class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        m = len(word1)
        n = len(word2)
        dp =[[0] * (n + 1) for _ in range(m+1)] # dp[m][n]
        for j in range(n+1):
            dp[0][j] = j
        for i in range(m+1):
            dp[i][0] = i
        for i in range(1, m+1):
            for j in range(1,n+1):
                if word1[i-1] == word2[j-1]:
                    dp[i][j] = dp[i-1][j-1]
                else:
                    dp[i][j] = min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1])+1
        return dp[m][n]

sol = Solution()
word1 = "horse"
word2 = "ros"
print(sol.minDistance(word1, word2))