72. Edit Distance

Description

Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.

You have the following three operations permitted on a word:

          Insert a character
          Delete a character
          Replace a character

Example

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

Tips

0 <= word1.length, word2.length <= 500
word1 and word2 consist of lowercase English letters.

分析

简单的 dp 题目

    def minDistance(self, word1, word2):
        """
        :type word1: str
        :type word2: str
        :rtype: int
        """
        N, M = len(word1), len(word2)
        dp = [[N+M+2 for j in range(M+1)]  for i in range(1+N)]
  
        dp[0][0] 
   
        for i in range(1, N+1):
            for j in range(1, M+1):
                d = 1
                if word1[i-1] == word2[j-1]:
                    d = 0
                dp[i][j] = min(dp[i-1][j-1] +d , dp[i][j-1] + 1, dp[i-1][j] + 1)

        return dp[-1][-1]
计算结果总是出错，主要是初始化出错了！！ 没有初始化 dp[0][j] 和 dp[i][0]