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:

• Insert a character
• Delete a character
• 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')

Tags: Math, String

给定两个单词 word1 和 word2 ,请问最少需要进行多少次操作可以将 word1 变成 word2 。

(动态规划) O(n2)

经典的编辑距离问题。

状态表示:f[i,j] 表示将 word1 的前 i 个字符变成 word2 的前 j 个字符,最少需要进行多少次操作。 状态转移,一共有四种情况:

• 将word1[i] 删除或在word2[j]后面添加word1[i],则其操作次数等于f[i−1,j]+1;
• 将word2[j]删除或在word1[i]后面添加word2[j],则其操作次数等于 f[i,j−1]+1;
• 如果word1[i]=word2[j],则其操作次数等于 f[i−1,j−1];
• 如果word1[i]≠word2[j],则其操作次数等于 f[i−1,j−1]+1;

时间复杂度分析:

• 状态数 O(n2)O(n2),状态转移复杂度是 O(1)O(1),所以总时间复杂度是 O(n2)O(n2)。

思路2

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