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Questions and Answers
What is the base case when inserting an item into a tree?
What is the base case when inserting an item into a tree?
What is the consequence of inserting elements into a tree in an uncalibrated order?
What is the consequence of inserting elements into a tree in an uncalibrated order?
Which statement about unbalanced trees is true?
Which statement about unbalanced trees is true?
Which of the following advanced tree structures guarantees balanced trees?
Which of the following advanced tree structures guarantees balanced trees?
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What must be preserved when deleting an item from a binary search tree?
What must be preserved when deleting an item from a binary search tree?
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What is a defining characteristic of the structure property in a binary search tree?
What is a defining characteristic of the structure property in a binary search tree?
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What does Tree-Search return when the key matches the key of the node x?
What does Tree-Search return when the key matches the key of the node x?
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Which algorithmic operation can be performed on a binary search tree?
Which algorithmic operation can be performed on a binary search tree?
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To find the smallest element in a binary search tree, one should look where?
To find the smallest element in a binary search tree, one should look where?
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What is the primary difference between recursive and iterative tree searches?
What is the primary difference between recursive and iterative tree searches?
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Which operation would be used to find the minimum node in a binary search tree?
Which operation would be used to find the minimum node in a binary search tree?
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What happens if you reach a leaf node while searching in a binary search tree and the item is not found?
What happens if you reach a leaf node while searching in a binary search tree and the item is not found?
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How does the binary search tree property assist in finding the minimum node?
How does the binary search tree property assist in finding the minimum node?
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What is the primary benefit of the order property of a binary search tree?
What is the primary benefit of the order property of a binary search tree?
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Which statement is true regarding binary trees and binary search trees?
Which statement is true regarding binary trees and binary search trees?
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In the Iterative-Tree-Search algorithm, how does the search continue?
In the Iterative-Tree-Search algorithm, how does the search continue?
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What is the running time complexity of the Tree-Search operation?
What is the running time complexity of the Tree-Search operation?
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Which operation is NOT typically associated with binary search trees?
Which operation is NOT typically associated with binary search trees?
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What will the Iterative-Tree-Search method return if the key is not found in the tree?
What will the Iterative-Tree-Search method return if the key is not found in the tree?
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What is the expected time complexity for searching an item in a balanced binary search tree?
What is the expected time complexity for searching an item in a balanced binary search tree?
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What does the operation findMax accomplish in a binary search tree?
What does the operation findMax accomplish in a binary search tree?
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What is the first step in deleting a node with two children from a binary tree?
What is the first step in deleting a node with two children from a binary tree?
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What happens when deleting a leaf node?
What happens when deleting a leaf node?
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How does the function Delete handle the case when the item to delete is less than the current node's info?
How does the function Delete handle the case when the item to delete is less than the current node's info?
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What is the role of the GetPredecessor function?
What is the role of the GetPredecessor function?
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Which case requires identifying the predecessor node during deletion?
Which case requires identifying the predecessor node during deletion?
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What defines the base case in the delete operation of a tree?
What defines the base case in the delete operation of a tree?
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When a node with only one child is deleted, what replaces that node?
When a node with only one child is deleted, what replaces that node?
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Which operation is performed after replacing a node's data with its predecessor's data?
Which operation is performed after replacing a node's data with its predecessor's data?
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What is indicated by the recursive nature of the Delete function?
What is indicated by the recursive nature of the Delete function?
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What does the DeleteNode function check for when deleting a node?
What does the DeleteNode function check for when deleting a node?
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What is the primary purpose of the find function in a binary search tree (BST)?
What is the primary purpose of the find function in a binary search tree (BST)?
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Which statement correctly describes the iterative version of the find function?
Which statement correctly describes the iterative version of the find function?
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What indicates that a search operation in a BST has failed?
What indicates that a search operation in a BST has failed?
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Which operation correctly utilizes the binary search tree property during insertion?
Which operation correctly utilizes the binary search tree property during insertion?
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In the recursive version of the find function, what happens when the current node is null?
In the recursive version of the find function, what happens when the current node is null?
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What is the time complexity of searching for a value in a balanced binary search tree?
What is the time complexity of searching for a value in a balanced binary search tree?
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Which of the following best describes the process of inserting a new item in a binary search tree recursively?
Which of the following best describes the process of inserting a new item in a binary search tree recursively?
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What underlying principle allows binary search trees to maintain their efficiency?
What underlying principle allows binary search trees to maintain their efficiency?
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Study Notes
Course Information
- Course Title: CSE-111 Data Structure
- Module: 01: Binary Search Tree (BST)
- Instructor: Dr. Omar Elzeki
- Course Level: Undergraduate
- Faculty: Faculty of Computer Science and Engineering, New Mansoura University
Objectives
- Learn about binary search trees
- Learn how to organize data in a binary search tree
- Explore various binary search tree algorithms
- Find items in a binary search tree
- Find maximum and minimum values
- Insert items in a binary search tree
- Delete items in a binary search tree
Binary Search Tree (BST) Data Structure
- Structure Property (Binary Tree): Each node has at most two children. This property simplifies operations.
- Order Property: Values in the left subtree are less than the value in the root node, and values in the right subtree are greater than the value in the root. This crucial property allows for efficient searching.
Finding Smallest and Largest Elements
- Smallest: Located at the leftmost node
- Largest: Located at the rightmost node
Binary Search Tree Search Algorithm
- Start at the root node.
- Compare the target value with the current node value.
- If equal, the item is found.
- If target is less, continue searching in the left subtree.
- If target is greater, continue searching in the right subtree.
- If a leaf node is reached without finding the target, the item is not in the tree.
Practice: Are These BSTs?
- The document shows examples of binary search trees and non-binary search trees.
Tree Search Algorithm (Recursive)
- Tree-Search(x, k): Searches for a key 'k' in a tree rooted at node 'x'.
- Algorithm steps involves checking the key against root key, and repeating based on whether or not the key is less than root key.
- Running time: O(h) where h is the height of the tree.
Tree Search Algorithm (Iterative)
- Iterative-Tree-Search(x, k): Iterative version of the search.
- Algorithm stops when the key is found, or if a null branch is encountered.
BST "Finding" Operations: Other Operations
- FindMin: Finds the minimum node in the tree
- FindMax: Finds the maximum node in the tree
Finding Minimum and Maximum (Algorithms)
- Tree-Minimum(x): Starts at x, moves left until left child is NIL, returns x
- Tree-Maximum(x): Starts at x, moves right until right child is NIL, returns x
- Both take O(h) time (h is the height of the tree)
How to Find a Value in BST
- The document illustrates how to locate a specific data value within a BST. Visual representations guide through the steps, and an algorithm is partially provided.
BST "Finding": Recursive and Iterative Versions
- These present algorithms for finding a value within a BST (recursive, then iterative). Running times are explained.
Function InsertItem
- Use the BST property to insert new items at the correct place in the tree. Examples illustrate insertion with step-by-step updates. A simple recursive implementation algorithm is provided.
Function InsertItem (Implementation Cont.)
- Key details of insertion algorithms are highlighted including recursive implementation. The documents give a brief explanation for recursion steps.
Function InsertItem (Cont.)
- Explanation of analysis of insertion algorithms, including size of the problem, and base and general case. A recursive implementation is described followed by an iterative one.
Does the Order of Inserting Element Matter?
- Yes, ordering elements influences tree balance. Unbalanced trees lead to increased search times.
Function Deleteltem
- Procedure for deleting items from the BST is outlined. Different cases (leaf, one child, two children) are highlighted and illustrated with diagrams.
Deleteltem: Cases, Procedures
- Three significant cases are detailed in deleting a node from a BST. These cases and algorithms for handling specific situations are described in details with illustrated diagrams to explain.
Function DeleteItem (Cont.)
- What is the size of the problem? (Number of nodes)
- What is the base case(s)? (Key found/Empty tree)
- What is the general case? (Select subtree)
- The content also gives an algorithm to implement deletion (recursive). Different cases of deletion are highlighted, and illustrative diagrams are given for each case.
Function Deleteltem (Cont.)
Detailed explanation for deletion algorithm, including steps and algorithm. Different cases for deletion of nodes, detailed illustrations for cases and the algorithms that implement each cases.
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Description
Test your knowledge on binary search trees with this quiz. It covers essential concepts such as insertion, deletion, and searching mechanisms. Each question aims to enhance your understanding of tree structures and their properties.