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1 | // -*- C++ -*- | |
2 | ||
3 | // Copyright (C) 2005-2014 Free Software Foundation, Inc. | |
4 | // | |
5 | // This file is part of the GNU ISO C++ Library. This library is free | |
6 | // software; you can redistribute it and/or modify it under the terms | |
7 | // of the GNU General Public License as published by the Free Software | |
8 | // Foundation; either version 3, or (at your option) any later | |
9 | // version. | |
10 | ||
11 | // This library is distributed in the hope that it will be useful, but | |
12 | // WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 | // General Public License for more details. | |
15 | ||
16 | // You should have received a copy of the GNU General Public License | |
17 | // along with this library; see the file COPYING3. If not see | |
18 | // <http://www.gnu.org/licenses/>. | |
19 | ||
20 | ||
21 | // Copyright (C) 2004 Ami Tavory and Vladimir Dreizin, IBM-HRL. | |
22 | ||
23 | // Permission to use, copy, modify, sell, and distribute this software | |
24 | // is hereby granted without fee, provided that the above copyright | |
25 | // notice appears in all copies, and that both that copyright notice | |
26 | // and this permission notice appear in supporting documentation. None | |
27 | // of the above authors, nor IBM Haifa Research Laboratories, make any | |
28 | // representation about the suitability of this software for any | |
29 | // purpose. It is provided "as is" without express or implied | |
30 | // warranty. | |
31 | ||
32 | /** | |
33 | * @file tree_intervals_example.cpp | |
34 | * An example showing how to augment a trees to support operations involving | |
35 | * line intervals. | |
36 | */ | |
37 | ||
38 | /** | |
39 | * In some cases tree structure can be used for various purposes other | |
40 | * than storing entries by key order. This example shows how a | |
41 | * tree-based container can be used for geometric-line intersection | |
42 | * determination. That is, the key of the container is a pair of | |
43 | * numbers representing a line interval. The container object can be | |
44 | * used to query whether a line interval intersects any line interval | |
45 | * it currently stores. | |
46 | * | |
47 | * This type of problem arises not only in geometric applications, but | |
48 | * also sometimes in distributed filesystems. Assume that "leases" are | |
49 | * taken for parts of files or LUNs. When a new lease is requested, it | |
50 | * is necessary to check that it does not conflict with a lease | |
51 | * already taken. In this case a file or LUN can be envisioned as a | |
52 | * line segment; leases requested and granted for contiguous parts of | |
53 | * the file or LUN can be represented as line intervals as well. | |
54 | */ | |
55 | ||
56 | #include <cassert> | |
57 | #include <cstdlib> | |
58 | #include <ext/pb_ds/assoc_container.hpp> | |
59 | ||
60 | using namespace std; | |
61 | using namespace __gnu_pbds; | |
62 | ||
63 | // Following are definitions of line intervals and functors operating | |
64 | // on them. As the purpose of this example is node invariants, and not | |
65 | // computational-geometry algorithms per-se, some simplifications are | |
66 | // made (e.g., intervals are defined by unsigned integers, and not by | |
67 | // a parameterized type, data members are public, etc.). | |
68 | ||
69 | // An interval of unsigned integers. | |
70 | typedef pair< unsigned int, unsigned int> interval; | |
71 | ||
72 | // Functor updating maximal endpoints of entries. Algorithm taken from | |
73 | // "Introduction to Algorithms" by Cormen, Leiserson, and Rivest. | |
74 | template<class Node_CItr, | |
75 | class Node_Itr, | |
76 | class Cmp_Fn, | |
77 | typename _Alloc> | |
78 | struct intervals_node_update | |
79 | { | |
80 | public: | |
81 | // The metadata that each node stores is the largest endpoint of an | |
82 | // interval in its subtree. In this case, this is an unsigned int. | |
83 | typedef unsigned int metadata_type; | |
84 | ||
85 | // Checks whether a set of intervals contains at least one interval | |
86 | // overlapping some interval. Algorithm taken from "Introduction to | |
87 | // Algorithms" by Cormen, Leiserson, and Rivest. | |
88 | bool | |
89 | overlaps(const interval& r_interval) | |
90 | { | |
91 | Node_CItr nd_it = node_begin(); | |
92 | Node_CItr end_it = node_end(); | |
93 | ||
94 | while (nd_it != end_it) | |
95 | { | |
96 | // Check whether r_interval overlaps the current interval. | |
97 | if (r_interval.second >= (*nd_it)->first&& | |
98 | r_interval.first <= (*nd_it)->second) | |
99 | return true; | |
100 | ||
101 | // Get the const node iterator of the node's left child. | |
102 | Node_CItr l_nd_it = nd_it.get_l_child(); | |
103 | ||
104 | // Calculate the maximal endpoint of the left child. If the | |
105 | // node has no left child, then this is the node's maximal | |
106 | // endpoint. | |
107 | const unsigned int l_max_endpoint =(l_nd_it == end_it)? | |
108 | 0 : l_nd_it.get_metadata(); | |
109 | ||
110 | // Now use the endpoint to determine which child to choose. | |
111 | if (l_max_endpoint >= r_interval.first) | |
112 | nd_it = l_nd_it; | |
113 | else | |
114 | nd_it = nd_it.get_r_child(); | |
115 | } | |
116 | ||
117 | return false; | |
118 | } | |
119 | ||
120 | protected: | |
121 | // Update predicate: nd_it is a node iterator to the node currently | |
122 | // updated; end_nd_it is a const node iterator to a just-after leaf | |
123 | // node. | |
124 | inline void | |
125 | operator()(Node_Itr nd_it, Node_CItr end_nd_it) | |
126 | { | |
127 | // The left maximal endpoint is 0 if there is no left child. | |
128 | const unsigned int l_max_endpoint =(nd_it.get_l_child() == end_nd_it)? | |
129 | 0 : nd_it.get_l_child().get_metadata(); | |
130 | ||
131 | // The right maximal endpoint is 0 if there is no right child. | |
132 | const unsigned int r_max_endpoint =(nd_it.get_r_child() == end_nd_it)? | |
133 | 0 : nd_it.get_r_child().get_metadata(); | |
134 | ||
135 | // The maximal endpoint is the endpoint of the node's interval, | |
136 | // and the maximal endpoints of its children. | |
137 | const_cast<unsigned int&>(nd_it.get_metadata()) = | |
138 | max((*nd_it)->second, max<unsigned int>(l_max_endpoint, r_max_endpoint)); | |
139 | } | |
140 | ||
141 | virtual Node_CItr | |
142 | node_begin() const = 0; | |
143 | ||
144 | virtual Node_CItr | |
145 | node_end() const = 0; | |
146 | ||
147 | virtual | |
148 | ~intervals_node_update() | |
149 | { } | |
150 | }; | |
151 | ||
152 | // The following function performs some operation sequence on a | |
153 | // generic associative container supporting order statistics. It | |
154 | // inserts some intervals, and checks for overlap. | |
155 | template<class Cntnr> | |
156 | void | |
157 | some_op_sequence(Cntnr r_c) | |
158 | { | |
159 | // Insert some entries. | |
160 | r_c.insert(make_pair(0, 100)); | |
161 | r_c.insert(make_pair(150, 160)); | |
162 | r_c.insert(make_pair(300, 1000)); | |
163 | r_c.insert(make_pair(10000, 100000)); | |
164 | r_c.insert(make_pair(200, 100200)); | |
165 | ||
166 | // Test overlaps. | |
167 | ||
168 | // Overlaps 150 - 160 | |
169 | assert(r_c.overlaps(make_pair(145, 165)) == true); | |
170 | // Overlaps 150 - 160 | |
171 | assert(r_c.overlaps(make_pair(145, 155)) == true); | |
172 | assert(r_c.overlaps(make_pair(165, 175)) == false); | |
173 | assert(r_c.overlaps(make_pair(100201, 100203)) == false); | |
174 | ||
175 | // Erase an interval | |
176 | r_c.erase(make_pair(150, 160)); | |
177 | ||
178 | // Test overlaps again. | |
179 | assert(r_c.overlaps(make_pair(145, 165)) == false); | |
180 | assert(r_c.overlaps(make_pair(165, 175)) == false); | |
181 | assert(r_c.overlaps(make_pair(0, 300000)) == true); | |
182 | } | |
183 | ||
184 | int main() | |
185 | { | |
186 | // Test a red-black tree. | |
187 | some_op_sequence(tree< | |
188 | interval, | |
189 | null_type, | |
190 | less<interval>, | |
191 | rb_tree_tag, | |
192 | intervals_node_update>()); | |
193 | ||
194 | // Test an ordered-vector tree. | |
195 | some_op_sequence(tree< | |
196 | interval, | |
197 | null_type, | |
198 | less<interval>, | |
199 | ov_tree_tag, | |
200 | intervals_node_update>()); | |
201 | ||
202 | // Test a splay tree. | |
203 | some_op_sequence(tree< | |
204 | interval, | |
205 | null_type, | |
206 | less<interval>, | |
207 | splay_tree_tag, | |
208 | intervals_node_update>()); | |
209 | ||
210 | return 0; | |
211 | } | |
212 |