1/*-
2 * Copyright (c) 2015 Nuxi, https://nuxi.nl/
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 * 1. Redistributions of source code must retain the above copyright
8 *    notice, this list of conditions and the following disclaimer.
9 * 2. Redistributions in binary form must reproduce the above copyright
10 *    notice, this list of conditions and the following disclaimer in the
11 *    documentation and/or other materials provided with the distribution.
12 *
13 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
14 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
15 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
16 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
17 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
18 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
19 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
20 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
21 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
22 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
23 * SUCH DAMAGE.
24 */
25
26#include <sys/cdefs.h>
27__FBSDID("$FreeBSD$");
28
29#define	_SEARCH_PRIVATE
30#include <search.h>
31#include <stdlib.h>
32
33#include "tsearch_path.h"
34
35void *
36tsearch(const void *key, void **rootp,
37    int (*compar)(const void *, const void *))
38{
39	struct path path;
40	node_t *root, **base, **leaf, *result, *n, *x, *y, *z;
41	int cmp;
42
43	/* POSIX requires that tsearch() returns NULL if rootp is NULL. */
44	if (rootp == NULL)
45	return (NULL);
46		root = *rootp;
47
48	/*
49	 * Find the leaf where the new key needs to be inserted. Return
50	 * if we've found an existing entry. Keep track of the path that
51	 * is taken to get to the node, as we will need it to adjust the
52	 * balances.
53	*/
54	path_init(&path);
55	base = &root;
56	leaf = &root;
57	while (*leaf != NULL) {
58		if ((*leaf)->balance != 0) {
59			/*
60			 * If we reach a node that has a non-zero
61			 * balance on the way, we know that we won't
62			 * need to perform any rotations above this
63			 * point. In this case rotations are always
64			 * capable of keeping the subtree in balance.
65			 * Make this the base node and reset the path.
66			 */
67			base = leaf;
68			path_init(&path);
69		}
70		cmp = compar(key, (*leaf)->key);
71		if (cmp < 0) {
72			path_taking_left(&path);
73			leaf = &(*leaf)->llink;
74		} else if (cmp > 0) {
75			path_taking_right(&path);
76			leaf = &(*leaf)->rlink;
77		} else {
78			return (&(*leaf)->key);
79		}
80	}
81
82	/* Did not find a matching key in the tree. Insert a new node. */
83	result = *leaf = malloc(sizeof(**leaf));
84	if (result == NULL)
85		return (NULL);
86	result->key = (void *)key;
87	result->llink = NULL;
88	result->rlink = NULL;
89	result->balance = 0;
90
91	/*
92	 * Walk along the same path a second time and adjust the
93	 * balances. Except for the first node, all of these nodes must
94	 * have a balance of zero, meaning that these nodes will not get
95	 * out of balance.
96	*/
97	for (n = *base; n != *leaf;) {
98		if (path_took_left(&path)) {
99			n->balance += 1;
100			n = n->llink;
101		} else {
102			n->balance -= 1;
103			n = n->rlink;
104		}
105	}
106
107	/*
108	 * Adjusting the balances may have pushed the balance of the
109	 * base node out of range. Perform a rotation to bring the
110	 * balance back in range.
111	 */
112	x = *base;
113	if (x->balance > 1) {
114		y = x->llink;
115		if (y->balance < 0) {
116			/*
117			 * Left-right case.
118			 *
119			 *         x
120			 *        / \            z
121			 *       y   D          / \
122			 *      / \     -->    y   x
123			 *     A   z          /|   |\
124			 *        / \        A B   C D
125			 *       B   C
126			 */
127			z = y->rlink;
128			y->rlink = z->llink;
129			z->llink = y;
130			x->llink = z->rlink;
131			z->rlink = x;
132			*base = z;
133
134			x->balance = z->balance > 0 ? -1 : 0;
135			y->balance = z->balance < 0 ? 1 : 0;
136			z->balance = 0;
137		} else {
138			/*
139			 * Left-left case.
140			 *
141			 *        x           y
142			 *       / \         / \
143			 *      y   C  -->  A   x
144			 *     / \             / \
145			 *    A   B           B   C
146			 */
147			x->llink = y->rlink;
148			y->rlink = x;
149			*base = y;
150
151			x->balance = 0;
152			y->balance = 0;
153		}
154	} else if (x->balance < -1) {
155		y = x->rlink;
156		if (y->balance > 0) {
157			/*
158			 * Right-left case.
159			 *
160			 *       x
161			 *      / \              z
162			 *     A   y            / \
163			 *        / \   -->    x   y
164			 *       z   D        /|   |\
165			 *      / \          A B   C D
166			 *     B   C
167			 */
168			node_t *z = y->llink;
169			x->rlink = z->llink;
170			z->llink = x;
171			y->llink = z->rlink;
172			z->rlink = y;
173			*base = z;
174
175			x->balance = z->balance < 0 ? 1 : 0;
176			y->balance = z->balance > 0 ? -1 : 0;
177			z->balance = 0;
178		} else {
179			/*
180			 * Right-right case.
181			 *
182			 *       x               y
183			 *      / \             / \
184			 *     A   y    -->    x   C
185			 *        / \         / \
186			 *       B   C       A   B
187			 */
188			x->rlink = y->llink;
189			y->llink = x;
190			*base = y;
191
192			x->balance = 0;
193			y->balance = 0;
194		}
195	}
196
197	/* Return the new entry. */
198	*rootp = root;
199	return (&result->key);
200}
201