Objectives. Upon completion you will be able to:
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1 Chapter 10 Multiway Trees Objectives Upon completion you will be able to: Define and discuss multiway tree structures Understand the operation and use of the B-tree ADT Discuss the use and implementation of simplified B-trees Compare and contrast B-trees, B*trees, and T+trees Discuss the design and use a lexical search trees (Tries) Data Structures: A Pseudocode Approach with C, Second Edition 1
2 10-1 M-way y( (Multiway) Search Trees An m-way tree is eith an empty or an non-empty search tree in which h each one can have from 0 to m subtrees, where m is defined as the B- tree order.. The properties of a nonempty m-way tree are as flows: 1. Each node have 0 to m subtrees (i.e. children). 2. A node with n subtrees, where n <= m, composes n-1 data entries. Every entry is assigned a key K i arranged in an ascending order: K 1 < K 2 <... < K i <... < K n-1, where 1 < i < n The keys S 1 in the 1 st subtree meet the inequality: S 1 < K 1. The keys S i in the i th subtree meet the inequality: K i-1 < S i < K i. The keys S n in the n th subtree meet the inequality: K n-1 < S n. 4. All subtrees are themselves m-way trees. Data Structures: A Pseudocode Approach with C, Second Edition 2
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6 10-2 B-trees A B-tree is an m-way search tree with the following additional properties: 1. The root is either a leaf or it has 2 ~ m subtrees. 2. The internal nodes have at least m/2 nonnull subtrees and at most m nonnull subtrees. 3. All leaf nodes are at the same level; that is, the tree is perfectly balanced. 4. A leaf node has at least m/2-11 and at most m-1 entries. Data Structures: A Pseudocode Approach with C, Second Edition 6
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86 10-1 Queue Operations This section discusses the four basic queue operations. Using diagrammatic figures, it shows how each of them work. It concludes with a comprehensive example that demonstrates each operation. Enqueue Dequeue Queue Front Queue Rear Queue Example Data Structures: A Pseudocode Approach with C, Second Edition 86
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Introduction p. 1 Pseudocode p. 2 Algorithm Header p. 2 Purpose, Conditions, and Return p. 3 Statement Numbers p. 4 Variables p. 4 Algorithm Analysis
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