1 /* tree.h -- AVL trees (in the spirit of BSD's 'queue.h')	-*- C -*-	*/
2 
3 /* Copyright (c) 2005 Ian Piumarta
4  *
5  * All rights reserved.
6  *
7  * Permission is hereby granted, free of charge, to any person obtaining a copy
8  * of this software and associated documentation files (the 'Software'), to deal
9  * in the Software without restriction, including without limitation the rights
10  * to use, copy, modify, merge, publish, distribute, and/or sell copies of the
11  * Software, and to permit persons to whom the Software is furnished to do so,
12  * provided that the above copyright notice(s) and this permission notice appear
13  * in all copies of the Software and that both the above copyright notice(s) and
14  * this permission notice appear in supporting documentation.
15  *
16  * THE SOFTWARE IS PROVIDED 'AS IS'.  USE ENTIRELY AT YOUR OWN RISK.
17  */
18 
19 /* This file defines an AVL balanced binary tree [Georgii M. Adelson-Velskii and
20  * Evgenii M. Landis, 'An algorithm for the organization of information',
21  * Doklady Akademii Nauk SSSR, 146:263-266, 1962 (Russian).  Also in Myron
22  * J. Ricci (trans.), Soviet Math, 3:1259-1263, 1962 (English)].
23  *
24  * An AVL tree is headed by pointers to the root node and to a function defining
25  * the ordering relation between nodes.  Each node contains an arbitrary payload
26  * plus three fields per tree entry: the depth of the subtree for which it forms
27  * the root and two pointers to child nodes (singly-linked for minimum space, at
28  * the expense of direct access to the parent node given a pointer to one of the
29  * children).  The tree is rebalanced after every insertion or removal.  The
30  * tree may be traversed in two directions: forward (in-order left-to-right) and
31  * reverse (in-order, right-to-left).
32  *
33  * Because of the recursive nature of many of the operations on trees it is
34  * necessary to define a number of helper functions for each type of tree node.
35  * The macro TREE_DEFINE(node_tag, entry_name) defines these functions with
36  * unique names according to the node_tag.  This macro should be invoked,
37  * thereby defining the necessary functions, once per node tag in the program.
38  *
39  * For details on the use of these macros, see the tree(3) manual page.
40  */
41 
42 #ifndef __tree_h
43 #define __tree_h
44 
45 
46 #define TREE_DELTA_MAX	1
47 #ifndef _HU_FUNCTION
48 # if defined(__GNUC__) || defined(__clang__)
49 #   define _HU_FUNCTION(x) __attribute__((__unused__)) x
50 # else
51 #   define _HU_FUNCTION(x) x
52 # endif
53 #endif
54 
55 #define TREE_ENTRY(type)			\
56   struct {					\
57     struct type	*avl_left;			\
58     struct type	*avl_right;			\
59     int		 avl_height;			\
60   }
61 
62 #define TREE_HEAD(name, type)				\
63   struct name {						\
64     struct type *th_root;				\
65     int  (*th_cmp)(struct type *lhs, struct type *rhs);	\
66   }
67 
68 #define TREE_INITIALIZER(cmp) { 0, cmp }
69 
70 #define TREE_DELTA(self, field)								\
71   (( (((self)->field.avl_left)  ? (self)->field.avl_left->field.avl_height  : 0))	\
72    - (((self)->field.avl_right) ? (self)->field.avl_right->field.avl_height : 0))
73 
74 /* Recursion prevents the following from being defined as macros. */
75 
76 #define TREE_DEFINE(node, field)									\
77 													\
78   static struct node *_HU_FUNCTION(TREE_BALANCE_##node##_##field)(struct node *);						\
79 													\
80   static struct node *_HU_FUNCTION(TREE_ROTL_##node##_##field)(struct node *self)						\
81   {													\
82     struct node *r= self->field.avl_right;								\
83     self->field.avl_right= r->field.avl_left;								\
84     r->field.avl_left= TREE_BALANCE_##node##_##field(self);						\
85     return TREE_BALANCE_##node##_##field(r);								\
86   }													\
87 													\
88   static struct node *_HU_FUNCTION(TREE_ROTR_##node##_##field)(struct node *self)						\
89   {													\
90     struct node *l= self->field.avl_left;								\
91     self->field.avl_left= l->field.avl_right;								\
92     l->field.avl_right= TREE_BALANCE_##node##_##field(self);						\
93     return TREE_BALANCE_##node##_##field(l);								\
94   }													\
95 													\
96   static struct node *_HU_FUNCTION(TREE_BALANCE_##node##_##field)(struct node *self)						\
97   {													\
98     int delta= TREE_DELTA(self, field);									\
99 													\
100     if (delta < -TREE_DELTA_MAX)									\
101       {													\
102 	if (TREE_DELTA(self->field.avl_right, field) > 0)						\
103 	  self->field.avl_right= TREE_ROTR_##node##_##field(self->field.avl_right);			\
104 	return TREE_ROTL_##node##_##field(self);							\
105       }													\
106     else if (delta > TREE_DELTA_MAX)									\
107       {													\
108 	if (TREE_DELTA(self->field.avl_left, field) < 0)						\
109 	  self->field.avl_left= TREE_ROTL_##node##_##field(self->field.avl_left);			\
110 	return TREE_ROTR_##node##_##field(self);							\
111       }													\
112     self->field.avl_height= 0;										\
113     if (self->field.avl_left && (self->field.avl_left->field.avl_height > self->field.avl_height))	\
114       self->field.avl_height= self->field.avl_left->field.avl_height;					\
115     if (self->field.avl_right && (self->field.avl_right->field.avl_height > self->field.avl_height))	\
116       self->field.avl_height= self->field.avl_right->field.avl_height;					\
117     self->field.avl_height += 1;									\
118     return self;											\
119   }													\
120 													\
121   static struct node *_HU_FUNCTION(TREE_INSERT_##node##_##field)								\
122     (struct node *self, struct node *elm, int (*compare)(struct node *lhs, struct node *rhs))		\
123   {													\
124     if (!self)												\
125       return elm;											\
126     if (compare(elm, self) < 0)										\
127       self->field.avl_left= TREE_INSERT_##node##_##field(self->field.avl_left, elm, compare);		\
128     else												\
129       self->field.avl_right= TREE_INSERT_##node##_##field(self->field.avl_right, elm, compare);		\
130     return TREE_BALANCE_##node##_##field(self);								\
131   }													\
132 													\
133   static struct node *_HU_FUNCTION(TREE_FIND_##node##_##field)								\
134     (struct node *self, struct node *elm, int (*compare)(struct node *lhs, struct node *rhs))		\
135   {													\
136     if (!self)												\
137       return 0;												\
138     if (compare(elm, self) == 0)									\
139       return self;											\
140     if (compare(elm, self) < 0)										\
141       return TREE_FIND_##node##_##field(self->field.avl_left, elm, compare);				\
142     else												\
143       return TREE_FIND_##node##_##field(self->field.avl_right, elm, compare);				\
144   }													\
145 													\
146   static struct node *_HU_FUNCTION(TREE_MOVE_RIGHT)(struct node *self, struct node *rhs)					\
147   {													\
148     if (!self)												\
149       return rhs;											\
150     self->field.avl_right= TREE_MOVE_RIGHT(self->field.avl_right, rhs);					\
151     return TREE_BALANCE_##node##_##field(self);								\
152   }													\
153 													\
154   static struct node *_HU_FUNCTION(TREE_REMOVE_##node##_##field)								\
155     (struct node *self, struct node *elm, int (*compare)(struct node *lhs, struct node *rhs))		\
156   {													\
157     if (!self) return 0;										\
158 													\
159     if (compare(elm, self) == 0)									\
160       {													\
161 	struct node *tmp= TREE_MOVE_RIGHT(self->field.avl_left, self->field.avl_right);			\
162 	self->field.avl_left= 0;									\
163 	self->field.avl_right= 0;									\
164 	return tmp;											\
165       }													\
166     if (compare(elm, self) < 0)										\
167       self->field.avl_left= TREE_REMOVE_##node##_##field(self->field.avl_left, elm, compare);		\
168     else												\
169       self->field.avl_right= TREE_REMOVE_##node##_##field(self->field.avl_right, elm, compare);		\
170     return TREE_BALANCE_##node##_##field(self);								\
171   }													\
172 													\
173   static void _HU_FUNCTION(TREE_FORWARD_APPLY_ALL_##node##_##field)								\
174     (struct node *self, void (*function)(struct node *node, void *data), void *data)			\
175   {													\
176     if (self)												\
177       {													\
178 	TREE_FORWARD_APPLY_ALL_##node##_##field(self->field.avl_left, function, data);			\
179 	function(self, data);										\
180 	TREE_FORWARD_APPLY_ALL_##node##_##field(self->field.avl_right, function, data);			\
181       }													\
182   }													\
183 													\
184   static void _HU_FUNCTION(TREE_REVERSE_APPLY_ALL_##node##_##field)								\
185     (struct node *self, void (*function)(struct node *node, void *data), void *data)			\
186   {													\
187     if (self)												\
188       {													\
189 	TREE_REVERSE_APPLY_ALL_##node##_##field(self->field.avl_right, function, data);			\
190 	function(self, data);										\
191 	TREE_REVERSE_APPLY_ALL_##node##_##field(self->field.avl_left, function, data);			\
192       }													\
193   }
194 
195 #define TREE_INSERT(head, node, field, elm)						\
196   ((head)->th_root= TREE_INSERT_##node##_##field((head)->th_root, (elm), (head)->th_cmp))
197 
198 #define TREE_FIND(head, node, field, elm)				\
199   (TREE_FIND_##node##_##field((head)->th_root, (elm), (head)->th_cmp))
200 
201 #define TREE_REMOVE(head, node, field, elm)						\
202   ((head)->th_root= TREE_REMOVE_##node##_##field((head)->th_root, (elm), (head)->th_cmp))
203 
204 #define TREE_DEPTH(head, field)			\
205   ((head)->th_root->field.avl_height)
206 
207 #define TREE_FORWARD_APPLY(head, node, field, function, data)	\
208   TREE_FORWARD_APPLY_ALL_##node##_##field((head)->th_root, function, data)
209 
210 #define TREE_REVERSE_APPLY(head, node, field, function, data)	\
211   TREE_REVERSE_APPLY_ALL_##node##_##field((head)->th_root, function, data)
212 
213 #define TREE_INIT(head, cmp) do {		\
214     (head)->th_root= 0;				\
215     (head)->th_cmp= (cmp);			\
216   } while (0)
217 
218 
219 #endif /* __tree_h */
220