#TC: O(mn)
#SC: O(mn)
#us dynamic programming
#dp[i][j] means the distance between word1[:i] and word2[:j]

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)]

        for i in range(1,m+1):
            dp[i][0] = i

        for j in range(1,n+1):
            dp[0][j] = j

        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-1], min(dp[i-1][j], dp[i][j-1])) + 1

        return dp[-1][-1]