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Huffman codes

Huffman codes

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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We are given the following set of 7 characters, with their relative frequencies (last one is a space): {('A', 10), ('E', 15), ('T', 12), ('S', 3), ('H', 4), ('T', 13), ('_', 1)} a) Showing all the steps, build the tree for the Huffman codes of these characters. Show the resulting binary encodings for each character after you are done. b) Compute the binary code for the following string: "THIS IS A TEST" c) Using your tree, decode the following bit string: 001111011111000111110110011111011011110111011001 d) What are the average encoding lengths (bits per character) in the two strings above? e) The problem with the strings in (b) and (c) is that the letters do not have the same distribution (relative frequencies) as stated in (a). If we instead had a string of length 58 (about one line of text) with the same relative frequencies of as stated in (a), what would be the length of the encoding and how many bits per character? What if this string was of length 2900 (about one page of text) instead of 58 -- what would be the length of the encoding and how many bits per character?
Transcribed Image Text:We are given the following set of 7 characters, with their relative frequencies (last one is a space): {('A', 10), ('E', 15), ('T', 12), ('S', 3), ('H', 4), ('T', 13), ('_', 1)} a) Showing all the steps, build the tree for the Huffman codes of these characters. Show the resulting binary encodings for each character after you are done. b) Compute the binary code for the following string: "THIS IS A TEST" c) Using your tree, decode the following bit string: 001111011111000111110110011111011011110111011001 d) What are the average encoding lengths (bits per character) in the two strings above? e) The problem with the strings in (b) and (c) is that the letters do not have the same distribution (relative frequencies) as stated in (a). If we instead had a string of length 58 (about one line of text) with the same relative frequencies of as stated in (a), what would be the length of the encoding and how many bits per character? What if this string was of length 2900 (about one page of text) instead of 58 -- what would be the length of the encoding and how many bits per character?
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