72. Edit Distance

Given two words word1 and word2, find the minimum number of operations required to convert word1 to word2.

You have the following 3 operations permitted on a word:

1. Insert a character
2. Delete a character
3. Replace a character

Example 1:

Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation: 
horse -> rorse (replace 'h' with 'r')
rorse -> rose (remove 'r')
rose -> ros (remove 'e')

Example 2:

Input: word1 = "intention", word2 = "execution"
Output: 5
Explanation: 
intention -> inention (remove 't')
inention -> enention (replace 'i' with 'e')
enention -> exention (replace 'n' with 'x')
exention -> exection (replace 'n' with 'c')
exection -> execution (insert 'u')

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