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Brute force method to find LCS

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• Brute force approach
  • Find longest common subsequence:

    X = BAA Y = BBAB

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  • Brute force solution:

    Generate every subsequence of X: X = BAA Subsequences: B A BA AA BAA Find the longest subsequence that is also a subsequence of Y: Y = BBAB BAA Not subsequence AA Not subsequence BA YES ! Subsequence

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• Running time for the Brute Force method
  • # of subsequences:

    X = x0 x1 x2 .... xn-1 Subsequence: pick x0 OR do not pick x0 pick x1 OR do not pick x1 .... pick xn-1 OR do not pick xn-1 =====> O(2n) # subsequence !!!

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  • Running time brute force method for LCS:

    O(2n)

    So: do not even try !!!

    You won't live long enough to see the answer....