DAA 07 – Huffman Coding and Prefix Codes | Optimal Encoding Using Binary Trees | CS F364

Описание: This lecture is DAA 07 in the Design and Analysis of Algorithms (DAA) course (CS F364). It introduces Huffman Coding and Prefix Codes as efficient techniques for data encoding, with the goal of minimizing the average number of bits required per symbol.

The lecture begins by comparing fixed-length encoding with variable-length encoding and formally defines prefix codes, explaining why they are uniquely decodable. Using symbol frequencies, the concept of Average Bit Length (ABL) is introduced, and examples are used to show how variable-length prefix codes improve encoding efficiency.

Next, the lecture explains how prefix codes can be represented using binary trees, where left and right edges correspond to 0 and 1. It also demonstrates how to construct a binary tree from a given prefix code and proves why such a construction always yields a valid prefix code. These ideas form the conceptual foundation for Huffman’s greedy algorithm, which is discussed in subsequent lectures.

📌 Topics Covered in This Lecture

Fixed-length encoding vs variable-length encoding

Definition and properties of prefix codes

Unique decodability of prefix codes

Symbol frequencies and probability distribution

Average Bit Length (ABL) calculation

Optimal prefix codes

Reduction of ABL using variable-length encoding

Representation of prefix codes using binary trees

Constructing binary trees from prefix codes

Conceptual basis of Huffman Coding

🎯 Who Should Watch

Students studying Design and Analysis of Algorithms (DAA)

B.Tech / BE / M.Sc. / MCA / GATE aspirants

Learners studying Huffman Coding, data compression, and greedy algorithms

Anyone seeking a clear conceptual foundation of prefix codes and optimal encoding

🔗 Playlist

This video is part of the playlist:
Design and Analysis of Algorithms – Complete DAA Course