jayantjpr's blog

Edit Distance using LCS
By jayantjpr, 11 years ago, In English

Hi friends,

I was solving a question on SPOJ (http://www.spoj.com/problems/EDIST) to calculate the Edit Distance between two strings (http://en.wikipedia.org/wiki/Levenshtein_distance).

My Claim is:

Given two strings A & B
 Edit Distance(A,B) = max(|A|,|B|) - |Longest common sub-sequence(A,B)|.
(where |A| means length of string A)

Is there something wrong with the above claim? If yes, could you help me find out a test case on which it fails?

I tried submitting the code (using the above claim), but got a wrong answer. I am already aware of the conventional DP solution as shown on the wikipedia page.

Thanks for you help!

Regards,

Jayant

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11 years ago, # |
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ABAC
ADEA
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    11 years ago, # ^ |
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    Yeah! Thanks for the test case!

    I realized my mistake. While claiming above, I was not considering the positions of the letters in the LCS.

    Thanks again! :)

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    8 years ago, # ^ |
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    Thanks :)

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11 years ago, # |
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I always thought:

|A| + |B| = |SES| + |LCS| * 2

Where SES — shortest edit script and LCS is longest common subsequence.

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