72. Edit Distance

Hard

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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

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.

class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        m = len(word1)
        n = len(word2)
        return self.edit_distance(word1, word2, m ,n)
    @lru_cache()
    def edit_distance(self, word1, word2, m, n):
        if m == 0:
            return n
        if n == 0:py
            return m
        if word1[m-1] == word2[n-1]:
            return self.edit_distance(word1, word2, m-1, n-1)
        return 1+min(self.edit_distance(word1, word2, m-1, n), self.edit_distance(word1, word2, m-1, n-1), self.edit_distance(word1, word2, m, n-1))