Huffman Algorithm
Huffman Coding is a popular algorithm used for lossless data compression. It generates variable-length codes based on the frequency of characters or symbols. The more frequently occurring symbols are assigned shorter codes, while less frequent ones get longer codes, reducing the total number of bits needed to represent the data.
Key Concepts:
Lossless Compression: Huffman coding allows you to compress data without any loss of information.
Prefix Codes: The code assigned to a character is unique and no code is a prefix of another, ensuring unambiguous decoding.
Binary Tree: Huffman codes are represented by traversing a binary tree where each left branch represents 0 and each right branch represents 1.
Steps:
Calculate the frequency of each character or symbol in the input.
Build a priority queue (min-heap) of nodes, where each node represents a character and its frequency.
Repeat the following steps until only one node remains in the queue:
Remove the two nodes with the lowest frequencies from the queue.
Combine them into a new node, where the new node's frequency is the sum of the two nodes' frequencies.
Insert the new node back into the queue.
The final node represents the root of the Huffman Tree.
Generate the Huffman codes by traversing the Huffman Tree, assigning a binary 0 for the left branch and 1 for the right branch.
Key Points:
Variable-Length Encoding: Huffman coding reduces the average length of the encoded messages based on character frequency.
Optimality: Huffman coding is an optimal greedy algorithm for lossless compression when dealing with known character frequencies.
Decoding: The prefix property ensures that decoding is straightforward by traversing the tree.
Huffman coding is widely used in applications like file compression (e.g., ZIP), multimedia encoding (e.g., JPEG, MP3), and other areas requiring efficient data encoding.