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

2. Nodes in a Binary Tree Representing tree nodes Array-based Link-based
Must contain both data and “pointers” to node’s children
Each node will be an object
Array-based
Pointers will be array indices
Link-based
Use C++ pointers
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3. Array-Based Representation
Class of array-based data members
Variable root is index to tree’s root node within the array tree
If tree is empty, root = -1
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4. Array-Based Representation
As tree changes (additions, removals) …
Nodes may not be in contiguous array elements
Thus, need list of available nodes
Called a free list
Node removed from tree
Placed in free list for later use
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5. Array-Based Representation
The class TreeNode for an array-based implementation of the ADT binary tree
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6. Array-Based Representation
(a) A binary tree of names; (b) its implementation using the array tree
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7. Link-Based Representation
The header file containing the class BinaryNode for a link-based implementation of the ADT binary tree
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8. Link-Based Representation
The header file containing the class BinaryNode for a link-based implementation of the ADT binary tree
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9. Link-Based Representation
A link-based implementation of a binary tree
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10. The Header File
A header file for the link-based implementation of the class BinaryNodeTree
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11. The Header File
A header file for the link-based implementation of the class BinaryNodeTree
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12. The Header File
A header file for the link-based implementation of the class BinaryNodeTree
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13. The Header File
A header file for the link-based implementation of the class BinaryNodeTree
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14. The Header File
A header file for the link-based implementation of the class BinaryNodeTree
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15. The Header File
A header file for the link-based implementation of the class BinaryNodeTree
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16. The Implementation Constructors
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17. The Implementation Constructors
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18. The Implementation
Protected method copyTree called by copy constructor
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19. The Implementation Copy constructor
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20. The Implementation
destroyTree used by destructor which simply calls this method
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21. The Implementation Protected method getHeightHelper
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22. The Implementation Method add
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23. The Implementation Adding nodes to an initially empty binary tree
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24. The Implementation Adding nodes to an initially empty binary tree
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25. The Implementation Protected method that enables recursive traversals.
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26. The Implementation
Contents of the implicit stack as treePtr progresses through a given tree during a recursive inorder traversal
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27. The Implementation
Steps during an inorder traversal of the subtrees of 20
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28. The Implementation
Steps during an inorder traversal of the subtrees of 20
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29. The Implementation Avoiding returns to nodes B and C
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30. The Implementation Nonrecursive inorder traversal
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31. The Implementation Nonrecursive inorder traversal
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32. Link-Based Implementation of the ADT Binary Search Tree
Uses same node objects as for binary-tree implementation
Class BinaryNode from Listing16-2 will be used
Recursive search algorithm from Section is basis for operations
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33. Link-Based Implementation of the ADT Binary Search Tree
Adding Kody to a binary search tree
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34. Link-Based Implementation of the ADT Binary Search Tree
Method add
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35. Link-Based Implementation of the ADT Binary Search Tree
Refinement of addition algorithm
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36. Link-Based Implementation of the ADT Binary Search Tree
Adding new data to a binary search tree
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37. Link-Based Implementation of the ADT Binary Search Tree
First draft of the removal algorithm
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38. Link-Based Implementation of the ADT Binary Search Tree
Cases for node N containing item to be removed
N is a leaf
Remove leaf containing target
Set pointer in parent to nullptr
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39. Link-Based Implementation of the ADT Binary Search Tree
Cases for node N containing item to be removed
N has only left (or right) child – cases are symmetrical
After N removed, all data items rooted at L (or R) are adopted by root of N
All items adopted are in correct order, binary search tree property preserved
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40. Link-Based Implementation of the ADT Binary Search Tree
Cases for node N containing item to be removed
N has two children
Locate another node M easier to remove from tree than N
Copy item that is in M to N
Remove M from tree
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41. Link-Based Implementation of the ADT Binary Search Tree
Case 2 for removeValue: The data item to remove is in a node N that has only a left child and whose parent is node P
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42. Link-Based Implementation of the ADT Binary Search Tree
Case 2 for removeValue: The data item to remove is in a node N that has only a left child and whose parent is node P
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43. Link-Based Implementation of the ADT Binary Search Tree
Case 2 for removeValue: The data item to remove is in a node N that has only a left child and whose parent is node P
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44. Link-Based Implementation of the ADT Binary Search Tree
Case 3: The data item to remove is in a node N that has two children
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45. Link-Based Implementation of the ADT Binary Search Tree
Not any node will do
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46. Link-Based Implementation of the ADT Binary Search Tree
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47. Link-Based Implementation of the ADT Binary Search Tree
Replacing the data item in node N with its inorder successor
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48. Link-Based Implementation of the ADT Binary Search Tree
Final draft of the removal algorithm
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49. Link-Based Implementation of the ADT Binary Search Tree
Final draft of the removal algorithm
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50. Link-Based Implementation of the ADT Binary Search Tree
Final draft of the removal algorithm
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51. Link-Based Implementation of the ADT Binary Search Tree
Final draft of the removal algorithm
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52. Link-Based Implementation of the ADT Binary Search Tree
Final draft of the removal algorithm
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53. Link-Based Implementation of the ADT Binary Search Tree
Recursive removal of node N
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54. Link-Based Implementation of the ADT Binary Search Tree
Recursive removal of node N
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55. Link-Based Implementation of the ADT Binary Search Tree
Recursive removal of node N
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56. Link-Based Implementation of the ADT Binary Search Tree
Algorithm for findNode
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57. The Class BinarySearchTree
A header file for the link-based implementation of the class BinarySearchTree
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58. The Class BinarySearchTree
A header file for the link-based implementation of the class BinarySearchTree
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59. The Class BinarySearchTree
A header file for the link-based implementation of the class BinarySearchTree
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60. The Class BinarySearchTree
A header file for the link-based implementation of the class BinarySearchTree
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61. The Class BinarySearchTree
A header file for the link-based implementation of the class BinarySearchTree
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62. Saving a Binary Search Tree in a File
An initially empty binary search tree after the addition of 60, 20, 10, 40, 30, 50, and 70
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63. Saving a Binary Search Tree in a File
Use preorder traversal to save binary search tree in a file
Restore to original shape by using method add
Balanced binary search tree increases efficiency of ADT operations
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64. Saving a Binary Search Tree in a File
A full tree saved in a file by using inorder traversal
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65. Saving a Binary Search Tree in a File
A tree of minimum height that is not complete
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66. Saving a Binary Search Tree in a File
Building a minimum-height binary search tree
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67. Saving a Binary Search Tree in a File
Building a minimum-height binary search tree
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68. Tree Sort Tree sort uses a binary search tree.
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69. General Trees A general tree or an n-ary tree with n = 3
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70. General Trees
An implementation of a general tree and its equivalent binary tree
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71. General Trees An implementation of the n-ary tree
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