# 72. Edit Distance

Medium
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 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')
Constraints:
• `0 <= word1.length, word2.length <= 500`
• `word1` and `word2` consist of lowercase English letters.

### 解題

func minDistance(word1 string, word2 string) int {
m, n := len(word1), len(word2)
dp := make([][]int, n + 1)
for i := range dp { dp[i] = make([]int, m + 1) }
for i := 1; i <= m; i++ { dp[i] += i }
for i := 1; i <= n; i++ { dp[i] += i }
for i := 1; i <= n; i++ {
for j := 1; j <= m; j++ {
if word1[j - 1] == word2[i - 1] {
dp[i][j] = dp[i - 1][j - 1] // no need to operate
} else {
dp[i][j] = min(dp[i - 1][j - 1], min(dp[i][j - 1], dp[i - 1][j])) + 1
// replace // insert // delete
}
}
}
return dp[n][m]
}
func min(a, b int) int {
if a < b { return a }
return b
}