ExpressionAddOperators.java

/**
* 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.
*
* Example 1:
*
* Input: num = "123", target = 6
* Output: ["1+2+3", "1*2*3"] 
* Example 2:
*
* Input: num = "232", target = 8
* Output: ["2*3+2", "2+3*2"]
* Example 3:
*
* Input: num = "105", target = 5
* Output: ["1*0+5","10-5"]
* Example 4:
*
* Input: num = "00", target = 0
* Output: ["0+0", "0-0", "0*0"]
* Example 5:
*
* Input: num = "3456237490", target = 9191
* Output: []
*/

class Solution {
  public List<String> addOperators(String num, int target) {
    List<String> rst = new ArrayList<>();
    if (num == null || num.length() == 0) return rst;
    helper(rst, "", num, target, 0, 0, 0);
    return rst;
  }

  public void helper(List<String> rst, String path, String num, int target, int pos, long eval, long multed) {
    if (pos == num.length()) {
      if (target == eval)
        rst.add(path);
      return;
    }
    for (int i = pos; i < num.length(); i++) {
      if (i != pos && num.charAt(pos) == '0') break;
      long cur = Long.parseLong(num.substring(pos, i + 1));
      if (pos == 0) {
        helper(rst, path + cur, num, target, i + 1, cur, cur);
      } else {
        helper(rst, path + "+" + cur, num, target, i + 1, eval + cur, cur);

        helper(rst, path + "-" + cur, num, target, i + 1, eval - cur, -cur);

        helper(rst, path + "*" + cur, num, target, i + 1, eval - multed + multed * cur, multed * cur);
      }
    }
  }
}