/***************************************************************************//**

Copyright (c) 2007, 2010, Innobase Oy. All Rights Reserved.

Portions of this file contain modifications contributed and copyrighted by
Sun Microsystems, Inc. Those modifications are gratefully acknowledged and
are described briefly in the InnoDB documentation. The contributions by
Sun Microsystems are incorporated with their permission, and subject to the
conditions contained in the file COPYING.Sun_Microsystems.

This program is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation; version 2 of the License.

This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 
51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

*****************************************************************************/
/********************************************************************//**
Red-Black tree implementation

(c) 2007 Oracle/Innobase Oy

Created 2007-03-20 Sunny Bains
***********************************************************************/

#include "ut0rbt.h"

/**********************************************************************//**
Definition of a red-black tree
==============================

A red-black tree is a binary search tree which has the following
red-black properties:

   1. Every node is either red or black.
   2. Every leaf (NULL - in our case tree->nil) is black.
   3. If a node is red, then both its children are black.
   4. Every simple path from a node to a descendant leaf contains the
      same number of black nodes.

   from (3) above, the implication is that on any path from the root
   to a leaf, red nodes must not be adjacent.

   However, any number of black nodes may appear in a sequence.
 */

#if	defined(IB_RBT_TESTING)
#warning "Testing enabled!"
#endif

#define ROOT(t)		(t->root->left)

/**********************************************************************//**
Print out the sub-tree recursively. */
static
void
rbt_print_subtree(
/*==============*/
	const ib_rbt_t*		tree,		/*!< in: tree to traverse */
	const ib_rbt_node_t*	node,		/*!< in: node to print */
	ib_rbt_print_node	print)		/*!< in: print key function */
{
	/* FIXME: Doesn't do anything yet */
	if (node != tree->nil) {
		print(node);
		rbt_print_subtree(tree, node->left, print);
		rbt_print_subtree(tree, node->right, print);
	}
}

/**********************************************************************//**
Verify that the keys are in order.
@return	TRUE of OK. FALSE if not ordered */
static
ibool
rbt_check_ordering(
/*===============*/
	const ib_rbt_t*		tree)		/*!< in: tree to verfify */
{
	const ib_rbt_node_t*	node;
	const ib_rbt_node_t*	prev = NULL;

	/* Iterate over all the nodes, comparing each node with the prev */
	for (node = rbt_first(tree); node; node = rbt_next(tree, prev)) {

		if (prev && tree->compare(prev->value, node->value) >= 0) {
			return(FALSE);
		}

		prev = node;
	}

	return(TRUE);
}

/**********************************************************************//**
Check that every path from the root to the leaves has the same count.
Count is expressed in the number of black nodes.
@return	0 on failure else black height of the subtree */
static
ibool
rbt_count_black_nodes(
/*==================*/
	const ib_rbt_t*		tree,		/*!< in: tree to verify */
	const ib_rbt_node_t*	node)		/*!< in: start of sub-tree */
{
	ulint	result;

	if (node != tree->nil) {
		ulint	left_height = rbt_count_black_nodes(tree, node->left);

		ulint	right_height = rbt_count_black_nodes(tree, node->right);

		if (left_height == 0
		    || right_height == 0
		    || left_height != right_height) {

			result = 0;
		} else if (node->color == IB_RBT_RED) {

			/* Case 3 */
			if (node->left->color != IB_RBT_BLACK
			    || node->right->color != IB_RBT_BLACK) {

				result = 0;
			} else {
				result = left_height;
			}
		/* Check if it's anything other than RED or BLACK. */
		} else if (node->color != IB_RBT_BLACK) {

			result = 0;
		} else {

			result = right_height + 1;
		}
	} else {
		result = 1;
	}

	return(result);
}

/**********************************************************************//**
Turn the node's right child's left sub-tree into node's right sub-tree.
This will also make node's right child it's parent. */
static
void
rbt_rotate_left(
/*============*/
	const ib_rbt_node_t*	nil,		/*!< in: nil node of the tree */
	ib_rbt_node_t*		node)		/*!< in: node to rotate */
{
	ib_rbt_node_t*	right = node->right;

	node->right = right->left;

	if (right->left != nil) {
		right->left->parent = node;
	}

	/* Right's new parent was node's parent. */
	right->parent = node->parent;

	/* Since root's parent is tree->nil and root->parent->left points
	back to root, we can avoid the check. */
	if (node == node->parent->left) {
		/* Node was on the left of its parent. */
		node->parent->left = right;
	} else {
		/* Node must have been on the right. */
		node->parent->right = right;
	}

	/* Finally, put node on right's left. */
	right->left = node;
	node->parent = right;
}

/**********************************************************************//**
Turn the node's left child's right sub-tree into node's left sub-tree.
This also make node's left child it's parent. */
static
void
rbt_rotate_right(
/*=============*/
	const ib_rbt_node_t*	nil,		/*!< in: nil node of tree */
	ib_rbt_node_t*		node)		/*!< in: node to rotate */
{
	ib_rbt_node_t*	left = node->left;

	node->left = left->right;

	if (left->right != nil) {
		left->right->parent = node;
	}

	/* Left's new parent was node's parent. */
	left->parent = node->parent;

	/* Since root's parent is tree->nil and root->parent->left points
	back to root, we can avoid the check. */
	if (node == node->parent->right) {
	    /* Node was on the left of its parent. */
            node->parent->right = left;
	} else {
	    /* Node must have been on the left. */
            node->parent->left = left;
	}

	/* Finally, put node on left's right. */
	left->right = node;
	node->parent = left;
}

/**********************************************************************//**
Append a node to the tree. */
static
ib_rbt_node_t*
rbt_tree_add_child(
/*===============*/
	const ib_rbt_t*	tree,
	ib_rbt_bound_t*	parent,
	ib_rbt_node_t*	node)
{
	/* Cast away the const. */
	ib_rbt_node_t*	last = (ib_rbt_node_t*) parent->last;

	if (last == tree->root || parent->result < 0) {
		last->left = node;
	} else {
		/* FIXME: We don't handle duplicates (yet)! */
		ut_a(parent->result != 0);

		last->right = node;
	}

	node->parent = last;

	return(node);
}

/**********************************************************************//**
Generic binary tree insert */
static
ib_rbt_node_t*
rbt_tree_insert(
/*============*/
	ib_rbt_t*	tree,
	const void*	key,
	ib_rbt_node_t*	node)
{
	ib_rbt_bound_t	parent;
	ib_rbt_node_t*	current = ROOT(tree);

	parent.result = 0;
	parent.last = tree->root;

	/* Regular binary search. */
	while (current != tree->nil) {

		parent.last = current;
		parent.result = tree->compare(key, current->value);

		if (parent.result < 0) {
			current = current->left;
		} else {
			current = current->right;
		}
	}

	ut_a(current == tree->nil);

	rbt_tree_add_child(tree, &parent, node);

	return(node);
}

/**********************************************************************//**
Balance a tree after inserting a node. */
static
void
rbt_balance_tree(
/*=============*/
	const ib_rbt_t*	tree,			/*!< in: tree to balance */
	ib_rbt_node_t*	node)			/*!< in: node that was inserted */
{
	const ib_rbt_node_t*	nil = tree->nil;
	ib_rbt_node_t*		parent = node->parent;

	/* Restore the red-black property. */
	node->color = IB_RBT_RED;

	while (node != ROOT(tree) && parent->color == IB_RBT_RED) {
		ib_rbt_node_t*	grand_parent = parent->parent;

		if (parent == grand_parent->left) {
			ib_rbt_node_t*	uncle = grand_parent->right;

			if (uncle->color == IB_RBT_RED) {

				/* Case 1 - change the colors. */
				uncle->color = IB_RBT_BLACK;
				parent->color = IB_RBT_BLACK;
				grand_parent->color = IB_RBT_RED;

				/* Move node up the tree. */
				node = grand_parent;

			} else {

				if (node == parent->right) {
					/* Right is a black node and node is
					to the right, case 2 - move node
					up and rotate. */
					node = parent;
					rbt_rotate_left(nil, node);
				}

				grand_parent = node->parent->parent;

				/* Case 3. */
				node->parent->color = IB_RBT_BLACK;
				grand_parent->color = IB_RBT_RED;

				rbt_rotate_right(nil, grand_parent);
			}

		} else {
			ib_rbt_node_t*	uncle = grand_parent->left;

			if (uncle->color == IB_RBT_RED) {

				/* Case 1 - change the colors. */
				uncle->color = IB_RBT_BLACK;
				parent->color = IB_RBT_BLACK;
				grand_parent->color = IB_RBT_RED;

				/* Move node up the tree. */
				node = grand_parent;

			} else {

				if (node == parent->left) {
					/* Left is a black node and node is to
					the right, case 2 - move node up and
					rotate. */
					node = parent;
					rbt_rotate_right(nil, node);
				}

				grand_parent = node->parent->parent;

				/* Case 3. */
				node->parent->color = IB_RBT_BLACK;
				grand_parent->color = IB_RBT_RED;

				rbt_rotate_left(nil, grand_parent);
			}
		}

		parent = node->parent;
	}

	/* Color the root black. */
	ROOT(tree)->color = IB_RBT_BLACK;
}

/**********************************************************************//**
Find the given node's successor.
@return	successor node or NULL if no successor */
static
ib_rbt_node_t*
rbt_find_successor(
/*===============*/
	const ib_rbt_t*		tree,		/*!< in: rb tree */
	const ib_rbt_node_t*	current)	/*!< in: this is declared const
						because it can be called via
						rbt_next() */
{
	const ib_rbt_node_t*	nil = tree->nil;
	ib_rbt_node_t*		next = current->right;

	/* Is there a sub-tree to the right that we can follow. */
	if (next != nil) {

		/* Follow the left most links of the current right child. */
		while (next->left != nil) {
			next = next->left;
		}

	} else { /* We will have to go up the tree to find the successor. */
		ib_rbt_node_t*	parent = current->parent;

		/* Cast away the const. */
		next = (ib_rbt_node_t*) current;

		while (parent != tree->root && next == parent->right) {
			next = parent;
			parent = next->parent;
		}

		next = (parent == tree->root) ? NULL : parent;
	}

	return(next);
}

/**********************************************************************//**
Find the given node's precedecessor.
@return	predecessor node or NULL if no predecesor */
static
ib_rbt_node_t*
rbt_find_predecessor(
/*=================*/
	const ib_rbt_t*		tree,		/*!< in: rb tree */
	const ib_rbt_node_t*	current)	/*!< in: this is declared const
						because it can be called via
						rbt_prev() */
{
	const ib_rbt_node_t*	nil = tree->nil;
	ib_rbt_node_t*		prev = current->left;

	/* Is there a sub-tree to the left that we can follow. */
	if (prev != nil) {

		/* Follow the right most links of the current left child. */
		while (prev->right != nil) {
			prev = prev->right;
		}

	} else { /* We will have to go up the tree to find the precedecessor. */
		ib_rbt_node_t*	parent = current->parent;

		/* Cast away the const. */
		prev = (ib_rbt_node_t*)current;

		while (parent != tree->root && prev == parent->left) {
			prev = parent;
			parent = prev->parent;
		}

		prev = (parent == tree->root) ? NULL : parent;
	}

	return(prev);
}

/**********************************************************************//**
Replace node with child. After applying transformations eject becomes
an orphan. */
static
void
rbt_eject_node(
/*===========*/
	ib_rbt_node_t*	eject,			/*!< in: node to eject */
	ib_rbt_node_t*	node)			/*!< in: node to replace with */
{
	/* Update the to be ejected node's parent's child pointers. */
	if (eject->parent->left == eject) {
		eject->parent->left = node;
	} else if (eject->parent->right == eject) {
		eject->parent->right = node;
	} else {
		ut_a(0);
	}
	/* eject is now an orphan but otherwise its pointers
	and color are left intact. */

	node->parent = eject->parent;
}

/**********************************************************************//**
Replace a node with another node. */
static
void
rbt_replace_node(
/*=============*/
	ib_rbt_node_t*	replace,		/*!< in: node to replace */
	ib_rbt_node_t*	node)			/*!< in: node to replace with */
{
	ib_rbt_color_t	color = node->color;

	/* Update the node pointers. */
	node->left = replace->left;
	node->right = replace->right;

	/* Update the child node pointers. */
	node->left->parent = node;
	node->right->parent = node;

	/* Make the parent of replace point to node. */
	rbt_eject_node(replace, node);

	/* Swap the colors. */
	node->color = replace->color;
	replace->color = color;
}

/**********************************************************************//**
Detach node from the tree replacing it with one of it's children.
@return	the child node that now occupies the position of the detached node */
static
ib_rbt_node_t*
rbt_detach_node(
/*============*/
	const ib_rbt_t*	tree,			/*!< in: rb tree */
	ib_rbt_node_t*	node)			/*!< in: node to detach */
{
	ib_rbt_node_t*		child;
	const ib_rbt_node_t*	nil = tree->nil;

	if (node->left != nil && node->right != nil) {
		/* Case where the node to be deleted has two children. */
		ib_rbt_node_t*	successor = rbt_find_successor(tree, node);

		ut_a(successor != nil);
		ut_a(successor->parent != nil);
		ut_a(successor->left == nil);

		child = successor->right;

		/* Remove the successor node and replace with its child. */
		rbt_eject_node(successor, child);

		/* Replace the node to delete with its successor node. */
		rbt_replace_node(node, successor);
	} else {
		ut_a(node->left == nil || node->right == nil);

		child = (node->left != nil) ? node->left : node->right;

		/* Replace the node to delete with one of it's children. */
		rbt_eject_node(node, child);
	}

	/* Reset the node links. */
	node->parent = node->right = node->left = tree->nil;

	return(child);
}

/**********************************************************************//**
Rebalance the right sub-tree after deletion.
@return	node to rebalance if more rebalancing required else NULL */
static
ib_rbt_node_t*
rbt_balance_right(
/*==============*/
	const ib_rbt_node_t*	nil,		/*!< in: rb tree nil node */
	ib_rbt_node_t*		parent,		/*!< in: parent node */
	ib_rbt_node_t*		sibling)	/*!< in: sibling node */
{
	ib_rbt_node_t*		node = NULL;

	ut_a(sibling != nil);

	/* Case 3. */
	if (sibling->color == IB_RBT_RED) {

		parent->color = IB_RBT_RED;
		sibling->color = IB_RBT_BLACK;

		rbt_rotate_left(nil, parent);

		sibling = parent->right;

		ut_a(sibling != nil);
	}

	/* Since this will violate case 3 because of the change above. */
	if (sibling->left->color == IB_RBT_BLACK
	    && sibling->right->color == IB_RBT_BLACK) {

		node = parent; /* Parent needs to be rebalanced too. */
		sibling->color = IB_RBT_RED;

	} else {
		if (sibling->right->color == IB_RBT_BLACK) {

			ut_a(sibling->left->color == IB_RBT_RED);

			sibling->color = IB_RBT_RED;
			sibling->left->color = IB_RBT_BLACK;

			rbt_rotate_right(nil, sibling);

			sibling = parent->right;
			ut_a(sibling != nil);
		}

		sibling->color = parent->color;
		sibling->right->color = IB_RBT_BLACK;

		parent->color = IB_RBT_BLACK;

		rbt_rotate_left(nil, parent);
	}

	return(node);
}

/**********************************************************************//**
Rebalance the left sub-tree after deletion.
@return	node to rebalance if more rebalancing required else NULL */
static
ib_rbt_node_t*
rbt_balance_left(
/*=============*/
	const ib_rbt_node_t*	nil,		/*!< in: rb tree nil node */
	ib_rbt_node_t*		parent,		/*!< in: parent node */
	ib_rbt_node_t*		sibling)	/*!< in: sibling node */
{
	ib_rbt_node_t*	node = NULL;

	ut_a(sibling != nil);

	/* Case 3. */
	if (sibling->color == IB_RBT_RED) {

		parent->color = IB_RBT_RED;
		sibling->color = IB_RBT_BLACK;

		rbt_rotate_right(nil, parent);
		sibling = parent->left;

		ut_a(sibling != nil);
	}

	/* Since this will violate case 3 because of the change above. */
	if (sibling->right->color == IB_RBT_BLACK
	    && sibling->left->color == IB_RBT_BLACK) {

		node = parent; /* Parent needs to be rebalanced too. */
		sibling->color = IB_RBT_RED;

	} else {
		if (sibling->left->color == IB_RBT_BLACK) {

			ut_a(sibling->right->color == IB_RBT_RED);

			sibling->color = IB_RBT_RED;
			sibling->right->color = IB_RBT_BLACK;

			rbt_rotate_left(nil, sibling);

			sibling = parent->left;

			ut_a(sibling != nil);
		}

		sibling->color = parent->color;
		sibling->left->color = IB_RBT_BLACK;

		parent->color = IB_RBT_BLACK;

		rbt_rotate_right(nil, parent);
	}

	return(node);
}

/**********************************************************************//**
Delete the node and rebalance the tree if necessary */
static
void
rbt_remove_node_and_rebalance(
/*==========================*/
	ib_rbt_t*		tree,		/*!< in: rb tree */
	ib_rbt_node_t*		node)		/*!< in: node to remove */
{
	/* Detach node and get the node that will be used
	as rebalance start. */
	ib_rbt_node_t*	child = rbt_detach_node(tree, node);

	if (node->color == IB_RBT_BLACK) {
		ib_rbt_node_t*	last = child;

		ROOT(tree)->color = IB_RBT_RED;

		while (child && child->color == IB_RBT_BLACK) {
			ib_rbt_node_t*	parent = child->parent;

			/* Did the deletion cause an imbalance in the
			parents left sub-tree. */
			if (parent->left == child) {

				child = rbt_balance_right(
					tree->nil, parent, parent->right);

			} else if (parent->right == child) {

				child = rbt_balance_left(
					tree->nil, parent, parent->left);

			} else {
				ut_error;
			}

			if (child) {
				last = child;
			}
		}

		ut_a(last);

		last->color = IB_RBT_BLACK;
		ROOT(tree)->color = IB_RBT_BLACK;
	}

	/* Note that we have removed a node from the tree. */
	--tree->n_nodes;
}

/**********************************************************************//**
Recursively free the nodes. */
static
void
rbt_free_node(
/*==========*/
	ib_rbt_node_t*	node,			/*!< in: node to free */
	ib_rbt_node_t*	nil)			/*!< in: rb tree nil node */
{
	if (node != nil) {
		rbt_free_node(node->left, nil);
		rbt_free_node(node->right, nil);

		ut_free(node);
	}
}

/**********************************************************************//**
Free all the nodes and free the tree. */
UNIV_INTERN
void
rbt_free(
/*=====*/
	ib_rbt_t*	tree)			/*!< in: rb tree to free */
{
	rbt_free_node(tree->root, tree->nil);
	ut_free(tree->nil);
	ut_free(tree);
}

/**********************************************************************//**
Create an instance of a red black tree.
@return	an empty rb tree */
UNIV_INTERN
ib_rbt_t*
rbt_create(
/*=======*/
	size_t		sizeof_value,		/*!< in: sizeof data item */
	ib_rbt_compare	compare)		/*!< in: fn to compare items */
{
	ib_rbt_t*	tree;
	ib_rbt_node_t*	node;

	tree = (ib_rbt_t*) ut_malloc(sizeof(*tree));
	memset(tree, 0, sizeof(*tree));

	tree->sizeof_value = sizeof_value;

	/* Create the sentinel (NIL) node. */
	node = tree->nil = (ib_rbt_node_t*) ut_malloc(sizeof(*node));
	memset(node, 0, sizeof(*node));

	node->color = IB_RBT_BLACK;
	node->parent = node->left = node->right = node;

	/* Create the "fake" root, the real root node will be the
	left child of this node. */
	node = tree->root = (ib_rbt_node_t*) ut_malloc(sizeof(*node));
	memset(node, 0, sizeof(*node));

	node->color = IB_RBT_BLACK;
	node->parent = node->left = node->right = tree->nil;

	tree->compare = compare;

	return(tree);
}

/**********************************************************************//**
Generic insert of a value in the rb tree.
@return	inserted node */
UNIV_INTERN
const ib_rbt_node_t*
rbt_insert(
/*=======*/
	ib_rbt_t*	tree,			/*!< in: rb tree */
	const void*	key,			/*!< in: key for ordering */
	const void*	value)			/*!< in: value of key, this value
						is copied to the node */
{
	ib_rbt_node_t*	node;

	/* Create the node that will hold the value data. */
	node = (ib_rbt_node_t*) ut_malloc(SIZEOF_NODE(tree));

	memcpy(node->value, value, tree->sizeof_value);
	node->parent = node->left = node->right = tree->nil;

	/* Insert in the tree in the usual way. */
	rbt_tree_insert(tree, key, node);
	rbt_balance_tree(tree, node);

	++tree->n_nodes;

	return(node);
}

/**********************************************************************//**
Add a new node to the tree, useful for data that is pre-sorted.
@return	appended node */
UNIV_INTERN
const ib_rbt_node_t*
rbt_add_node(
/*=========*/
	ib_rbt_t*	tree,			/*!< in: rb tree */
	ib_rbt_bound_t*	parent,			/*!< in: bounds */
	const void*	value)			/*!< in: this value is copied
						to the node */
{
	ib_rbt_node_t*	node;

	/* Create the node that will hold the value data */
	node = (ib_rbt_node_t*) ut_malloc(SIZEOF_NODE(tree));

	memcpy(node->value, value, tree->sizeof_value);
	return(rbt_add_preallocated_node(tree, parent, node));
}

/****************************************************************//**
Add a new caller-provided node to tree at the specified position.
The node must have its key fields initialized correctly.
@return added node */
UNIV_INTERN
const ib_rbt_node_t*
rbt_add_preallocated_node(
/*======================*/
	ib_rbt_t*	tree,			/*!< in: rb tree */
	ib_rbt_bound_t*	parent,			/*!< in: parent */
	ib_rbt_node_t*	node)			/*!< in: node */
{
	node->parent = node->left = node->right = tree->nil;

	/* If tree is empty */
	if (parent->last == NULL) {
		parent->last = tree->root;
	}

	/* Append the node, the hope here is that the caller knows
	   what s/he is doing. */
	rbt_tree_add_child(tree, parent, node);
	rbt_balance_tree(tree, node);

	++tree->n_nodes;

#if	defined(IB_RBT_TESTING)
	ut_a(rbt_validate(tree));
#endif
	return(node);
}


/**********************************************************************//**
Find a matching node in the rb tree.
@return	NULL if not found else the node where key was found */
UNIV_INTERN
const ib_rbt_node_t*
rbt_lookup(
/*=======*/
	const ib_rbt_t*	tree,			/*!< in: rb tree */
	const void*	key)			/*!< in: key to use for search */
{
	const ib_rbt_node_t*	current = ROOT(tree);

	/* Regular binary search. */
	while (current != tree->nil) {
		int	result = tree->compare(key, current->value);

		if (result < 0) {
			current = current->left;
		} else if (result > 0) {
			current = current->right;
		} else {
			break;
		}
	}

	return(current != tree->nil ? current : NULL);
}

/**********************************************************************//**
Delete a node indentified by key.
@return	TRUE if success FALSE if not found */
UNIV_INTERN
ibool
rbt_delete(
/*=======*/
	ib_rbt_t*	tree,			/*!< in: rb tree */
	const void*	key)			/*!< in: key to delete */
{
	ibool		deleted = FALSE;
	ib_rbt_node_t*	node = (ib_rbt_node_t*) rbt_lookup(tree, key);

	if (node) {
		rbt_remove_node_and_rebalance(tree, node);

		ut_free(node);
		deleted = TRUE;
	}

	return(deleted);
}

/**********************************************************************//**
Remove a node from the rb tree, the node is not free'd, that is the
callers responsibility.
@return	deleted node but without the const */
UNIV_INTERN
ib_rbt_node_t*
rbt_remove_node(
/*============*/
	ib_rbt_t*		tree,		/*!< in: rb tree */
	const ib_rbt_node_t*	const_node)	/*!< in: node to delete, this
						is a fudge and declared const
						because the caller can access
						only const nodes */
{
	/* Cast away the const. */
	rbt_remove_node_and_rebalance(tree, (ib_rbt_node_t*) const_node);

	/* This is to make it easier to do something like this:
		ut_free(rbt_remove_node(node));
	*/

	return((ib_rbt_node_t*) const_node);
}

/**********************************************************************//**
Find the node that has the lowest key that is >= key.
@return	node satisfying the lower bound constraint or NULL */
UNIV_INTERN
const ib_rbt_node_t*
rbt_lower_bound(
/*============*/
	const ib_rbt_t*	tree,			/*!< in: rb tree */
	const void*	key)			/*!< in: key to search */
{
	ib_rbt_node_t*	lb_node = NULL;
	ib_rbt_node_t*	current = ROOT(tree);

	while (current != tree->nil) {
		int result = tree->compare(key, current->value);

		if (result > 0) {

			current = current->right;

		} else if (result < 0) {

			lb_node = current;
			current = current->left;

		} else {
			lb_node = current;
			break;
		}
	}

	return(lb_node);
}

/**********************************************************************//**
Find the node that has the greatest key that is <= key.
@return	node satisfying the upper bound constraint or NULL */
UNIV_INTERN
const ib_rbt_node_t*
rbt_upper_bound(
/*============*/
	const ib_rbt_t*	tree,			/*!< in: rb tree */
	const void*	key)			/*!< in: key to search */
{
	ib_rbt_node_t*	ub_node = NULL;
	ib_rbt_node_t*	current = ROOT(tree);

	while (current != tree->nil) {
		int result = tree->compare(key, current->value);

		if (result > 0) {

			ub_node = current;
			current = current->right;

		} else if (result < 0) {

			current = current->left;

		} else {
			ub_node = current;
			break;
		}
	}

	return(ub_node);
}

/**********************************************************************//**
Find the node that has the greatest key that is <= key.
@return	value of result */
UNIV_INTERN
int
rbt_search(
/*=======*/
	const ib_rbt_t*	tree,			/*!< in: rb tree */
	ib_rbt_bound_t*	parent,			/*!< in: search bounds */
	const void*	key)			/*!< in: key to search */
{
	ib_rbt_node_t*	current = ROOT(tree);

	/* Every thing is greater than the NULL root. */
	parent->result = 1;
	parent->last = NULL;

	while (current != tree->nil) {

		parent->last = current;
		parent->result = tree->compare(key, current->value);

		if (parent->result > 0) {
			current = current->right;
		} else if (parent->result < 0) {
			current = current->left;
		} else {
			break;
		}
	}

	return(parent->result);
}

/**********************************************************************//**
Find the node that has the greatest key that is <= key. But use the
supplied comparison function.
@return	value of result */
UNIV_INTERN
int
rbt_search_cmp(
/*===========*/
	const ib_rbt_t*	tree,			/*!< in: rb tree */
	ib_rbt_bound_t*	parent,			/*!< in: search bounds */
	const void*	key,			/*!< in: key to search */
	ib_rbt_compare	compare)		/*!< in: fn to compare items */
{
	ib_rbt_node_t*	current = ROOT(tree);

	/* Every thing is greater than the NULL root. */
	parent->result = 1;
	parent->last = NULL;

	while (current != tree->nil) {

		parent->last = current;
		parent->result = compare(key, current->value);

		if (parent->result > 0) {
			current = current->right;
		} else if (parent->result < 0) {
			current = current->left;
		} else {
			break;
		}
	}

	return(parent->result);
}

/**********************************************************************//**
Return the left most node in the tree. */
UNIV_INTERN
const ib_rbt_node_t*
rbt_first(
/*======*/
						/* out leftmost node or NULL */
	const ib_rbt_t*	tree)			/* in: rb tree */
{
	ib_rbt_node_t*	first = NULL;
	ib_rbt_node_t*	current = ROOT(tree);

	while (current != tree->nil) {
		first = current;
		current = current->left;
	}

	return(first);
}

/**********************************************************************//**
Return the right most node in the tree.
@return	the rightmost node or NULL */
UNIV_INTERN
const ib_rbt_node_t*
rbt_last(
/*=====*/
	const ib_rbt_t*	tree)			/*!< in: rb tree */
{
	ib_rbt_node_t*	last = NULL;
	ib_rbt_node_t*	current = ROOT(tree);

	while (current != tree->nil) {
		last = current;
		current = current->right;
	}

	return(last);
}

/**********************************************************************//**
Return the next node.
@return	node next from current */
UNIV_INTERN
const ib_rbt_node_t*
rbt_next(
/*=====*/
	const ib_rbt_t*		tree,		/*!< in: rb tree */
	const ib_rbt_node_t*	current)	/*!< in: current node */
{
	return(current ? rbt_find_successor(tree, current) : NULL);
}

/**********************************************************************//**
Return the previous node.
@return	node prev from current */
UNIV_INTERN
const ib_rbt_node_t*
rbt_prev(
/*=====*/
	const ib_rbt_t*		tree,		/*!< in: rb tree */
	const ib_rbt_node_t*	current)	/*!< in: current node */
{
	return(current ? rbt_find_predecessor(tree, current) : NULL);
}

/**********************************************************************//**
Reset the tree. Delete all the nodes. */
UNIV_INTERN
void
rbt_clear(
/*======*/
	ib_rbt_t*	tree)			/*!< in: rb tree */
{
	rbt_free_node(ROOT(tree), tree->nil);
	rbt_reset(tree);
}

/****************************************************************//**
Clear the tree without deleting and freeing its nodes. */
UNIV_INTERN
void
rbt_reset(
/*======*/
	ib_rbt_t*	tree)			/*!< in: rb tree */
{
	tree->n_nodes = 0;
	tree->root->left = tree->root->right = tree->nil;
}

/**********************************************************************//**
Merge the node from dst into src. Return the number of nodes merged.
@return	no. of recs merged */
UNIV_INTERN
ulint
rbt_merge_uniq(
/*===========*/
	ib_rbt_t*	dst,			/*!< in: dst rb tree */
	const ib_rbt_t*	src)			/*!< in: src rb tree */
{
	ib_rbt_bound_t		parent;
	ulint			n_merged = 0;
	const	ib_rbt_node_t*	src_node = rbt_first(src);

	if (rbt_empty(src) || dst == src) {
		return(0);
	}

	for (/* No op */; src_node; src_node = rbt_next(src, src_node)) {

		if (rbt_search(dst, &parent, src_node->value) != 0) {
			rbt_add_node(dst, &parent, src_node->value);
			++n_merged;
		}
	}

	return(n_merged);
}

/**********************************************************************//**
Merge the node from dst into src. Return the number of nodes merged.
Delete the nodes from src after copying node to dst. As a side effect
the duplicates will be left untouched in the src.
@return	no. of recs merged */
UNIV_INTERN
ulint
rbt_merge_uniq_destructive(
/*=======================*/
	ib_rbt_t*	dst,			/*!< in: dst rb tree */
	ib_rbt_t*	src)			/*!< in: src rb tree */
{
	ib_rbt_bound_t	parent;
	ib_rbt_node_t*	src_node;
	ulint		old_size = rbt_size(dst);

	if (rbt_empty(src) || dst == src) {
		return(0);
	}

	for (src_node = (ib_rbt_node_t*) rbt_first(src); src_node; /* */) {
		ib_rbt_node_t*	prev = src_node;

		src_node = (ib_rbt_node_t*)rbt_next(src, prev);

		/* Skip duplicates. */
		if (rbt_search(dst, &parent, prev->value) != 0) {

			/* Remove and reset the node but preserve
			the node (data) value. */
			rbt_remove_node_and_rebalance(src, prev);

			/* The nil should be taken from the dst tree. */
			prev->parent = prev->left = prev->right = dst->nil;
			rbt_tree_add_child(dst, &parent, prev);
			rbt_balance_tree(dst, prev);

			++dst->n_nodes;
		}
	}

#if	defined(IB_RBT_TESTING)
	ut_a(rbt_validate(dst));
	ut_a(rbt_validate(src));
#endif
	return(rbt_size(dst) - old_size);
}

/**********************************************************************//**
Check that every path from the root to the leaves has the same count and
the tree nodes are in order.
@return	TRUE if OK FALSE otherwise */
UNIV_INTERN
ibool
rbt_validate(
/*=========*/
	const ib_rbt_t*	tree)		/*!< in: RB tree to validate */
{
	if (rbt_count_black_nodes(tree, ROOT(tree)) > 0) {
		return(rbt_check_ordering(tree));
	}

	return(FALSE);
}

/**********************************************************************//**
Iterate over the tree in depth first order. */
UNIV_INTERN
void
rbt_print(
/*======*/
	const ib_rbt_t*		tree,		/*!< in: tree to traverse */
	ib_rbt_print_node	print)		/*!< in: print function */
{
	rbt_print_subtree(tree, ROOT(tree), print);
}