Data Structures: Huffman Coding & Trees

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Questions and Answers

What is the primary purpose of Huffman Coding in data compression?

To prevent any form of data loss

To assign longer codes to more frequent characters

To increase the size of the data

To assign shorter codes to more frequent characters (correct)

Which step occurs immediately after creating leaf nodes in the Huffman tree construction?

Assign codes to characters

Traverse the tree

Create a new internal node

Arrange nodes by their frequency values (correct)

How is the frequency of a newly created internal node determined in the Huffman tree construction?

It is the average of its child nodes' frequencies

It is the frequency of the most frequent character

It is set to zero

It is the sum of its child nodes' frequencies (correct)

What is the correct sequence of nodes in the in-order traversal of the provided binary tree?

D→B→E→A→F→C→G Signup and view all the answers

Which of the following statements accurately describes the prefix rule in Huffman Coding?

No character's code can be a prefix of another's code Signup and view all the answers

Which traversal method will yield the root node last in the visited sequence?

Post-order Traversal Signup and view all the answers

What is the assigned Huffman Code for the character 'u'?

1101 Signup and view all the answers

In the construction of the Huffman Tree, when is a new internal node created?

By combining the two nodes with the lowest frequencies Signup and view all the answers

When performing a pre-order traversal, which node would be visited first?

The root node A Signup and view all the answers

Which of the following accurately describes a post-order traversal?

Left-Right-Root Signup and view all the answers

Which of the following best describes the relationship between character frequency and code length in Huffman Coding?

Higher frequency results in shorter code Signup and view all the answers

What is the resulting output of a pre-order traversal of the binary tree?

A→B→D→E→C→F→G Signup and view all the answers

What weight is assigned to the left edges in a Huffman Tree?

0 Signup and view all the answers

What would be the last node visited in an in-order traversal of the binary tree?

Node A Signup and view all the answers

Which step does not occur during the post-order traversal process?

Visit the root node first Signup and view all the answers

During which traversal is the output sorted in ascending order?

In-order Traversal Signup and view all the answers

What defines a tree data structure as non-linear?

It contains nodes connected in a hierarchical form. Signup and view all the answers

Which of the following statements about nodes in a tree is true?

Nodes can contain any type of data. Signup and view all the answers

What is the depth of a node in a tree?

The length of the path from the root to that node. Signup and view all the answers

How many edges are there in a tree with n nodes?

n - 1 Signup and view all the answers

Why is a tree referred to as a recursive data structure?

It can be defined by its root and its subtrees. Signup and view all the answers

Which node in a tree contains no incoming edges?

Root node Signup and view all the answers

In a tree structure, how are nodes typically represented?

By a combination of data types. Signup and view all the answers

What feature differentiates a tree from linear data structures like arrays?

Trees display a hierarchical organization of nodes. Signup and view all the answers

What type of rotation is performed when a node is inserted into the left-subtree of the left-subtree?

Right-Left rotation Signup and view all the answers

In the deletion process of an AVL tree, which type of rotation is applied if the node being deleted is in the left subtree of the critical node?

Left rotation Signup and view all the answers

When a node A becomes unbalanced due to an insertion in its right subtree, which rotation is needed first?

Right rotation on C Signup and view all the answers

Which operation may lead to a violation of the AVL tree property requiring balancing?

Deletion Signup and view all the answers

What are the two types of rotations used in an AVL tree during rebalancing?

L rotation and R rotation Signup and view all the answers

What happens to node A after a right rotation on node C during the rebalancing process?

It becomes the right subtree of node B. Signup and view all the answers

What condition characterizes node B when using R0 rotation?

It has a balance factor of 0. Signup and view all the answers

What guarantees that an AVL tree remains balanced after node insertions and deletions?

Performing rotations when necessary Signup and view all the answers

What happens to node B when R0 rotation is performed?

Node B becomes the new root. Signup and view all the answers

Which balance factor condition triggers an R1 rotation?

Balance factor of Node B is 1. Signup and view all the answers

Which node becomes the root when R-1 rotation is executed?

Node C. Signup and view all the answers

What is a key characteristic of a B-Tree?

It has a small height relative to the number of keys. Signup and view all the answers

During R1 rotation, where does T1 get placed?

As the left child of Node B. Signup and view all the answers

What effect does deleting node 60 have on the AVL tree?

It disturbs the balance factor of node 50. Signup and view all the answers

Which scenario leads to an R-1 rotation?

Node B has a balance factor of -1. Signup and view all the answers

Why is a B-Tree preferred for disk access?

Because it can store a large number of keys within a single node. Signup and view all the answers

Study Notes

Huffman Coding

Huffman coding is a method of data compression that assigns shorter codes to frequently occurring characters and longer codes to less frequent characters.
This method follows the prefix rule, where the code of a character is not the prefix of any other character.
The Huffman Tree is built by creating leaf nodes for each character, ordering them by frequency, combining the two nodes with the lowest frequencies into a new internal node, and repeating this process until all nodes are combined.

Tree Data Structure

A tree is a non-linear hierarchical data structure where nodes are connected by edges.
The topmost node is called the root node.
Each node in a tree contains data and references to its child nodes.
A tree can be defined recursively, as the root node contains links to the roots of its subtrees.

Tree Traversals

In-order: Left subtree → Root → Right subtree. The output order of an in-order traversal of a binary search tree is the sorted key values in ascending order.
Pre-order: Root → Left subtree → Right subtree.
Post-order: Left subtree → Right subtree → Root.

Binary Search Tree (BST)

A binary search tree is a binary tree where each node's key is greater than all keys in its left subtree and less than all keys in its right subtree.

AVL Trees

An AVL tree is a self-balancing binary search tree where the height difference between the two subtrees of any node is at most 1.
Rotations are used to maintain balance after insertion or deletion.
LR Rotations: This type of rotation is performed when a node is inserted into the right subtree of the left subtree, causing an imbalance.
RL Rotations: This type of rotation is performed when a node is inserted into the left subtree of the right subtree, causing an imbalance.

B-Tree

A B-Tree is an m-way search tree specifically designed for disk access.
It allows for a large number of keys in a single node and relatively small height, improving disk efficiency.

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Description

Explore the concepts of Huffman coding and tree data structures in this quiz. Learn how Huffman coding compresses data and the fundamental properties of trees, including different traversal methods. Test your understanding of these key topics in computer science and data management.