Trees in java.util. A set is an object that stores unique elements In Java, two implementations are available:
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1 Trees in java.util A set is an object that stores unique elements In Java, two implementations are available: The class HashSet implements the set with a hash table and a hash function The class TreeSet, which keeps elements of a set in a sorted order Data Structures and Algorithms in Java 1
2 Trees in java.util (continued) Figure 3-32 Methods of the class TreeSet Data Structures and Algorithms in Java 2
3 Trees in java.util (continued) Figure 3-32 Methods of the class TreeSet (continued) Data Structures and Algorithms in Java 3
4 Trees in java.util (continued) Figure 3-32 Methods of the class TreeSet (continued) Data Structures and Algorithms in Java 4
5 Trees in java.util (continued) Figure 3-32 Methods of the class TreeSet (continued) Data Structures and Algorithms in Java 5
6 Trees in java.util (continued) Figure 3-32 Methods of the class TreeSet (continued) Data Structures and Algorithms in Java 6
7 Trees in java.util (continued) Figure 7-33 An example of application of the TreeSet methods Data Structures and Algorithms in Java 7
8 Trees in java.util (continued) Figure 7-33 An example of application of the TreeSet methods (continued) Data Structures and Algorithms in Java 8
9 Trees in java.util (continued) Figure 7-33 An example of application of the TreeSet methods (continued) Data Structures and Algorithms in Java 9
10 Trees in java.util (continued) Figure 7-33 An example of application of the TreeSet methods (continued) Data Structures and Algorithms in Java 10
11 Trees in java.util (continued) Figure 7-33 An example of application of the TreeSet methods (continued) Data Structures and Algorithms in Java 11
12 Trees in java.util (continued) Figure 7-33 An example of application of the TreeSet methods (continued) Data Structures and Algorithms in Java 12
13 Trees in java.util (continued) Figure 7-33 An example of application of the TreeSet methods (continued) Data Structures and Algorithms in Java 13
14 Trees in java.util (continued) Figure 7-33 An example of application of the TreeSet methods (continued) Data Structures and Algorithms in Java 14
15 TreeMap Maps are tables that can be indexed with any type of data Maps use keys that are used as indexes and elements (values) to be accessed through the keys Keys in maps are unique in that one key is associated with one value only Tree maps implement maps store pairs (key, value) called entries that can be operated on by methods specified in the interface Map.Entry Data Structures and Algorithms in Java 15
16 TreeMap (continued) Figure 7-34 (a) Methods in the interface Map.Entry; (b) methods of the class TreeMap Data Structures and Algorithms in Java 16
17 TreeMap (continued) Figure 7-34 (a) Methods in the interface Map.Entry; (b) methods of the class TreeMap (continued) Data Structures and Algorithms in Java 17
18 TreeMap (continued) Figure 7-34 (a) Methods in the interface Map.Entry; (b) methods of the class TreeMap (continued) Data Structures and Algorithms in Java 18
19 TreeMap (continued) Figure 7-34 (a) Methods in the interface Map.Entry; (b) methods of the class TreeMap (continued) Data Structures and Algorithms in Java 19
20 TreeMap (continued) Figure 7-34 (a) Methods in the interface Map.Entry; (b) methods of the class TreeMap (continued) Data Structures and Algorithms in Java 20
21 TreeMap (continued) Figure 7-35 An example of application of the TreeMap methods. The class PersonByName is the same as in Figure Data Structures and Algorithms in Java 21
22 TreeMap (continued) Figure 7-35 An example of application of the TreeMap methods (continued) Data Structures and Algorithms in Java 22
23 Tries A tree that uses parts of the key to navigate the search is called a trie Each key is a sequence of characters; a trie is organized around these characters rather than entire keys Data Structures and Algorithms in Java 23
24 Tries (continued) Figure 7-36 A trie of some words composed of the five letters A, E, I, R, and P Data Structures and Algorithms in Java 24
25 Tries (continued) Figure 7-37 The trie in Figure 7.36 with all unused reference fields removed Data Structures and Algorithms in Java 25
26 Tries (continued) Figure 7-38 The trie from Figure 7.37 implemented as a binary tree Data Structures and Algorithms in Java 26
27 Tries (continued) Figure 7-39 A part of a trie (a) before and (b) after compression using the compresstrie() algorithm and (c) after compressing it in an optimal way Data Structures and Algorithms in Java 27
28 Tries (continued) Figure 7-39 A part of a trie (a) before and (b) after compression using the compresstrie() algorithm and (c) after compressing it in an optimal way (continued) Data Structures and Algorithms in Java 28
29 Tries (continued) Figure 7-40 A fragment of the C-trie representation of the trie from Figure 7-36 Data Structures and Algorithms in Java 29
30 Case Study: Spell Checker Figure 7-41 An implementation of a trie that uses pseudoflexible arrays. The trie has the same words as the trie in Figure Data Structures and Algorithms in Java 30
31 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries Data Structures and Algorithms in Java 31
32 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 32
33 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 33
34 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 34
35 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 35
36 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 36
37 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 37
38 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 38
39 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 39
40 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 40
41 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 41
42 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 42
43 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 43
44 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 44
45 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 45
46 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 46
47 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 47
48 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 48
49 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 49
50 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 50
51 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 51
52 Case Study: Spell Checker (continued) Figure 7-42 Implementation of a spell checker using tries (continued) Data Structures and Algorithms in Java 52
53 Summary B + -trees are commonly used in the implementation of indexes in today s relational databases Seek time depends on the mechanical movement of the disk head to position the head at the correct track of the disk Latency is the time required to position the head above the correct block and is equal to the time needed to make one-half of a revolution Data Structures and Algorithms in Java 53
54 Summary (continued) In a B*-tree, all nodes except the root are required to be at least two-thirds full, not just half full as in a B-tree A simple prefix B + -tree is a B + -tree in which the chosen separators are the shortest prefixes that allow us to distinguish two neighboring index keys A set is an object that stores unique elements. Maps are tables that can be indexed with any type of data Data Structures and Algorithms in Java 54
55 Summary (continued) The bit-tree is based on the concept of a distinction bit (D-bit) A variant of B-trees, 2 4 trees, is useful in processing information in memory A tree that uses parts of the key to navigate the search is called a trie Data Structures and Algorithms in Java 55
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