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", "123"]
• "232", 8 -> ["23+2", "2+32"]
• "105", 5 -> ["1*0+5","10-5"]
• "00", 0 -> ["0+0", "0-0", "0*0"]
• "3456237490", 9191 -> []

https://leetcode.com/problems/expression-add-operators/

Solution:

note: how to handle the multiply

public List<String> addOperators(String num, int target) {
    List<String> res = new ArrayList<>();
    StringBuilder sb = new StringBuilder();
    dfs(res, sb, num, 0, target, 0, 0);
    return res;

}
public void dfs(List<String> res, StringBuilder sb, String num, int pos, int target, long prev, long multi) { 
    if(pos == num.length()) {
        if(target == prev) res.add(sb.toString());
        return;
    }
    for(int i = pos; i < num.length(); i++) {
        if(num.charAt(pos) == '0' && i != pos) break;
        long curr = Long.parseLong(num.substring(pos, i + 1));
        int len = sb.length();
        if(pos == 0) {
            dfs(res, sb.append(curr), num, i + 1, target, curr, curr); 
            sb.setLength(len);
        } else {
            dfs(res, sb.append("+").append(curr), num, i + 1, target, prev + curr, curr); 
            sb.setLength(len);
            dfs(res, sb.append("-").append(curr), num, i + 1, target, prev - curr, -curr); 
            sb.setLength(len);
            dfs(res, sb.append("*").append(curr), num, i + 1, target, prev - multi + multi * curr, multi * curr); // why is this ??? 
            sb.setLength(len);
        }
    }
}