Thetwosmallestare8and11 combinethem 19 8 11 a b c d e

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Unformatted text preview: hem into a new tree. 8 A C D E 4 B 4 5 6 12 Label the new vertex with the sum of the frequencies (4+4 = 8) Repeat Repeat Now, we consider 8, 5, 6, and 12. The two smallest are 5 and 6 Combine them as in the first step, yielding new vertex with frequency label 11 8 11 A B C D E 4 4 5 6 12 Repeat Repeat Now, we consider 8, 11, and 12. The two smallest are 8 and 11 Combine them 19 8 11 A B C D E 4 4 5 6 12 Finally, combine the two remaining vertices (12 and 19) to get a single tree. 31 19 8 11 A B C D E 4 4 5 6 12 The final code Letter Code A B C D E 4 4 5 6 12 010 D B 001 C A 000 011 E 1 Length of entire encoding of text…. 4 A’s, 4 B’s, 5 C’s, 6 D’s, and 12 E’s 4x3 + 4x3 + 5x3 + 6x3 + 12x1 = 12 + 12 + 15 + 18 + 12 = 69 bits Letter Code A 000 5 characters: need 3 bits each 4x3 + 4x3 + 5x3 + 6x3 + 12x3 = 12 + 12 + 15 + 18 + 36 = 93 bits B 001 C 010 D 011 A savings of 24 bits. Longer text would mean more savings E 1 Compare to fixed length code Summary Summary Text encoded in natural way using binary n bits allows 2n chars to be represented (or: need log2 n bits to represent n chars) ASCII 8 bit encoding, Unicode 16 bits Fixed length codes are simple, but not necessarily compact Run­length coding takes advantage of repeated sequential characters Lempel­Ziv compression takes advantage of repeating patterns previously occurring Huffman coding chooses variable length code with short codewords for most frequent letters...
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