3102_14

# 3102_14 - CSC 3102 Longest Common Subsequence 1 Subsequence...

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1 CSC 3102 Longest Common Subsequence

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2 Subsequence of a String • Let S = s 1 s 2 …s m be a string of length m • Any string of the form s i 1 s i 2 … s i k with i 1 < i 2 < < i k is a subsequence of S • E.g., if S = farmers b fame , arm , mrs , farmers , are some of the subsequences of S
3 Longest Common Subsequence • Let S and T be two strings • If a string is both • a subsequence of S and • a subsequence of T , it is a common subsequence of S and T • In addition, if it is the longest possible one, it is a longest common subsequence

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4 Longest Common Subsequence • E.g., S = algorithms T = logarithms • Then, aim , lots , ohms , grit , are some of the common subsequences of S and T • Longest common subsequences: lorithms , lgrithms
5 Longest Common Subsequence • Let S = s 1 s 2 …s m be a string of length m • Let T = t 1 t 2 …t n be a string of length n Can we quickly find a longest common subsequence (LCS) of S and T ?

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Let X = x 1 x 2 …x k be an LCS of S 1,i = s 1 s 2 s i and T 1,j = t 1 t 2 t j . Lemma: • If s i = t j , then x k = s i = t j , and x 1 x 2 …x k-1 must be the LCS of S 1,i-1 and T 1,j-1 • If s i t j , then X must either be
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## This note was uploaded on 11/16/2011 for the course CSC 3102 taught by Professor Kraft,d during the Fall '08 term at LSU.

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3102_14 - CSC 3102 Longest Common Subsequence 1 Subsequence...

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