1. HUFFMAN TREES CSC 172 SPRING 2002 LECTURE 24

2. Prefix Codes Consider a binary trie representing a code 1 0 1 1 0 0 00 01 1011

3. A possible code Suppose we have to transmit messages made up of {A,B,C,D,R} How many bits per character do we need?

4. 1 0 1 0 11 0 0 000001 010 011 1 0 1 1 0 0 100101 110111 A B C DR How many bits for “ABRACADABRA”

5. Prefix Code To prevent ambiguities in decoding, we require the encoding tree satisfies the prefix rule “No code is a prefix of another” A=“0”,j=“11”,v=“10” satisfies the prefix code

6. 0 1 0 1 11 10 0 1 01 011010 00 C A R D How many bits for “ABRACADABRA” B A = 101 B = 11 C = 00 D = 10 R = 011 01011011010000101001011011010 29 bits

7. 0 1 0 1 11 10 0 1 01 011010 00 A C D B How many bits for “ABRACADABRA” R A = 00 B = 10 C = 010 D = 011 R = 11 001011000100001100101100 24 bits

8. Huffman Encoding Trie ABRACADABRA ABRCD 52211

9. Huffman Encoding Trie ABRACADABRA ABRCD 52211 42611

10. Huffman Encoding Trie ABRACADABRA ABRCD 52211 42611 0 0 0 0 1 1 11 ABRACADABRA = 0 100 101 0 110 0 111 0 100 101 0 (23 bits)