1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 2007, 2009, 2011 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
18 #define LIBPSPP_ABT_H 1
20 /* Augmented binary tree (ABT) data structure.
22 A data structure can be "augmented" by defining new
23 information for it to maintain. One commonly useful way to
24 augment a binary search tree-based data structure is to define
25 part of its data as a function of its immediate children's
26 data. Furthermore, augmented data defined in this way can be
27 efficiently maintained as the tree changes over time.
29 For example, suppose we define the "size" of a node as the sum
30 of the "size" of its immediate children, plus 1. In such an
31 annotated BST with height H, we can find the node that would
32 be Kth in in-order traversal in O(H) time, instead of O(K)
33 time, which is a significant saving for balanced trees.
35 The ABT data structure partially abstracts augmentation. The
36 client passes in a "reaugmentation" function that accepts a
37 node. This function must recalculate the node's augmentation
38 data based on its own contents and the contents of its
39 children, and store the new augmentation data in the node.
41 The ABT automatically calls the reaugmentation function
42 whenever it can tell that a node's augmentation data might
43 need to be updated: when the node is inserted or when a node's
44 descendants change due to insertion or deletion. The ABT does
45 not know to call the reaugmentation function if a node's data
46 is updated while it is in the ABT. In such a case, call the
47 abt_reaugmented or abt_changed function to update the
50 Augmentation is only partially abstracted: we do not provide
51 any way to search an ABT based on its augmentations. The
52 tree structure is thus exposed to the client to allow it to
55 To allow for optimization, the ABT implementation assumes that
56 the augmentation function in use is unaffected by the shape of
57 a binary search tree. That is, if a given subtree within a
58 larger tree is rearranged, e.g. via a series of rotations,
59 then the implementation will not call the reaugmentation
60 function outside of the subtree, because the overall
61 augmentation data for the subtree is assumed not to change.
62 This optimization is valid for the forms of augmentation
63 described in CLR and Knuth (see below), and it is possible
64 that it is valid for every efficient binary search tree
67 The client should not need to be aware of the form of
68 balancing applied to the ABT, as its operation should be fully
69 encapsulated by the reaugmentation function. The current
70 implementation uses an AA (Arne Andersson) tree, but this is
73 The following example illustrates how to use an ABT to build a
74 tree that can be searched either by a data value or in-order
80 struct abt_node node; // Embedded binary tree element.
81 int data; // Primary value.
82 int count; // Number of nodes in subtree,
83 // including this node.
86 // Returns the `struct element' that NODE is embedded within.
87 static struct element *
88 node_to_element (const struct abt_node *node)
90 return abt_data (node, struct element, node);
93 // Compares the DATA values in A and B and returns a
94 // strcmp-type return value.
96 compare_elements (const struct abt_node *a_, const struct abt_node *b_,
99 const struct element *a = node_to_element (a_);
100 const struct element *b = node_to_element (b_);
102 return a->data < b->data ? -1 : a->data > b->data;
105 // Recalculates the count for NODE's subtree by adding up the
106 // counts for its left and right child subtrees.
108 reaugment_elements (struct abt_node *node_, const void *aux)
110 struct element *node = node_to_element (node_);
112 if (node->node.down[0] != NULL)
113 node->count += node_to_element (node->node.down[0])->count;
114 if (node->node.down[1] != NULL)
115 node->count += node_to_element (node->node.down[1])->count;
118 // Finds and returns the element in ABT that is in the given
119 // 0-based POSITION in in-order.
120 static struct element *
121 find_by_position (struct abt *abt, int position)
124 for (p = abt->root; p != NULL; )
126 int p_pos = p->down[0] ? node_to_element (p->down[0])->count : 0;
127 if (position == p_pos)
128 return node_to_element (p);
129 else if (position < p_pos)
134 position -= p_pos + 1;
140 For more information on augmenting binary search tree-based
141 data structures, see Cormen-Leiserson-Rivest, chapter 15, or
142 Knuth vol. 3, section 6.2.3, under "Linear list
143 representation." For more information on AA trees, see
144 <http://en.wikipedia.org/wiki/AA_tree>, which includes source
145 code and links to other resources, such as the original AA
149 #include "libpspp/cast.h"
151 /* Returns the data structure corresponding to the given NODE,
152 assuming that NODE is embedded as the given MEMBER name in
154 #define abt_data(NODE, STRUCT, MEMBER) \
155 (CHECK_POINTER_HAS_TYPE (NODE, struct abt_node *), \
156 UP_CAST (NODE, STRUCT, MEMBER))
158 /* Node in an augmented binary tree. */
161 struct abt_node *up; /* Parent (NULL for root). */
162 struct abt_node *down[2]; /* Left child, right child. */
163 int level; /* AA tree level (not ordinary BST level). */
166 /* Compares nodes A and B, with the tree's AUX.
167 Returns a strcmp-like result. */
168 typedef int abt_compare_func (const struct abt_node *a,
169 const struct abt_node *b,
172 /* Recalculates NODE's augmentation based on NODE's data and that of its left
173 and right children NODE->down[0] and NODE[1], respectively, with the tree's
175 typedef void abt_reaugment_func (struct abt_node *node, const void *aux);
177 /* An augmented binary tree. */
180 struct abt_node *root; /* Tree's root, NULL if empty. */
181 abt_compare_func *compare; /* To compare nodes. */
182 abt_reaugment_func *reaugment; /* To augment a node using its children. */
183 const void *aux; /* Auxiliary data. */
186 void abt_init (struct abt *, abt_compare_func *, abt_reaugment_func *,
189 struct abt_node *abt_insert (struct abt *, struct abt_node *);
190 void abt_insert_after (struct abt *,
191 const struct abt_node *, struct abt_node *);
192 void abt_insert_before (struct abt *,
193 const struct abt_node *, struct abt_node *);
194 void abt_delete (struct abt *, struct abt_node *);
196 struct abt_node *abt_first (const struct abt *);
197 struct abt_node *abt_last (const struct abt *);
198 struct abt_node *abt_find (const struct abt *, const struct abt_node *);
199 struct abt_node *abt_next (const struct abt *, const struct abt_node *);
200 struct abt_node *abt_prev (const struct abt *, const struct abt_node *);
202 void abt_reaugmented (const struct abt *, struct abt_node *);
203 struct abt_node *abt_changed (struct abt *, struct abt_node *);
204 void abt_moved (struct abt *, struct abt_node *);
206 #endif /* libpspp/abt.h */