Expression Add Operators

Expression Add Operators

What is this problem about?

The Expression Add Operators interview question asks you to find all possible strings formed by inserting binary operators (+, -, or *) between the digits of a string num such that the expression evaluates to a target value. You cannot change the order of digits, but you can concatenate them to form multi-digit numbers.

Why is this asked in interviews?

Companies like Meta, Amazon, and Google ask this Hard difficulty Backtracking problem to test a candidate's mastery of recursion and mathematical evaluation. It requires careful handling of operator precedence (especially multiplication) and leading zeros. It's an excellent test of a candidate's ability to maintain complex state (the current expression, current value, and the "last operand" for multiplication) through a recursive search.

Algorithmic pattern used

This problem is solved using Backtracking with a "prev_operand" state to handle multiplication precedence.

1. Recursion: Explore all possible split points for the current number.
2. State: Pass the current_val and prev_val through the recursion.
3. Multiplication Logic: To evaluate a + b * c, you cannot simply do (a + b) * c. Instead, you subtract b from the running total and add b * c.
   • new_val = current_val - prev_val + (prev_val * next_num)
4. Pruning: Handle leading zeros (e.g., "05" is not a valid number, but "0" is).

Example explanation

num = "123", target = 6

1. Try "1+2+3": 1+2=3, 3+3=6. (Match!)
2. Try "123": 12=2, 23=6. (Match!)
3. Try "12-3": 12-3=9. (No match) ...and so on. The backtracking explores all combinations of [1, 2, 3] with [+, -, *, ""].

Common mistakes candidates make

• Precedence Error: Failing to correctly handle the multiplication operator, which must be evaluated before addition and subtraction.
• Integer Overflow: Not using 64-bit integers (long) for the evaluation, as intermediate products can exceed 32-bit limits.
• Leading Zeros: Allowing numbers like "05" which are usually prohibited by the problem statement.

Interview preparation tip

Practice the multiplication trick: total - prev + (prev * current). This is a very common requirement for any problem where you need to evaluate math expressions on the fly without a full parser.