282. Expression Add Operators

Description

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", "123"]

Example 2:

Input: *num* = "232", target = 8
Output: ["23+2", "2+32"]

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: []

Solution

Backtracking, O(4 ^ n)

class Solution {
    public List addOperators(String num, int target) {
        List res = new ArrayList<>();
        if (num == null || num.isEmpty()) {
            return res;
        }
        
        helper(num, 0, target, 0l, 0l, "", res);
        return res;
    }
    
    private void helper(String s, int start, int target, long eval, long multi, String path, List res) {
        if (start >= s.length()) {
            if (eval == target) {
                res.add(path);
            }
            return;
        }
        
        for (int i = start; i < s.length(); ++i) {
            if (i > start && s.charAt(start) == '0') {  // check if multiple digits started with zero
                break;
            }
            long val = Long.parseLong(s.substring(start, i + 1));   // avoid overflow
            // add operator before s.substring(start, i + 1)
            if (start == 0) {
                helper(s, i + 1, target, eval + val, val, String.valueOf(val), res);
            } else {
                helper(s, i + 1, target, eval + val, val, path + "+" + val, res);
                helper(s, i + 1, target, eval - val, -val, path + "-" + val, res);
                helper(s, i + 1, target, eval - multi + multi * val, multi * val, path + "*" + val, res);
            }
        }
    }
}