[LintCode] #119 Edit Distance

public class Solution {
    /**
     * @param word1 & word2: Two string.
     * @return: The minimum number of steps.
     */
    
    // state: f[i][j] - min steps to convert word1.substring(0,i) to word2.substring(0,j) , Attn: when i = 0, j = 0
    // function: f[i][j] = f[i - 1][j - 1], word1[i] == word2[j]
    //                   = Min(f[i - 1][j - 1], f[i - 1][j], f[i][j - 1]) + 1, word1[i] != word2[j]
    // initialze: f[i][0] = i - 1, word1[0] != word2[0]
    //            f[0][i] = i - 1
    // result: f[m][n]
    
    public int minDistance(String word1, String word2) {
        // write your code here
        if (word1 == null || word2 == null || (word1.length() == 0 && word2.length() == 0)) {
            return 0;
        }
        if (word1.length() == 0 || word2.length() == 0) {
            return word1.length() == 0 ? word2.length() : word1.length();
        }
        int[][] f = new int[word1.length() + 1][word2.length() + 1]; // Attn:Why +1?
        for (int i = 0; i <= word1.length(); i++) {
            f[i][0] = i;
        }
        for (int j = 0; j <= word2.length(); j++) {
            f[0][j] = j;
        }
        for (int i = 1; i <= word1.length(); i++) {
            for (int j = 1; j <= word2.length(); j++) {
                if (word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    f[i][j] = f[i - 1][j - 1];
                } else {
                    f[i][j] = Math.min(f[i - 1][j - 1], Math.min(f[i][j - 1], f[i - 1][j])) + 1;
                }
            }
        }
        return f[word1.length()][word2.length()];
    }
}