1. Chapter 16 Tree Implementations
CS Data Structures
Mehmet H Gunes
Modified from authors’ slides

2. Contents The Nodes in a Binary Tree
A Link-Based Implementation of the ADT Binary Tree
A Link-Based Implementation of the ADT Binary Search Tree
Saving a Binary Search Tree in a File
Tree Sort
General Trees
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

3. Array-Based Representation
Consider required data members
View class TreeNode, Listing 16-1
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

4. Array-Based Representation
(a) A binary tree of names;
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

5. Array-Based Representation
(b) its implementation using the array tree
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

6. Link-Based Representation
Listing 16-2 shows the class BinaryNode for a link-based implementation
A link-based implementation of a binary tree
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

7. Link-Based Implementation
View header file for the link-based implementation of the class BinaryNodeTree, Listing 16-3
Note significant portions of the implementation file, Listing 16-A
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

8. Link-Based Implementation
Adding nodes to an initially empty binary tree
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

9. Link-Based Implementation
Adding nodes to an initially empty binary tree
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

10. Link-Based Implementation
Avoiding returns to nodes B and C
View pseudocode for non recursive traversal, Listing 16-B
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

11. Algorithms for the ADT Binary Search Tree Operations
(a) A binary search tree;
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

12. Algorithms for the ADT Binary Search Tree Operations
(b) empty subtree where the search algorithm terminates when looking for Kody
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

13. Algorithms for the ADT Binary Search Tree Operations
(c) the tree after Kody is inserted as a new leaf
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

14. Algorithms for the ADT Binary Search Tree Operations
(a) Insertion into an empty tree; (b) search for Frank terminates at a leaf; (c) insertion at a leaf
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

15. Algorithms for the ADT Binary Search Tree Operations
(a) N with only a left child— N can be either the left child or right child of P ;
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

16. Algorithms for the ADT Binary Search Tree Operations
(b) after removing node N
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

17. Algorithms for the ADT Binary Search Tree Operations
N with two children
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

18. Algorithms for the ADT Binary Search Tree Operations
(a) Not any node will do; (b) no longer a binary search tree
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

19. Algorithms for the ADT Binary Search Tree Operations
Search key x can be replaced by y
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

20. Algorithms for the ADT Binary Search Tree Operations
Copying the item whose search key is the inorder successor of N ’s search key
View final draft of remove algorithm, Listing 16-C
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

21. Algorithms for the ADT Binary Search Tree Operations
Recursive deletion of node N
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

22. Algorithms for the ADT Binary Search Tree Operations
Recursive deletion of node N
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

23. Algorithms for the ADT Binary Search Tree Operations
Recursive deletion of node N
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

24. Algorithms for the ADT Binary Search Tree Operations
findNode as a refinement of search
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

25. The Class BinarySearchTree
View header file for the link-based implementation of the class BinarySearchTree, Listing 16-4
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013`

26. Saving Binary Search Tree in a File
An initially empty binary search tree after the insertion of 60, 20, 10, 40, 30, 50, and 70
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

27. Saving Binary Search Tree in a File
Recursive algorithm to create full binary search tree with n nodes
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

28. Saving Binary Search Tree in a File
A full tree saved in a file by using inorder traversal
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

29. Saving Binary Search Tree in a File
A tree of minimum height that is not complete
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

30. Saving Binary Search Tree in a File
Building a minimum height binary search tree
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

31. Tree Sort Algorithm for tree sort
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

32. General Trees A general tree
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

33. General Trees
(a) A link-based implementation of the general tree in Figure ;
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

34. General Trees (b) the binary tree that part a represents
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

35. General Trees An implementation of the n -ary tree in Figure 16-18
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013