Binary Search Trees Quiz

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Questions and Answers

What is the base case when inserting an item into a tree?

The item matches the root node.

The tree is full.

The tree contains one node.

The tree is empty. (correct)

What is the consequence of inserting elements into a tree in an uncalibrated order?

It may lead to a balanced tree.

It only affects the retrieval speed.

It can produce very unbalanced trees. (correct)

It has no impact on the tree structure.

Which statement about unbalanced trees is true?

They minimize the number of nodes.

They are always easier to manage.

They guarantee a shorter search time.

They result in longer search times. (correct)

Which of the following advanced tree structures guarantees balanced trees?

AVL trees (A) Signup and view all the answers

What must be preserved when deleting an item from a binary search tree?

The binary search tree property. (D) Signup and view all the answers

What is a defining characteristic of the structure property in a binary search tree?

Each node can have at most 2 children. (C) Signup and view all the answers

What does Tree-Search return when the key matches the key of the node x?

Returns the node x (A) Signup and view all the answers

Which algorithmic operation can be performed on a binary search tree?

Inserting items (C) Signup and view all the answers

To find the smallest element in a binary search tree, one should look where?

At the leftmost element (B) Signup and view all the answers

What is the primary difference between recursive and iterative tree searches?

Recursive tree search is easier to implement. (A) Signup and view all the answers

Which operation would be used to find the minimum node in a binary search tree?

Tree-Minimum (B) Signup and view all the answers

What happens if you reach a leaf node while searching in a binary search tree and the item is not found?

The search concludes that the item is not found. (C) Signup and view all the answers

How does the binary search tree property assist in finding the minimum node?

Minimum is at the left-most node (A) Signup and view all the answers

What is the primary benefit of the order property of a binary search tree?

It allows for straightforward value searching. (D) Signup and view all the answers

Which statement is true regarding binary trees and binary search trees?

Binary search trees are a specific type of binary tree. (B) Signup and view all the answers

In the Iterative-Tree-Search algorithm, how does the search continue?

Until x is equal to NIL or k matches key[x] (D) Signup and view all the answers

What is the running time complexity of the Tree-Search operation?

O(h) (B) Signup and view all the answers

Which operation is NOT typically associated with binary search trees?

Calculate the average of all nodes (C) Signup and view all the answers

What will the Iterative-Tree-Search method return if the key is not found in the tree?

Returns NIL (B) Signup and view all the answers

What is the expected time complexity for searching an item in a balanced binary search tree?

O(log n) (D) Signup and view all the answers

What does the operation findMax accomplish in a binary search tree?

Locates the node with the largest key (C) Signup and view all the answers

What is the first step in deleting a node with two children from a binary tree?

Find the predecessor node (A) Signup and view all the answers

What happens when deleting a leaf node?

The leaf node is simply removed from the tree (C) Signup and view all the answers

How does the function Delete handle the case when the item to delete is less than the current node's info?

It calls Delete on the left subtree (A) Signup and view all the answers

What is the role of the GetPredecessor function?

To find the rightmost node in the left subtree (B) Signup and view all the answers

Which case requires identifying the predecessor node during deletion?

Deleting a node with two children (C) Signup and view all the answers

What defines the base case in the delete operation of a tree?

Key to be deleted was found (D) Signup and view all the answers

When a node with only one child is deleted, what replaces that node?

The node's right child (B) Signup and view all the answers

Which operation is performed after replacing a node's data with its predecessor's data?

Delete the predecessor node (C) Signup and view all the answers

What is indicated by the recursive nature of the Delete function?

All nodes are processed in a depth-first manner (B) Signup and view all the answers

What does the DeleteNode function check for when deleting a node?

If the node has one or two children (D) Signup and view all the answers

What is the primary purpose of the find function in a binary search tree (BST)?

To locate a specific value within the tree (A) Signup and view all the answers

Which statement correctly describes the iterative version of the find function?

It continues traversing until the value is found or root is null. (B) Signup and view all the answers

What indicates that a search operation in a BST has failed?

When the root becomes null during the search (D) Signup and view all the answers

Which operation correctly utilizes the binary search tree property during insertion?

Insert a new item in a sorted order based on value comparison (B) Signup and view all the answers

In the recursive version of the find function, what happens when the current node is null?

The function returns null. (B) Signup and view all the answers

What is the time complexity of searching for a value in a balanced binary search tree?

O(log n) (C) Signup and view all the answers

Which of the following best describes the process of inserting a new item in a binary search tree recursively?

The insertion follows the tree's structure based on value comparisons. (A) Signup and view all the answers

What underlying principle allows binary search trees to maintain their efficiency?

Nodes are organized such that for every node, values in the left subtree are less and in the right subtree are greater. (D) Signup and view all the answers

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.