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+/* ========================================================================== **
+ * ubi_AVLtree.c
+ *
+ * Copyright (C) 1991-1997 by Christopher R. Hertel
+ *
+ * Email: crh@ubiqx.mn.org
+ * -------------------------------------------------------------------------- **
+ *
+ * This module provides an implementation of AVL height balanced binary
+ * trees. (Adelson-Velskii, Landis 1962)
+ *
+ * This file implements the core of the height-balanced (AVL) tree management
+ * routines. The header file, ubi_AVLtree.h, contains function prototypes
+ * for all "exported" functions.
+ *
+ * -------------------------------------------------------------------------- **
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Library General Public
+ * License as published by the Free Software Foundation; either
+ * version 2 of the License, or (at your option) any later version.
+ *
+ * This library 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
+ * Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with this library; if not, write to the Free
+ * Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+ *
+ * -------------------------------------------------------------------------- **
+ *
+ * $Log: ubi_AVLtree.c,v $
+ * Revision 1.1 1997/10/10 14:46:36 crh
+ * This is the ubiqx binary tree and linked list library.
+ * This library is being included as part of the Samba distribution.
+ * (Hurray!)
+ *
+ * Revision 2.4 1997/07/26 04:36:20 crh
+ * Andrew Leppard, aka "Grazgur", discovered that I still had my brains tied
+ * on backwards with respect to node deletion. I did some more digging and
+ * discovered that I was not changing the balance values correctly in the
+ * single rotation functions. Double rotation was working correctly because
+ * the formula for changing the balance values is the same for insertion or
+ * deletion. Not so for single rotation.
+ *
+ * I have tested the fix by loading the tree with over 44 thousand names,
+ * deleting 2,629 of them (all those in which the second character is 'u')
+ * and then walking the tree recursively to verify that the balance factor of
+ * each node is correct. Passed.
+ *
+ * Thanks Andrew!
+ *
+ * Also:
+ * + Changed ubi_TRUE and ubi_FALSE to ubi_trTRUE and ubi_trFALSE.
+ * + Rewrote the ubi_tr<func> macros because they weren't doing what I'd
+ * hoped they would do (see the bottom of the header file). They work now.
+ *
+ * Revision 2.3 1997/06/03 04:41:35 crh
+ * Changed TRUE and FALSE to ubi_TRUE and ubi_FALSE to avoid causing
+ * problems.
+ *
+ * Revision 2.2 1995/10/03 22:16:01 CRH
+ * Ubisized!
+ *
+ * Revision 2.1 95/03/09 23:45:59 CRH
+ * Added the ModuleID static string and function. These modules are now
+ * self-identifying.
+ *
+ * Revision 2.0 95/03/05 14:10:51 CRH
+ * This revision of ubi_AVLtree coincides with revision 2.0 of ubi_BinTree,
+ * and so includes all of the changes to that module. In addition, a bug in
+ * the node deletion process has been fixed.
+ *
+ * After rewriting the Locate() function in ubi_BinTree, I decided that it was
+ * time to overhaul this module. In the process, I discovered a bug related
+ * to node deletion. To fix the bug, I wrote function Debalance(). A quick
+ * glance will show that it is very similar to the Rebalance() function. In
+ * previous versions of this module, I tried to include the functionality of
+ * Debalance() within Rebalance(), with poor results.
+ *
+ * Revision 1.0 93/10/15 22:58:56 CRH
+ * With this revision, I have added a set of #define's that provide a single,
+ * standard API to all existing tree modules. Until now, each of the three
+ * existing modules had a different function and typedef prefix, as follows:
+ *
+ * Module Prefix
+ * ubi_BinTree ubi_bt
+ * ubi_AVLtree ubi_avl
+ * ubi_SplayTree ubi_spt
+ *
+ * To further complicate matters, only those portions of the base module
+ * (ubi_BinTree) that were superceeded in the new module had the new names.
+ * For example, if you were using ubi_AVLtree, the AVL node structure was
+ * named "ubi_avlNode", but the root structure was still "ubi_btRoot". Using
+ * SplayTree, the locate function was called "ubi_sptLocate", but the next
+ * and previous functions remained "ubi_btNext" and "ubi_btPrev".
+ *
+ * This was not too terrible if you were familiar with the modules and knew
+ * exactly which tree model you wanted to use. If you wanted to be able to
+ * change modules (for speed comparisons, etc), things could get messy very
+ * quickly.
+ *
+ * So, I have added a set of defined names that get redefined in any of the
+ * descendant modules. To use this standardized interface in your code,
+ * simply replace all occurances of "ubi_bt", "ubi_avl", and "ubi_spt" with
+ * "ubi_tr". The "ubi_tr" names will resolve to the correct function or
+ * datatype names for the module that you are using. Just remember to
+ * include the header for that module in your program file. Because these
+ * names are handled by the preprocessor, there is no added run-time
+ * overhead.
+ *
+ * Note that the original names do still exist, and can be used if you wish
+ * to write code directly to a specific module. This should probably only be
+ * done if you are planning to implement a new descendant type, such as
+ * red/black trees. CRH
+ *
+ * V0.0 - May, 1990 - Written by Christopher R. Hertel (CRH).
+ *
+ * ========================================================================= **
+ */
+
+#include "ubi_AVLtree.h" /* Header for THIS module. */
+#include <stdlib.h> /* Standard C definitions, etc. */
+
+/* ========================================================================== **
+ * Static data.
+ */
+
+static char ModuleID[] = "ubi_AVLtree\n\
+\t$Revision: 1.1 $\n\
+\t$Date: 1997/10/10 14:46:36 $\n\
+\t$Author: crh $\n";
+
+/* ========================================================================== **
+ * The next set of functions are the AVL balancing routines. There are left
+ * and right, single and double rotations. The rotation routines handle the
+ * rotations and reconnect all tree pointers that might get confused by the
+ * rotations. A pointer to the new subtree root node is returned.
+ *
+ * Note that L1 and R1 are identical, except that all the RIGHTs and LEFTs
+ * are reversed. The same is true for L2 and R2. I'm sure that there is
+ * a clever way to reduce the amount of code by combining these functions,
+ * but it might involve additional overhead, and it would probably be a pain
+ * to read, debug, etc.
+ * -------------------------------------------------------------------------- **
+ */
+
+static ubi_avlNodePtr L1( ubi_avlNodePtr p )
+ /* ------------------------------------------------------------------------ **
+ * Single rotate left.
+ *
+ * Input: p - Pointer to the root of a tree (possibly a subtree).
+ * Output: A pointer to the new root of the same subtree (now that node
+ * p has been moved).
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ ubi_avlNodePtr tmp;
+
+ tmp = p->Link[RIGHT];
+ p->Link[RIGHT] = tmp->Link[LEFT];
+ tmp->Link[LEFT] = p;
+
+ tmp->Link[PARENT] = p->Link[PARENT];
+ tmp->gender = p->gender;
+ if(tmp->Link[PARENT])
+ (tmp->Link[PARENT])->Link[(tmp->gender)] = tmp;
+ p->Link[PARENT] = tmp;
+ p->gender = LEFT;
+ if( p->Link[RIGHT] )
+ {
+ p->Link[RIGHT]->Link[PARENT] = p;
+ (p->Link[RIGHT])->gender = RIGHT;
+ }
+ p->balance -= Normalize( tmp->balance );
+ (tmp->balance)--;
+ return( tmp );
+ } /* L1 */
+
+static ubi_avlNodePtr R1( ubi_avlNodePtr p )
+ /* ------------------------------------------------------------------------ **
+ * Single rotate right.
+ *
+ * Input: p - Pointer to the root of a tree (possibly a subtree).
+ * Output: A pointer to the new root of the same subtree (now that node
+ * p has been moved).
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ ubi_avlNodePtr tmp;
+
+ tmp = p->Link[LEFT];
+ p->Link[LEFT] = tmp->Link[RIGHT];
+ tmp->Link[RIGHT] = p;
+
+ tmp->Link[PARENT] = p->Link[PARENT];
+ tmp->gender = p->gender;
+ if(tmp->Link[PARENT])
+ (tmp->Link[PARENT])->Link[(tmp->gender)] = tmp;
+ p->Link[PARENT] = tmp;
+ p->gender = RIGHT;
+ if(p->Link[LEFT])
+ {
+ p->Link[LEFT]->Link[PARENT] = p;
+ p->Link[LEFT]->gender = LEFT;
+ }
+ p->balance -= Normalize( tmp->balance );
+ (tmp->balance)++;
+ return( tmp );
+ } /* R1 */
+
+static ubi_avlNodePtr L2( ubi_avlNodePtr tree )
+ /* ------------------------------------------------------------------------ **
+ * Double rotate left.
+ *
+ * Input: p - Pointer to the root of a tree (possibly a subtree).
+ * Output: A pointer to the new root of the same subtree (now that node
+ * p has been moved).
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ ubi_avlNodePtr tmp, newroot;
+
+ tmp = tree->Link[RIGHT];
+ newroot = tmp->Link[LEFT];
+ tmp->Link[LEFT] = newroot->Link[RIGHT];
+ newroot->Link[RIGHT] = tmp;
+ tree->Link[RIGHT] = newroot->Link[LEFT];
+ newroot->Link[LEFT] = tree;
+
+ newroot->Link[PARENT] = tree->Link[PARENT];
+ newroot->gender = tree->gender;
+ tree->Link[PARENT] = newroot;
+ tree->gender = LEFT;
+ tmp->Link[PARENT] = newroot;
+ tmp->gender = RIGHT;
+
+ if( tree->Link[RIGHT] )
+ {
+ tree->Link[RIGHT]->Link[PARENT] = tree;
+ tree->Link[RIGHT]->gender = RIGHT;
+ }
+ if( tmp->Link[LEFT] )
+ {
+ tmp->Link[LEFT]->Link[PARENT] = tmp;
+ tmp->Link[LEFT]->gender = LEFT;
+ }
+ if(newroot->Link[PARENT])
+ newroot->Link[PARENT]->Link[newroot->gender] = newroot;
+
+ switch( newroot->balance )
+ {
+ case LEFT :
+ tree->balance = EQUAL; tmp->balance = RIGHT; break;
+ case EQUAL:
+ tree->balance = EQUAL; tmp->balance = EQUAL; break;
+ case RIGHT:
+ tree->balance = LEFT; tmp->balance = EQUAL; break;
+ }
+ newroot->balance = EQUAL;
+ return( newroot );
+ } /* L2 */
+
+static ubi_avlNodePtr R2( ubi_avlNodePtr tree )
+ /* ------------------------------------------------------------------------ **
+ * Double rotate right.
+ *
+ * Input: p - Pointer to the root of a tree (possibly a subtree).
+ * Output: A pointer to the new root of the same subtree (now that node
+ * p has been moved).
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ ubi_avlNodePtr tmp, newroot;
+
+ tmp = tree->Link[LEFT];
+ newroot = tmp->Link[RIGHT];
+ tmp->Link[RIGHT] = newroot->Link[LEFT];
+ newroot->Link[LEFT] = tmp;
+ tree->Link[LEFT] = newroot->Link[RIGHT];
+ newroot->Link[RIGHT] = tree;
+
+ newroot->Link[PARENT] = tree->Link[PARENT];
+ newroot->gender = tree->gender;
+ tree->Link[PARENT] = newroot;
+ tree->gender = RIGHT;
+ tmp->Link[PARENT] = newroot;
+ tmp->gender = LEFT;
+
+ if( tree->Link[LEFT] )
+ {
+ tree->Link[LEFT]->Link[PARENT] = tree;
+ tree->Link[LEFT]->gender = LEFT;
+ }
+ if( tmp->Link[RIGHT] )
+ {
+ tmp->Link[RIGHT]->Link[PARENT] = tmp;
+ tmp->Link[RIGHT]->gender = RIGHT;
+ }
+ if(newroot->Link[PARENT])
+ newroot->Link[PARENT]->Link[newroot->gender] = newroot;
+
+ switch( newroot->balance )
+ {
+ case LEFT :
+ tree->balance = RIGHT; tmp->balance = EQUAL; break;
+ case EQUAL :
+ tree->balance = EQUAL; tmp->balance = EQUAL; break;
+ case RIGHT :
+ tree->balance = EQUAL; tmp->balance = LEFT; break;
+ }
+ newroot->balance = EQUAL;
+ return( newroot );
+ } /* R2 */
+
+
+static ubi_avlNodePtr Adjust( ubi_avlNodePtr p, char LorR )
+ /* ------------------------------------------------------------------------ **
+ * Adjust the balance value at node *p. If necessary, rotate the subtree
+ * rooted at p.
+ *
+ * Input: p - A pointer to the node to be adjusted. One of the
+ * subtrees of this node has changed height, so the
+ * balance value at this node must be adjusted, possibly
+ * by rotating the tree at this node.
+ * LorR - Indicates the TALLER subtree.
+ *
+ * Output: A pointer to the (possibly new) root node of the subtree.
+ *
+ * Notes: This function may be called after a node has been added *or*
+ * deleted, so LorR indicates the TALLER subtree.
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ if( p->balance != LorR )
+ p->balance += Normalize(LorR);
+ else
+ {
+ char tallerbal; /* Balance value of the root of the taller subtree of p. */
+
+ tallerbal = p->Link[LorR]->balance;
+ if( ( EQUAL == tallerbal ) || ( p->balance == tallerbal ) )
+ p = ( (LEFT==LorR) ? R1(p) : L1(p) ); /* single rotation */
+ else
+ p = ( (LEFT==LorR) ? R2(p) : L2(p) ); /* double rotation */
+ }
+ return( p );
+ } /* Adjust */
+
+static ubi_avlNodePtr Rebalance( ubi_avlNodePtr Root,
+ ubi_avlNodePtr subtree,
+ char LorR )
+ /* ------------------------------------------------------------------------ **
+ * Rebalance the tree following an insertion.
+ *
+ * Input: Root - A pointer to the root node of the whole tree.
+ * subtree - A pointer to the node that has just gained a new
+ * child.
+ * LorR - Gender of the child that has just been gained.
+ *
+ * Output: A pointer to the (possibly new) root of the AVL tree.
+ * Rebalancing the tree moves nodes around a bit, so the node
+ * that *was* the root, may not be the root when we're finished.
+ *
+ * Notes: Rebalance() must walk up the tree from where we are (which is
+ * where the latest change occurred), rebalancing the subtrees
+ * along the way. The rebalancing operation can stop if the
+ * change at the current subtree root won't affect the rest of
+ * the tree. In the case of an addition, if a subtree root's
+ * balance becomes EQUAL, then we know that the height of that
+ * subtree has not changed, so we can exit.
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ while( subtree )
+ {
+ subtree = Adjust( subtree, LorR );
+ if( PARENT == subtree->gender )
+ return( subtree );
+ if( EQUAL == subtree->balance )
+ return( Root );
+ LorR = subtree->gender;
+ subtree = subtree->Link[PARENT];
+ }
+ return( Root );
+ } /* Rebalance */
+
+static ubi_avlNodePtr Debalance( ubi_avlNodePtr Root,
+ ubi_avlNodePtr subtree,
+ char LorR )
+ /* ------------------------------------------------------------------------ **
+ * Rebalance the tree following a deletion.
+ *
+ * Input: Root - A pointer to the root node of the whole tree.
+ * subtree - A pointer to the node who's child has just "left the
+ * nest".
+ * LorR - Gender of the child that left.
+ *
+ * Output: A pointer to the (possibly new) root of the AVL tree.
+ * Rebalancing the tree moves nodes around a bit, so the node
+ * that *was* the root, may not be the root when we're finished.
+ *
+ * Notes: Debalance() is subtly different from Rebalance() (above) in
+ * two respects.
+ * * When it calls Adjust(), it passes the *opposite* of LorR.
+ * This is because LorR, as passed into Debalance() indicates
+ * the shorter subtree. As we move up the tree, LorR is
+ * assigned the gender of the node that we are leaving (i.e.,
+ * the subtree that we just rebalanced).
+ * * We know that a subtree has not changed height if the
+ * balance becomes LEFT or RIGHT. This is the *opposite* of
+ * what happens in Rebalance().
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ while( subtree )
+ {
+ subtree = Adjust( subtree, RevWay(LorR) );
+ if( PARENT == subtree->gender )
+ return( subtree );
+ if( EQUAL != subtree->balance )
+ return( Root );
+ LorR = subtree->gender;
+ subtree = subtree->Link[PARENT];
+ }
+ return( Root );
+ } /* Debalance */
+
+
+/* -------------------------------------------------------------------------- **
+ * The next two functions are used for general tree manipulation. They are
+ * each slightly different from their ubi_BinTree counterparts.
+ * -------------------------------------------------------------------------- **
+ */
+
+static void ReplaceNode( ubi_avlNodePtr *parent,
+ ubi_avlNodePtr oldnode,
+ ubi_avlNodePtr newnode )
+ /* ------------------------------------------------------------------------ **
+ * Remove node oldnode from the tree, replacing it with node newnode.
+ *
+ * Input:
+ * parent - A pointer to he parent pointer of the node to be
+ * replaced. <parent> may point to the Link[] field of
+ * a parent node, or it may indicate the root pointer at
+ * the top of the tree.
+ * oldnode - A pointer to the node that is to be replaced.
+ * newnode - A pointer to the node that is to be installed in the
+ * place of <*oldnode>.
+ *
+ * Notes: Don't forget to free oldnode.
+ * The only difference between this function and the ubi_bt
+ * version is that the node size is sizeof( ubi_avlNode ), not
+ * sizeof( ubi_btNode ).
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ register int i;
+ register int avlNodeSize = sizeof( ubi_avlNode );
+
+ for( i = 0; i < avlNodeSize; i++ )
+ ((unsigned char *)newnode)[i] = ((unsigned char *)oldnode)[i];
+ (*parent) = newnode;
+
+ if(oldnode->Link[LEFT ] )
+ (oldnode->Link[LEFT ])->Link[PARENT] = newnode;
+ if(oldnode->Link[RIGHT] )
+ (oldnode->Link[RIGHT])->Link[PARENT] = newnode;
+ } /* ReplaceNode */
+
+static void SwapNodes( ubi_btRootPtr RootPtr,
+ ubi_avlNodePtr Node1,
+ ubi_avlNodePtr Node2 )
+ /* ------------------------------------------------------------------------ **
+ * This function swaps two nodes in the tree. Node1 will take the place of
+ * Node2, and Node2 will fill in the space left vacant by Node 1.
+ *
+ * Input:
+ * RootPtr - pointer to the tree header structure for this tree.
+ * Node1 - \
+ * > These are the two nodes which are to be swapped.
+ * Node2 - /
+ *
+ * Notes:
+ * This function does a three step swap, using a dummy node as a place
+ * holder. This function is used by ubi_avlRemove().
+ * The only difference between this function and its ubi_bt counterpart
+ * is that the nodes are ubi_avlNodes, not ubi_btNodes.
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ ubi_avlNodePtr *Parent;
+ ubi_avlNode dummy;
+ ubi_avlNodePtr dummy_p = &dummy;
+
+ if( Node1->Link[PARENT] )
+ Parent = &((Node1->Link[PARENT])->Link[Node1->gender]);
+ else
+ Parent = (ubi_avlNodePtr *)&(RootPtr->root);
+ ReplaceNode( Parent, Node1, dummy_p );
+
+ if( Node2->Link[PARENT] )
+ Parent = &((Node2->Link[PARENT])->Link[Node2->gender]);
+ else
+ Parent = (ubi_avlNodePtr *)&(RootPtr->root);
+ ReplaceNode( Parent, Node2, Node1 );
+
+ if( dummy_p->Link[PARENT] )
+ Parent = &((dummy_p->Link[PARENT])->Link[dummy_p->gender]);
+ else
+ Parent = (ubi_avlNodePtr *)&(RootPtr->root);
+ ReplaceNode( Parent, dummy_p, Node2 );
+ } /* SwapNodes */
+
+
+/* ========================================================================== **
+ * Public, exported (ie. not static-ly declared) functions...
+ * -------------------------------------------------------------------------- **
+ */
+
+ubi_avlNodePtr ubi_avlInitNode( ubi_avlNodePtr NodePtr )
+ /* ------------------------------------------------------------------------ **
+ * Initialize a tree node.
+ *
+ * Input: NodePtr - pointer to a ubi_btNode structure to be
+ * initialized.
+ * Output: a pointer to the initialized ubi_avlNode structure (ie. the
+ * same as the input pointer).
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ (void)ubi_btInitNode( (ubi_btNodePtr)NodePtr );
+ NodePtr->balance = EQUAL;
+ return( NodePtr );
+ } /* ubi_avlInitNode */
+
+ubi_trBool ubi_avlInsert( ubi_btRootPtr RootPtr,
+ ubi_avlNodePtr NewNode,
+ ubi_btItemPtr ItemPtr,
+ ubi_avlNodePtr *OldNode )
+ /* ------------------------------------------------------------------------ **
+ * This function uses a non-recursive algorithm to add a new element to
+ * the tree.
+ *
+ * Input: RootPtr - a pointer to the ubi_btRoot structure that indicates
+ * the root of the tree to which NewNode is to be added.
+ * NewNode - a pointer to an ubi_avlNode structure that is NOT
+ * part of any tree.
+ * ItemPtr - A pointer to the sort key that is stored within
+ * *NewNode. ItemPtr MUST point to information stored
+ * in *NewNode or an EXACT DUPLICATE. The key data
+ * indicated by ItemPtr is used to place the new node
+ * into the tree.
+ * OldNode - a pointer to an ubi_btNodePtr. When searching
+ * the tree, a duplicate node may be found. If
+ * duplicates are allowed, then the new node will
+ * be simply placed into the tree. If duplicates
+ * are not allowed, however, then one of two things
+ * may happen.
+ * 1) if overwritting *is not* allowed, this
+ * function will return FALSE (indicating that
+ * the new node could not be inserted), and
+ * *OldNode will point to the duplicate that is
+ * still in the tree.
+ * 2) if overwritting *is* allowed, then this
+ * function will swap **OldNode for *NewNode.
+ * In this case, *OldNode will point to the node
+ * that was removed (thus allowing you to free
+ * the node).
+ * ** If you are using overwrite mode, ALWAYS **
+ * ** check the return value of this parameter! **
+ * Note: You may pass NULL in this parameter, the
+ * function knows how to cope. If you do this,
+ * however, there will be no way to return a
+ * pointer to an old (ie. replaced) node (which is
+ * a problem if you are using overwrite mode).
+ *
+ * Output: a boolean value indicating success or failure. The function
+ * will return FALSE if the node could not be added to the tree.
+ * Such failure will only occur if duplicates are not allowed,
+ * nodes cannot be overwritten, AND a duplicate key was found
+ * within the tree.
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ ubi_avlNodePtr OtherP;
+
+ if( !(OldNode) ) OldNode = &OtherP;
+ if( ubi_btInsert( RootPtr,
+ (ubi_btNodePtr)NewNode,
+ ItemPtr,
+ (ubi_btNodePtr *)OldNode ) )
+ {
+ if( (*OldNode) )
+ NewNode->balance = (*OldNode)->balance;
+ else
+ {
+ NewNode->balance = EQUAL;
+ RootPtr->root = (ubi_btNodePtr)Rebalance( (ubi_avlNodePtr)RootPtr->root,
+ NewNode->Link[PARENT],
+ NewNode->gender );
+ }
+ return( ubi_trTRUE );
+ }
+ return( ubi_trFALSE ); /* Failure: could not replace an existing node. */
+ } /* ubi_avlInsert */
+
+ubi_avlNodePtr ubi_avlRemove( ubi_btRootPtr RootPtr,
+ ubi_avlNodePtr DeadNode )
+ /* ------------------------------------------------------------------------ **
+ * This function removes the indicated node from the tree, after which the
+ * tree is rebalanced.
+ *
+ * Input: RootPtr - A pointer to the header of the tree that contains
+ * the node to be removed.
+ * DeadNode - A pointer to the node that will be removed.
+ *
+ * Output: This function returns a pointer to the node that was removed
+ * from the tree (ie. the same as DeadNode).
+ *
+ * Note: The node MUST be in the tree indicated by RootPtr. If not,
+ * strange and evil things will happen to your trees.
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ ubi_btNodePtr p,
+ *parentp;
+
+ /* if the node has both left and right subtrees, then we have to swap
+ * it with another node.
+ */
+ if( (DeadNode->Link[LEFT]) && (DeadNode->Link[RIGHT]) )
+ SwapNodes( RootPtr, DeadNode, ubi_trPrev( DeadNode ) );
+
+ /* The parent of the node to be deleted may be another node, or it may be
+ * the root of the tree. Since we're not sure, it's best just to have
+ * a pointer to the parent pointer, whatever it is.
+ */
+ if( DeadNode->Link[PARENT] )
+ parentp = (ubi_btNodePtr *)
+ &((DeadNode->Link[PARENT])->Link[(DeadNode->gender)]);
+ else
+ parentp = &( RootPtr->root );
+
+ /* Now link the parent to the only grand-child. Patch up the gender and
+ * such, and rebalance.
+ */
+ if( EQUAL == DeadNode->balance )
+ (*parentp) = NULL;
+ else
+ {
+ p = (ubi_btNodePtr)(DeadNode->Link[(DeadNode->balance)]);
+ p->Link[PARENT] = (ubi_btNodePtr)DeadNode->Link[PARENT];
+ p->gender = DeadNode->gender;
+ (*parentp) = p;
+ }
+ RootPtr->root = (ubi_btNodePtr)Debalance( (ubi_avlNodePtr)RootPtr->root,
+ DeadNode->Link[PARENT],
+ DeadNode->gender );
+
+ (RootPtr->count)--;
+ return( DeadNode );
+ } /* ubi_avlRemove */
+
+int ubi_avlModuleID( int size, char *list[] )
+ /* ------------------------------------------------------------------------ **
+ * Returns a set of strings that identify the module.
+ *
+ * Input: size - The number of elements in the array <list>.
+ * list - An array of pointers of type (char *). This array
+ * should, initially, be empty. This function will fill
+ * in the array with pointers to strings.
+ * Output: The number of elements of <list> that were used. If this value
+ * is less than <size>, the values of the remaining elements are
+ * not guaranteed.
+ *
+ * Notes: Please keep in mind that the pointers returned indicate strings
+ * stored in static memory. Don't free() them, don't write over
+ * them, etc. Just read them.
+ * ------------------------------------------------------------------------ **
+ */
+ {
+ if( size > 0 )
+ {
+ list[0] = ModuleID;
+ if( size > 1 )
+ return( 1 + ubi_btModuleID( --size, &(list[1]) ) );
+ return( 1 );
+ }
+ return( 0 );
+ } /* ubi_avlModuleID */
+
+/* ============================== The End ============================== */