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

可以看花花的影片，解釋得很清楚

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[0][i] += i }
    for i := 1; i <= n; i++ { dp[i][0] += 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
}