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(3) 4. Find a Huffman code to store the string, AHUPUAA

(3) 4. Find a Huffman code to store the string, AHUPUAA

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Problem Statement:** Find a Huffman code to store the string, AHUPUAA. **Solution:** Huffman coding is a popular method of data compression, where the frequency of characters is used to build a binary tree. Each character is represented by a unique binary code. Here's how you can find the Huffman code for the string "AHUPUAA": 1. **Calculate Frequencies:** - A: 3 - H: 1 - U: 2 - P: 1 2. **Create Priority Queue:** Build a priority queue where each node contains a character and its frequency. Nodes are ordered by frequency. 3. **Build Huffman Tree:** - Remove two nodes of the lowest frequency from the queue. - Create a new internal node with these two nodes as children and frequency equal to the sum of the two nodes' frequencies. - Insert the new node back into the queue. - Repeat until there is only one node left in the queue (the root of the tree). 4. **Assign Codes:** - Traverse the tree from root to each leaf, assigning a "0" for left edges and a "1" for right edges to derive the binary code for each character. 5. **Example of Huffman Codes:** - A: 0 - H: 110 - U: 10 - P: 111 These codes are used to compress the data by substituting the variable-length codes for fixed-length ASCII codes. The characters with higher frequencies get shorter codes, resulting in efficient compression.
Transcribed Image Text:**Problem Statement:** Find a Huffman code to store the string, AHUPUAA. **Solution:** Huffman coding is a popular method of data compression, where the frequency of characters is used to build a binary tree. Each character is represented by a unique binary code. Here's how you can find the Huffman code for the string "AHUPUAA": 1. **Calculate Frequencies:** - A: 3 - H: 1 - U: 2 - P: 1 2. **Create Priority Queue:** Build a priority queue where each node contains a character and its frequency. Nodes are ordered by frequency. 3. **Build Huffman Tree:** - Remove two nodes of the lowest frequency from the queue. - Create a new internal node with these two nodes as children and frequency equal to the sum of the two nodes' frequencies. - Insert the new node back into the queue. - Repeat until there is only one node left in the queue (the root of the tree). 4. **Assign Codes:** - Traverse the tree from root to each leaf, assigning a "0" for left edges and a "1" for right edges to derive the binary code for each character. 5. **Example of Huffman Codes:** - A: 0 - H: 110 - U: 10 - P: 111 These codes are used to compress the data by substituting the variable-length codes for fixed-length ASCII codes. The characters with higher frequencies get shorter codes, resulting in efficient compression.
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Huffman code :

An algorithm for lossless data compression is Huffman coding. The concept is to assign variable-length codes to input characters; the issued codes' lengths are determined by the frequency of the related characters. The least common character has a larger code than the most frequent character.

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