给定2个字符串，求最少经过多少步变成第二个字符串

//  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:
//  a) Insert a character
//  b) Delete a character
//  c) Replace a character
public int minDistance(String word1, String word2) {
        int[][] dp = new int[word1.length() + 1][word2.length() + 1];
        for (int i = 0; i <= word1.length(); i++) {
            dp[i][0] = i;
        }
        for (int j = 0; j <= word2.length(); j++) {
            dp[0][j] = j;
        }
        for (int i = 1; i < dp.length; i++) {
            for (int j = 1; j < dp[0].length; j++) {
                if (word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1];
                } else {                              //删         //增              //改
                    dp[i][j] = 1 + Math.min(Math.min(dp[i - 1][j], dp[i][j - 1]), dp[i - 1][j - 1]);
                }
            }
        }
        return dp[word1.length()][word2.length()];
    }