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')

 

 

 

 1 class Solution:
 2 
 3     def minDistance(self, x, y):
 4         """
 5         :type word1: str
 6         :type word2: str
 7         :rtype: int
 8         """
 9         m = len(x)
10         n = len(y)
11         dp = [[' '] * (n + 1) for i in range(m + 1)]
12 
13         for i in range(m + 1):
14             dp[i][0] = i
15         for j in range(n + 1):
16             dp[0][j] = j
17 
18         for i in range(1, m + 1):
19             for j in range(1, n + 1):
20                 if x[i - 1] == y[j - 1]:
21                     dp[i][j] = dp[i - 1][j - 1]
22                 else:
23                     dp[i][j] = 1 + min(dp[i - 1][j], dp[i]
24                                        [j - 1], dp[i - 1][j - 1])
25         return dp[m][n]

 

来源：oschina

链接：https://my.oschina.net/u/4415286/blog/4004318