    // Copyright (C) 2003  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_SEQUENCE_KERNEl_1_
    #define DLIB_SEQUENCE_KERNEl_1_

    #include "sequence_kernel_abstract.h"
    #include "../algs.h"
    #include "../interfaces/enumerable.h"
    #include "../interfaces/remover.h"
    #include "../serialize.h"

    namespace dlib
    {

        template <
            typename T,
            typename mem_manager = default_memory_manager
            >
        class sequence_kernel_1 : public enumerable<T>,
                                  public remover<T>
        {

            /*!
                INITIAL VALUE
                    - tree_root == 0
                    - tree_size == 0
                    - at_start_ == true
                    - current_element == 0
                    - stack == array of 50 node pointers
                    - stack_pos == 0

                CONVENTION

                    - if (tree_size > 0)
                        - tree_root == pointer to the root node of the binary search tree
                    - else
                        - tree_root == 0

                    - stack[stack_pos-1] == pop()

                    - current_element_valid() == (current_element != 0)

                    - at_start_ == at_start()
                    - if (current_element != 0 && current_element != tree_root) then
                        - stack[stack_pos-1] == the parent of the node pointed to by current_element

                    - if (current_element_valid()) then
                        - element() == current_element->item

                    - tree_size == size()
                    - (*this)[i] == return_reference(i)

                    - for all nodes:
                        - left_size == the number of elements in the left subtree.
                        - left points to the left subtree or 0 if there is no left subtree.
                        - right points to the right subtree or 0 if there is no right subtree.

                        - all elements in a left subtree have a position in the sequence < that
                          of the root of the current tree.

                        - all elements in a right subtree have a position in the
                          sequence > that of the root of the current tree.

                        - item is the sequence element for that node.
                        - balance:
                            - balance == 0 if both subtrees have the same height
                            - balance == -1 if the left subtree has a height that is
                              greater than the height of the right subtree by 1
                            - balance == 1 if the right subtree has a height that is
                              greater than the height of the left subtree by 1
                        - for all subtrees:
                            - the height of the left and right subtrees differ by at most one

            !*/

            class node
            {
            public:
                node* left;
                node* right;
                unsigned long left_size;
                T item;
                signed char balance;
            };

            public:

                typedef T type;
                typedef mem_manager mem_manager_type;

                sequence_kernel_1 (
                ) :
                    tree_root(0),
                    tree_size(0),
                    stack(ppool.allocate_array(50)),
                    current_element(0),
                    at_start_(true),
                    stack_pos(0)
                {}

                virtual ~sequence_kernel_1 (
                );

                inline void clear (
                );

                void add (
                    unsigned long pos,
                    T& item
                );

                void remove (
                    unsigned long pos,
                    T& item
                );

                void cat (
                    sequence_kernel_1& item
                );

                const T& operator[] (
                    unsigned long pos
                ) const;

                T& operator[] (
                    unsigned long pos
                );

                inline void swap (
                    sequence_kernel_1& item
                );

                // functions from the remover interface
                inline void remove_any (
                    T& item
                );

                // functions from the enumerable interface
                inline unsigned long size (
                ) const;

                bool at_start (
                ) const;

                inline void reset (
                ) const;

                bool current_element_valid (
                ) const;

                const T& element (
                ) const;

                T& element (
                );

                bool move_next (
                ) const;

            private:

                void delete_nodes (
                    node* t
                );
                /*!
                    requires
                        - t == a pointer to a valid node
                    ensures
                        - deletes t and all its sub nodes.
                !*/

                inline void rotate_left (
                    node*& t
                );
                /*!
                    requires
                        - t->balance == 2
                        - t->right->balance == 0 or 1
                    ensures
                        - #t is still a binary search tree
                        - #t->balance is between 1 and -1
                        - #t now has a height smaller by 1 if #t->balance == 0
                !*/

                inline void rotate_right (
                    node*& t
                );
                /*!
                    requires
                        - t->balance == -2
                        - t->left->balance == 0 or -1
                    ensures
                        - #t is still a binary search tree
                        - #t->balance is between 1 and -1
                        - #t now has a height smaller by 1 if #t->balance == 0

                !*/

                inline void double_rotate_right (
                    node*& t
                );
                /*!
                    requires
                        - #t->balance == -2
                        - #t->left->balance == 1
                    ensures
                        - #t is still a binary search tree
                        - #t now has a balance of 0
                        - #t now has a height smaller by 1
                !*/

                inline void double_rotate_left (
                    node*& t
                );
                /*!
                    requires
                        - #t->balance == 2
                        - #t->right->balance == -1
                    ensures
                        - #t is still a binary search tree
                        - #t now has a balance of 0 and
                        - #t now has a height smaller by 1
                !*/

                bool remove_least_element_in_tree (
                    node*& t,
                    T& item
                );
                /*!
                    requires
                        - t != 0  (i.e. there must be something in the tree to remove)
                    ensures
                        - the least node in t has been removed
                        - the least node element in t has been put into #item
                        - #t is still a binary search tree
                        - returns false if the height of the tree has not changed
                        - returns true if the height of the tree has shrunk by one
                !*/

                bool add_to_tree (
                    node*& t,
                    unsigned long pos,
                    T& item
                );
                /*!
                    requires
                        - pos <= the number of items in the tree
                    ensures
                        - item has been added to #t
                        - #return_reference(pos) == item
                        - the convention is still satisfied
                        - #item has an initial value for its type
                        - returns false if the height of the tree has not changed
                        - returns true if the height of the tree has grown by one
                !*/

                bool remove_from_tree (
                    node*& t,
                    unsigned long pos,
                    T& item
                );
                /*!
                    requires
                        - there is an item in the tree associated with pos
                    ensures
                        - the element in the tree associated with pos has been removed
                          and put into #item
                        - the convention is still satisfied
                        - returns false if the height of the tree has not changed
                        - returns true if the height of the tree has shrunk by one
                !*/

                const T& return_reference (
                    const node* t,
                    unsigned long pos
                ) const;
                /*!
                    requires
                        - there is an item in the tree associated with pos
                    ensures
                        - returns a const reference to the item in the tree associated with pos
                !*/

                T& return_reference (
                    node* t,
                    unsigned long pos
                );
                /*!
                    requires
                        - there is an item in the tree associated with pos
                    ensures
                        - returns a non-const reference to the item in the tree associated
                          with pos
                !*/

                inline bool keep_node_balanced (
                    node*& t
                );
                /*!
                    requires
                        - t != 0
                    ensures
                        - if (t->balance is < 1 or > 1) then
                            - keep_node_balanced() will ensure that t->balance == 0, -1, or 1
                        - returns true if it made the tree one height shorter
                        - returns false if it didn't change the height
                !*/

                void push (
                    node* n
                ) const { stack[stack_pos] = n; ++stack_pos; }
                /*!
                    ensures
                        - pushes n onto the stack
                !*/

                node* pop (
                ) const { --stack_pos; return stack[stack_pos]; }
                /*!
                    ensures
                        - pops the top of the stack and returns it
                !*/

                // data members
                typename mem_manager::template rebind<node>::other pool;
                typename mem_manager::template rebind<node*>::other ppool;

                node* tree_root;
                unsigned long tree_size;

                mutable node** stack;
                mutable node* current_element;
                mutable bool at_start_;
                mutable unsigned char stack_pos;

                // restricted functions
                sequence_kernel_1(sequence_kernel_1&);        // copy constructor
                sequence_kernel_1& operator=(sequence_kernel_1&); // assignment operator

        };

        template <
            typename T,
            typename mem_manager
            >
        inline void swap (
            sequence_kernel_1<T,mem_manager>& a,
            sequence_kernel_1<T,mem_manager>& b
        ) { a.swap(b); }

        template <
            typename T,
            typename mem_manager
            >
        void deserialize (
            sequence_kernel_1<T,mem_manager>& item,
            std::istream& in
        )
        {
            try
            {
                item.clear();
                unsigned long size;
                deserialize(size,in);
                T temp;
                for (unsigned long i = 0; i < size; ++i)
                {
                    deserialize(temp,in);
                    item.add(i,temp);
                }
            }
            catch (serialization_error e)
            {
                item.clear();
                throw serialization_error(e.info + "\n   while deserializing object of type sequence_kernel_1");
            }
        }

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
        // member function definitions
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        sequence_kernel_1<T,mem_manager>::
        ~sequence_kernel_1 (
        )
        {
            ppool.deallocate_array(stack);
            if (tree_size > 0)
            {
                delete_nodes(tree_root);
            }
        }

    // ----------------------------------------------------------------------------------------
        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        swap (
            sequence_kernel_1<T,mem_manager>& item
        )
        {
            exchange(stack,item.stack);
            exchange(stack_pos,item.stack_pos);

            pool.swap(item.pool);
            ppool.swap(item.ppool);

            node* tree_root_temp            = item.tree_root;
            unsigned long tree_size_temp    = item.tree_size;
            node* current_element_temp      = item.current_element;
            bool at_start_temp              = item.at_start_;

            item.tree_root = tree_root;
            item.tree_size = tree_size;
            item.current_element = current_element;
            item.at_start_   = at_start_;

            tree_root = tree_root_temp;
            tree_size = tree_size_temp;
            current_element = current_element_temp;
            at_start_   = at_start_temp;

        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        unsigned long sequence_kernel_1<T,mem_manager>::
        size (
        ) const
        {
            return tree_size;
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        const T& sequence_kernel_1<T,mem_manager>::
        operator[] (
            unsigned long pos
        ) const
        {
            return return_reference(tree_root,pos);
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        T& sequence_kernel_1<T,mem_manager>::
        operator[] (
            unsigned long pos
        )
        {
            return return_reference(tree_root,pos);
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        add (
            unsigned long pos,
            T& item
        )
        {
            add_to_tree(tree_root,pos,item);
            ++tree_size;
            // reset the enumerator
            reset();
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        remove (
            unsigned long pos,
            T& item
        )
        {
            remove_from_tree(tree_root,pos,item);
            --tree_size;
            // reset the enumerator
            reset();
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        cat (
            sequence_kernel_1<T,mem_manager>& item
        )
        {
            for (unsigned long i = 0; i < item.tree_size; ++i)
            {
                add_to_tree(
                    tree_root,
                    tree_size,
                    return_reference(item.tree_root,i)
                );

                ++tree_size;
            }

            item.clear();
            // reset the enumerator
            reset();
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        clear (
        )
        {
            if (tree_size > 0)
            {
                delete_nodes(tree_root);
                tree_root = 0;
                tree_size = 0;
            }
            // reset the enumerator
            reset();
        }

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
        // enumerable function definitions
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        bool sequence_kernel_1<T,mem_manager>::
        at_start (
        ) const
        {
            return at_start_;
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        reset (
        ) const
        {
            at_start_ = true;
            current_element = 0;
            stack_pos = 0;
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        bool sequence_kernel_1<T,mem_manager>::
        current_element_valid (
        ) const
        {
            return (current_element != 0);
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        const T& sequence_kernel_1<T,mem_manager>::
        element (
        ) const
        {
            return current_element->item;
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        T& sequence_kernel_1<T,mem_manager>::
        element (
        )
        {
            return current_element->item;
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        bool sequence_kernel_1<T,mem_manager>::
        move_next (
        ) const
        {
            // if we haven't started iterating yet
            if (at_start_)
            {
                at_start_ = false;
                if (tree_size == 0)
                {
                    return false;
                }
                else
                {
                    // find the first element in the tree
                    current_element = tree_root;
                    node* temp = current_element->left;
                    while (temp != 0)
                    {
                        push(current_element);
                        current_element = temp;
                        temp = current_element->left;
                    }
                    return true;
                }
            }
            else
            {
                if (current_element == 0)
                {
                    return false;
                }
                else
                {
                    node* temp;
                    bool went_up;  // true if we went up the tree from a child node to parent
                    bool from_left = false; // true if we went up and were coming from a left child node
                    // find the next element in the tree
                    if (current_element->right != 0)
                    {
                        // go right and down
                        temp = current_element;
                        push(current_element);
                        current_element = temp->right;
                        went_up = false;
                    }
                    else
                    {
                        // go up to the parent if we can
                        if (current_element == tree_root)
                        {
                            // in this case we have iterated over all the element of the tree
                            current_element = 0;
                            return false;
                        }
                        went_up = true;
                        node* parent = pop();

                        from_left = (parent->left == current_element);
                        // go up to parent
                        current_element = parent;
                    }

                    while (true)
                    {
                        if (went_up)
                        {
                            if (from_left)
                            {
                                // in this case we have found the next node
                                break;
                            }
                            else
                            {
                                if (current_element == tree_root)
                                {
                                    // in this case we have iterated over all the elements
                                    // in the tree
                                    current_element = 0;
                                    return false;
                                }
                                // we should go up
                                node* parent = pop();
                                from_left = (parent->left == current_element);
                                current_element = parent;
                            }
                        }
                        else
                        {
                            // we just went down to a child node
                            if (current_element->left != 0)
                            {
                                // go left
                                went_up = false;
                                temp = current_element;
                                push(current_element);
                                current_element = temp->left;
                            }
                            else
                            {
                                // if there is no left child then we have found the next node
                                break;
                            }
                        }
                    }

                    return true;
                }
            }

        }

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
        // remover function definitions
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        remove_any (
            T& item
        )
        {
            remove(0,item);
        }

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
        // private member function definitions
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        rotate_left (
            node*& t
        )
        {

            // set the new balance numbers
            if (t->right->balance == 1)
            {
                t->balance = 0;
                t->right->balance = 0;
            }
            else
            {
                t->balance = 1;
                t->right->balance = -1;
            }

            // perform the rotation
            node* temp = t->right;
            t->right = temp->left;
            temp->left = t;
            t = temp;

            // set left_size to its correct value
            t->left_size += t->left->left_size + 1;
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        rotate_right (
            node*& t
        )
        {
            // set the new balance numbers
            if (t->left->balance == -1)
            {
                t->balance = 0;
                t->left->balance = 0;
            }
            else
            {
                t->balance = -1;
                t->left->balance = 1;
            }

            // preform the rotation
            node* temp = t->left;
            t->left = temp->right;
            temp->right = t;
            t = temp;

            // set left_size to its correct value
            t->right->left_size -= t->left_size + 1;

        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        double_rotate_right (
            node*& t
        )
        {

            node* temp = t;
            t = t->left->right;

            temp->left->right = t->left;
            t->left = temp->left;

            temp->left = t->right;
            t->right = temp;

            if (t->balance < 0)
            {
                t->left->balance = 0;
                t->right->balance = 1;
            }
            else if (t->balance > 0)
            {
                t->left->balance = -1;
                t->right->balance = 0;
            }
            else
            {
                t->left->balance = 0;
                t->right->balance = 0;
            }
            t->balance = 0;

            // set left_size to its correct value
            t->left_size += t->left->left_size + 1;
            t->right->left_size -= t->left_size + 1;

        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        double_rotate_left (
            node*& t
        )
        {
            node* temp = t;
            t = t->right->left;

            temp->right->left = t->right;
            t->right = temp->right;

            temp->right = t->left;
            t->left = temp;

            if (t->balance < 0)
            {
                t->left->balance = 0;
                t->right->balance = 1;
            }
            else if (t->balance > 0)
            {
                t->left->balance = -1;
                t->right->balance = 0;
            }
            else
            {
                t->left->balance = 0;
                t->right->balance = 0;
            }

            t->balance = 0;

            // set left_size to its correct value
            t->right->left_size -= t->left_size + 1;
            t->left_size += t->left->left_size + 1;
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        bool sequence_kernel_1<T,mem_manager>::
        remove_least_element_in_tree (
            node*& t,
            T& item
        )
        {
            // make a reference to the current node so we don't have to dereference
            // a pointer a bunch of times
            node& tree = *t;

            // if the left tree is an empty tree
            if ( tree.left == 0)
            {
                // swap nodes element into item
                exchange(tree.item,item);

                // plug hole left by removing this node
                t = tree.right;

                // delete the node that was just removed
                tree.right = 0;
                delete_nodes(&tree);

                // return that the height of this part of the tree has decreased
                return true;
            }
            else
            {
                // subtract one from the left size
                --tree.left_size;

                // keep going left

                // if remove made the tree one height shorter
                if ( remove_least_element_in_tree(tree.left,item) )
                {
                    // if this caused the current tree to strink then report that
                    if ( tree.balance == -1)
                    {
                        ++tree.balance;
                        return true;
                    }
                    else
                    {
                        ++tree.balance;
                        return keep_node_balanced(t);
                    }
                }

                return false;
            }
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        bool sequence_kernel_1<T,mem_manager>::
        add_to_tree (
            node*& t,
            unsigned long pos,
            T& item
        )
        {
            // if found place to add
            if (t == 0)
            {
                // create a node to add new item into
                t = pool.allocate();

                // make a reference to the current node so we don't have to dereference
                // a pointer a bunch of times
                node& tree = *t;

                // set left and right pointers to 0 to indicate that there are no
                // left or right subtrees
                tree.left = 0;
                tree.right = 0;
                tree.balance = 0;
                tree.left_size = 0;

                // put item into t
                exchange(item,tree.item);

                // indicate that the height of this tree has increased
                return true;
            }
            else  // keep looking for a place to add the new item
            {
                // make a reference to the current node so we don't have to dereference
                // a pointer a bunch of times
                node& tree = *t;
                signed char old_balance = tree.balance;

                // add the new item to whatever subtree it should go into
                if ( pos < tree.left_size + 1 )
                {
                    tree.balance -= add_to_tree(tree.left,pos,item);
                    ++tree.left_size;
                }
                else
                    tree.balance += add_to_tree(tree.right,pos - tree.left_size - 1,item);

                // if the tree was balanced to start with
                if (old_balance == 0)
                {
                    // if its not balanced anymore then it grew in height
                    if (tree.balance != 0)
                        return true;
                    else
                        return false;
                }
                else
                {
                    // if the tree is now balanced then it didn't grow
                    if (tree.balance == 0)
                    {
                        return false;
                    }
                    else
                    {
                        // if the tree needs to be balanced
                        if (tree.balance != old_balance)
                        {
                            return !keep_node_balanced(t);
                        }
                        // if there has been no change in the heights
                        else
                        {
                            return false;
                        }
                    }
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        bool sequence_kernel_1<T,mem_manager>::
        remove_from_tree (
            node*& t,
            unsigned long pos,
            T& item
        )
        {

            // make a reference to the current node so we don't have to dereference
            // a pointer a bunch of times
            node& tree = *t;

            // if item is on the left
            if (pos < tree.left_size)
            {
                // adjust the left size
                --tree.left_size;

                // if the left side of the tree has the greatest height
                if (tree.balance == -1)
                {
                    tree.balance += remove_from_tree(tree.left,pos,item);
                    return !tree.balance;
                }
                else
                {
                    tree.balance += remove_from_tree(tree.left,pos,item);
                    return keep_node_balanced(t);
                }

            }
            // if item is found
            else if (pos == tree.left_size)
            {
                // if there is no left node
                if (tree.left == 0)
                {
                    // swap nodes element into item
                    exchange(tree.item,item);

                    // plug hole left by removing this node and free memory
                    t = tree.right;  // plug hole with right subtree

                    // delete old node
                    tree.right = 0;
                    delete_nodes(&tree);

                    // indicate that the height has changed
                    return true;
                }
                // if there is no right node
                else if (tree.right == 0)
                {
                    // swap nodes element into item
                    exchange(tree.item,item);

                    // plug hole left by removing this node and free memory
                    t = tree.left;  // plug hole with left subtree

                    // delete old node
                    tree.left = 0;
                    delete_nodes(&tree);

                    // indicate that the height of this tree has changed
                    return true;
                }
                // if there are both a left and right sub node
                else
                {
                    // get an element that can replace the one being removed and do this
                    // if it made the right subtree shrink by one
                    if (remove_least_element_in_tree(tree.right,item))
                    {
                        // adjust the tree height
                        --tree.balance;

                        // put the element into item copy and also plug the
                        // hole with the smallest element from the right.
                        exchange(item,tree.item);

                        // if the height of the current tree has dropped by one
                        if (tree.balance == 0)
                        {
                            return true;
                        }
                        else
                        {
                            return keep_node_balanced(t);
                        }
                    }
                    // else this remove did not effect the height of this tree
                    else
                    {
                        // put the element into item copy and also plug the
                        // hole with the smallest element from the right.
                        exchange(item,tree.item);

                        return false;
                    }

                }
            }
            // if item is on the right
            else
            {

                // if the right side of the tree has the greatest height
                if (tree.balance == 1)
                {
                    tree.balance -= remove_from_tree(tree.right,pos - tree.left_size - 1,item);
                    return !tree.balance;
                }
                else
                {
                    tree.balance -= remove_from_tree(tree.right,pos - tree.left_size - 1,item);
                    return keep_node_balanced(t);
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        T& sequence_kernel_1<T,mem_manager>::
        return_reference (
            node* t,
            unsigned long pos
        )
        {
            while (true)
            {
                // if we have found the node
                if (pos == t->left_size)
                    return t->item;

                if (pos < t->left_size)
                {
                    // go left
                    t = t->left;
                }
                else
                {
                    // go right
                    pos -= t->left_size+1;
                    t = t->right;
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        const T& sequence_kernel_1<T,mem_manager>::
        return_reference (
            const node* t,
            unsigned long pos
        ) const
        {
            while (true)
            {
                // if we have found the node
                if (pos == t->left_size)
                    return t->item;

                if (pos < t->left_size)
                {
                    // go left
                    t = t->left;
                }
                else
                {
                    // go right
                    pos -= t->left_size+1;
                    t = t->right;
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        bool sequence_kernel_1<T,mem_manager>::
        keep_node_balanced (
            node*& t
        )
        {
            // make a reference to the current node so we don't have to dereference
            // a pointer a bunch of times
            node& tree = *t;

            // if tree does not need to be balanced then return false
            if (tree.balance == 0)
                return false;

            // if tree needs to be rotated left
            if (tree.balance == 2)
            {
                if (tree.right->balance >= 0)
                    rotate_left(t);
                else
                    double_rotate_left(t);
            }
            // else if the tree needs to be rotated right
            else if (tree.balance == -2)
            {
                if (tree.left->balance <= 0)
                    rotate_right(t);
                else
                    double_rotate_right(t);
            }

            if (t->balance == 0)
                return true;
            else
                return false;
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename T,
            typename mem_manager
            >
        void sequence_kernel_1<T,mem_manager>::
        delete_nodes (
            node* t
        )
        {
            if (t->left)
                delete_nodes(t->left);
            if (t->right)
                delete_nodes(t->right);
            pool.deallocate(t);
        }

    // ----------------------------------------------------------------------------------------
    }

    #endif // DLIB_SEQUENCE_KERNEl_1_