Lecture 36 Log into Linux. Copy files on csserver from - PowerPoint PPT Presentation

Lecture 36  Log into Linux. Copy files on csserver from /home/hwang/cs215/lecture36/*.* into a subdirectory.  Reminder: Homework 8 due on Friday.  Questions? Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 1

Outline  Review binary search trees  Example class: Bag class  Attributes  Reimplementation of operations Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 2

Binary Search Trees  Review: A BST is defined as a binary tree with the following ordering :  For each node, the data values in the left subtree are less than or equal to the node value.  For each node, the data values in the right subtree are greater than the node value. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 3

Binary Search Trees  To find an item, start at root node. Compare item to node value. If equal, then done. Otherwise, go down the appropriate subtree and repeat. If reach null, item is not present.  To insert an item, start at a root node. Use the same algorithm as finding an item also maintaining a parent pointer that points to the parent of the node being examined. When reach a null pointer, create a new node with item and attach it to the parent on that side. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 4

Binary Search Trees  To erase an item, start at root node. Using the same algorithm as inserting an item, stop when find a node with the item value. Identify case:  Node is a leaf. Delete node and set child pointer in parent to null.  Node has one child. Set the child pointer is parent to point to the child of the node. Delete node.  Node has two children. Find the immediate predecessor. Replace node value with immediate predecessor. Erase the immediate predecessor node. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 5

In-class Exercise  Starting with an empty BST, draw the tree that results from inserting the following integers: 30, 67, 17, 47, 15, 25, 50, 45, 19, 27  Continuing with this tree, draw the result of deleting (in order): 50, 67, 17 Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 6

Bag Class Attributes  This bag class will be implemented using a binary search tree. There is one attribute:  rootPtr – a pointer to the head node of the linked list that contains the bag items  Note that the textbook chooses to compute the size of the data structure rather than keep track of the size as items are inserted and removed, making the Size operation O(n) rather than O(1). Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 7

Bag Object  Here is a way to think about how this works. Bag b; b.Insert(15); b.Insert(34); rootPtr 15 34 Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 8

BTNode Class File  Note that today's bintree.h file is enhanced from what we had last class, and you may use it in your project. In this version, non-const Left( ) and Right( ) operations return references to the children pointers so that they may be modified using code like: ptr->Left( ) = new BTNode<T> (entry); TreeClear(ptr->Left());  Note that since BTNode is a template, we do not need to change anything to use it. However, it is in namespace BinaryTreeToolkit. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 9

Bag Class Definition  Examine the Bag template class definition in file bag6.h  Has the same typedefs as the other Bag classes.  Otherwise operation prototypes are the exactly the same as the previous Bag classes. Note that a Bag only receives and returns data items; never pointers to the nodes. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 10

Bag Class Usage  Examine file bag6test.cpp  This is an example of an interactive test program. Note that using the Bag object is the same as previous usages. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 11

Bag Class Implementation  Examine the rest of file bag6.h  In addition to the Bag class operation implementations, there are several BST utility functions that encapsulate BST operations on BTNodes. Various parts are left as exercises to be completed today during class.  As before, we will ignore any bad_alloc exceptions. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 12

Constructors, Destructor, Assignment operator=  The default constructor simply sets rootPtr to null to indicate an empty tree.  The copy constructor simply uses TreeCopy to make a copy of the source's tree.  The destructor simply uses TreeClear to destroy the tree's nodes.  The assignment operator= makes a self- assignment test, then uses TreeClear and TreeCopy. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 13

Count  Since the storage representation is a BST, we can use an iterative algorithm to provide count of a particular element.  Since the left subtree contains items less than or equal to the node value, we need to find the first node that equals the target. Once there we need to count the node containing the target as we continue down the left subtree. Eventually, we get to a null child.  Complete the Count function in bag6.h Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 14

Insert  Special case: empty tree  Create a node with the entry and make it the root node  Otherwise, want to find the place the entry goes. Use a boolean flag done to know when to stop the loop that looks for this place. Need a pointer to the node where the new entry node is attached. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 15

Insert  Basic find algorithm 1. Initialize cursor to rootPtr and done to false 2. While not done do 2.1. Check if entry <= cursor node value 2.1.1. If so, check if left child exists 2.1.1.1. Attach new node with entry as left child 2.1.1.2. Set done to true 2.1.2. Else 2.1.2.1. Move cursor to left child 2.2. Else 2.2.1. Do the same for the right child  Complete the Insert function in bag6.h Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 16

EraseOne  The erasing algorithm for BSTs can be implemented directly, and is not too difficult. However, a parent pointer must be maintained in order to delete a node from a tree in a manner similar to linked lists.  The textbook presents an indirect method using recursion. Two auxilliary functions, BSTRemove and BSTRemoveMax, are used. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 17

BSTRemove  This function takes advantage of the fact that we can use the Left( ) and Right( ) operations to change the values of the left and right children pointers, respectively. The function receives a root pointer and a target, and passes back the root of the tree with the target removed as well as returning true if it removed the target.  As usual, we handle the empty tree first and return false. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 18

BSTRemove  Otherwise, if the target is less than or greater than the node value, we call BSTRemove with the left or right child pointer, respectively.  When the target is found, there are two cases:  If there is no left child, we can just make the right child the new root and delete the node.  If there is a left child, we need to replace the root node value with its immediate predecessor and delete that node. This is done using BSTRemoveMax. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 19

BSTRemoveMax  BSTRemoveMax receives a root pointer and passes back the root of the tree with the maximum element removed. It also passes back the item whose node was delete in removed . (Since we call BSTRemoveMax with the data field of the node where we want the maximum value to go, this causes that value to be stored in the correct place.) Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 20

BSTRemoveMax  There are two cases to consider  The node has no right child, which means we have found the maximum value in the tree. We set removed to the value in this node and then replace it with its left child.  The node has a right child, so the maximum is still farther down the right subtree and we call BSTRemoveMax with the right child.  Complete the BSTRemoveMax function in bag6.h Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 21

Erase  Erase is similar to EraseOne, except that it must delete all of the nodes containing the target.  It uses BSTRemoveAll, which is left as a bonus exercise. Wednesday, November 17 CS 215 Fundamentals of Programming II - Lecture 36 22