282. Expression Add Operators

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 -> []

Solution:

The idea is using DFS and cut the string to numbers.

When we cut and get a number, we have three choices:

1. multiply
2. add
3. subtract

Therefore we maintains lastFactor to deal with these cases:

1.
sum = sum - lastFactor + lastFactor * currNum
lastFactor = lastFactor * currNum

2.
sum = sum + currNum
lastFactor = currNum

3.
sum = sum - currNum
lastFactor = -currNum

Corner case:
1. No sign at the beginning of the string.
2. After a cut, the number cannot start with '0'.



Code:

public class Solution {
    public List<String> addOperators(String num, int target) {
        List<String> result = new ArrayList<>();
        if (num == null || num.length() == 0) {
            return result;
        }
        helper(num, result, target, "", 0, 0, 0);
        return result;
    }
    public void helper(String num, List<String> result, int target, String path, long factor, long sum, int pos) {
        if (pos == num.length() && sum == target) {
            result.add(path);
            return;
        }
        
        for (int i = pos; i < num.length(); i++) {
            if (i != pos && num.charAt(pos) == '0') {
                break;
            }
            String currStr = num.substring(pos, i + 1);
            long currNum = Long.parseLong(currStr);
            if (pos == 0) {
                helper(num, result, target, currStr, currNum, currNum, i + 1);
            }
            else {
                helper(num, result, target, path + "*" + currStr, factor * currNum, sum - factor + factor * currNum, i + 1);
                helper(num, result, target, path + "+" + currStr, currNum, sum + currNum, i + 1);
                helper(num, result, target, path + "-" + currStr, -currNum, sum - currNum, i + 1);
            }
        }
    }
}