| 1 | /* $Id: avl_Base.cpp.h 98103 2023-01-17 14:15:46Z vboxsync $ */
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| 2 | /** @file
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| 3 | * kAVLBase - basic routines for all AVL trees.
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| 4 | */
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| 5 |
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| 6 | /*
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| 7 | * Copyright (C) 2006-2023 Oracle and/or its affiliates.
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| 8 | *
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| 9 | * This file is part of VirtualBox base platform packages, as
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| 10 | * available from https://www.virtualbox.org.
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| 11 | *
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| 12 | * This program is free software; you can redistribute it and/or
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| 13 | * modify it under the terms of the GNU General Public License
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| 14 | * as published by the Free Software Foundation, in version 3 of the
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| 15 | * License.
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| 16 | *
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| 17 | * This program is distributed in the hope that it will be useful, but
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| 18 | * WITHOUT ANY WARRANTY; without even the implied warranty of
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| 19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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| 20 | * General Public License for more details.
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| 21 | *
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| 22 | * You should have received a copy of the GNU General Public License
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| 23 | * along with this program; if not, see <https://www.gnu.org/licenses>.
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| 24 | *
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| 25 | * The contents of this file may alternatively be used under the terms
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| 26 | * of the Common Development and Distribution License Version 1.0
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| 27 | * (CDDL), a copy of it is provided in the "COPYING.CDDL" file included
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| 28 | * in the VirtualBox distribution, in which case the provisions of the
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| 29 | * CDDL are applicable instead of those of the GPL.
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| 30 | *
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| 31 | * You may elect to license modified versions of this file under the
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| 32 | * terms and conditions of either the GPL or the CDDL or both.
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| 33 | *
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| 34 | * SPDX-License-Identifier: GPL-3.0-only OR CDDL-1.0
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| 35 | */
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| 36 |
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| 37 | #ifndef _kAVLBase_h_
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| 38 | #define _kAVLBase_h_
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| 39 |
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| 40 |
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| 41 | /** @page pg_rt_kAVL kAVL Template configuration.
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| 42 | * @internal
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| 43 | *
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| 44 | * This is a template made to implement multiple AVL trees. The differences
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| 45 | * among the implementations are related to the key used.
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| 46 | *
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| 47 | * \#define KAVL_FN
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| 48 | * Use this to alter the names of the AVL functions.
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| 49 | * Must be defined.
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| 50 | *
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| 51 | * \#define KAVL_EQUAL_ALLOWED
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| 52 | * Define this to tell us that equal keys are allowed.
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| 53 | * Then Equal keys will be put in a list pointed to by pList in the KAVLNODECORE.
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| 54 | * This is by default not defined.
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| 55 | *
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| 56 | * \#define KAVL_CHECK_FOR_EQUAL_INSERT
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| 57 | * Define this to enable insert check for equal nodes.
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| 58 | * This is by default not defined.
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| 59 | *
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| 60 | * \#define KAVL_MAX_STACK
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| 61 | * Use this to specify the number of stack entries the stack will use when inserting
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| 62 | * and removing nodes from the tree. I think the size should be about
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| 63 | * log2(<max nodes>) + 3
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| 64 | * Must be defined.
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| 65 | *
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| 66 | */
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| 67 |
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| 68 | /*******************************************************************************
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| 69 | * Defined Constants And Macros *
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| 70 | *******************************************************************************/
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| 71 | #define AVL_HEIGHTOF(pNode) ((unsigned char)((pNode) != NULL ? pNode->uchHeight : 0))
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| 72 |
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| 73 | /** @def KAVL_GET_POINTER
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| 74 | * Reads a 'pointer' value.
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| 75 | *
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| 76 | * @returns The native pointer.
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| 77 | * @param pp Pointer to the pointer to read.
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| 78 | */
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| 79 |
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| 80 | /** @def KAVL_GET_POINTER_NULL
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| 81 | * Reads a 'pointer' value which can be KAVL_NULL.
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| 82 | *
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| 83 | * @returns The native pointer.
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| 84 | * @returns NULL pointer if KAVL_NULL.
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| 85 | * @param pp Pointer to the pointer to read.
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| 86 | */
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| 87 |
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| 88 | /** @def KAVL_SET_POINTER
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| 89 | * Writes a 'pointer' value.
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| 90 | * For offset-based schemes offset relative to pp is calculated and assigned to *pp.
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| 91 | *
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| 92 | * @returns stored pointer.
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| 93 | * @param pp Pointer to where to store the pointer.
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| 94 | * @param p Native pointer to assign to *pp.
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| 95 | */
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| 96 |
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| 97 | /** @def KAVL_SET_POINTER_NULL
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| 98 | * Writes a 'pointer' value which can be KAVL_NULL.
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| 99 | *
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| 100 | * For offset-based schemes offset relative to pp is calculated and assigned to *pp,
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| 101 | * if p is not KAVL_NULL of course.
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| 102 | *
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| 103 | * @returns stored pointer.
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| 104 | * @param pp Pointer to where to store the pointer.
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| 105 | * @param pp2 Pointer to where to pointer to assign to pp. This can be KAVL_NULL
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| 106 | */
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| 107 |
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| 108 | #ifndef KAVL_GET_POINTER
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| 109 | # ifdef KAVL_OFFSET
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| 110 | # define KAVL_GET_POINTER(pp) ( (PKAVLNODECORE)((intptr_t)(pp) + *(pp)) )
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| 111 | # define KAVL_GET_POINTER_NULL(pp) ( *(pp) != KAVL_NULL ? KAVL_GET_POINTER(pp) : NULL )
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| 112 | # define KAVL_SET_POINTER(pp, p) ( (*(pp)) = ((intptr_t)(p) - (intptr_t)(pp)) )
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| 113 | # define KAVL_SET_POINTER_NULL(pp, pp2) ( (*(pp)) = *(pp2) != KAVL_NULL ? (intptr_t)KAVL_GET_POINTER(pp2) - (intptr_t)(pp) : KAVL_NULL )
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| 114 | # else
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| 115 | # define KAVL_GET_POINTER(pp) ( *(pp) )
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| 116 | # define KAVL_GET_POINTER_NULL(pp) ( *(pp) )
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| 117 | # define KAVL_SET_POINTER(pp, p) ( (*(pp)) = (p) )
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| 118 | # define KAVL_SET_POINTER_NULL(pp, pp2) ( (*(pp)) = *(pp2) )
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| 119 | # endif
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| 120 | #endif
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| 121 |
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| 122 |
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| 123 | /** @def KAVL_NULL
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| 124 | * The NULL 'pointer' equivalent.
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| 125 | */
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| 126 | #ifndef KAVL_NULL
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| 127 | # ifdef KAVL_OFFSET
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| 128 | # define KAVL_NULL 0
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| 129 | # else
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| 130 | # define KAVL_NULL NULL
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| 131 | # endif
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| 132 | #endif
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| 133 |
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| 134 | #ifndef KAVL_RANGE
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| 135 | # define KAVL_R_IS_INTERSECTING(key1B, key2B, key1E, key2E) KAVL_E(key1B, key2B)
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| 136 | # define KAVL_R_IS_IDENTICAL(key1B, key2B, key1E, key2E) KAVL_E(key1B, key2B)
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| 137 | #endif
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| 138 |
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| 139 | /** @def KAVL_DECL
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| 140 | * Function declation macro in the RTDECL tradition.
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| 141 | * @param a_Type The function return type. */
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| 142 | #ifndef KAVL_DECL
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| 143 | # define KAVL_DECL(a_Type) RTDECL(a_Type)
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| 144 | #endif
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| 145 |
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| 146 |
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| 147 | /*******************************************************************************
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| 148 | * Structures and Typedefs *
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| 149 | *******************************************************************************/
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| 150 | /*
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| 151 | * A stack used to avoid recursive calls...
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| 152 | */
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| 153 | typedef struct _kAvlStack
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| 154 | {
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| 155 | unsigned cEntries;
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| 156 | PPKAVLNODECORE aEntries[KAVL_MAX_STACK];
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| 157 | } KAVLSTACK, *PKAVLSTACK;
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| 158 |
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| 159 | typedef struct _kAvlStack2
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| 160 | {
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| 161 | unsigned cEntries;
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| 162 | PKAVLNODECORE aEntries[KAVL_MAX_STACK];
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| 163 | char achFlags[KAVL_MAX_STACK];
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| 164 | } KAVLSTACK2, *PLAVLSTACK2;
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| 165 |
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| 166 |
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| 167 |
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| 168 | /**
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| 169 | * Rewinds a stack of pointers to pointers to nodes, rebalancing the tree.
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| 170 | * @param pStack Pointer to stack to rewind.
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| 171 | * @sketch LOOP thru all stack entries
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| 172 | * BEGIN
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| 173 | * Get pointer to pointer to node (and pointer to node) from the stack.
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| 174 | * IF 2 higher left subtree than in right subtree THEN
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| 175 | * BEGIN
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| 176 | * IF higher (or equal) left-sub-subtree than right-sub-subtree THEN
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| 177 | * * n+2|n+3
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| 178 | * / \ / \
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| 179 | * n+2 n ==> n+1 n+1|n+2
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| 180 | * / \ / \
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| 181 | * n+1 n|n+1 n|n+1 n
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| 182 | *
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| 183 | * Or with keys:
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| 184 | *
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| 185 | * 4 2
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| 186 | * / \ / \
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| 187 | * 2 5 ==> 1 4
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| 188 | * / \ / \
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| 189 | * 1 3 3 5
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| 190 | *
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| 191 | * ELSE
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| 192 | * * n+2
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| 193 | * / \ / \
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| 194 | * n+2 n n+1 n+1
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| 195 | * / \ ==> / \ / \
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| 196 | * n n+1 n L R n
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| 197 | * / \
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| 198 | * L R
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| 199 | *
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| 200 | * Or with keys:
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| 201 | * 6 4
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| 202 | * / \ / \
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| 203 | * 2 7 ==> 2 6
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| 204 | * / \ / \ / \
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| 205 | * 1 4 1 3 5 7
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| 206 | * / \
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| 207 | * 3 5
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| 208 | * END
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| 209 | * ELSE IF 2 higher in right subtree than in left subtree THEN
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| 210 | * BEGIN
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| 211 | * Same as above but left <==> right. (invert the picture)
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| 212 | * ELSE
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| 213 | * IF correct height THEN break
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| 214 | * ELSE correct height.
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| 215 | * END
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| 216 | */
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| 217 | DECLINLINE(void) KAVL_FN(Rebalance)(PKAVLSTACK pStack)
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| 218 | {
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| 219 | while (pStack->cEntries > 0)
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| 220 | {
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| 221 | /** @todo Perhaps some of these KAVL_SET_POINTER_NULL() cases could be optimized away.. */
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| 222 | PPKAVLNODECORE ppNode = pStack->aEntries[--pStack->cEntries];
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| 223 | PKAVLNODECORE pNode = KAVL_GET_POINTER(ppNode);
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| 224 | PKAVLNODECORE pLeftNode = KAVL_GET_POINTER_NULL(&pNode->pLeft);
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| 225 | unsigned char uchLeftHeight = AVL_HEIGHTOF(pLeftNode);
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| 226 | PKAVLNODECORE pRightNode = KAVL_GET_POINTER_NULL(&pNode->pRight);
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| 227 | unsigned char uchRightHeight = AVL_HEIGHTOF(pRightNode);
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| 228 |
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| 229 | if (uchRightHeight + 1 < uchLeftHeight)
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| 230 | {
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| 231 | PKAVLNODECORE pLeftLeftNode = KAVL_GET_POINTER_NULL(&pLeftNode->pLeft);
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| 232 | PKAVLNODECORE pLeftRightNode = KAVL_GET_POINTER_NULL(&pLeftNode->pRight);
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| 233 | unsigned char uchLeftRightHeight = AVL_HEIGHTOF(pLeftRightNode);
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| 234 |
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| 235 | if (AVL_HEIGHTOF(pLeftLeftNode) >= uchLeftRightHeight)
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| 236 | {
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| 237 | KAVL_SET_POINTER_NULL(&pNode->pLeft, &pLeftNode->pRight);
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| 238 | KAVL_SET_POINTER(&pLeftNode->pRight, pNode);
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| 239 | pLeftNode->uchHeight = (unsigned char)(1 + (pNode->uchHeight = (unsigned char)(1 + uchLeftRightHeight)));
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| 240 | KAVL_SET_POINTER(ppNode, pLeftNode);
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| 241 | }
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| 242 | else
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| 243 | {
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| 244 | KAVL_SET_POINTER_NULL(&pLeftNode->pRight, &pLeftRightNode->pLeft);
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| 245 | KAVL_SET_POINTER_NULL(&pNode->pLeft, &pLeftRightNode->pRight);
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| 246 | KAVL_SET_POINTER(&pLeftRightNode->pLeft, pLeftNode);
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| 247 | KAVL_SET_POINTER(&pLeftRightNode->pRight, pNode);
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| 248 | pLeftNode->uchHeight = pNode->uchHeight = uchLeftRightHeight;
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| 249 | pLeftRightNode->uchHeight = uchLeftHeight;
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| 250 | KAVL_SET_POINTER(ppNode, pLeftRightNode);
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| 251 | }
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| 252 | }
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| 253 | else if (uchLeftHeight + 1 < uchRightHeight)
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| 254 | {
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| 255 | PKAVLNODECORE pRightLeftNode = KAVL_GET_POINTER_NULL(&pRightNode->pLeft);
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| 256 | unsigned char uchRightLeftHeight = AVL_HEIGHTOF(pRightLeftNode);
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| 257 | PKAVLNODECORE pRightRightNode = KAVL_GET_POINTER_NULL(&pRightNode->pRight);
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| 258 |
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| 259 | if (AVL_HEIGHTOF(pRightRightNode) >= uchRightLeftHeight)
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| 260 | {
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| 261 | KAVL_SET_POINTER_NULL(&pNode->pRight, &pRightNode->pLeft);
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| 262 | KAVL_SET_POINTER(&pRightNode->pLeft, pNode);
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| 263 | pRightNode->uchHeight = (unsigned char)(1 + (pNode->uchHeight = (unsigned char)(1 + uchRightLeftHeight)));
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| 264 | KAVL_SET_POINTER(ppNode, pRightNode);
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| 265 | }
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| 266 | else
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| 267 | {
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| 268 | KAVL_SET_POINTER_NULL(&pRightNode->pLeft, &pRightLeftNode->pRight);
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| 269 | KAVL_SET_POINTER_NULL(&pNode->pRight, &pRightLeftNode->pLeft);
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| 270 | KAVL_SET_POINTER(&pRightLeftNode->pRight, pRightNode);
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| 271 | KAVL_SET_POINTER(&pRightLeftNode->pLeft, pNode);
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| 272 | pRightNode->uchHeight = pNode->uchHeight = uchRightLeftHeight;
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| 273 | pRightLeftNode->uchHeight = uchRightHeight;
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| 274 | KAVL_SET_POINTER(ppNode, pRightLeftNode);
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| 275 | }
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| 276 | }
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| 277 | else
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| 278 | {
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| 279 | unsigned char uchHeight = (unsigned char)(KMAX(uchLeftHeight, uchRightHeight) + 1);
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| 280 | if (uchHeight == pNode->uchHeight)
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| 281 | break;
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| 282 | pNode->uchHeight = uchHeight;
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| 283 | }
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| 284 | }
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| 285 |
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| 286 | }
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| 287 |
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| 288 |
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| 289 |
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| 290 |
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| 291 | /**
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| 292 | * Inserts a node into the AVL-tree.
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| 293 | * @returns TRUE if inserted.
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| 294 | * FALSE if node exists in tree.
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| 295 | * @param ppTree Pointer to the AVL-tree root node pointer.
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| 296 | * @param pNode Pointer to the node which is to be added.
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| 297 | * @sketch Find the location of the node (using binary tree algorithm.):
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| 298 | * LOOP until KAVL_NULL leaf pointer
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| 299 | * BEGIN
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| 300 | * Add node pointer pointer to the AVL-stack.
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| 301 | * IF new-node-key < node key THEN
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| 302 | * left
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| 303 | * ELSE
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| 304 | * right
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| 305 | * END
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| 306 | * Fill in leaf node and insert it.
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| 307 | * Rebalance the tree.
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| 308 | */
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| 309 | KAVL_DECL(bool) KAVL_FN(Insert)(PPKAVLNODECORE ppTree, PKAVLNODECORE pNode)
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| 310 | {
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| 311 | KAVLSTACK AVLStack;
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| 312 | PPKAVLNODECORE ppCurNode = ppTree;
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| 313 | PKAVLNODECORE pCurNode;
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| 314 | KAVLKEY Key = pNode->Key; NOREF(Key);
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| 315 | #ifdef KAVL_RANGE
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| 316 | KAVLKEY KeyLast = pNode->KeyLast; NOREF(KeyLast);
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| 317 | #endif
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| 318 |
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| 319 | AVLStack.cEntries = 0;
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| 320 |
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| 321 | #ifdef KAVL_RANGE
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| 322 | if (Key > KeyLast)
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| 323 | return false;
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| 324 | #endif
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| 325 |
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| 326 | for (;;)
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| 327 | {
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| 328 | if (*ppCurNode != KAVL_NULL)
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| 329 | pCurNode = KAVL_GET_POINTER(ppCurNode);
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| 330 | else
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| 331 | break;
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| 332 | Assert(pCurNode->uchHeight == RT_MAX(AVL_HEIGHTOF(KAVL_GET_POINTER_NULL(&pCurNode->pLeft)),
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| 333 | AVL_HEIGHTOF(KAVL_GET_POINTER_NULL(&pCurNode->pRight))) + 1);
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| 334 |
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| 335 | kASSERT(AVLStack.cEntries < KAVL_MAX_STACK);
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| 336 | AVLStack.aEntries[AVLStack.cEntries++] = ppCurNode;
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| 337 | #ifdef KAVL_EQUAL_ALLOWED
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| 338 | if (KAVL_R_IS_IDENTICAL(pCurNode->Key, Key, pCurNode->KeyLast, KeyLast))
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| 339 | {
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| 340 | /*
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| 341 | * If equal then we'll use a list of equal nodes.
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| 342 | */
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| 343 | pNode->pLeft = pNode->pRight = KAVL_NULL;
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| 344 | pNode->uchHeight = 0;
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| 345 | KAVL_SET_POINTER_NULL(&pNode->pList, &pCurNode->pList);
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| 346 | KAVL_SET_POINTER(&pCurNode->pList, pNode);
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| 347 | return true;
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| 348 | }
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| 349 | #endif
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| 350 | #ifdef KAVL_CHECK_FOR_EQUAL_INSERT
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| 351 | if (KAVL_R_IS_INTERSECTING(pCurNode->Key, Key, pCurNode->KeyLast, KeyLast))
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| 352 | return false;
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| 353 | #endif
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| 354 | if (KAVL_G(pCurNode->Key, Key))
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| 355 | ppCurNode = &pCurNode->pLeft;
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| 356 | else
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| 357 | ppCurNode = &pCurNode->pRight;
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| 358 | }
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| 359 |
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| 360 | pNode->pLeft = pNode->pRight = KAVL_NULL;
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| 361 | #ifdef KAVL_EQUAL_ALLOWED
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| 362 | pNode->pList = KAVL_NULL;
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| 363 | #endif
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| 364 | pNode->uchHeight = 1;
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| 365 | KAVL_SET_POINTER(ppCurNode, pNode);
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| 366 |
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| 367 | KAVL_FN(Rebalance)(SSToDS(&AVLStack));
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| 368 | return true;
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| 369 | }
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| 370 |
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| 371 |
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| 372 | /**
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| 373 | * Removes a node from the AVL-tree.
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| 374 | * @returns Pointer to the node.
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| 375 | * @param ppTree Pointer to the AVL-tree root node pointer.
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| 376 | * @param Key Key value of the node which is to be removed.
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| 377 | * @sketch Find the node which is to be removed:
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| 378 | * LOOP until not found
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| 379 | * BEGIN
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| 380 | * Add node pointer pointer to the AVL-stack.
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| 381 | * IF the keys matches THEN break!
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| 382 | * IF remove key < node key THEN
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| 383 | * left
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| 384 | * ELSE
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| 385 | * right
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| 386 | * END
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| 387 | * IF found THEN
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| 388 | * BEGIN
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| 389 | * IF left node not empty THEN
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| 390 | * BEGIN
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| 391 | * Find the right most node in the left tree while adding the pointer to the pointer to it's parent to the stack:
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| 392 | * Start at left node.
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| 393 | * LOOP until right node is empty
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| 394 | * BEGIN
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| 395 | * Add to stack.
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| 396 | * go right.
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| 397 | * END
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| 398 | * Link out the found node.
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| 399 | * Replace the node which is to be removed with the found node.
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| 400 | * Correct the stack entry for the pointer to the left tree.
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| 401 | * END
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| 402 | * ELSE
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| 403 | * BEGIN
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| 404 | * Move up right node.
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| 405 | * Remove last stack entry.
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| 406 | * END
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| 407 | * Balance tree using stack.
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| 408 | * END
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| 409 | * return pointer to the removed node (if found).
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| 410 | */
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| 411 | KAVL_DECL(PKAVLNODECORE) KAVL_FN(Remove)(PPKAVLNODECORE ppTree, KAVLKEY Key)
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| 412 | {
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| 413 | KAVLSTACK AVLStack;
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| 414 | PPKAVLNODECORE ppDeleteNode = ppTree;
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| 415 | PKAVLNODECORE pDeleteNode;
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| 416 |
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| 417 | AVLStack.cEntries = 0;
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| 418 |
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| 419 | for (;;)
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| 420 | {
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| 421 | if (*ppDeleteNode != KAVL_NULL)
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| 422 | pDeleteNode = KAVL_GET_POINTER(ppDeleteNode);
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| 423 | else
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| 424 | return NULL;
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| 425 | Assert(pDeleteNode->uchHeight == RT_MAX(AVL_HEIGHTOF(KAVL_GET_POINTER_NULL(&pDeleteNode->pLeft)),
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| 426 | AVL_HEIGHTOF(KAVL_GET_POINTER_NULL(&pDeleteNode->pRight))) + 1);
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| 427 |
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| 428 | kASSERT(AVLStack.cEntries < KAVL_MAX_STACK);
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| 429 | AVLStack.aEntries[AVLStack.cEntries++] = ppDeleteNode;
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| 430 | if (KAVL_E(pDeleteNode->Key, Key))
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| 431 | break;
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|---|
| 432 |
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| 433 | if (KAVL_G(pDeleteNode->Key, Key))
|
|---|
| 434 | ppDeleteNode = &pDeleteNode->pLeft;
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|---|
| 435 | else
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|---|
| 436 | ppDeleteNode = &pDeleteNode->pRight;
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|---|
| 437 | }
|
|---|
| 438 |
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|---|
| 439 | if (pDeleteNode->pLeft != KAVL_NULL)
|
|---|
| 440 | {
|
|---|
| 441 | /* find the rightmost node in the left tree. */
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|---|
| 442 | const unsigned iStackEntry = AVLStack.cEntries;
|
|---|
| 443 | PPKAVLNODECORE ppLeftLeast = &pDeleteNode->pLeft;
|
|---|
| 444 | PKAVLNODECORE pLeftLeast = KAVL_GET_POINTER(ppLeftLeast);
|
|---|
| 445 |
|
|---|
| 446 | while (pLeftLeast->pRight != KAVL_NULL)
|
|---|
| 447 | {
|
|---|
| 448 | kASSERT(AVLStack.cEntries < KAVL_MAX_STACK);
|
|---|
| 449 | AVLStack.aEntries[AVLStack.cEntries++] = ppLeftLeast;
|
|---|
| 450 | ppLeftLeast = &pLeftLeast->pRight;
|
|---|
| 451 | pLeftLeast = KAVL_GET_POINTER(ppLeftLeast);
|
|---|
| 452 | }
|
|---|
| 453 |
|
|---|
| 454 | /* link out pLeftLeast */
|
|---|
| 455 | KAVL_SET_POINTER_NULL(ppLeftLeast, &pLeftLeast->pLeft);
|
|---|
| 456 |
|
|---|
| 457 | /* link it in place of the delete node. */
|
|---|
| 458 | KAVL_SET_POINTER_NULL(&pLeftLeast->pLeft, &pDeleteNode->pLeft);
|
|---|
| 459 | KAVL_SET_POINTER_NULL(&pLeftLeast->pRight, &pDeleteNode->pRight);
|
|---|
| 460 | pLeftLeast->uchHeight = pDeleteNode->uchHeight;
|
|---|
| 461 | KAVL_SET_POINTER(ppDeleteNode, pLeftLeast);
|
|---|
| 462 | AVLStack.aEntries[iStackEntry] = &pLeftLeast->pLeft;
|
|---|
| 463 | }
|
|---|
| 464 | else
|
|---|
| 465 | {
|
|---|
| 466 | KAVL_SET_POINTER_NULL(ppDeleteNode, &pDeleteNode->pRight);
|
|---|
| 467 | AVLStack.cEntries--;
|
|---|
| 468 | }
|
|---|
| 469 |
|
|---|
| 470 | KAVL_FN(Rebalance)(SSToDS(&AVLStack));
|
|---|
| 471 | return pDeleteNode;
|
|---|
| 472 | }
|
|---|
| 473 |
|
|---|
| 474 | #endif
|
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