282. Expression Add Operators

Problem:

Given a string that contains only digits 0-9 and a target value, return all possibilities to add binary operators (not unary) +, -, or *between the digits so they evaluate to the target value.

Examples: 

"123", 6 -> ["1+2+3", "1*2*3"] 
"232", 8 -> ["2*3+2", "2+3*2"]
"105", 5 -> ["1*0+5","10-5"]
"00", 0 -> ["0+0", "0-0", "0*0"]
"3456237490", 9191 -> []

Analysis:
The idea is plain DFS, the difficulty lies in how to deal with multiply.
2+3*2, the prev value is 5, we cant simply multiply 5 by 2.
The correct formula is 5   -    3    +      3 *  2
                                    val - prev  + prev * cur

So we need to maintain prev value. When the previous operator is - or * =, the previous value is -cur or cur * pre respectively.
Another point worth to mention is that leading 0 is not allowed.


Solution:
Use StringBuilder is much faster than plus Strings.

class Solution {
    public List<String> addOperators(String num, int target) {
        List<String> res = new ArrayList<>();
        if (num == null && num.length() == 0)
            return res;
        dfs(res, num, new StringBuilder(), 0, target, 0, 0);
        return res;
    }
    
    private void dfs(List<String> res, String num, StringBuilder sb, int pos, int target, long val, long pre) {
        if (pos == num.length() && val == target) {
            res.add(sb.toString());    
            return;
        }
        int len = sb.length();
        for (int i = pos; i < num.length(); i++) {
            // leading 0 with 2 and more digits
            if (i != pos && num.charAt(pos) == '0') break;
            long cur = Long.parseLong(num.substring(pos, i + 1));

            if (pos == 0) {
                dfs(res, num, sb.append(cur), i + 1, target, cur, cur);
                sb.setLength(len);
            } else {
                dfs(res, num, sb.append("+").append(cur), i + 1, target, val + cur, cur);
                sb.setLength(len);
                dfs(res, num, sb.append("-").append(cur), i + 1, target, val - cur, -cur);
                sb.setLength(len);
                dfs(res, num, sb.append("*").append(cur), i + 1, target, val - pre + pre * cur, cur * pre);
                sb.setLength(len);
            }
        }
    }
}