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72. Edit Distance

Description

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

``````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')
``````

Translation

• 插入一个字符
• 删除一个字符
• 替换一个字符
``````示例 1:

horse -> rorse (将 'h' 替换为 'r')
rorse -> rose (删除 'r')
rose -> ros (删除 'e')

intention -> inention (删除 't')
inention -> enention (将 'i' 替换为 'e')
enention -> exention (将 'n' 替换为 'x')
exention -> exection (将 'n' 替换为 'c')
exection -> execution (插入 'u')
``````

Ideas

dp[i+1][j+1] 的意义为 word1 从 0 到 i 的字符转换成 word2 从 0 到 j 的字符需要的最少步数。

``````如果 word1[i] == word2[j] 则：

dp[i + 1][j + 1] = dp[i][j]

dp[i + 1][j + 1] = Math.min(dp[i][j] + 1, Math.min(dp[i][j + 1] + 1, dp[i + 1][j] + 1));
``````

Note

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