CSC 1061: More Trees Quiz

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Questions and Answers

What is the primary advantage of using a B-tree over traditional binary search trees?

B-trees are less efficient for storing large amounts of data.

B-trees decrease the height of the tree, allowing faster disk accesses. (correct)

B-trees require more disk accesses for data retrieval.

B-trees can store only single key per node.

Which property of a B-tree ensures that all leaves are at the same depth?

All leaves have the same depth, defined as the height of the tree. (correct)

Each internal node can have a maximum of MAX-1 keys.

All leaves must contain at least one key.

The root must contain at least 2 children.

What is the minimum number of child nodes that each internal node (except the root) in a B-tree can have?

At least MAX keys.

At least MAX/2 children. (correct)

At least 1 key.

At least 2 children.

How does searching for a value in a B-tree typically work?

Using binary tree search followed by searching the array inside the node. Signup and view all the answers

Which scenario best exemplifies the use of a B-tree?

Manipulating a large, undetermined amount of data in a database system. Signup and view all the answers

Which traversal method visits the nodes in the order of left child, parent, and then right child?

In-Order Signup and view all the answers

What is a distinguishing property of a binary search tree compared to a regular binary tree?

All nodes of the left subtree are less than or equal to the parent node. Signup and view all the answers

Which of the following is the correct order for a pre-order traversal?

4, 2, 5, 1, 3 Signup and view all the answers

Which tree type is characterized by having filled levels and only the last level occupied from left to right?

Complete Tree Signup and view all the answers

In the context of passing a function as an argument, which option represents the function signature correctly?

returnType functionName(dataType, ...) Signup and view all the answers

Which of these traversal methods lists the nodes in a manner where the parent node is visited after its children?

Post-Order Signup and view all the answers

Which of the following sequences corresponds to the backwards in-order traversal?

1, 2, 4, 5, 3 Signup and view all the answers

What is the process called to create a heap data structure from a binary tree?

Heapify Signup and view all the answers

In a Min-Heap, how does the relationship between parent and child nodes work?

Each parent node is smaller than its child nodes. Signup and view all the answers

Which indices correctly represent the parent and child nodes in a binary tree stored as an array?

Parent: array[(i - 1) / 2], Left child: array[2 * i + 1], Right child: array[2 * i + 2] Signup and view all the answers

What is a defining characteristic of a B-tree?

Each node can contain more than one key and more than two children. Signup and view all the answers

Which types of trees are NOT mentioned in relation to binary trees?

B-Trees and Red-Black Trees Signup and view all the answers

What occurs during re-heapification upward in a heap?

Nodes are compared and reordered to maintain heap properties. Signup and view all the answers

Which statement is true for a complete binary tree?

The lowest level can have gaps in its leaves. Signup and view all the answers

In a full binary tree, how many children does each parent node have?

Either two children or zero children. Signup and view all the answers

What does the inOrder function do in a binary tree traversal?

Visits nodes in left-root-right order. Signup and view all the answers

Which is the correct representation of relationships in a binary tree stored as an array with root at index 0?

Current node: array[i], Parent: array[(i - 1) / 2], Children: array[2i + 1] and array[2i + 2] Signup and view all the answers

Study Notes

Course Information

Course code: CSC 1061
Topic: More Trees

Objectives

Follow and explain tree-based algorithms
Explain common binary tree traversals (in-order, pre-order, post-order, backwards in-order)
List binary search tree rules and determine if a tree satisfies them
Perform searches and insertions on binary search trees
Implement algorithms using binary tree class

Agenda - Week 13

Review Binary Tree
Review Binary Search Tree
Binary Tree as Array
Function as Arguments
Other Trees (Full Tree, Complete Tree, Heap, B-Trees)

Binary Tree Traversals

A binary tree is a data structure where each parent node has at most two children.
Traversal names match ordered sets:
- In-Order: 4, 5, 2, 3, 1
- Pre-Order: 4, 2, 5, 1, 3
- Post-Order: 3, 1, 5, 2, 4
- Backward In-Order: 1, 2, 4, 5, 3

Binary Search Tree

A data structure that efficiently maintains a sorted list.
Properties:
- All left subtree nodes are less than or equal to the parent node
- All right subtree nodes are greater than the parent node

Passing a Function as an Argument

Templates don't know about special processing for one data type.
To keep templates generic, functions can take other functions as arguments.
To pass a function as an argument, specify the full function signature in the prototype and header.
Only the function name is passed, but it must match the signature of the function being passed.

Binary Tree Traversal: Generic Process

process is a placeholder function, not a real function.
inOrder function performs in-order traversal using recursion.

Binary Trees as Arrays

Binary trees in arrays offer direct random access.
Each node has a direct index, allowing easy access to parents and children based on the current node's index.
The root node is at index [0]

Other Types of Trees

Besides binary search trees, there are:
- Full Trees
- Heaps
- Complete Trees
- B-Trees

Full Binary Tree

Every parent node has either two or no children.

Complete Binary Tree

All levels are filled except possibly the lowest one (which is filled from left to right).

Heap

A complete binary tree that satisfies either max-heap or min-heap properties.
Every level, excluding possibly the last, is filled.
All nodes are as far left as possible in the tree.

Max Heap Property

Each node is always greater than its child nodes.
The root node has the largest key among all other nodes.

Min Heap Property

Each node is always smaller than its child nodes.
The root node has the smallest key among all other nodes.

Heapify

Creating a heap data structure from a binary tree (creating a min-heap or max-heap).
Adding an element involves re-heapification upward.
Removing an element involves re-heapification downward.

B-Tree

A self-balancing search tree where each node can contain more than one key and has more than two children.
It's a generalization of a binary search tree.

Why B-Tree

The need for B-trees arose due to the need for faster access to physical storage media (like hard disks).
Secondary storage devices are slower, and B-trees can store multiple keys in a single node and have multiple children, significantly reducing the height of the tree (which improves access time).

B-Tree Properties

Keys in a node are stored in increasing order.
Each node has a boolean value x.leaf, which is true if the node is a leaf.
An internal node holds a maximum of MAX - 1 keys and pointers to each child.
Nodes except the root have a maximum of MAX children and a minimum of MAX/2 children.
All leaves have the same depth.
The root node has at least two children and contains one key.

B-Tree Idea

B-trees combine the advantages of dynamic memory and static arrays.
Searches use binary tree traversal to find the range containing the value, then a standard array-searching algorithm like a binary search.

Post-Review

Review glossary terms and complete matching questions.

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Description

This quiz covers key concepts from CSC 1061, focusing on tree-based algorithms, binary tree traversals, and binary search tree properties. You will be tested on your ability to identify traversal types, perform search and insertion operations, and understand various tree structures. Prepare to demonstrate your understanding of binary trees and their applications.