Binary Search Trees Chapter 7 Objectives

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Presentation transcript:

Binary Search Trees Chapter 7 Objectives Upon completion you will be able to: 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 Design and implement threaded trees Data Structures: A Pseudocode Approach with C, Second Edition

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

Introduction there are 2 standard trees structures for search trees binary search trees AVL trees both of these trees are used when data need to be ordered they differ only in that AVL trees are balanced while binary search trees are not Data Structures: A Pseudocode Approach with C, Second Edition

Binary Search Trees 1. ordered data in array structure binary search is efficient for searching but very poor for insertion and deletion since it require shifting data in the array 2. linked list structure efficient insertion and deletion but poor for searching because we have to use sequential search (cannot use binary search) Data Structures: A Pseudocode Approach with C, Second Edition

Binary Search Trees (2) therefore, we really need a data structure that has an efficient search, insert and delete algorithms binary search trees provide that structure Data Structures: A Pseudocode Approach with C, Second Edition

Definition a binary search tree is a binary tree with the following properties 1. all items in the left subtree are less than the root 2. all items in the right subtree are greater than or equal to the root 3. each subtree is itself a binary search tree Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

7-2 BST Operations Traversals Searches Insertion Deletion We discuss four basic BST operations: traversal, search, insert, and delete; and develop algorithms for searches, insertion, and deletion. Traversals Searches Insertion Deletion Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Binary Search Tree Traversals from figure 7-4, traverse the tree: using a preorder traversal 23 18 12 20 44 35 52 using a postorder traversal 12 20 18 35 52 44 23 using a inorder traversal 12 18 20 23 35 44 52 the inorder traversal produces an ordered list what happens if we traverse the tree using a right-node-left sequence? Data Structures: A Pseudocode Approach with C, Second Edition

Binary Search Tree Search Algs we study 3 binary search tree search algs 1. find the smallest node 2. find the largest node 3. find a requested node Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

(continued) Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

7-3 Binary Search Tree ADT We begin this section with a discussion of the BST data structure and write the header file for the ADT. We then develop 14 programs that we include in the ADT. Data Structure Algorithms Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

7-4 BST Applications Integer Application Student List Application 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

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

7-5 Threaded Trees 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. Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition