Description

Given two wordsword1_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.

Solution

初始化dp[i][0] = i; dp[0][j] = j; insert or delete: A[i - 1][j] + 1 or A[i][j - 1] replace: when A[i] == B[j]: dp[i - 1][j - 1], otherwise: dp[i - 1][j - 1] + 1

public class Solution {
    /*
     * @param word1: A string
     * @param word2: A string
     * @return: The minimum number of steps.
     */
    public int minDistance(String word1, String word2) {
        // write your code here
        if (word1 == null || word2 == null) {
            return 0;
        }

        int n = word1.length();
        int m = word2.length();
        int[][] dp = new int[n + 1][m + 1];
        for (int i = 1; i <= n; i++) {
            dp[i][0] = i;
        }

        for (int j = 1; j <= m; j++) {
            dp[0][j] = j;
        }

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                dp[i][j] = word1.charAt(i - 1) == word2.charAt(j - 1) ? dp[i - 1][j - 1] : dp[i - 1][j - 1] + 1;
                dp[i][j] = Math.min(dp[i][j], Math.min(dp[i - 1][j], dp[i][j - 1]) + 1);
            }
        }

        return dp[n][m];
    }
}