dp[i][j] = dp[i-1][j-1], if word1[i] == word2[j]dp[i][j] = max{dp[i-1][j], dp[i][j-1], dp[i-1][j-1]} + 1, otherwise

 1 public int minDistance(String word1, String word2) {
 2     int len1 = word1.length();
 3     int len2 = word2.length();
 4
 5     //distance[i][j] is the distance converse word1(1~ith) to word2(1~jth)
 6     int[][] distance = new int[len1 + 1][len2 + 1];
 7     for (int j = 0; j <= len2; j++)
 8         {distance[0][j] = j;} //delete all characters in word2
 9     for (int i = 0; i <= len1; i++)
10         {distance[i][0] = i;}
11
12     for (int i = 1; i <= len1; i++) {
13         for (int j = 1; j <= len2; j++) {
14             if (word1.charAt(i - 1) == word2.charAt(j - 1)) { //ith & jth
15                 distance[i][j] = distance[i - 1][j - 1];
16             } else {
17                 distance[i][j] = Math.min(Math.min(distance[i][j - 1], distance[i - 1][j]), distance[i - 1][j - 1]) + 1;
18             }
19         }
20     }
21     return distance[len1][len2];
22 }

 1     public int minDistance(String word1, String word2) {
 2         if(word1 == null || word2 == null) {
 3             return -1;
 4         }
 5         int len1 = word1.length();
 6         int len2 = word2.length();
 7         int[] distance = new int[len2 + 1];
 8         for(int i = 0; i <= len2; i++) {
 9             distance[i] = i;
10         }
11         for(int i = 1; i <= len1; i++) {
12             int pre = i;
13             for(int j = 1; j <= len2; j++) {
14                 int cur = 0;
15                 if(word1.charAt(i - 1) == word2.charAt(j - 1)) {
16                     cur = distance[j - 1];
17                 } else {
18                     cur = Math.min(pre, Math.min(distance[j], distance[j - 1])) + 1;
19                 }
20                 distance[j - 1] = pre;
21                 pre = cur;
22             }
23             distance[len2] = pre;
24         }
25         return distance[len2];
26     }