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A question on Longest common Substring (Not subsequence)
By hari6988, 13 years ago, In English
I was studying the Longest common substring problem using DP ...

LCS(s1--p, t1--q) = 1+ LCS(s1--p-1, t1--q-1) if s[p]=t[q]

                                 0 otherwise

This was the solution given in wikipedia... This would give an answer of 0 for the strings "to" and "tom" ... But, shouldnt it be 2 ?? the "to" matches with "to" in tom . But, it compares only the last character and gives the answer`
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13 years ago, # |
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LCS(1,1) = 1
LCS(2,2) = LCS(1,1) + 1 = 2
Other LCS(i,j) = 0
So it seems to be right.
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  • 13 years ago, # ^ |
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    No, i am talking about LCS(2,3) . It will be 0 ,right ? Shouldnt it be 2 ??

    to
    tom

    In this, to matches in both strings ...
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    • 13 years ago, # ^ |
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      Yes, you right, but answer is maximum among all LCS(i,j), not LCS(n,m).
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