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

27. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.20 A 2-3-4 tree with the same items as the 2-3 tree in Figure 12-6b

28. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.21 A 4-node in a 2-3-4 tree

29. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.22 Inserting 20 into a one-node 2-3-4 tree

30. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.23 After inserting 50 and 40

31. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.24 The steps for inserting 70

32. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.25 After inserting 80 and 15

33. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.26 The steps for inserting 90

34. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.27 The steps for inserting 100

35. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.28 Splitting a 4-node root during insertion

36. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.29 Splitting a 4-node whose parent is a 2-node during insertion

37. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.30 Splitting a 4-node whose parent is a 3-node during insertion

38. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.31 Red-black representation of a 4-node

39. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.32 Red-black representation of a 3-node

40. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.33 A red-black tree that represents the 2-3-4 tree in Figure 12.20

41. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.34 Splitting a red-black representation of a 4-node that is the root

42. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.35 Splitting a red-black representation of a 4-node whose parent is a 2-node

43. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.36a Splitting a red-black representation of a 4-node whose parent is a 3-node

44. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.36b Splitting a red-black representation of a 4-node whose parent is a 3-node

45. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.36c Splitting a red-black representation of a 4-node whose parent is a 3-node

46. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.37 a) An unbalanced binary search tree; b) balanced tree after rotation; c) a balanced tree after insertion

47. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.38 a) An unbalanced binary search tree; b) a balanced tree after a single left rotation

48. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.39 Before and after a single left rotation that decreases the tree’s height

49. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.40 a) An unbalanced binary search tree; b) a balanced tree after a single left rotation

50. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.41 Before and after a single left rotation that does not affect the tree’s height

51. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.42 a) Before; b) during; and c) after a double rotation

52. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.43 Before and after a double rotation that decreases the tree’s height

53. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.44 Address calculator

54. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.45 A collision

55. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.46 Linear probing with h(x) = x mod 101

56. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.47 Quadratic probing with h(x) = x mod 101

57. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.48 Double hashing during the insertion of 58, 14, and 91

58. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.49 Separate chaining

59. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.50 The relative efficiency of four collision-resolution methods

60. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.51 Two data structures that share the same data: a) a sorted linked list; b) a reference-based queue

61. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.52 A queue referencing a sorted linked list

62. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.53 A queue referencing into a doubly linked list

63. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.54 A queue referencing a double linked binary search tree

64. Data Abstraction and Problem Solving with JAVA Walls and Mirrors; Frank M. Carrano and Janet J. Prichard © 2001 Addison Wesley Figure 12.55 A red-black tree for Exercise 7