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Edit Distance

Problem Statement​

Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.

You have the following three operations permitted on a word:

  • Insert a character
  • Delete a character
  • Replace a character

Leetcode Link

Example 1:​

Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation:
horse -> rorse (replace 'h' with 'r')
rorse -> rose (remove 'r')
rose -> ros (remove 'e')

Example 2:​

Input: word1 = "intention", word2 = "execution"
Output: 5
Explanation:
intention -> inention (remove 't')
inention -> enention (replace 'i' with 'e')
enention -> exention (replace 'n' with 'x')
exention -> exection (replace 'n' with 'c')
exection -> execution (insert 'u')

Constraints:​

  • 0 <= word1.length, word2.length <= 500
  • word1 and word2 consist of lowercase English letters.

Code​

Python Code

class Solution(object):
    def minDistance(self, w1, w2):
        """
        :type word1: str
        :type word2: str
        :rtype: int
        """
        m,n,d = len(w1),len(w2),{}
        def mds(w1, w2, i, j):
        if i\*j==0: return i+j
        if (i,j) in d: return d[(i,j)]
        val = 0
        if w1[i-1]==w2[j-1]:
        val = mds(w1, w2, i-1, j-1)
        else:
        val = 1+min(mds(w1,w2,i,j-1),mds(w1,w2,i-1,j-1),mds(w1,w2,i-1,j))
        d[(i,j)]=val
        return val
        return mds(w1,w2,m,n)