class_4_greedy_algorithms_Huffman_Kruskal_Prim.pdf

class_4_greedy_algorithms_Huffman_Kruskal_Prim.pdf - Greedy...

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Greedy algorithms Huffman codes Existence of prefix codes Shannon’s theorem Huffman algorithm Minimal spanning trees Graphs (some concepts and definitions) Minimal spanning trees Kruskal algorithm for MST Prim’s algorithm Greedy algorithms July 16, 2017
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Greedy algorithms Huffman codes Existence of prefix codes Shannon’s theorem Huffman algorithm Minimal spanning trees Graphs (some concepts and definitions) Minimal spanning trees Kruskal algorithm for MST Prim’s algorithm Overview 1 Huffman codes Existence of prefix codes Shannon’s theorem Huffman algorithm 2 Minimal spanning trees Graphs (some concepts and definitions) Minimal spanning trees Kruskal algorithm for MST Prim’s algorithm
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Greedy algorithms Huffman codes Existence of prefix codes Shannon’s theorem Huffman algorithm Minimal spanning trees Graphs (some concepts and definitions) Minimal spanning trees Kruskal algorithm for MST Prim’s algorithm Encoding a text file The problem: Suppose we have a text file made out of some finite alphabet x 1 , ..., x n and we want to encode it to a binary code. It should look like: abcdefgh -→ 110110001010101110110011010101 We would like to encode the file such that: 1 It is possible to reconstruct the original file from the encoded file (to decode the file). 2 The encoded file is of minimal length.
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Greedy algorithms Huffman codes Existence of prefix codes Shannon’s theorem Huffman algorithm Minimal spanning trees Graphs (some concepts and definitions) Minimal spanning trees Kruskal algorithm for MST Prim’s algorithm Encoding a text file The problem: Suppose we have a text file made out of some finite alphabet x 1 , ..., x n and we want to encode it to a binary code. It should look like: abcdefgh -→ 110110001010101110110011010101 We would like to encode the file such that: 1 It is possible to reconstruct the original file from the encoded file (to decode the file). 2 The encoded file is of minimal length.
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Greedy algorithms Huffman codes Existence of prefix codes Shannon’s theorem Huffman algorithm Minimal spanning trees Graphs (some concepts and definitions) Minimal spanning trees Kruskal algorithm for MST Prim’s algorithm Encoding a text file The problem: Suppose we have a text file made out of some finite alphabet x 1 , ..., x n and we want to encode it to a binary code. It should look like: abcdefgh -→ 110110001010101110110011010101 We would like to encode the file such that: 1 It is possible to reconstruct the original file from the encoded file (to decode the file). 2 The encoded file is of minimal length.
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Greedy algorithms Huffman codes Existence of prefix codes Shannon’s theorem Huffman algorithm Minimal spanning trees Graphs (some concepts and definitions) Minimal spanning trees Kruskal algorithm for MST Prim’s algorithm Encoding a text file - an example Suppose the file has N characters all of them from the set { A , B , C , D } and we know that the frequencies in which they appear in the file are: character A B C D frequency 1 2 1 4 1 8 1 8 One possible encoding is: character A B C D Codeword 00 01 10 11 In this case, the length of the encoded file will be N 2 · 2 + N 4 · 2 + N 8 ·
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