#1

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: []
```

#2

The below code uses backtracking to exhaustively search for all possible combinations of numbers and put in the operator between them.

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

private void helper(String num, int target, List<String> result, StringBuilder expr, int pos, long eval, long last){
if(pos == num.length()){
if(target == eval)
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));
int len = expr.length();
if(pos==0){
helper(num, target, result, expr.append(cur), i+1, cur, cur);
expr.setLength(len);
} else{
helper(num, target, result, expr.append("+").append(cur), i+1, eval+cur, cur);
expr.setLength(len);
helper(num, target, result, expr.append("-").append(cur), i+1, eval-cur, -cur);
expr.setLength(len);
helper(num, target, result, expr.append("*").append(cur), i+1, eval-last+last*cur, last*cur);
expr.setLength(len);
}
}
}
}
``````