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| 1 | 13 | up20180614 | /* $NetBSD: tree.h,v 1.20 2013/09/14 13:20:45 joerg Exp $ */
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| 2 | /* $OpenBSD: tree.h,v 1.13 2011/07/09 00:19:45 pirofti Exp $ */
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| 3 | /*
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| 4 | * Copyright 2002 Niels Provos <provos@citi.umich.edu>
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| 5 | * All rights reserved.
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| 6 | *
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| 7 | * Redistribution and use in source and binary forms, with or without
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| 8 | * modification, are permitted provided that the following conditions
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| 9 | * are met:
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| 10 | * 1. Redistributions of source code must retain the above copyright
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| 11 | * notice, this list of conditions and the following disclaimer.
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| 12 | * 2. Redistributions in binary form must reproduce the above copyright
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| 13 | * notice, this list of conditions and the following disclaimer in the
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| 14 | * documentation and/or other materials provided with the distribution.
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| 15 | *
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| 16 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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| 17 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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| 18 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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| 19 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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| 20 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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| 21 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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| 22 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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| 23 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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| 24 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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| 25 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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| 26 | */
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| 27 | |||
| 28 | #ifndef _SYS_TREE_H_
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| 29 | #define _SYS_TREE_H_
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| 30 | |||
| 31 | /*
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| 32 | * This file defines data structures for different types of trees:
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| 33 | * splay trees and red-black trees.
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| 34 | *
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| 35 | * A splay tree is a self-organizing data structure. Every operation
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| 36 | * on the tree causes a splay to happen. The splay moves the requested
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| 37 | * node to the root of the tree and partly rebalances it.
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| 38 | *
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| 39 | * This has the benefit that request locality causes faster lookups as
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| 40 | * the requested nodes move to the top of the tree. On the other hand,
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| 41 | * every lookup causes memory writes.
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| 42 | *
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| 43 | * The Balance Theorem bounds the total access time for m operations
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| 44 | * and n inserts on an initially empty tree as O((m + n)lg n). The
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| 45 | * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
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| 46 | *
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| 47 | * A red-black tree is a binary search tree with the node color as an
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| 48 | * extra attribute. It fulfills a set of conditions:
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| 49 | * - every search path from the root to a leaf consists of the
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| 50 | * same number of black nodes,
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| 51 | * - each red node (except for the root) has a black parent,
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| 52 | * - each leaf node is black.
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| 53 | *
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| 54 | * Every operation on a red-black tree is bounded as O(lg n).
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| 55 | * The maximum height of a red-black tree is 2lg (n+1).
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| 56 | */
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| 57 | |||
| 58 | #define SPLAY_HEAD(name, type) \
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| 59 | struct name { \
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| 60 | struct type *sph_root; /* root of the tree */ \ |
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| 61 | } |
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| 62 | |||
| 63 | #define SPLAY_INITIALIZER(root) \
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| 64 | { NULL }
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| 65 | |||
| 66 | #define SPLAY_INIT(root) do { \ |
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| 67 | (root)->sph_root = NULL; \
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| 68 | } while (/*CONSTCOND*/ 0) |
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| 69 | |||
| 70 | #define SPLAY_ENTRY(type) \
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| 71 | struct { \
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| 72 | struct type *spe_left; /* left element */ \ |
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| 73 | struct type *spe_right; /* right element */ \ |
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| 74 | } |
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| 75 | |||
| 76 | #define SPLAY_LEFT(elm, field) (elm)->field.spe_left
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| 77 | #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
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| 78 | #define SPLAY_ROOT(head) (head)->sph_root
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| 79 | #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL) |
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| 80 | |||
| 81 | /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
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| 82 | #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \ |
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| 83 | SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \ |
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| 84 | SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ |
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| 85 | (head)->sph_root = tmp; \ |
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| 86 | } while (/*CONSTCOND*/ 0) |
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| 87 | |||
| 88 | #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \ |
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| 89 | SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \ |
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| 90 | SPLAY_LEFT(tmp, field) = (head)->sph_root; \ |
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| 91 | (head)->sph_root = tmp; \ |
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| 92 | } while (/*CONSTCOND*/ 0) |
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| 93 | |||
| 94 | #define SPLAY_LINKLEFT(head, tmp, field) do { \ |
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| 95 | SPLAY_LEFT(tmp, field) = (head)->sph_root; \ |
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| 96 | tmp = (head)->sph_root; \ |
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| 97 | (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \ |
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| 98 | } while (/*CONSTCOND*/ 0) |
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| 99 | |||
| 100 | #define SPLAY_LINKRIGHT(head, tmp, field) do { \ |
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| 101 | SPLAY_RIGHT(tmp, field) = (head)->sph_root; \ |
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| 102 | tmp = (head)->sph_root; \ |
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| 103 | (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \ |
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| 104 | } while (/*CONSTCOND*/ 0) |
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| 105 | |||
| 106 | #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \ |
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| 107 | SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \ |
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| 108 | SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\ |
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| 109 | SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \ |
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| 110 | SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \ |
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| 111 | } while (/*CONSTCOND*/ 0) |
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| 112 | |||
| 113 | /* Generates prototypes and inline functions */
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| 114 | |||
| 115 | #define SPLAY_PROTOTYPE(name, type, field, cmp) \
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| 116 | void name##_SPLAY(struct name *, struct type *); \ |
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| 117 | void name##_SPLAY_MINMAX(struct name *, int); \ |
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| 118 | struct type *name##_SPLAY_INSERT(struct name *, struct type *); \ |
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| 119 | struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \ |
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| 120 | \ |
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| 121 | /* Finds the node with the same key as elm */ \
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| 122 | static __inline struct type * \ |
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| 123 | name##_SPLAY_FIND(struct name *head, struct type *elm) \ |
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| 124 | { \
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| 125 | if (SPLAY_EMPTY(head)) \
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| 126 | return(NULL); \ |
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| 127 | name##_SPLAY(head, elm); \ |
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| 128 | if ((cmp)(elm, (head)->sph_root) == 0) \ |
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| 129 | return (head->sph_root); \
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| 130 | return (NULL); \ |
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| 131 | } \ |
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| 132 | \ |
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| 133 | static __inline __unused struct type * \ |
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| 134 | name##_SPLAY_NEXT(struct name *head, struct type *elm) \ |
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| 135 | { \
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| 136 | name##_SPLAY(head, elm); \ |
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| 137 | if (SPLAY_RIGHT(elm, field) != NULL) { \ |
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| 138 | elm = SPLAY_RIGHT(elm, field); \ |
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| 139 | while (SPLAY_LEFT(elm, field) != NULL) { \ |
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| 140 | elm = SPLAY_LEFT(elm, field); \ |
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| 141 | } \ |
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| 142 | } else \
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| 143 | elm = NULL; \
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| 144 | return (elm); \
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| 145 | } \ |
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| 146 | \ |
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| 147 | static __unused __inline struct type * \ |
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| 148 | name##_SPLAY_MIN_MAX(struct name *head, int val) \ |
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| 149 | { \
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| 150 | name##_SPLAY_MINMAX(head, val); \ |
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| 151 | return (SPLAY_ROOT(head)); \
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| 152 | } |
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| 153 | |||
| 154 | /* Main splay operation.
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| 155 | * Moves node close to the key of elm to top
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| 156 | */
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| 157 | #define SPLAY_GENERATE(name, type, field, cmp) \
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| 158 | struct type * \
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| 159 | name##_SPLAY_INSERT(struct name *head, struct type *elm) \ |
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| 160 | { \
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| 161 | if (SPLAY_EMPTY(head)) { \
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| 162 | SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
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| 163 | } else { \
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| 164 | int __comp; \
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| 165 | name##_SPLAY(head, elm); \ |
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| 166 | __comp = (cmp)(elm, (head)->sph_root); \ |
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| 167 | if(__comp < 0) { \ |
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| 168 | SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\ |
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| 169 | SPLAY_RIGHT(elm, field) = (head)->sph_root; \ |
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| 170 | SPLAY_LEFT((head)->sph_root, field) = NULL; \
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| 171 | } else if (__comp > 0) { \ |
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| 172 | SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\ |
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| 173 | SPLAY_LEFT(elm, field) = (head)->sph_root; \ |
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| 174 | SPLAY_RIGHT((head)->sph_root, field) = NULL; \
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| 175 | } else \
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| 176 | return ((head)->sph_root); \
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| 177 | } \ |
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| 178 | (head)->sph_root = (elm); \ |
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| 179 | return (NULL); \ |
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| 180 | } \ |
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| 181 | \ |
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| 182 | struct type * \
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| 183 | name##_SPLAY_REMOVE(struct name *head, struct type *elm) \ |
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| 184 | { \
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| 185 | struct type *__tmp; \
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| 186 | if (SPLAY_EMPTY(head)) \
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| 187 | return (NULL); \ |
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| 188 | name##_SPLAY(head, elm); \ |
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| 189 | if ((cmp)(elm, (head)->sph_root) == 0) { \ |
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| 190 | if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \ |
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| 191 | (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\ |
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| 192 | } else { \
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| 193 | __tmp = SPLAY_RIGHT((head)->sph_root, field); \ |
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| 194 | (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\ |
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| 195 | name##_SPLAY(head, elm); \ |
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| 196 | SPLAY_RIGHT((head)->sph_root, field) = __tmp; \ |
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| 197 | } \ |
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| 198 | return (elm); \
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| 199 | } \ |
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| 200 | return (NULL); \ |
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| 201 | } \ |
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| 202 | \ |
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| 203 | void \
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| 204 | name##_SPLAY(struct name *head, struct type *elm) \ |
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| 205 | { \
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| 206 | struct type __node, *__left, *__right, *__tmp; \
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| 207 | int __comp; \
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| 208 | \ |
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| 209 | SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
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| 210 | __left = __right = &__node; \ |
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| 211 | \ |
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| 212 | while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \ |
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| 213 | if (__comp < 0) { \ |
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| 214 | __tmp = SPLAY_LEFT((head)->sph_root, field); \ |
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| 215 | if (__tmp == NULL) \ |
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| 216 | break; \
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| 217 | if ((cmp)(elm, __tmp) < 0){ \ |
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| 218 | SPLAY_ROTATE_RIGHT(head, __tmp, field); \ |
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| 219 | if (SPLAY_LEFT((head)->sph_root, field) == NULL)\ |
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| 220 | break; \
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| 221 | } \ |
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| 222 | SPLAY_LINKLEFT(head, __right, field); \ |
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| 223 | } else if (__comp > 0) { \ |
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| 224 | __tmp = SPLAY_RIGHT((head)->sph_root, field); \ |
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| 225 | if (__tmp == NULL) \ |
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| 226 | break; \
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| 227 | if ((cmp)(elm, __tmp) > 0){ \ |
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| 228 | SPLAY_ROTATE_LEFT(head, __tmp, field); \ |
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| 229 | if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\ |
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| 230 | break; \
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| 231 | } \ |
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| 232 | SPLAY_LINKRIGHT(head, __left, field); \ |
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| 233 | } \ |
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| 234 | } \ |
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| 235 | SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ |
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| 236 | } \ |
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| 237 | \ |
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| 238 | /* Splay with either the minimum or the maximum element \
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| 239 | * Used to find minimum or maximum element in tree. \
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| 240 | */ \
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| 241 | void name##_SPLAY_MINMAX(struct name *head, int __comp) \ |
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| 242 | { \
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| 243 | struct type __node, *__left, *__right, *__tmp; \
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| 244 | \ |
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| 245 | SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
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| 246 | __left = __right = &__node; \ |
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| 247 | \ |
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| 248 | while (1) { \ |
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| 249 | if (__comp < 0) { \ |
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| 250 | __tmp = SPLAY_LEFT((head)->sph_root, field); \ |
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| 251 | if (__tmp == NULL) \ |
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| 252 | break; \
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| 253 | if (__comp < 0){ \ |
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| 254 | SPLAY_ROTATE_RIGHT(head, __tmp, field); \ |
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| 255 | if (SPLAY_LEFT((head)->sph_root, field) == NULL)\ |
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| 256 | break; \
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| 257 | } \ |
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| 258 | SPLAY_LINKLEFT(head, __right, field); \ |
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| 259 | } else if (__comp > 0) { \ |
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| 260 | __tmp = SPLAY_RIGHT((head)->sph_root, field); \ |
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| 261 | if (__tmp == NULL) \ |
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| 262 | break; \
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| 263 | if (__comp > 0) { \ |
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| 264 | SPLAY_ROTATE_LEFT(head, __tmp, field); \ |
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| 265 | if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\ |
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| 266 | break; \
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| 267 | } \ |
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| 268 | SPLAY_LINKRIGHT(head, __left, field); \ |
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| 269 | } \ |
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| 270 | } \ |
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| 271 | SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \ |
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| 272 | } |
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| 273 | |||
| 274 | #define SPLAY_NEGINF -1 |
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| 275 | #define SPLAY_INF 1 |
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| 276 | |||
| 277 | #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y) |
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| 278 | #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y) |
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| 279 | #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y) |
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| 280 | #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y) |
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| 281 | #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \ |
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| 282 | : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF)) |
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| 283 | #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \ |
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| 284 | : name##_SPLAY_MIN_MAX(x, SPLAY_INF)) |
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| 285 | |||
| 286 | #define SPLAY_FOREACH(x, name, head) \
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| 287 | for ((x) = SPLAY_MIN(name, head); \
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| 288 | (x) != NULL; \
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| 289 | (x) = SPLAY_NEXT(name, head, x)) |
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| 290 | |||
| 291 | /* Macros that define a red-black tree */
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| 292 | #define RB_HEAD(name, type) \
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| 293 | struct name { \
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| 294 | struct type *rbh_root; /* root of the tree */ \ |
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| 295 | } |
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| 296 | |||
| 297 | #define RB_INITIALIZER(root) \
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| 298 | { NULL }
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| 299 | |||
| 300 | #define RB_INIT(root) do { \ |
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| 301 | (root)->rbh_root = NULL; \
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| 302 | } while (/*CONSTCOND*/ 0) |
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| 303 | |||
| 304 | #define RB_BLACK 0 |
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| 305 | #define RB_RED 1 |
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| 306 | #define RB_ENTRY(type) \
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| 307 | struct { \
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| 308 | struct type *rbe_left; /* left element */ \ |
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| 309 | struct type *rbe_right; /* right element */ \ |
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| 310 | struct type *rbe_parent; /* parent element */ \ |
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| 311 | int rbe_color; /* node color */ \ |
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| 312 | } |
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| 313 | |||
| 314 | #define RB_LEFT(elm, field) (elm)->field.rbe_left
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| 315 | #define RB_RIGHT(elm, field) (elm)->field.rbe_right
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| 316 | #define RB_PARENT(elm, field) (elm)->field.rbe_parent
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| 317 | #define RB_COLOR(elm, field) (elm)->field.rbe_color
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| 318 | #define RB_ROOT(head) (head)->rbh_root
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| 319 | #define RB_EMPTY(head) (RB_ROOT(head) == NULL) |
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| 320 | |||
| 321 | #define RB_SET(elm, parent, field) do { \ |
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| 322 | RB_PARENT(elm, field) = parent; \ |
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| 323 | RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
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| 324 | RB_COLOR(elm, field) = RB_RED; \ |
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| 325 | } while (/*CONSTCOND*/ 0) |
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| 326 | |||
| 327 | #define RB_SET_BLACKRED(black, red, field) do { \ |
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| 328 | RB_COLOR(black, field) = RB_BLACK; \ |
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| 329 | RB_COLOR(red, field) = RB_RED; \ |
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| 330 | } while (/*CONSTCOND*/ 0) |
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| 331 | |||
| 332 | #ifndef RB_AUGMENT
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| 333 | #define RB_AUGMENT(x) do {} while (/*CONSTCOND*/ 0) |
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| 334 | #endif
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| 335 | |||
| 336 | #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \ |
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| 337 | (tmp) = RB_RIGHT(elm, field); \ |
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| 338 | if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \ |
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| 339 | RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \ |
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| 340 | } \ |
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| 341 | RB_AUGMENT(elm); \ |
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| 342 | if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \ |
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| 343 | if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
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| 344 | RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ |
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| 345 | else \
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| 346 | RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ |
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| 347 | } else \
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| 348 | (head)->rbh_root = (tmp); \ |
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| 349 | RB_LEFT(tmp, field) = (elm); \ |
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| 350 | RB_PARENT(elm, field) = (tmp); \ |
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| 351 | RB_AUGMENT(tmp); \ |
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| 352 | if ((RB_PARENT(tmp, field))) \
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| 353 | RB_AUGMENT(RB_PARENT(tmp, field)); \ |
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| 354 | } while (/*CONSTCOND*/ 0) |
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| 355 | |||
| 356 | #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \ |
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| 357 | (tmp) = RB_LEFT(elm, field); \ |
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| 358 | if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \ |
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| 359 | RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \ |
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| 360 | } \ |
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| 361 | RB_AUGMENT(elm); \ |
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| 362 | if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \ |
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| 363 | if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
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| 364 | RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ |
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| 365 | else \
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| 366 | RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ |
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| 367 | } else \
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| 368 | (head)->rbh_root = (tmp); \ |
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| 369 | RB_RIGHT(tmp, field) = (elm); \ |
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| 370 | RB_PARENT(elm, field) = (tmp); \ |
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| 371 | RB_AUGMENT(tmp); \ |
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| 372 | if ((RB_PARENT(tmp, field))) \
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| 373 | RB_AUGMENT(RB_PARENT(tmp, field)); \ |
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| 374 | } while (/*CONSTCOND*/ 0) |
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| 375 | |||
| 376 | /* Generates prototypes and inline functions */
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| 377 | #define RB_PROTOTYPE(name, type, field, cmp) \
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| 378 | RB_PROTOTYPE_INTERNAL(name, type, field, cmp,) |
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| 379 | #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \
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| 380 | RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
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| 381 | #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \
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| 382 | attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \ |
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| 383 | attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\ |
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| 384 | attr struct type *name##_RB_REMOVE(struct name *, struct type *); \ |
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| 385 | attr struct type *name##_RB_INSERT(struct name *, struct type *); \ |
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| 386 | attr struct type *name##_RB_FIND(struct name *, struct type *); \ |
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| 387 | attr struct type *name##_RB_NFIND(struct name *, struct type *); \ |
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| 388 | attr struct type *name##_RB_NEXT(struct type *); \ |
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| 389 | attr struct type *name##_RB_PREV(struct type *); \ |
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| 390 | attr struct type *name##_RB_MINMAX(struct name *, int); \ |
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| 391 | \ |
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| 392 | |||
| 393 | /* Main rb operation.
|
||
| 394 | * Moves node close to the key of elm to top
|
||
| 395 | */
|
||
| 396 | #define RB_GENERATE(name, type, field, cmp) \
|
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| 397 | RB_GENERATE_INTERNAL(name, type, field, cmp,) |
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| 398 | #define RB_GENERATE_STATIC(name, type, field, cmp) \
|
||
| 399 | RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
|
||
| 400 | #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
|
||
| 401 | attr void \
|
||
| 402 | name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \ |
||
| 403 | { \
|
||
| 404 | struct type *parent, *gparent, *tmp; \
|
||
| 405 | while ((parent = RB_PARENT(elm, field)) != NULL && \ |
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| 406 | RB_COLOR(parent, field) == RB_RED) { \
|
||
| 407 | gparent = RB_PARENT(parent, field); \ |
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| 408 | if (parent == RB_LEFT(gparent, field)) { \
|
||
| 409 | tmp = RB_RIGHT(gparent, field); \ |
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| 410 | if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
|
||
| 411 | RB_COLOR(tmp, field) = RB_BLACK; \ |
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| 412 | RB_SET_BLACKRED(parent, gparent, field);\ |
||
| 413 | elm = gparent; \ |
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| 414 | continue; \
|
||
| 415 | } \ |
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| 416 | if (RB_RIGHT(parent, field) == elm) { \
|
||
| 417 | RB_ROTATE_LEFT(head, parent, tmp, field);\ |
||
| 418 | tmp = parent; \ |
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| 419 | parent = elm; \ |
||
| 420 | elm = tmp; \ |
||
| 421 | } \ |
||
| 422 | RB_SET_BLACKRED(parent, gparent, field); \ |
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| 423 | RB_ROTATE_RIGHT(head, gparent, tmp, field); \ |
||
| 424 | } else { \
|
||
| 425 | tmp = RB_LEFT(gparent, field); \ |
||
| 426 | if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
|
||
| 427 | RB_COLOR(tmp, field) = RB_BLACK; \ |
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| 428 | RB_SET_BLACKRED(parent, gparent, field);\ |
||
| 429 | elm = gparent; \ |
||
| 430 | continue; \
|
||
| 431 | } \ |
||
| 432 | if (RB_LEFT(parent, field) == elm) { \
|
||
| 433 | RB_ROTATE_RIGHT(head, parent, tmp, field);\ |
||
| 434 | tmp = parent; \ |
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| 435 | parent = elm; \ |
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| 436 | elm = tmp; \ |
||
| 437 | } \ |
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| 438 | RB_SET_BLACKRED(parent, gparent, field); \ |
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| 439 | RB_ROTATE_LEFT(head, gparent, tmp, field); \ |
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| 440 | } \ |
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| 441 | } \ |
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| 442 | RB_COLOR(head->rbh_root, field) = RB_BLACK; \ |
||
| 443 | } \ |
||
| 444 | \ |
||
| 445 | attr void \
|
||
| 446 | name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \ |
||
| 447 | { \
|
||
| 448 | struct type *tmp; \
|
||
| 449 | while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \ |
||
| 450 | elm != RB_ROOT(head)) { \
|
||
| 451 | if (RB_LEFT(parent, field) == elm) { \
|
||
| 452 | tmp = RB_RIGHT(parent, field); \ |
||
| 453 | if (RB_COLOR(tmp, field) == RB_RED) { \
|
||
| 454 | RB_SET_BLACKRED(tmp, parent, field); \ |
||
| 455 | RB_ROTATE_LEFT(head, parent, tmp, field);\ |
||
| 456 | tmp = RB_RIGHT(parent, field); \ |
||
| 457 | } \ |
||
| 458 | if ((RB_LEFT(tmp, field) == NULL || \ |
||
| 459 | RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\ |
||
| 460 | (RB_RIGHT(tmp, field) == NULL || \
|
||
| 461 | RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
|
||
| 462 | RB_COLOR(tmp, field) = RB_RED; \ |
||
| 463 | elm = parent; \ |
||
| 464 | parent = RB_PARENT(elm, field); \ |
||
| 465 | } else { \
|
||
| 466 | if (RB_RIGHT(tmp, field) == NULL || \ |
||
| 467 | RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
|
||
| 468 | struct type *oleft; \
|
||
| 469 | if ((oleft = RB_LEFT(tmp, field)) \
|
||
| 470 | != NULL) \
|
||
| 471 | RB_COLOR(oleft, field) = RB_BLACK;\ |
||
| 472 | RB_COLOR(tmp, field) = RB_RED; \ |
||
| 473 | RB_ROTATE_RIGHT(head, tmp, oleft, field);\ |
||
| 474 | tmp = RB_RIGHT(parent, field); \ |
||
| 475 | } \ |
||
| 476 | RB_COLOR(tmp, field) = RB_COLOR(parent, field);\ |
||
| 477 | RB_COLOR(parent, field) = RB_BLACK; \ |
||
| 478 | if (RB_RIGHT(tmp, field)) \
|
||
| 479 | RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\ |
||
| 480 | RB_ROTATE_LEFT(head, parent, tmp, field);\ |
||
| 481 | elm = RB_ROOT(head); \ |
||
| 482 | break; \
|
||
| 483 | } \ |
||
| 484 | } else { \
|
||
| 485 | tmp = RB_LEFT(parent, field); \ |
||
| 486 | if (RB_COLOR(tmp, field) == RB_RED) { \
|
||
| 487 | RB_SET_BLACKRED(tmp, parent, field); \ |
||
| 488 | RB_ROTATE_RIGHT(head, parent, tmp, field);\ |
||
| 489 | tmp = RB_LEFT(parent, field); \ |
||
| 490 | } \ |
||
| 491 | if ((RB_LEFT(tmp, field) == NULL || \ |
||
| 492 | RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\ |
||
| 493 | (RB_RIGHT(tmp, field) == NULL || \
|
||
| 494 | RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
|
||
| 495 | RB_COLOR(tmp, field) = RB_RED; \ |
||
| 496 | elm = parent; \ |
||
| 497 | parent = RB_PARENT(elm, field); \ |
||
| 498 | } else { \
|
||
| 499 | if (RB_LEFT(tmp, field) == NULL || \ |
||
| 500 | RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
|
||
| 501 | struct type *oright; \
|
||
| 502 | if ((oright = RB_RIGHT(tmp, field)) \
|
||
| 503 | != NULL) \
|
||
| 504 | RB_COLOR(oright, field) = RB_BLACK;\ |
||
| 505 | RB_COLOR(tmp, field) = RB_RED; \ |
||
| 506 | RB_ROTATE_LEFT(head, tmp, oright, field);\ |
||
| 507 | tmp = RB_LEFT(parent, field); \ |
||
| 508 | } \ |
||
| 509 | RB_COLOR(tmp, field) = RB_COLOR(parent, field);\ |
||
| 510 | RB_COLOR(parent, field) = RB_BLACK; \ |
||
| 511 | if (RB_LEFT(tmp, field)) \
|
||
| 512 | RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\ |
||
| 513 | RB_ROTATE_RIGHT(head, parent, tmp, field);\ |
||
| 514 | elm = RB_ROOT(head); \ |
||
| 515 | break; \
|
||
| 516 | } \ |
||
| 517 | } \ |
||
| 518 | } \ |
||
| 519 | if (elm) \
|
||
| 520 | RB_COLOR(elm, field) = RB_BLACK; \ |
||
| 521 | } \ |
||
| 522 | \ |
||
| 523 | attr struct type * \
|
||
| 524 | name##_RB_REMOVE(struct name *head, struct type *elm) \ |
||
| 525 | { \
|
||
| 526 | struct type *child, *parent, *old = elm; \
|
||
| 527 | int color; \
|
||
| 528 | if (RB_LEFT(elm, field) == NULL) \ |
||
| 529 | child = RB_RIGHT(elm, field); \ |
||
| 530 | else if (RB_RIGHT(elm, field) == NULL) \ |
||
| 531 | child = RB_LEFT(elm, field); \ |
||
| 532 | else { \
|
||
| 533 | struct type *left; \
|
||
| 534 | elm = RB_RIGHT(elm, field); \ |
||
| 535 | while ((left = RB_LEFT(elm, field)) != NULL) \ |
||
| 536 | elm = left; \ |
||
| 537 | child = RB_RIGHT(elm, field); \ |
||
| 538 | parent = RB_PARENT(elm, field); \ |
||
| 539 | color = RB_COLOR(elm, field); \ |
||
| 540 | if (child) \
|
||
| 541 | RB_PARENT(child, field) = parent; \ |
||
| 542 | if (parent) { \
|
||
| 543 | if (RB_LEFT(parent, field) == elm) \
|
||
| 544 | RB_LEFT(parent, field) = child; \ |
||
| 545 | else \
|
||
| 546 | RB_RIGHT(parent, field) = child; \ |
||
| 547 | RB_AUGMENT(parent); \ |
||
| 548 | } else \
|
||
| 549 | RB_ROOT(head) = child; \ |
||
| 550 | if (RB_PARENT(elm, field) == old) \
|
||
| 551 | parent = elm; \ |
||
| 552 | (elm)->field = (old)->field; \ |
||
| 553 | if (RB_PARENT(old, field)) { \
|
||
| 554 | if (RB_LEFT(RB_PARENT(old, field), field) == old)\
|
||
| 555 | RB_LEFT(RB_PARENT(old, field), field) = elm;\ |
||
| 556 | else \
|
||
| 557 | RB_RIGHT(RB_PARENT(old, field), field) = elm;\ |
||
| 558 | RB_AUGMENT(RB_PARENT(old, field)); \ |
||
| 559 | } else \
|
||
| 560 | RB_ROOT(head) = elm; \ |
||
| 561 | RB_PARENT(RB_LEFT(old, field), field) = elm; \ |
||
| 562 | if (RB_RIGHT(old, field)) \
|
||
| 563 | RB_PARENT(RB_RIGHT(old, field), field) = elm; \ |
||
| 564 | if (parent) { \
|
||
| 565 | left = parent; \ |
||
| 566 | do { \
|
||
| 567 | RB_AUGMENT(left); \ |
||
| 568 | } while ((left = RB_PARENT(left, field)) != NULL); \ |
||
| 569 | } \ |
||
| 570 | goto color; \
|
||
| 571 | } \ |
||
| 572 | parent = RB_PARENT(elm, field); \ |
||
| 573 | color = RB_COLOR(elm, field); \ |
||
| 574 | if (child) \
|
||
| 575 | RB_PARENT(child, field) = parent; \ |
||
| 576 | if (parent) { \
|
||
| 577 | if (RB_LEFT(parent, field) == elm) \
|
||
| 578 | RB_LEFT(parent, field) = child; \ |
||
| 579 | else \
|
||
| 580 | RB_RIGHT(parent, field) = child; \ |
||
| 581 | RB_AUGMENT(parent); \ |
||
| 582 | } else \
|
||
| 583 | RB_ROOT(head) = child; \ |
||
| 584 | color: \ |
||
| 585 | if (color == RB_BLACK) \
|
||
| 586 | name##_RB_REMOVE_COLOR(head, parent, child); \ |
||
| 587 | return (old); \
|
||
| 588 | } \ |
||
| 589 | \ |
||
| 590 | /* Inserts a node into the RB tree */ \
|
||
| 591 | attr struct type * \
|
||
| 592 | name##_RB_INSERT(struct name *head, struct type *elm) \ |
||
| 593 | { \
|
||
| 594 | struct type *tmp; \
|
||
| 595 | struct type *parent = NULL; \ |
||
| 596 | int comp = 0; \ |
||
| 597 | tmp = RB_ROOT(head); \ |
||
| 598 | while (tmp) { \
|
||
| 599 | parent = tmp; \ |
||
| 600 | comp = (cmp)(elm, parent); \ |
||
| 601 | if (comp < 0) \ |
||
| 602 | tmp = RB_LEFT(tmp, field); \ |
||
| 603 | else if (comp > 0) \ |
||
| 604 | tmp = RB_RIGHT(tmp, field); \ |
||
| 605 | else \
|
||
| 606 | return (tmp); \
|
||
| 607 | } \ |
||
| 608 | RB_SET(elm, parent, field); \ |
||
| 609 | if (parent != NULL) { \ |
||
| 610 | if (comp < 0) \ |
||
| 611 | RB_LEFT(parent, field) = elm; \ |
||
| 612 | else \
|
||
| 613 | RB_RIGHT(parent, field) = elm; \ |
||
| 614 | RB_AUGMENT(parent); \ |
||
| 615 | } else \
|
||
| 616 | RB_ROOT(head) = elm; \ |
||
| 617 | name##_RB_INSERT_COLOR(head, elm); \ |
||
| 618 | return (NULL); \ |
||
| 619 | } \ |
||
| 620 | \ |
||
| 621 | /* Finds the node with the same key as elm */ \
|
||
| 622 | attr struct type * \
|
||
| 623 | name##_RB_FIND(struct name *head, struct type *elm) \ |
||
| 624 | { \
|
||
| 625 | struct type *tmp = RB_ROOT(head); \
|
||
| 626 | int comp; \
|
||
| 627 | while (tmp) { \
|
||
| 628 | comp = cmp(elm, tmp); \ |
||
| 629 | if (comp < 0) \ |
||
| 630 | tmp = RB_LEFT(tmp, field); \ |
||
| 631 | else if (comp > 0) \ |
||
| 632 | tmp = RB_RIGHT(tmp, field); \ |
||
| 633 | else \
|
||
| 634 | return (tmp); \
|
||
| 635 | } \ |
||
| 636 | return (NULL); \ |
||
| 637 | } \ |
||
| 638 | \ |
||
| 639 | /* Finds the first node greater than or equal to the search key */ \
|
||
| 640 | attr struct type * \
|
||
| 641 | name##_RB_NFIND(struct name *head, struct type *elm) \ |
||
| 642 | { \
|
||
| 643 | struct type *tmp = RB_ROOT(head); \
|
||
| 644 | struct type *res = NULL; \ |
||
| 645 | int comp; \
|
||
| 646 | while (tmp) { \
|
||
| 647 | comp = cmp(elm, tmp); \ |
||
| 648 | if (comp < 0) { \ |
||
| 649 | res = tmp; \ |
||
| 650 | tmp = RB_LEFT(tmp, field); \ |
||
| 651 | } \ |
||
| 652 | else if (comp > 0) \ |
||
| 653 | tmp = RB_RIGHT(tmp, field); \ |
||
| 654 | else \
|
||
| 655 | return (tmp); \
|
||
| 656 | } \ |
||
| 657 | return (res); \
|
||
| 658 | } \ |
||
| 659 | \ |
||
| 660 | /* ARGSUSED */ \
|
||
| 661 | attr struct type * \
|
||
| 662 | name##_RB_NEXT(struct type *elm) \ |
||
| 663 | { \
|
||
| 664 | if (RB_RIGHT(elm, field)) { \
|
||
| 665 | elm = RB_RIGHT(elm, field); \ |
||
| 666 | while (RB_LEFT(elm, field)) \
|
||
| 667 | elm = RB_LEFT(elm, field); \ |
||
| 668 | } else { \
|
||
| 669 | if (RB_PARENT(elm, field) && \
|
||
| 670 | (elm == RB_LEFT(RB_PARENT(elm, field), field))) \ |
||
| 671 | elm = RB_PARENT(elm, field); \ |
||
| 672 | else { \
|
||
| 673 | while (RB_PARENT(elm, field) && \
|
||
| 674 | (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\ |
||
| 675 | elm = RB_PARENT(elm, field); \ |
||
| 676 | elm = RB_PARENT(elm, field); \ |
||
| 677 | } \ |
||
| 678 | } \ |
||
| 679 | return (elm); \
|
||
| 680 | } \ |
||
| 681 | \ |
||
| 682 | /* ARGSUSED */ \
|
||
| 683 | attr struct type * \
|
||
| 684 | name##_RB_PREV(struct type *elm) \ |
||
| 685 | { \
|
||
| 686 | if (RB_LEFT(elm, field)) { \
|
||
| 687 | elm = RB_LEFT(elm, field); \ |
||
| 688 | while (RB_RIGHT(elm, field)) \
|
||
| 689 | elm = RB_RIGHT(elm, field); \ |
||
| 690 | } else { \
|
||
| 691 | if (RB_PARENT(elm, field) && \
|
||
| 692 | (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \ |
||
| 693 | elm = RB_PARENT(elm, field); \ |
||
| 694 | else { \
|
||
| 695 | while (RB_PARENT(elm, field) && \
|
||
| 696 | (elm == RB_LEFT(RB_PARENT(elm, field), field)))\ |
||
| 697 | elm = RB_PARENT(elm, field); \ |
||
| 698 | elm = RB_PARENT(elm, field); \ |
||
| 699 | } \ |
||
| 700 | } \ |
||
| 701 | return (elm); \
|
||
| 702 | } \ |
||
| 703 | \ |
||
| 704 | attr struct type * \
|
||
| 705 | name##_RB_MINMAX(struct name *head, int val) \ |
||
| 706 | { \
|
||
| 707 | struct type *tmp = RB_ROOT(head); \
|
||
| 708 | struct type *parent = NULL; \ |
||
| 709 | while (tmp) { \
|
||
| 710 | parent = tmp; \ |
||
| 711 | if (val < 0) \ |
||
| 712 | tmp = RB_LEFT(tmp, field); \ |
||
| 713 | else \
|
||
| 714 | tmp = RB_RIGHT(tmp, field); \ |
||
| 715 | } \ |
||
| 716 | return (parent); \
|
||
| 717 | } |
||
| 718 | |||
| 719 | #define RB_NEGINF -1 |
||
| 720 | #define RB_INF 1 |
||
| 721 | |||
| 722 | #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y) |
||
| 723 | #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y) |
||
| 724 | #define RB_FIND(name, x, y) name##_RB_FIND(x, y) |
||
| 725 | #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y) |
||
| 726 | #define RB_NEXT(name, x, y) name##_RB_NEXT(y) |
||
| 727 | #define RB_PREV(name, x, y) name##_RB_PREV(y) |
||
| 728 | #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF) |
||
| 729 | #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF) |
||
| 730 | |||
| 731 | #define RB_FOREACH(x, name, head) \
|
||
| 732 | for ((x) = RB_MIN(name, head); \
|
||
| 733 | (x) != NULL; \
|
||
| 734 | (x) = name##_RB_NEXT(x)) |
||
| 735 | |||
| 736 | #define RB_FOREACH_FROM(x, name, y) \
|
||
| 737 | for ((x) = (y); \
|
||
| 738 | ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ |
||
| 739 | (x) = (y)) |
||
| 740 | |||
| 741 | #define RB_FOREACH_SAFE(x, name, head, y) \
|
||
| 742 | for ((x) = RB_MIN(name, head); \
|
||
| 743 | ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ |
||
| 744 | (x) = (y)) |
||
| 745 | |||
| 746 | #define RB_FOREACH_REVERSE(x, name, head) \
|
||
| 747 | for ((x) = RB_MAX(name, head); \
|
||
| 748 | (x) != NULL; \
|
||
| 749 | (x) = name##_RB_PREV(x)) |
||
| 750 | |||
| 751 | #define RB_FOREACH_REVERSE_FROM(x, name, y) \
|
||
| 752 | for ((x) = (y); \
|
||
| 753 | ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ |
||
| 754 | (x) = (y)) |
||
| 755 | |||
| 756 | #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
|
||
| 757 | for ((x) = RB_MAX(name, head); \
|
||
| 758 | ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ |
||
| 759 | (x) = (y)) |
||
| 760 | |||
| 761 | #endif /* _SYS_TREE_H_ */ |