//-----------------------------------------------------------------------------
// Copyright © 2003 - Philip Howard - All rights reserved
//
// 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; either version 2
// of the License, or (at your option) any later version.
//
// 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., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
//-----------------------------------------------------------------------------
// package	libh/avl
// homepage	http://libh.slashusr.org/
//-----------------------------------------------------------------------------
// author	Philip Howard
// email	libh at ipal dot org
// homepage	http://phil.ipal.org/
//-----------------------------------------------------------------------------
// This file is best viewed using a fixed spaced font such as Courier
// and in a display at least 120 columns wide.
//-----------------------------------------------------------------------------

//-----------------------------------------------------------------------------
// G. M. Adelson-Velskii and E. M. Landis are the inventors of the algorithm
// bearing their initials, AVL.  Their algorithm for height-balanced binary
// search trees is the basis of the code in this package.  Some modification
// is made to the balancing operations, and features are added for practical
// purposes.
//-----------------------------------------------------------------------------

#include "avl_lib.h"

__PROTO_BEGIN__
//-----------------------------------------------------------------------------
// function	avl_delete
//
// purpose	Delete a specified node or the current node from a given
//		binary tree.
//
// arguments	1 (AVL *) pointer to root of the binary tree
//		2 (void *) pointer to node to delete, or NULL to delete the
//			currently selected node
//
// returns	(void *) pointer to deleted node.
//		(void *) NULL if no node deleted.
//
// note		The caller is responsible for returning the memory space
//		occupied by the deleted node if it was dynamically allocated.
//-----------------------------------------------------------------------------
void *
avl_delete (
    AVL *		arg_tree
    ,
    void *		arg_node
    )
__PROTO_END__
{
    avl_link *		link_p		;
    avl_link *		bal_p		;
    avl_link *		rep_p		;
    avl_link *		pa_p		;


#if AVL_CHECK_ARGS
    //---------------------------------
    // Make sure we have a binary tree.
    //---------------------------------
    if ( ! arg_tree ) return NULL;
#endif

    //--------------------------
    // Make sure we have a node.
    //--------------------------
    if ( arg_node ) {
	link_p = avl_node_to_link( arg_tree, arg_node );
    } else {
	if ( ! ( link_p = arg_tree->select ) ) return NULL;
    }

#if AVL_PARANOID_LOGIC
#if AVL_COUNT_ENABLE
    //------------------------------------------------------
    // Make sure there are supposed to be nodes in the tree.
    //------------------------------------------------------
    if ( avl_count_get_nodes( arg_tree ) < 1 ) return NULL;
#endif /* AVL_COUNT_ENABLE */
#endif /* AVL_PARANOID_LOGIC */

    //-----------------------------------------------
    // If this node is the selected one, unselect it.
    //-----------------------------------------------
    if ( link_p == arg_tree->select ) {
	arg_tree->select = NULL;
    }

    //-------------------------------
    // Get the deleted node's parent.
    //-------------------------------
    pa_p = link_p->pa;
    bal_p = pa_p;

    //-------------------------------------------------------------------
    // Decide which of several scenarios exists and handle appropriately.
    // In the midst of these changes, the tree structure is incomplete.
    // Thus calls to check or print the tree cannot be made here.
    //-------------------------------------------------------------------
    if ( ! link_p->lo ) {

	if ( ! link_p->hi ) {

	    //----------------------------------------------------------------
	    // Since the node to be deleted is a leaf node, having no lo link
	    // nor hi link, deletion involves finding which side the parent
	    // links to the deleted node and making it nil.  That side becomes
	    // shorter.  Re-balance from the parent.
	    //
	    //  _P_  ->  _P         _P_  -> _P_ <-- balance changed here
	    // O   D    O    -or-  D   O       O
	    //----------------------------------------------------------------
	    if ( bal_p->lo == link_p ) bal_p->lo = NULL;
#if AVL_PARANOID_LOGIC
	    else if ( bal_p->hi != link_p ) {
		avl_abort( arg_tree, link_p, "avl_delete: orphan node being deleted\n" );
		return NULL;
	    }
#endif /* AVL_PARANOID_LOGIC */
	    else bal_p->hi = NULL;

	} else {

	    //-------------------------------------------------------------
	    // Since the node to be deleted has a hi link but no lo link,
	    // deletion involves pulling up the hi link as the replacement.
	    // The side of the parent where the deleted node was linked is
	    // now shorter.  Re-balance from the parent.
	    //
	    //  _P_      _P_          _P_      _P_ <-- balance changed here
	    // O   D -> O   R  -or-  D   O -> R   O
	    //      R                 R
	    //-------------------------------------------------------------
	    ( rep_p = link_p->hi )->pa = bal_p;

	    //-- Link the parent to the replacement on the same side.
	    if ( bal_p->lo == link_p ) bal_p->lo = rep_p;
#if AVL_PARANOID_LOGIC
	    else if ( bal_p->hi != link_p ) {
		avl_abort( arg_tree, link_p, "avl_delete: orphan node being deleted\n" );
		return NULL;
	    }
#endif /* AVL_PARANOID_LOGIC */
	    else bal_p->hi = rep_p;

	}

    } else {

	if ( ! link_p->hi ) {

	    //-------------------------------------------------------------
	    // Since the node to be deleted has a lo link but no hi link,
	    // deletion involves pulling up the lo link as the replacement.
	    // The side of the parent where the deleted node was linked is
	    // now shorter.  Re-balance from the parent.
	    //
	    //  _P_      _P_          _P_      _P_ <-- balance changed here
	    // O   D -> O   R  -or-  D   O -> R   O
	    //    R                 R
	    //-------------------------------------------------------------
	    ( rep_p = link_p->lo )->pa = bal_p;

	    //-- Link the parent to the replacement on the same side.
	    if ( bal_p->hi == link_p ) bal_p->hi = rep_p;
#if AVL_PARANOID_LOGIC
	    else if ( bal_p->lo != link_p ) {
		avl_abort( arg_tree, link_p, "avl_delete: orphan node being deleted\n" );
		return NULL;
	    }
#endif /* AVL_PARANOID_LOGIC */
	    else bal_p->lo = rep_p;

	} else {

	    //----------------------------------------------------------------
	    // Since the node to be deleted has both a lo link and a hi link,
	    // deletion may or may not be simple, depending on whether one of
	    // the links can still be pulled up.  Such a link can be pulled up
	    // if it preserves the order of the tree.  That is only the case
	    // if its link on the nearer side (hi->lo or lo->hi) is nil.
	    //
	    // If the simple case does not exist, the nearest order node must
	    // be found to replace the deleted node.  That node will be either
	    // a leaf or a simple case itself, so extraction will be easy.
	    // Finding the nearest node involves stepping down the links on
	    // the side in the direction of the deleted node until one is nil.
	    //
	    // The simple case does not optimize the algorithm.  Instead, it
	    // may be an optimization to choose the side which is currently
	    // longer, as that may reduce the number of re-shuffles done to
	    // maintain balance.  The tree order can be preserved either way.
	    //----------------------------------------------------------------
	    if ( link_p->lo->depth < link_p->hi->depth ) {

		//--------------------------------------------------
		// This way is a choice to use the hi branch.  Check
		// to see if it has a lo link or is the simple case.
		//--------------------------------------------------
		if ( ( rep_p = link_p->hi )->lo ) {

		    //---------------------------------------------------------
		    // Since the hi branch has a lo link, we must follow down
		    // the lo links until we find a node with no lo link.  This
		    // is the lowest keyed node in the hi branch and thus will
		    // preserve the order of the tree when it replaces the
		    // deleted node.  Extract it by pulling up its hi branch.
		    //
		    //  _D__________       _R__________
		    // Y        ____O_ -> Y        ____O_
		    //      ___B_                _B_ <---balance changed here
		    //     R_                   X
		    //       X
		    //
		    // The above illustration shows only the case where the
		    // replacement is found 2 levels down.  Real cases may
		    // involve any number of levels.
		    //---------------------------------------------------------
		    while ( rep_p->lo ) rep_p = rep_p->lo;
		    bal_p = rep_p->pa;
		    bal_p->lo = rep_p->hi;
		    if ( rep_p->hi ) {
			rep_p->hi->pa = bal_p;
		    }

		    //-- Replacement inherits hi link, which is linked back.
		    ( rep_p->hi = link_p->hi )->pa = rep_p;

		} else {

		    //-------------------------------------------------------
		    // Since the hi branch has no lo link, its apex is the
		    // lowest keyed node in the hi branch and thus will
		    // preserve the order of the tree when it replaces the
		    // deleted node.  Extract it by pulling up its hi branch.
		    //
		    //  _D___        _R_ <---balance changed here
		    // Y     R_  -> Y   X
		    //         X
		    //-------------------------------------------------------
		    bal_p = rep_p;

		    //-- Replacement already has hi link.
		}

		//-- Replacement inherits lo link, which is linked back.
		( rep_p->lo = link_p->lo )->pa = rep_p;

	    } else {

		//--------------------------------------------------
		// This way is a choice to use the lo branch.  Check
		// to see if it has a hi link or is the simple case.
		//--------------------------------------------------
		if ( ( rep_p = link_p->lo )->hi ) {

		    //---------------------------------------------------------
		    // Since the lo branch has a hi link, we must follow down
		    // the hi links until we find a node with no hi link.  This
		    // is the highest keyed node in the lo branch and thus will
		    // preserve the order of the tree when it replaces the
		    // deleted node.  Extract it by pulling up its lo branch.
		    //
		    //   __________D_       __________R_
		    // _O____        Y -> _O____        Y
		    //      _O___              _O_ <---balance changed here
		    //          _R                X
		    //         X
		    //
		    // The above illustration shows only the case where the
		    // replacement is found 2 levels down.  Real cases may
		    // involve any number of levels.
		    //---------------------------------------------------------
		    while ( rep_p->hi ) rep_p = rep_p->hi;
		    bal_p = rep_p->pa;
		    bal_p->hi = rep_p->lo;
		    if ( rep_p->lo ) {
			rep_p->lo->pa = bal_p;
		    }

		    //-- Replacement inherits lo link, which is linked back.
		    ( rep_p->lo = link_p->lo )->pa = rep_p;

		} else {

		    //-------------------------------------------------------
		    // Since the lo branch has no hi link, its apex is the
		    // highest keyed node in the lo branch and thus will
		    // preserve the order of the tree when it replaces the
		    // deleted node.  Extract it by pulling up its lo branch.
		    //
		    //    ___D_      _R_ <---balance changed here
		    //  _R     Y -> X   Y
		    // X
		    //-------------------------------------------------------
		    bal_p = rep_p;

		    //-- Replacement already has lo link.
		}

		//-- Replacement inherits hi link, which is linked back.
		( rep_p->hi = link_p->hi )->pa = rep_p;
	    }

	    //-- Replacement inherits pa link, which is linked back (lo or hi).
	    rep_p->pa = pa_p;
	    if ( pa_p->lo == link_p ) pa_p->lo = rep_p;
#if AVL_PARANOID_LOGIC
	    else if ( pa_p->hi != link_p ) {
		avl_abort( arg_tree, link_p, "avl_delete: orphan node being deleted\n" );
		return NULL;
	    }
#endif /* AVL_PARANOID_LOGIC */
	    else pa_p->hi = rep_p;

	    //-- Replacement inherits depth.
	    rep_p->depth = link_p->depth;

	}
    }

    //-- Balance the tree from the determined point of possible imbalance.
    avl_balance( arg_tree, bal_p );

#if AVL_CLEAN_NODE
    //-- Clean the deleted node to detect misuse.
    link_p->pa		= NULL;
    link_p->lo		= NULL;
    link_p->hi		= NULL;
    link_p->depth	= 0;
#endif

    //-- Keep statistical counts.
    avl_count_dec_nodes( arg_tree );

    //-- Return deleted node.
    return avl_link_to_node( arg_tree, link_p );
}