72 Edit Distance

🔀 Pick One

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.
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class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        m, n = len(word1)+1, len(word2)+1
        dp = [[0] * n for _ in range(m)]

        for i in range(m):
            for j in range(n):
                if i == 0:
                    dp[i][j] = j
                elif j == 0:
                    dp[i][j] = i
                else:
                    if word1[i-1] == word2[j-1]:
                        dp[i][j] = min(
                            dp[i-1][j] + 1,
                            dp[i][j-1] + 1,
                            dp[i-1][j-1]
                        )
                    else:
                        dp[i][j] = 1 + min(
                            dp[i-1][j],
                            dp[i][j-1],
                            dp[i-1][j-1]
                        )
        return dp[m-1][n-1]

# can reduce space to O(min(m, n))