Transcript Lecture 10
Chapter 7 Binary Search Trees 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 Data Structures: A Pseudocode Approach with C, Second Edition 1 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 right subtree are greater than or equal to the root. •Each subtree is itself a binary search tree. Data Structures: A Pseudocode Approach with C, Second Edition 2 Data Structures: A Pseudocode Approach with C, Second Edition 3 Data Structures: A Pseudocode Approach with C, Second Edition 4 7-2 BST Operations There are four basic BST operations: traversal, search, insert, and delete. Traversals • Searches • Insertion • Deletion Data Structures: A Pseudocode Approach with C, Second Edition 5 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 Data Structures: A Pseudocode Approach with C, Second Edition 6 Searches Data Structures: A Pseudocode Approach with C, Second Edition 7 Data Structures: A Pseudocode Approach with C, Second Edition 8 Data Structures: A Pseudocode Approach with C, Second Edition 9 Data Structures: A Pseudocode Approach with C, Second Edition 10 Data Structures: A Pseudocode Approach with C, Second Edition 11 Data Structures: A Pseudocode Approach with C, Second Edition 12 Data Structures: A Pseudocode Approach with C, Second Edition 13 Data Structures: A Pseudocode Approach with C, Second Edition 14 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. Data Structures: A Pseudocode Approach with C, Second Edition 15 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. 2. We can find the largest node in the deleted node’s left subtree and move its data to replace the deleted node’s data 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. Data Structures: A Pseudocode Approach with C, Second Edition 16 Data Structures: A Pseudocode Approach with C, Second Edition 17 (continued) Data Structures: A Pseudocode Approach with C, Second Edition 18 Data Structures: A Pseudocode Approach with C, Second Edition 19 7-3 Binary Search Tree ADT Discussion of the BST data structure includes: • Data Structure • Algorithms Data Structures: A Pseudocode Approach with C, Second Edition 20 Data Structures: A Pseudocode Approach with C, Second Edition 21 Data Structures: A Pseudocode Approach with C, Second Edition 22 Data Structures: A Pseudocode Approach with C, Second Edition 23 Data Structures: A Pseudocode Approach with C, Second Edition 24 Data Structures: A Pseudocode Approach with C, Second Edition 25 Data Structures: A Pseudocode Approach with C, Second Edition 26 Data Structures: A Pseudocode Approach with C, Second Edition 27 Data Structures: A Pseudocode Approach with C, Second Edition 28 Data Structures: A Pseudocode Approach with C, Second Edition 29 Data Structures: A Pseudocode Approach with C, Second Edition 30 Data Structures: A Pseudocode Approach with C, Second Edition 31 Data Structures: A Pseudocode Approach with C, Second Edition 32 Data Structures: A Pseudocode Approach with C, Second Edition 33 Data Structures: A Pseudocode Approach with C, Second Edition 34 Data Structures: A Pseudocode Approach with C, Second Edition 35 Data Structures: A Pseudocode Approach with C, Second Edition 36 Data Structures: A Pseudocode Approach with C, Second Edition 37 Data Structures: A Pseudocode Approach with C, Second Edition 38 Data Structures: A Pseudocode Approach with C, Second Edition 39 Data Structures: A Pseudocode Approach with C, Second Edition 40 Data Structures: A Pseudocode Approach with C, Second Edition 41 Data Structures: A Pseudocode Approach with C, Second Edition 42 Data Structures: A Pseudocode Approach with C, Second Edition 43 Data Structures: A Pseudocode Approach with C, Second Edition 44 Data Structures: A Pseudocode Approach with C, Second Edition 45 Data Structures: A Pseudocode Approach with C, Second Edition 46 Data Structures: A Pseudocode Approach with C, Second Edition 47 Data Structures: A Pseudocode Approach with C, Second Edition 48 Data Structures: A Pseudocode Approach with C, Second Edition 49 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 Data Structures: A Pseudocode Approach with C, Second Edition 50 Data Structures: A Pseudocode Approach with C, Second Edition 51 Data Structures: A Pseudocode Approach with C, Second Edition 52 Data Structures: A Pseudocode Approach with C, Second Edition 53 Data Structures: A Pseudocode Approach with C, Second Edition 54 Data Structures: A Pseudocode Approach with C, Second Edition 55 Data Structures: A Pseudocode Approach with C, Second Edition 56 Data Structures: A Pseudocode Approach with C, Second Edition 57 Data Structures: A Pseudocode Approach with C, Second Edition 58 Data Structures: A Pseudocode Approach with C, Second Edition 59 Data Structures: A Pseudocode Approach with C, Second Edition 60 Data Structures: A Pseudocode Approach with C, Second Edition 61 Data Structures: A Pseudocode Approach with C, Second Edition 62 Data Structures: A Pseudocode Approach with C, Second Edition 63 Data Structures: A Pseudocode Approach with C, Second Edition 64 Data Structures: A Pseudocode Approach with C, Second Edition 65 Data Structures: A Pseudocode Approach with C, Second Edition 66 Data Structures: A Pseudocode Approach with C, Second Edition 67 Data Structures: A Pseudocode Approach with C, Second Edition 68 Data Structures: A Pseudocode Approach with C, Second Edition 69 Data Structures: A Pseudocode Approach with C, Second Edition 70 Data Structures: A Pseudocode Approach with C, Second Edition 71 Data Structures: A Pseudocode Approach with C, Second Edition 72 Data Structures: A Pseudocode Approach with C, Second Edition 73