t9ans - CS3230 Tutorial 9 1. Compute the longest common...

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CS3230 Tutorial 9 1. Compute the longest common subsequence of (a) SLWOV NNDK and ALWGQV NBBK . Ans: LWV NK (b) AGCGATAGC and ACAGATGAG Ans: ACGATAG 2. Show that if X and Y are two sequences starting with a , then the longest common subsequence of X and Y starts with an a . Ans: Consider any longest common subsequence of X and Y , say s 1 s 2 ...s k . Then, for some 1 r 1 < r 2 < ... < r k ≤ | X | and for some 1 r 0 1 < r 0 2 < ... < r 0 k ≤ | Y | , s i = X [ r i ] = Y [ r 0 i ]. If s 1 6 = a , then r 1 > 1 and r 0 1 > 1. But then as 1 s 2 ...s k is also a common subsequence of X and Y which is of length greater than k . A contradiction. 3. Give a counterexample to the following claims: (a) If X = X [1] ...X [ m ] and Y = Y [1] ...Y [ n ], and X [ m ] 6 = Y [ n ], then the longest common subsequence of X and Y must end in either X [ m ] or Y [ n ]. Ans: Let X = abac and Y = abab . (b) If X = X [1] ...X [ m ] and Y = Y [1] ...Y [ n ], and X [ m ] 6 = Y [ n ], then the longest common subsequence of
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t9ans - CS3230 Tutorial 9 1. Compute the longest common...

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