7 longest common subsequence lcs alignment without

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Unformatted text preview: nputs. 7 Longest Common Subsequence (LCS) – Alignment without Mismatches Substrings and Subsequences Definition: A string x’ is a substring of a string x, " " "if x = ux’v for some prefix string u and suffix string v " " " " " "(x’ = xi…xj, for some 1 ≤ i ≤ j ≤ |x|) •  Given two sequences v = v1 v2…vm and w = w1 w2…wn A string x’ is a subsequence of a string x "if x’ can be obtained from x by deleting 0 or more letters " " " " " " " " " " " "Example: " " " " •  The LCS of v and w is a sequence of positions in v : 1 < i1 < i 2 < … < i t < m "(x’ = xi1…xik, for some 1 ≤ i1 ≤ … ≤ ik ≤ |x|) and a sequence of positions in Note: a substring is always a subsequence w: 1 < j1 < j2 < … < jt < n "x = abracadabra "y = cadabr; "substring "z = brcdbr; "subseqence, not substring such that ik -th letter of v equals to jk-th letter of w and t is maximal LCS: Example i...
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This note was uploaded on 02/10/2014 for the course CS 548 taught by Professor Asaben-hur during the Spring '12 term at Colorado State.

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