72. Edit Distance

Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

You have the following 3 operations permitted on a word:

• Insert a character
• Delete a character
• Replace a character

Example

Given word1 = "mart" and word2 = "karma", return 3.

分析：

经典的DP问题。

public class Solution {
    public int minDistance(String word1, String word2) {
        int word2Length = word2.length();
        int word1Length = word1.length();

        int[][] distance = new int[word1Length + 1][word2Length + 1];

        for (int i = 0; i <= word1Length; i++) {
            distance[i][0] = i;
        }

        for (int i = 0; i <= word2Length; i++) {
            distance[0][i] = i;
        }

        for (int i = 1; i <= word1Length; i++) {
            for (int j = 1; j <= word2Length; j++) {
                if (word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    distance[i][j] = distance[i-1][j-1];
                } else {
                    //                           delete                       add                   replace
                    distance[i][j] = Math.min(distance[i-1][j], Math.min(distance[i][j-1], distance[i-1][j-1])) + 1;
                }
            }
        }
        return distance[word1Length][word2Length];
    }
}