CSCOE 1501 Recitation 3 Dynamic Programming: Edit Distance Problemhw1

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CS/COE 1501 Recitation 3Dynamic Programming
Edit Distance Problem(hw1)

• Zhoulan Zhang
• http//www.cs.pitt.edu/zzl

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Problem Definition

• Spell checker finding the closest match of a
  misspelled word
• Edit Distance Problem for 2 strings, finding the
  length of their shortest alignment
• ( of mismatched columns).
• abc acde
• shoes socks

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Dynamic Programming

• Recall the Knapsack Problem
• Construct a matrix of size j i
• ( of items capacity limit M)
• Bottom- up
• How about this Edit Distance Problem?

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Base Case

• When either s1 or s2 is null
• s1 is null distance(s1,s2) s2.length()
• s2 is null distance(s1,s2) s1.length()
• We can fill the first row and first column of our
  matrix

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Recursive Case

• s11...i s21...j.
• 3 possibilities for the last column
• ... s1i - ... s1i
• ... - ... s2j ... s2j

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Wrap Up

• Constructs a matrix of edit distance for all
  prefixes of 2 strings
• Fill out 1st row and 1st column
• Fill out the other slots according to the
  recursive definition