1. CS-2852 Data Structures LECTURE 13B Andrew J. Wozniewicz Image copyright © 2010 andyjphoto.com

2. CS-2852 Data Structures, Andrew J. Wozniewicz Agenda Encodings Morse Code Huffman Trees

3. CS-2852 Data Structures, Andrew J. Wozniewicz Character Encodings UNICODE (6.0): Different Encodings – UTF-8 8-bits per character for ASCII chars Up to 4 bytes per character for other chars – UTF-16 2 bytes per character Some characters encoded with 4 bytes

4. CS-2852 Data Structures, Andrew J. Wozniewicz Character Encodings Standard ASCII – 7 bits per character – 128 distinct values Extended ASCII – 8 bits per character – 256 distinct values EBCDIC (“manifestation of purest evil” – E. Raymond) – 8 bits per character – IBM-mainframe specific

5. CS-2852 Data Structures, Andrew J. Wozniewicz Fixed-Length Encoding UTF-8, Extended ASCII: – 8 bits per character Always the same number of bits per symbol Log 2 n bits per symbol to distinguish among n symbols More efficient encoding possible, if not all characters are equally likely to appear

6. CS-2852 Data Structures, Andrew J. Wozniewicz Variable-Length Encoding

7. CS-2852 Data Structures, Andrew J. Wozniewicz Morse Code The length of each character in Morse is approximately inversely proportional to its frequency of occurrence in English. The most common letter in English, the letter "E," has the shortest code, a single dot.

8. CS-2852 Data Structures, Andrew J. Wozniewicz Prefix Codes Design a code in such a way that no complete code for any symbol is the beginning (prefix) for any other symbol. If the relative frequency of symbols in a message is known: efficient prefix encoding can be found Huffman encoding is a prefix code

9. CS-2852 Data Structures, Andrew J. Wozniewicz Huffman Encoding Lossless data compression algorithm “Minimum-redundancy” code by David Huffman (1952) Variable-length code table The technique works by creating a binary tree of nodes. The symbols with the lowest frequency appear farthest away from the root. The tree can itself be efficiently encoded and attached with the message to enable decoding.

10. CS-2852 Data Structures, Andrew J. Wozniewicz Example of a Huffman Tree http://mitpress.mit.edu/sicp/full-text/sicp/book/node41.html left=0, right=1

11. CS-2852 Data Structures, Andrew J. Wozniewicz Huffman Algorithm Begin with the set of leaf nodes, containing symbols and their frequencies Find two leaves with the lowest weights and merge them to produce a node that has these two nodes as its left and right branches. – The weight of the new node is the sum of the two weights Remove the two leaves from the original set and replace them by this new node.

12. CS-2852 Data Structures, Andrew J. Wozniewicz Example of Huffman Tree-Building Initial leaves{(A 8) (B 3) (C 1) (D 1) (E 1) (F 1) (G 1) (H 1)} Merge{(A 8) (B 3) ({C D} 2) (E 1) (F 1) (G 1) (H 1)} Merge{(A 8) (B 3) ({C D} 2) ({E F} 2) (G 1) (H 1)} Merge{(A 8) (B 3) ({C D} 2) ({E F} 2) ({G H} 2)} Merge{(A 8) (B 3) ({C D} 2) ({E F G H} 4)} Merge{(A 8) ({B C D} 5) ({E F G H} 4)} Merge{(A 8) ({B C D E F G H} 9)} Final merge{({A B C D E F G H} 17)}

13. CS-2852 Data Structures, Andrew J. Wozniewicz Summary Encodings Morse Code Huffman Trees

14. Questions? Image copyright © 2010 andyjphoto.com