1. Data Structures: A Pseudocode Approach with C, Second Edition 1 Chapter 7 Objectives Create and implement binary search trees Understand the operation of the binary search tree ADT Write application programs using the binary search tree ADT Design and implement a list using a BST Binary Search Trees

2. Data Structures: A Pseudocode Approach with C, Second Edition 2 7-1 Basic Concepts Binary search trees provide an excellent structure for searching a list and at the same time for inserting and deleting data into the list. A binary search tree (BST) is a binary tree with following properties: All items in the left of the tree are less than the root.All items in the left of the tree are less than the root. All items in the right subtree are greater than or equal to the root.All items in the right subtree are greater than or equal to the root. Each subtree is itself a binary search tree.Each subtree is itself a binary search tree.

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5. 5 7-2 BST Operations There are four basic BST operations: traversal, search, insert, and delete. Traversals Searches Insertion Deletion

6. Data Structures: A Pseudocode Approach with C, Second Edition 6 Preorder Traversal : 23 18 12 20 44 35 52 Postorder Traversal: 12 20 8 35 52 44 23 Inorder Traversal: 12 18 20 23 35 44 52

7. Data Structures: A Pseudocode Approach with C, Second Edition 7 Searches

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15. Data Structures: A Pseudocode Approach with C, Second Edition 15 Deletion To delete a node from a binary search tree, we must first locate it. There are four cases for deletion: 1.The node to be deleted has no children. All we need to do is delete the node. 2.The node to be deleted has only a right subtree. We need to delete the node and attach the right subtree to the deleted node’s parent. 3.The node to be deleted has only a left subtree. We need to delete the node and attach the left subtree to the deleted node’s parent. 4.The node to deleted has two subtrees. It is possible to delete a node from the middle of a tree, but the result tends to a very unbalanced trees. Rather, we try to maintain existing structure by finding data to take place of the deleted data.

16. Data Structures: A Pseudocode Approach with C, Second Edition 16 When the node to deleted has two subtrees. It is possible to delete a node from the middle of a tree, but the result tends to a very unbalanced trees. Rather, we try to maintain existing structure by finding data to take place of the deleted data. 1.We can find the largest node in the deleted node’s left subtree and move its data to replace the deleted node’s data 2.Or we can find the smallest node in the deleted node’s right subtree and move its data to replace the deleted node’s data Regardless of which logic we choose, we will be moving data from a leaf or leaf-like node that can be deleted.

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20. Data Structures: A Pseudocode Approach with C, Second Edition 20 7-3 Binary Search Tree ADT Discussion of the BST data structure includes: Data Structure Algorithms

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50. Data Structures: A Pseudocode Approach with C, Second Edition 50 7-4 BST Applications This section develops two applications that use the BST ADT. We begin the discussion of BST Applications with a simple application that manipulates integers. The second application, student list, requires a structure to hold the student's data. Integer Application Student List Application

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