defined::reference        reference;
    typedef typename implementation_defined::const_reference  const_reference;
    typedef typename implementation_defined::pointer          pointer;
    typedef typename implementation_defined::const_pointer    const_pointer;
    /// \copydoc boost::heap::priority_queue::iterator
    typedef typename implementation_defined::iterator         iterator;
    typedef typename implementation_defined::const_iterator   const_iterator;
    typedef typename implementation_defined::ordered_iterator ordered_iterator;

    typedef typename implementation_defined::handle_type handle_type;

private:
    typedef typename implementation_defined::node_type                node_type;
    typedef typename implementation_defined::node_list_type           node_list_type;
    typedef typename implementation_defined::node_pointer             node_pointer;
    typedef typename implementation_defined::const_node_pointer       const_node_pointer;
    typedef typename implementation_defined::node_list_iterator       node_list_iterator;
    typedef typename implementation_defined::node_list_const_iterator node_list_const_iterator;

    typedef typename super_t::internal_compare internal_compare;

public:
    /// \copydoc boost::heap::priority_queue::priority_queue(value_compare const &)
    explicit binomial_heap( value_compare const& cmp = value_compare() ) :
        super_t( cmp ),
        top_element( 0 )
    {}

    /// \copydoc boost::heap::priority_queue::priority_queue(allocator_type const &)
    explicit binomial_heap( allocator_type const& alloc ) :
        super_t( alloc ),
        top_element( 0 )
    {}

    /// \copydoc boost::heap::priority_queue::priority_queue(priority_queue const &)
    binomial_heap( binomial_heap const& rhs ) :
        super_t( rhs ),
        top_element( 0 )
    {
        if ( rhs.empty() )
            return;

        clone_forest( rhs );
        size_holder::set_size( rhs.get_size() );
    }

    /// \copydoc boost::heap::priority_queue::operator=(priority_queue const &)
    binomial_heap& operator=( binomial_heap const& rhs )
    {
        clear();
        size_holder::set_size( rhs.get_size() );
        static_cast< super_t& >( *this ) = rhs;

        if ( rhs.empty() )
            top_element = NULL;
        else
            clone_forest( rhs );
        return *this;
    }

#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
    /// \copydoc boost::heap::priority_queue::priority_queue(priority_queue &&)
    binomial_heap( binomial_heap&& rhs ) :
        super_t( std::move( rhs ) ),
        top_element( rhs.top_element )
    {
        trees.splice( trees.begin(), rhs.trees );
        rhs.top_element = NULL;
    }

    /// \copydoc boost::heap::priority_queue::operator=(priority_queue &&)
    binomial_heap& operator=( binomial_heap&& rhs )
    {
        clear();
        super_t::operator=( std::move( rhs ) );
        trees.splice( trees.begin(), rhs.trees );
        top_element     = rhs.top_element;
        rhs.top_element = NULL;
        return *this;
    }
#endif

    ~binomial_heap( void )
    {
        clear();
    }

    /// \copydoc boost::heap::priority_queue::empty
    bool empty( void ) const
    {
        return top_element == NULL;
    }

    /**
     * \b Effects: Returns the number of elements contained in the priority queue.
     *
     * \b Complexity: Constant, if configured with constant_time_size<true>, otherwise linear.
     *
     * */
    size_type size( void ) const
    {
        if ( constant_time_size )
            return size_holder::get_size();

        if ( empty() )
            return 0;
        else
            return detail::count_list_nodes< node_type, node_list_type >( trees );
    }

    /// \copydoc boost::heap::priority_queue::max_size
    size_type max_size( void ) const
    {
        const allocator_type& alloc = *this;
        return boost::allocator_max_size( alloc );
    }

    /// \copydoc boost::heap::priority_queue::clear
    void clear( void )
    {
        typedef detail::node_disposer< node_type, typename node_list_type::value_type, allocator_type > disposer;
        trees.clear_and_dispose( disposer( *this ) );

        size_holder::set_size( 0 );
        top_element = NULL;
    }

    /// \copydoc boost::heap::priority_queue::get_allocator
    allocator_type get_allocator( void ) const
    {
        return *this;
    }

    /// \copydoc boost::heap::priority_queue::swap
    void swap( binomial_heap& rhs )
    {
        super_t::swap( rhs );
        std::swap( top_element, rhs.top_element );
        trees.swap( rhs.trees );
    }

    /// \copydoc boost::heap::priority_queue::top
    const_reference top( void ) const
    {
        BOOST_ASSERT( !empty() );

        return super_t::get_value( top_element->value );
    }

    /**
     * \b Effects: Adds a new element to the priority queue. Returns handle to element
     *
     * \b Complexity: Logarithmic.
     *
     * */
    handle_type push( value_type const& v )
    {
        allocator_type& alloc = *this;
        node_pointer    n     = alloc.allocate( 1 );
        new ( n ) node_type( super_t::make_node( v ) );
        insert_node( trees.begin(), n );

        if ( !top_element || super_t::operator()( top_element->value, n->value ) )
            top_element = n;

        size_holder::increment();
        sanity_check();
        return handle_type( n );
    }

#if !defined( BOOST_NO_CXX11_RVALUE_REFERENCES ) && !defined( BOOST_NO_CXX11_VARIADIC_TEMPLATES )
    /**
     * \b Effects: Adds a new element to the priority queue. The element is directly constructed in-place. Returns
     * handle to element.
     *
     * \b Complexity: Logarithmic.
     *
     * */
    template < class... Args >
    handle_type emplace( Args&&... args )
    {
        allocator_type& alloc = *this;
        node_pointer    n     = alloc.allocate( 1 );
        new ( n ) node_type( super_t::make_node( std::forward< Args >( args )... ) );
        insert_node( trees.begin(), n );

        if ( !top_element || super_t::operator()( top_element->value, n->value ) )
            top_element = n;

        size_holder::increment();
        sanity_check();
        return handle_type( n );
    }
#endif

    /**
     * \b Effects: Removes the top element from the priority queue.
     *
     * \b Complexity: Logarithmic.
     *
     * */
    void pop( void )
    {
        BOOST_ASSERT( !empty() );

        node_pointer element = top_element;

        trees.erase( node_list_type::s_iterator_to( *element ) );
        size_holder::decrement();

        if ( element->child_count() ) {
            size_type sz = ( 1 << element->child_count() ) - 1;

            binomial_heap children( value_comp(), element->children, sz );
            if ( trees.empty() ) {
                stability_counter_type stability_count = super_t::get_stability_count();
                size_t                 size            = constant_time_size ? size_holder::get_size() : 0;
                swap( children );
                super_t::set_stability_count( stability_count );

                if ( constant_time_size )
                    size_holder::set_size( size );
            } else
                merge_and_clear_nodes( children );
        }

        if ( trees.empty() )
            top_element = NULL;
        else
            update_top_element();

        element->~node_type();
        allocator_type& alloc = *this;
        alloc.deallocate( element, 1 );
        sanity_check();
    }

    /**
     * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
     *
     * \b Complexity: Logarithmic.
     *
     * */
    void update( handle_type handle, const_reference v )
    {
        if ( super_t::operator()( super_t::get_value( handle.node_->value ), v ) )
            increase( handle, v );
        else
            decrease( handle, v );
    }

    /**
     * \b Effects: Updates the heap after the element handled by \c handle has been changed.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: If this is not called, after a handle has been updated, the behavior of the data structure is undefined!
     * */
    void update( handle_type handle )
    {
        node_pointer this_node = handle.node_;

        if ( this_node->parent ) {
            if ( super_t::operator()( super_t::get_value( this_node->parent->value ),
                                      super_t::get_value( this_node->value ) ) )
                increase( handle );
            else
                decrease( handle );
        } else
            decrease( handle );
    }

    /**
     * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: The new value is expected to be greater than the current one
     * */
    void increase( handle_type handle, const_reference v )
    {
        handle.node_->value = super_t::make_node( v );
        increase( handle );
    }

    /**
     * \b Effects: Updates the heap after the element handled by \c handle has been changed.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: If this is not called, after a handle has been updated, the behavior of the data structure is undefined!
     * */
    void increase( handle_type handle )
    {
        node_pointer n = handle.node_;
        siftup( n, *this );

        update_top_element();
        sanity_check();
    }

    /**
     * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: The new value is expected to be less than the current one
     * */
    void decrease( handle_type handle, const_reference v )
    {
        handle.node_->value = super_t::make_node( v );
        decrease( handle );
    }

    /**
     * \b Effects: Updates the heap after the element handled by \c handle has been changed.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: The new value is expected to be less than the current one. If this is not called, after a handle has
     * been updated, the behavior of the data structure is undefined!
     * */
    void decrease( handle_type handle )
    {
        node_pointer n = handle.node_;

        siftdown( n );

        update_top_element();
    }

    /**
     * \b Effects: Merge with priority queue rhs.
     *
     * \b Complexity: Logarithmic.
     *
     * */
    void merge( binomial_heap& rhs )
    {
        if ( rhs.empty() )
            return;

        if ( empty() ) {
            swap( rhs );
            return;
        }

        size_type new_size = size_holder::get_size() + rhs.get_size();
        merge_and_clear_nodes( rhs );

        size_holder::set_size( new_size );
        rhs.set_size( 0 );
        rhs.top_element = NULL;

        super_t::set_stability_count( ( std::max )( super_t::get_stability_count(), rhs.get_stability_count() ) );
        rhs.set_stability_count( 0 );
    }

public:
    /// \copydoc boost::heap::priority_queue::begin
    iterator begin( void ) const
    {
        return iterator( trees.begin() );
    }

    /// \copydoc boost::heap::priority_queue::end
    iterator end( void ) const
    {
        return iterator( trees.end() );
    }

    /// \copydoc boost::heap::fibonacci_heap::ordered_begin
    ordered_iterator ordered_begin( void ) const
    {
        return ordered_iterator( trees.begin(), trees.end(), top_element, super_t::value_comp() );
    }

    /// \copydoc boost::heap::fibonacci_heap::ordered_end
    ordered_iterator ordered_end( void ) const
    {
        return ordered_iterator( NULL, super_t::value_comp() );
    }

    /**
     * \b Effects: Removes the element handled by \c handle from the priority_queue.
     *
     * \b Complexity: Logarithmic.
     * */
    void erase( handle_type handle )
    {
        node_pointer n = handle.node_;
        siftup( n, force_inf() );
        top_element = n;
        pop();
    }

    /// \copydoc boost::heap::d_ary_heap_mutable::s_handle_from_iterator
    static handle_type s_handle_from_iterator( iterator const& it )
    {
        node_type* ptr = const_cast< node_type* >( it.get_node() );
        return handle_type( ptr );
    }

    /// \copydoc boost::heap::priority_queue::value_comp
    value_compare const& value_comp( void ) const
    {
        return super_t::value_comp();
    }

    /// \copydoc boost::heap::priority_queue::operator<(HeapType const & rhs) const
    template < typename HeapType >
    bool operator<( HeapType const& rhs ) const
    {
        return detail::heap_compare( *this, rhs );
    }

    /// \copydoc boost::heap::priority_queue::operator>(HeapType const & rhs) const
    template < typename HeapType >
    bool operator>( HeapType const& rhs ) const
    {
        return detail::heap_compare( rhs, *this );
    }

    /// \copydoc boost::heap::priority_queue::operator>=(HeapType const & rhs) const
    template < typename HeapType >
    bool operator>=( HeapType const& rhs ) const
    {
        return !operator<( rhs );
    }

    /// \copydoc boost::heap::priority_queue::operator<=(HeapType const & rhs) const
    template < typename HeapType >
    bool operator<=( HeapType const& rhs ) const
    {
        return !operator>( rhs );
    }

    /// \copydoc boost::heap::priority_queue::operator==(HeapType const & rhs) const
    template < typename HeapType >
    bool operator==( HeapType const& rhs ) const
    {
        return detail::heap_equality( *this, rhs );
    }

    /// \copydoc boost::heap::priority_queue::operator!=(HeapType const & rhs) const
    template < typename HeapType >
    bool operator!=( HeapType const& rhs ) const
    {
        return !( *this == rhs );
    }

private:
#if !defined( BOOST_DOXYGEN_INVOKED )
    void merge_and_clear_nodes( binomial_heap& rhs )
    {
        BOOST_HEAP_ASSERT( !empty() );
        BOOST_HEAP_ASSERT( !rhs.empty() );

        node_list_iterator this_iterator = trees.begin();
        node_pointer       carry_node    = NULL;

        while ( !rhs.trees.empty() ) {
            node_pointer rhs_node   = static_cast< node_pointer >( &rhs.trees.front() );
            size_type    rhs_degree = rhs_node->child_count();

            if ( super_t::operator()( top_element->value, rhs_node->value ) )
                top_element = rhs_node;

try_again:
            node_pointer this_node   = static_cast< node_pointer >( &*this_iterator );
            size_type    this_degree = this_node->child_count();
            sorted_by_degree();
            rhs.sorted_by_degree();

            if ( this_degree == rhs_degree ) {
                if ( carry_node ) {
                    if ( carry_node->child_count() < this_degree ) {
                        trees.insert( this_iterator, *carry_node );
                        carry_node = NULL;
                    } else {
                        rhs.trees.pop_front();
                        carry_node = merge_trees( carry_node, rhs_node );
                    }
                    ++this_iterator;
                } else {
                    this_iterator = trees.erase( this_iterator );
                    rhs.trees.pop_front();
                    carry_node = merge_trees( this_node, rhs_node );
                }

                if ( this_iterator == trees.end() )
                    break;
                else
                    continue;
            }

            if ( this_degree < rhs_degree ) {
                if ( carry_node ) {
                    if ( carry_node->child_count() < this_degree ) {
                        trees.insert( this_iterator, *carry_node );
                        carry_node = NULL;
                        ++this_iterator;
                    } else if ( carry_node->child_count() == rhs_degree ) {
                        rhs.trees.pop_front();
                        carry_node = merge_trees( carry_node, rhs_node );
                        continue;
                    } else {
                        this_iterator = trees.erase( this_iterator );
                        carry_node    = merge_trees( this_node, carry_node );
                    }
                    goto try_again;
                } else {
                    ++this_iterator;
                    if ( this_iterator == trees.end() )
                        break;
                    goto try_again;
                }

                if ( this_iterator == trees.end() )
                    break;
                else
                    continue;
            }

            if ( this_degree > rhs_degree ) {
                rhs.trees.pop_front();
                if ( carry_node ) {
                    if ( carry_node->child_count() < rhs_degree ) {
                        trees.insert( this_iterator, *carry_node );
                        trees.insert( this_iterator, *rhs_node );
                        carry_node = NULL;
                    } else
                        carry_node = merge_trees( rhs_node, carry_node );
                } else
                    trees.insert( this_iterator, *rhs_node );
            }
        }

        if ( !rhs.trees.empty() ) {
            if ( carry_node ) {
                node_list_iterator rhs_it = rhs.trees.begin();
                while ( static_cast< node_pointer >( &*rhs_it )->child_count() < carry_node->child_count() )
                    ++rhs_it;
                rhs.insert_node( rhs_it, carry_node );
                rhs.increment();
                sorted_by_degree();
                rhs.sorted_by_degree();
                if ( trees.empty() ) {
                    trees.splice( trees.end(), rhs.trees, rhs.trees.begin(), rhs.trees.end() );
                    update_top_element();
                } else
                    merge_and_clear_nodes( rhs );
            } else
                trees.splice( trees.end(), rhs.trees, rhs.trees.begin(), rhs.trees.end() );
            return;
        }

        if ( carry_node )
            insert_node( this_iterator, carry_node );
    }

    void clone_forest( binomial_heap const& rhs )
    {
        BOOST_HEAP_ASSERT( trees.empty() );
        typedef typename node_type::template node_cloner< allocator_type > node_cloner;
        trees.clone_from( rhs.trees, node_cloner( *this, NULL ), detail::nop_disposer() );

        update_top_element();
    }

    struct force_inf
    {
        template < typename X >
        bool operator()( X const&, X const& ) const
        {
            return false;
        }
    };

    template < typename Compare >
    void siftup( node_pointer n, Compare const& cmp )
    {
        while ( n->parent ) {
            node_pointer parent       = n->parent;
            node_pointer grand_parent = parent->parent;
            if ( cmp( n->value, parent->value ) )
                return;

            n->remove_from_parent();

            n->swap_children( parent );
            n->update_children();
            parent->update_children();

            if ( grand_parent ) {
                parent->remove_from_parent();
                grand_parent->add_child( n );
            } else {
                node_list_iterator it = trees.erase( node_list_type::s_iterator_to( *parent ) );
                trees.insert( it, *n );
            }
            n->add_child( parent );
        }
    }

    void siftdown( node_pointer n )
    {
        while ( n->child_count() ) {
            node_pointer max_child
                = detail::find_max_child< node_list_type, node_type, internal_compare >( n->children,
                                                                                         super_t::get_internal_cmp() );

            if ( super_t::operator()( max_child->value, n->value ) )
                return;

            max_child->remove_from_parent();

            n->swap_children( max_child );
            n->update_children();
            max_child->update_children();

            node_pointer parent = n->parent;
            if ( parent ) {
                n->remove_from_parent();
                max_child->add_child( n );
                parent->add_child( max_child );
            } else {
                node_list_iterator position = trees.erase( node_list_type::s_iterator_to( *n ) );
                max_child->add_child( n );
                trees.insert( position, *max_child );
            }
        }
    }

    void insert_node( node_list_iterator it, node_pointer n )
    {
        if ( it != trees.end() )
            BOOST_HEAP_ASSERT( static_cast< node_pointer >( &*it )->child_count() >= n->child_count() );

        while ( true ) {
            BOOST_HEAP_ASSERT( !n->is_linked() );
            if ( it == trees.end() )
                break;

            node_pointer this_node   = static_cast< node_pointer >( &*it );
            size_type    this_degree = this_node->child_count();
            size_type    n_degree    = n->child_count();
            if ( this_degree == n_degree ) {
                BOOST_HEAP_ASSERT( it->is_linked() );
                it = trees.erase( it );

                n = merge_trees( n, this_node );
            } else
                break;
        }
        trees.insert( it, *n );
    }

    // private constructor, just used in pop()
    explicit binomial_heap( value_compare const& cmp, node_list_type& child_list, size_type size ) :
        super_t( cmp )
    {
        size_holder::set_size( size );
        if ( size )
            top_element = static_cast< node_pointer >( &*child_list.begin() ); // not correct, but we will reset it later
        else
            top_element = NULL;

        for ( node_list_iterator it = child_list.begin(); it != child_list.end(); ++it ) {
            node_pointer n = static_cast< node_pointer >( &*it );
            n->parent      = NULL;
        }

        trees.splice( trees.end(), child_list, child_list.begin(), child_list.end() );

        trees.sort( detail::cmp_by_degree< node_type >() );
    }

    node_pointer merge_trees( node_pointer node1, node_pointer node2 )
    {
        BOOST_HEAP_ASSERT( node1->child_count() == node2->child_count() );

        if ( super_t::operator()( node1->value, node2->value ) )
            std::swap( node1, node2 );

        if ( node2->parent )
            node2->remove_from_parent();

        node1->add_child( node2 );
        return node1;
    }

    void update_top_element( void )
    {
        top_element
            = detail::find_max_child< node_list_type, node_type, internal_compare >( trees,
                                                                                     super_t::get_internal_cmp() );
    }

    void sorted_by_degree( void ) const
    {
#    ifdef BOOST_HEAP_SANITYCHECKS
        int degree = -1;

        for ( node_list_const_iterator it = trees.begin(); it != trees.end(); ++it ) {
            const_node_pointer n = static_cast< const_node_pointer >( &*it );
            BOOST_HEAP_ASSERT( int( n->child_count() ) > degree );
            degree = n->child_count();

            BOOST_HEAP_ASSERT( ( detail::is_heap< node_type, super_t >( n, *this ) ) );

            size_type child_nodes = detail::count_nodes< node_type >( n );
            BOOST_HEAP_ASSERT( child_nodes
                               == size_type( 1 << static_cast< const_node_pointer >( &*it )->child_count() ) );
        }
#    endif
    }

    void sanity_check( void )
    {
#    ifdef BOOST_HEAP_SANITYCHECKS
        sorted_by_degree();

        if ( !empty() ) {
            node_pointer found_top
                = detail::find_max_child< node_list_type, node_type, internal_compare >( trees,
                                                                                         super_t::get_internal_cmp() );
            BOOST_HEAP_ASSERT( top_element == found_top );
        }

        if ( constant_time_size ) {
            size_t counted = detail::count_list_nodes< node_type, node_list_type >( trees );
            size_t stored  = size_holder::get_size();
            BOOST_HEAP_ASSERT( counted == stored );
        }
#    endif
    }

    node_pointer   top_element;
    node_list_type trees;
#endif // BOOST_DOXYGEN_INVOKED
};


}} // namespace boost::heap

#undef BOOST_HEAP_ASSERT

#endif /* BOOST_HEAP_D_ARY_HEAP_HPP */
