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Data Abstraction and Problem Solving with JAVA Walls and Mirrors Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Data Abstraction and Problem.

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Presentation on theme: "Data Abstraction and Problem Solving with JAVA Walls and Mirrors Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Data Abstraction and Problem."— Presentation transcript:

1 Data Abstraction and Problem Solving with JAVA Walls and Mirrors Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Data Abstraction and Problem Solving with JAVA: Walls and Mirrors Carrano / Prichard Advanced Implementations of Tables

2 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.1 A binary search tree of a) maximum height; b) minimum height

3 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.2 A 2-3 tree of height 3

4 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.3 Nodes in a 2-3 tree a) a 2-node; b) a 3-node

5 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.4 A 2-3 tree

6 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.5 a) A balanced binary search tree; b) a 2-3 tree with the same elements

7 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.6 a) The binary search tree of Figure 12.5a after a sequence of insertions; b) the 2-3 tree of Figure 12.5b after the same insertions

8 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.7 After inserting 39

9 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.8 a), b) The steps for inserting 38; c) the resulting tree

10 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.9 After inserting 37

11 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.10 a), b), c) The steps for inserting 36; d) the resulting tree

12 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.11 The tree after the insertion of 35, 34, and 33

13 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.12 Splitting a leaf in a 2-3 tree

14 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.13 Splitting an internal node in a 2-3 tree

15 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.14 Splitting the root of a 2-3 tree

16 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.15a a), b), c), d) The steps for deleting 70

17 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.15b-d a), b), c), d) The steps for deleting 70

18 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.15e e) the resulting tree

19 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.16 a), b), c) The steps for deleting 100; d) the resulting tree

20 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.17a The steps for deleting 80

21 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.17b and 12.17c The steps for deleting 80

22 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.17d and 12.17e The steps for deleting 80

23 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.18 Results of deleting 70, 100, and 80 from a) the binary search tree of Figure 12.5a and b) the 2-3 tree of Figure 12.5b

24 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.19a and 12.19b a) Redistributing values; b) merging a leaf

25 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.19c and 12.19d c) redistributing values and children; d) merging internal nodes

26 Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.19e e) deleting the root

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