Simple JAVA DP solution


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    P
        public int minDistance(String word1, String word2) {
            int len1 = word1.length();
            int len2 = word2.length();
            char[] str1 = word1.toCharArray();
            char[] str2 = word2.toCharArray();
            int[][] dp = new int[len1 + 1][len2 + 1];
            
            // first row
            for (int i = 1; i <= len2; i++) {
                dp[0][i] = i;
            }
            
            // first column
            for (int i = 1; i <= len1; i++) {
                dp[i][0] = i;
            }
            
            for (int i = 1; i <= len1; i++) {
                for (int j = 1; j <= len2; j++) {
                    if (str1[i - 1] == str2[j - 1]) {
                        dp[i][j] = dp[i - 1][j - 1];
                    } else {
                        dp[i][j] = 1 + Math.min(dp[i - 1][j - 1], 
                                                Math.min(dp[i - 1][j], dp[i][j - 1]));
                    }
                }
            }
            
            return dp[len1][len2];
        }
    

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