Chapter 7

Data Structures: A Pseudocode Approach with C, Second Edition 1

Chapter 7Chapter 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 TreesBinary Search Trees


7-1 Basic Concepts

Binary search trees provide an excellent structure for searching Binary search trees provide an excellent structure for searching a list and at the same time for inserting and deleting data into a list and at the same time for inserting and deleting data into the list.the list.

A A binary search treebinary search tree (BST) is a binary tree with following properties: (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.


7-2 BST Operations

There are four basic BST operations: traversal, search, insert, There are four basic BST operations: traversal, search, insert, and delete.and delete.

Traversals• Searches• Insertion• Deletion


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


Searches


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.


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.


(continued)


7-3 Binary Search Tree ADT

Discussion of the BST data structure includes:Discussion of the BST data structure includes:

• Data Structure• Algorithms


7-4 BST Applications

This section develops two applications that use the BST ADT. We This section develops two applications that use the BST ADT. We begin the discussion of BST Applications with a simple begin the discussion of BST Applications with a simple application that manipulates integers. The second application, application that manipulates integers. The second application, student list, requires a structure to hold the student's data.student list, requires a structure to hold the student's data.

• Integer Application• Student List Application

Chapter 7

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Transcript of Chapter 7