The Levenshtein distance between two character strings a and b is defined as the minimum number...

Transcribed Image Text:

The Levenshtein distance between two character strings a and b is defined as the minimum number of single-character insertions, deletions, or substitutions (so-called edit operations) required to transform string a into string b. Let a[1...m] and b[1...n] be character strings. Formally, the Levenshtein distance between a and b is defined as: n, m, LD(a,b) = LD (a[2...m], b[2...n]), LD(a[2...m], b), min LD(a, b[2...n]), if m = 0, if n = 0, if a[1] = b[1] +1, otherwise. LD(a[2...m], b[2...n]) Consider the problem of computing the Levenshtein distance. 10. (1 point) Write an algorithm in pseudo-code from the above self-reduction. 11. (2 points) Obtain a recurrence expressing the worst-case runtime complex- ity of this algorithm as a function T(N) of the total number N:= m + n of input characters. Hint: take the maximum number of recursive calls the algorithm performs and the maximum number of elements that are passed to them. 12. (4 points) (a) Solve that recurrence. Hint: guess-and-prove works, but the Master Theorem can be applied to a related recurrence after a suitable change of variable. The Levenshtein distance between two character strings a and b is defined as the minimum number of single-character insertions, deletions, or substitutions (so-called edit operations) required to transform string a into string b. Let a[1...m] and b[1...n] be character strings. Formally, the Levenshtein distance between a and b is defined as: n, m, LD(a,b) = LD (a[2...m], b[2...n]), LD(a[2...m], b), min LD(a, b[2...n]), if m = 0, if n = 0, if a[1] = b[1] +1, otherwise. LD(a[2...m], b[2...n]) Consider the problem of computing the Levenshtein distance. 10. (1 point) Write an algorithm in pseudo-code from the above self-reduction. 11. (2 points) Obtain a recurrence expressing the worst-case runtime complex- ity of this algorithm as a function T(N) of the total number N:= m + n of input characters. Hint: take the maximum number of recursive calls the algorithm performs and the maximum number of elements that are passed to them. 12. (4 points) (a) Solve that recurrence. Hint: guess-and-prove works, but the Master Theorem can be applied to a related recurrence after a suitable change of variable.

Answer rating: 100% (QA)

10 Pseudocode for computing the Levenshtein distance function LevenshteinDistancea1m b1n if m 0 retu... View the full answer