avltree.h

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    int get_bf(handle h) { return abs.get_balance_factor(h); }
    void set_bf(handle h, int bf) { abs.set_balance_factor(h, bf); }

    int cmp_k_n(key k, handle h) { return abs.compare_key_node(k, h); }
    int cmp_n_n(handle h1, handle h2) { return abs.compare_node_node(h1, h2); }

    handle null() { return abs.null(); }

private:

    // Balances subtree, returns handle of root node of subtree
    // after balancing.
    handle balance(handle bal_h)
    {
        handle deep_h;

        // Either the "greater than" or the "less than" subtree of
        // this node has to be 2 levels deeper (or else it wouldn't
        // need balancing).

        if (get_bf(bal_h) > 0) {
            // "Greater than" subtree is deeper.

            deep_h = get_gt(bal_h);

            if (get_bf(deep_h) < 0) {
                handle old_h = bal_h;
                bal_h = get_lt(deep_h);

                set_gt(old_h, get_lt(bal_h));
                set_lt(deep_h, get_gt(bal_h));
                set_lt(bal_h, old_h);
                set_gt(bal_h, deep_h);

                int bf = get_bf(bal_h);
                if (bf != 0) {
                    if (bf > 0) {
                        set_bf(old_h, -1);
                        set_bf(deep_h, 0);
                    } else {
                        set_bf(deep_h, 1);
                        set_bf(old_h, 0);
                    }
                    set_bf(bal_h, 0);
                } else {
                    set_bf(old_h, 0);
                    set_bf(deep_h, 0);
                }
            } else {
                set_gt(bal_h, get_lt(deep_h));
                set_lt(deep_h, bal_h);
                if (get_bf(deep_h) == 0) {
                    set_bf(deep_h, -1);
                    set_bf(bal_h, 1);
                } else {
                    set_bf(deep_h, 0);
                    set_bf(bal_h, 0);
                }
                bal_h = deep_h;
            }
        } else {
            // "Less than" subtree is deeper.

            deep_h = get_lt(bal_h);

            if (get_bf(deep_h) > 0) {
                handle old_h = bal_h;
                bal_h = get_gt(deep_h);
                set_lt(old_h, get_gt(bal_h));
                set_gt(deep_h, get_lt(bal_h));
                set_gt(bal_h, old_h);
                set_lt(bal_h, deep_h);

                int bf = get_bf(bal_h);
                if (bf != 0) {
                    if (bf < 0) {
                        set_bf(old_h, 1);
                        set_bf(deep_h, 0);
                    } else {
                        set_bf(deep_h, -1);
                        set_bf(old_h, 0);
                    }
                    set_bf(bal_h, 0);
                } else {
                    set_bf(old_h, 0);
                    set_bf(deep_h, 0);
                }
            } else {
                set_lt(bal_h, get_gt(deep_h));
                set_gt(deep_h, bal_h);
                if (get_bf(deep_h) == 0) {
                    set_bf(deep_h, 1);
                    set_bf(bal_h, -1);
                } else {
                    set_bf(deep_h, 0);
                    set_bf(bal_h, 0);
                }
                bal_h = deep_h;
            }
        }

        return bal_h;
    }

};

template <class Abstractor, unsigned maxDepth, class BSet>
inline typename AVLTree<Abstractor, maxDepth, BSet>::handle
AVLTree<Abstractor, maxDepth, BSet>::insert(handle h)
{
    set_lt(h, null());
    set_gt(h, null());
    set_bf(h, 0);

    if (abs.root == null())
        abs.root = h;
    else {
        // Last unbalanced node encountered in search for insertion point.
        handle unbal = null();
        // Parent of last unbalanced node.
        handle parent_unbal = null();
        // Balance factor of last unbalanced node.
        int unbal_bf;

        // Zero-based depth in tree.
        unsigned depth = 0, unbal_depth = 0;

        // Records a path into the tree.  If branch[n] is true, indicates
        // take greater branch from the nth node in the path, otherwise
        // take the less branch.  branch[0] gives branch from root, and
        // so on.
        BSet branch;

        handle hh = abs.root;
        handle parent = null();
        int cmp;

        do {
            if (get_bf(hh) != 0) {
                unbal = hh;
                parent_unbal = parent;
                unbal_depth = depth;
            }
            cmp = cmp_n_n(h, hh);
            if (cmp == 0)
                // Duplicate key.
                return hh;
            parent = hh;
            hh = cmp < 0 ? get_lt(hh) : get_gt(hh);
            branch[depth++] = cmp > 0;
        } while (hh != null());

        //  Add node to insert as leaf of tree.
        if (cmp < 0)
            set_lt(parent, h);
        else
            set_gt(parent, h);

        depth = unbal_depth;

        if (unbal == null())
            hh = abs.root;
        else {
            cmp = branch[depth++] ? 1 : -1;
            unbal_bf = get_bf(unbal);
            if (cmp < 0)
                unbal_bf--;
            else  // cmp > 0
                unbal_bf++;
            hh = cmp < 0 ? get_lt(unbal) : get_gt(unbal);
            if ((unbal_bf != -2) && (unbal_bf != 2)) {
                // No rebalancing of tree is necessary.
                set_bf(unbal, unbal_bf);
                unbal = null();
            }
        }

        if (hh != null())
            while (h != hh) {
                cmp = branch[depth++] ? 1 : -1;
                if (cmp < 0) {
                    set_bf(hh, -1);
                    hh = get_lt(hh);
                } else { // cmp > 0
                    set_bf(hh, 1);
                    hh = get_gt(hh);
                }
            }

        if (unbal != null()) {
            unbal = balance(unbal);
            if (parent_unbal == null())
                abs.root = unbal;
            else {
                depth = unbal_depth - 1;
                cmp = branch[depth] ? 1 : -1;
                if (cmp < 0)
                    set_lt(parent_unbal, unbal);
                else  // cmp > 0
                    set_gt(parent_unbal, unbal);
            }
        }
    }

    return h;
}

template <class Abstractor, unsigned maxDepth, class BSet>
inline typename AVLTree<Abstractor, maxDepth, BSet>::handle
AVLTree<Abstractor, maxDepth, BSet>::search(key k, typename AVLTree<Abstractor, maxDepth, BSet>::SearchType st)
{
    const int MASK_HIGH_BIT = (int) ~ ((~ (unsigned) 0) >> 1);

    int cmp, target_cmp;
    handle match_h = null();
    handle h = abs.root;

    if (st & LESS)
        target_cmp = 1;
    else if (st & GREATER)
        target_cmp = -1;
    else
        target_cmp = 0;

    while (h != null()) {
        cmp = cmp_k_n(k, h);
        if (cmp == 0) {
            if (st & EQUAL) {
                match_h = h;
                break;
            }
            cmp = -target_cmp;
        } else if (target_cmp != 0)
            if (!((cmp ^ target_cmp) & MASK_HIGH_BIT))
                // cmp and target_cmp are both positive or both negative.
                match_h = h;
        h = cmp < 0 ? get_lt(h) : get_gt(h);
    }

    return match_h;
}

template <class Abstractor, unsigned maxDepth, class BSet>
inline typename AVLTree<Abstractor, maxDepth, BSet>::handle
AVLTree<Abstractor, maxDepth, BSet>::search_least()
{
    handle h = abs.root, parent = null();

    while (h != null()) {
        parent = h;
        h = get_lt(h);
    }

    return parent;
}

template <class Abstractor, unsigned maxDepth, class BSet>
inline typename AVLTree<Abstractor, maxDepth, BSet>::handle
AVLTree<Abstractor, maxDepth, BSet>::search_greatest()
{
    handle h = abs.root, parent = null();

    while (h != null()) {
        parent = h;
        h = get_gt(h);
    }

    return parent;
}

template <class Abstractor, unsigned maxDepth, class BSet>
inline typename AVLTree<Abstractor, maxDepth, BSet>::handle
AVLTree<Abstractor, maxDepth, BSet>::remove(key k)
{
    // Zero-based depth in tree.
    unsigned depth = 0, rm_depth;

    // Records a path into the tree.  If branch[n] is true, indicates
    // take greater branch from the nth node in the path, otherwise
    // take the less branch.  branch[0] gives branch from root, and
    // so on.
    BSet branch;

    handle h = abs.root;
    handle parent = null(), child;
    int cmp, cmp_shortened_sub_with_path;

    for (;;) {
        if (h == null())
            // No node in tree with given key.
            return null();
        cmp = cmp_k_n(k, h);
        if (cmp == 0)
            // Found node to remove.
            break;
        parent = h;
        h = cmp < 0 ? get_lt(h) : get_gt(h);
        branch[depth++] = cmp > 0;
        cmp_shortened_sub_with_path = cmp;
    }
    handle rm = h;
    handle parent_rm = parent;
    rm_depth = depth;

    // If the node to remove is not a leaf node, we need to get a
    // leaf node, or a node with a single leaf as its child, to put
    // in the place of the node to remove.  We will get the greatest
    // node in the less subtree (of the node to remove), or the least
    // node in the greater subtree.  We take the leaf node from the
    // deeper subtree, if there is one.

    if (get_bf(h) < 0) {
        child = get_lt(h);
        branch[depth] = false;
        cmp = -1;
    } else {
        child = get_gt(h);
        branch[depth] = true;
        cmp = 1;
    }
    depth++;

    if (child != null()) {
        cmp = -cmp;
        do {
            parent = h;
            h = child;
            if (cmp < 0) {
                child = get_lt(h);
                branch[depth] = false;
            } else {
                child = get_gt(h);
                branch[depth] = true;
            }
            depth++;
        } while (child != null());

        if (parent == rm)
            // Only went through do loop once.  Deleted node will be replaced
            // in the tree structure by one of its immediate children.
            cmp_shortened_sub_with_path = -cmp;
        else
            cmp_shortened_sub_with_path = cmp;

        // Get the handle of the opposite child, which may not be null.
        child = cmp > 0 ? get_lt(h) : get_gt(h);
    }

    if (parent == null())
        // There were only 1 or 2 nodes in this tree.
        abs.root = child;
    else if (cmp_shortened_sub_with_path < 0)
        set_lt(parent, child);
    else
        set_gt(parent, child);

    // "path" is the parent of the subtree being eliminated or reduced
    // from a depth of 2 to 1.  If "path" is the node to be removed, we
    // set path to the node we're about to poke into the position of the
    // node to be removed.
    handle path = parent == rm ? h : parent;

    if (h != rm) {
        // Poke in the replacement for the node to be removed.
        set_lt(h, get_lt(rm));
        set_gt(h, get_gt(rm));
        set_bf(h, get_bf(rm));
        if (parent_rm == null())
            abs.root = h;
        else {
            depth = rm_depth - 1;
            if (branch[depth])
                set_gt(parent_rm, h);
            else
                set_lt(parent_rm, h);
        }
    }

    if (path != null()) {
        // Create a temporary linked list from the parent of the path node
        // to the root node.
        h = abs.root;
        parent = null();
        depth = 0;
        while (h != path) {
            if (branch[depth++]) {
                child = get_gt(h);
                set_gt(h, parent);
            } else {
                child = get_lt(h);
                set_lt(h, parent);
            }
            parent = h;
            h = child;
        }

        // Climb from the path node to the root node using the linked
        // list, restoring the tree structure and rebalancing as necessary.
        bool reduced_depth = true;
        int bf;
        cmp = cmp_shortened_sub_with_path;
        for (;;) {
            if (reduced_depth) {
                bf = get_bf(h);
                if (cmp < 0)
                    bf++;
                else  // cmp > 0
                    bf--;
                if ((bf == -2) || (bf == 2)) {
                    h = balance(h);
                    bf = get_bf(h);
                } else
                    set_bf(h, bf);
                reduced_depth = (bf == 0);
            }
            if (parent == null())
                break;
            child = h;
            h = parent;
            cmp = branch[--depth] ? 1 : -1;
            if (cmp < 0)    {
                parent = get_lt(h);
                set_lt(h, child);
            } else {
                parent = get_gt(h);
                set_gt(h, child);
            }
        }
        abs.root = h;
    }

    return rm;
}

template <class Abstractor, unsigned maxDepth, class BSet>
inline typename AVLTree<Abstractor, maxDepth, BSet>::handle
AVLTree<Abstractor, maxDepth, BSet>::subst(handle new_node)
{
    handle h = abs.root;
    handle parent = null();
    int cmp, last_cmp;

    /* Search for node already in tree with same key. */
    for (;;) {
        if (h == null())
            /* No node in tree with same key as new node. */
            return null();
        cmp = cmp_n_n(new_node, h);
        if (cmp == 0)
            /* Found the node to substitute new one for. */
            break;
        last_cmp = cmp;
        parent = h;
        h = cmp < 0 ? get_lt(h) : get_gt(h);
    }

    /* Copy tree housekeeping fields from node in tree to new node. */
    set_lt(new_node, get_lt(h));
    set_gt(new_node, get_gt(h));
    set_bf(new_node, get_bf(h));

    if (parent == null())
        /* New node is also new root. */
        abs.root = new_node;
    else {
        /* Make parent point to new node. */
        if (last_cmp < 0)
            set_lt(parent, new_node);
        else
            set_gt(parent, new_node);
    }

    return h;
}

}

#endif