72. Edit Distance

Problem Link

Description

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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.

Solution

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Python3

class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        N, M = len(word1), len(word2)
 
        @cache
        def go(i, j):
            if i == N:
                return M - j
            
            if j == M:
                return N - i
            
            if word1[i] == word2[j]:
                return go(i + 1, j + 1)
            else:
                return 1 + min(go(i + 1, j), go(i, j + 1), go(i + 1, j + 1))
        
        return go(0, 0)