072 Edit Distance.py

'''
Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

You have the following 3 operations permitted on a word:

a) Insert a character
b) Delete a character
c) Replace a character
'''

class Solution(object):
    def minDistance(self, word1, word2):
        """
        :type word1: str
        :type word2: str
        :rtype: int
        """
        m = len(word1)
        n = len(word2)
        dp = [[0 for __ in range(m + 1)] for __ in range(n + 1)]
        for j in range(m + 1):
            dp[0][j] = j
        for i in range(n + 1):
            dp[i][0] = i
        for i in range(1, n + 1):
            for j in range(1, m + 1):
                onemore = 1 if word1[j - 1] != word2[i - 1] else 0
                dp[i][j] = min(dp[i - 1][j] + 1, dp[i][j - 1] + 1, dp[i - 1][j - 1] + onemore)
        return dp[n][m]


if __name__ == "__main__":
    assert Solution().minDistance("", "a") == 1
    assert Solution().minDistance("faf", "efef") == 2