/* ========================================================================== ** * ubi_AVLtree.c * * Copyright (C) 1991-1998 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 4.0 1998/03/10 03:37:09 crh * Major changes. * By adding the AVL balance field to the base ubi_btNode structure, I no * longer need AVL-specific ReplaceNode(), SwapNodes(), and InitNode() * functions. The Remove() function is also simplified. It's all much * cleaner. * This is rev. 4.0. The 3.x series was dropped. * * Revision 2.5 1997/12/23 04:00:42 crh * In this version, all constants & macros defined in the header file have * the ubi_tr prefix. Also cleaned up anything that gcc complained about * when run with '-pedantic -fsyntax-only -Wall'. * * 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 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_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 /* Standard C definitions, etc. */ /* ========================================================================== ** * Static data. */ static char ModuleID[] = "ubi_AVLtree\n\ \tRevision: 4.0\n\ \tDate: 1998/03/10 03:37:09\n\ \tAuthor: 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_btNodePtr L1( ubi_btNodePtr 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_btNodePtr tmp; tmp = p->Link[ubi_trRIGHT]; p->Link[ubi_trRIGHT] = tmp->Link[ubi_trLEFT]; tmp->Link[ubi_trLEFT] = p; tmp->Link[ubi_trPARENT] = p->Link[ubi_trPARENT]; tmp->gender = p->gender; if(tmp->Link[ubi_trPARENT]) (tmp->Link[ubi_trPARENT])->Link[(int)(tmp->gender)] = tmp; p->Link[ubi_trPARENT] = tmp; p->gender = ubi_trLEFT; if( p->Link[ubi_trRIGHT] ) { p->Link[ubi_trRIGHT]->Link[ubi_trPARENT] = p; (p->Link[ubi_trRIGHT])->gender = ubi_trRIGHT; } p->balance -= ubi_trNormalize( tmp->balance ); (tmp->balance)--; return( tmp ); } /* L1 */ static ubi_btNodePtr R1( ubi_btNodePtr 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_btNodePtr tmp; tmp = p->Link[ubi_trLEFT]; p->Link[ubi_trLEFT] = tmp->Link[ubi_trRIGHT]; tmp->Link[ubi_trRIGHT] = p; tmp->Link[ubi_trPARENT] = p->Link[ubi_trPARENT]; tmp->gender = p->gender; if(tmp->Link[ubi_trPARENT]) (tmp->Link[ubi_trPARENT])->Link[(int)(tmp->gender)] = tmp; p->Link[ubi_trPARENT] = tmp; p->gender = ubi_trRIGHT; if(p->Link[ubi_trLEFT]) { p->Link[ubi_trLEFT]->Link[ubi_trPARENT] = p; p->Link[ubi_trLEFT]->gender = ubi_trLEFT; } p->balance -= ubi_trNormalize( tmp->balance ); (tmp->balance)++; return( tmp ); } /* R1 */ static ubi_btNodePtr L2( ubi_btNodePtr 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_btNodePtr tmp, newroot; tmp = tree->Link[ubi_trRIGHT]; newroot = tmp->Link[ubi_trLEFT]; tmp->Link[ubi_trLEFT] = newroot->Link[ubi_trRIGHT]; newroot->Link[ubi_trRIGHT] = tmp; tree->Link[ubi_trRIGHT] = newroot->Link[ubi_trLEFT]; newroot->Link[ubi_trLEFT] = tree; newroot->Link[ubi_trPARENT] = tree->Link[ubi_trPARENT]; newroot->gender = tree->gender; tree->Link[ubi_trPARENT] = newroot; tree->gender = ubi_trLEFT; tmp->Link[ubi_trPARENT] = newroot; tmp->gender = ubi_trRIGHT; if( tree->Link[ubi_trRIGHT] ) { tree->Link[ubi_trRIGHT]->Link[ubi_trPARENT] = tree; tree->Link[ubi_trRIGHT]->gender = ubi_trRIGHT; } if( tmp->Link[ubi_trLEFT] ) { tmp->Link[ubi_trLEFT]->Link[ubi_trPARENT] = tmp; tmp->Link[ubi_trLEFT]->gender = ubi_trLEFT; } if(newroot->Link[ubi_trPARENT]) newroot->Link[ubi_trPARENT]->Link[(int)(newroot->gender)] = newroot; switch( newroot->balance ) { case ubi_trLEFT : tree->balance = ubi_trEQUAL; tmp->balance = ubi_trRIGHT; break; case ubi_trEQUAL: tree->balance = ubi_trEQUAL; tmp->balance = ubi_trEQUAL; break; case ubi_trRIGHT: tree->balance = ubi_trLEFT; tmp->balance = ubi_trEQUAL; break; } newroot->balance = ubi_trEQUAL; return( newroot ); } /* L2 */ static ubi_btNodePtr R2( ubi_btNodePtr 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_btNodePtr tmp, newroot; tmp = tree->Link[ubi_trLEFT]; newroot = tmp->Link[ubi_trRIGHT]; tmp->Link[ubi_trRIGHT] = newroot->Link[ubi_trLEFT]; newroot->Link[ubi_trLEFT] = tmp; tree->Link[ubi_trLEFT] = newroot->Link[ubi_trRIGHT]; newroot->Link[ubi_trRIGHT] = tree; newroot->Link[ubi_trPARENT] = tree->Link[ubi_trPARENT]; newroot->gender = tree->gender; tree->Link[ubi_trPARENT] = newroot; tree->gender = ubi_trRIGHT; tmp->Link[ubi_trPARENT] = newroot; tmp->gender = ubi_trLEFT; if( tree->Link[ubi_trLEFT] ) { tree->Link[ubi_trLEFT]->Link[ubi_trPARENT] = tree; tree->Link[ubi_trLEFT]->gender = ubi_trLEFT; } if( tmp->Link[ubi_trRIGHT] ) { tmp->Link[ubi_trRIGHT]->Link[ubi_trPARENT] = tmp; tmp->Link[ubi_trRIGHT]->gender = ubi_trRIGHT; } if(newroot->Link[ubi_trPARENT]) newroot->Link[ubi_trPARENT]->Link[(int)(newroot->gender)] = newroot; switch( newroot->balance ) { case ubi_trLEFT : tree->balance = ubi_trRIGHT; tmp->balance = ubi_trEQUAL; break; case ubi_trEQUAL : tree->balance = ubi_trEQUAL; tmp->balance = ubi_trEQUAL; break; case ubi_trRIGHT : tree->balance = ubi_trEQUAL; tmp->balance = ubi_trLEFT; break; } newroot->balance = ubi_trEQUAL; return( newroot ); } /* R2 */ static ubi_btNodePtr Adjust( ubi_btNodePtr 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 += ubi_trNormalize(LorR); else { char tallerbal; /* Balance value of the root of the taller subtree of p. */ tallerbal = p->Link[(int)LorR]->balance; if( ( ubi_trEQUAL == tallerbal ) || ( p->balance == tallerbal ) ) p = ( (ubi_trLEFT==LorR) ? R1(p) : L1(p) ); /* single rotation */ else p = ( (ubi_trLEFT==LorR) ? R2(p) : L2(p) ); /* double rotation */ } return( p ); } /* Adjust */ static ubi_btNodePtr Rebalance( ubi_btNodePtr Root, ubi_btNodePtr 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( ubi_trPARENT == subtree->gender ) return( subtree ); if( ubi_trEQUAL == subtree->balance ) return( Root ); LorR = subtree->gender; subtree = subtree->Link[ubi_trPARENT]; } return( Root ); } /* Rebalance */ static ubi_btNodePtr Debalance( ubi_btNodePtr Root, ubi_btNodePtr 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, ubi_trRevWay(LorR) ); if( ubi_trPARENT == subtree->gender ) return( subtree ); if( ubi_trEQUAL != subtree->balance ) return( Root ); LorR = subtree->gender; subtree = subtree->Link[ubi_trPARENT]; } return( Root ); } /* Debalance */ /* ========================================================================== ** * Public, exported (ie. not static-ly declared) functions... * -------------------------------------------------------------------------- ** */ ubi_trBool ubi_avlInsert( ubi_btRootPtr RootPtr, ubi_btNodePtr NewNode, ubi_btItemPtr ItemPtr, ubi_btNodePtr *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_btNode 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_btNodePtr 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 = ubi_trEQUAL; RootPtr->root = (ubi_btNodePtr)Rebalance( (ubi_btNodePtr)RootPtr->root, NewNode->Link[ubi_trPARENT], NewNode->gender ); } return( ubi_trTRUE ); } return( ubi_trFALSE ); /* Failure: could not replace an existing node. */ } /* ubi_avlInsert */ ubi_btNodePtr ubi_avlRemove( ubi_btRootPtr RootPtr, ubi_btNodePtr 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. * * ------------------------------------------------------------------------ ** */ { /* Let the base binary tree module do the removal, then rebalance. */ if( ubi_btRemove( RootPtr, DeadNode ) ) RootPtr->root = Debalance( RootPtr->root, DeadNode->Link[ubi_trPARENT], DeadNode->gender ); 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 - 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 that were used. If this value * is less than , 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 ============================== */