If X denotes the length of string s1 and Y denotes the length of the string s2, then the edit distance between s1 and s2 is never more than
Min(X,Y) or Max(X,Y)?
Please explain.

  • $\begingroup$ The worst case is when they have nothing in common. If I gave you the 5-char string "AAAAA", and the 8-char string "BBBBBBBB", what's the edit distance between them? Why? Because this is a "worst case", if you extend that reasoning, you'll have an answer and a proof. $\endgroup$ – Alex Meiburg Aug 29 '15 at 6:04

It depends on the exact definition of edit distance:

Let, $s1=a$, $s2=bb$

The edit distance between $s1,s2$ is 3 if allowed only insertions and deletions; but it is 2 if allowed insertions, deletions and substitutions.

With substitutions, it is clear that the number of letters you need to change is at most the length of the longer string.


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