72. Edit Distance(编辑距离 动态规划)

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:

     def minDistance(self, x, y):
         """
         :type word1: str
         :type word2: str
         :rtype: int
         """
         m = len(x)
         n = len(y)
         dp = [[' '] * (n + 1) for i in range(m + 1)]

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

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