class Solution:
    def minDistance(self, a: str, b: str) -> int:
        n = len(a)
        m = len(b)

        dp = [[0] * (m + 1) for i in range(n + 1)]
        for i in range(n + 1):
            for j in range(m + 1):
                if j == 0:
                    dp[i][0] = i
                if i == 0:
                    dp[0][j] = j

        for i in range(1, n + 1):
            for j in range(1, m + 1):
                if a[i - 1] == b[j - 1]:
                    dp[i][j] = dp[i - 1][j - 1]
                else:
                    dp[i][j] = 1 + min(dp[i - 1][j - 1], dp[i - 1][j], dp[i][j - 1])

        return dp[-1][-1]

