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