Expression Add Operators
Given a string that contains only digits 0-9 and a target value, find all possibilities to insert binary operators (+, -, *) between the digits to evaluate to the target value. Use Backtracking.
Why Interviewers Ask This
Stripe asks this problem to evaluate a candidate's mastery of backtracking algorithms and their ability to handle complex state management. It specifically tests how well you manage edge cases like leading zeros, operator precedence, and integer overflow while maintaining clean, readable code under pressure.
How to Answer This Question
1. Clarify constraints: Confirm if the input string can be empty or contain only zeros, and verify the target range to discuss overflow handling early.
2. Define the recursive state: Explain that your backtracking function needs the current index, the running total, the last operand (for multiplication logic), and the current expression path.
3. Outline the branching logic: Detail how you will iterate through possible splits for the next number segment, handling multi-digit numbers and skipping invalid ones starting with '0'.
4. Implement operator logic: Describe adding '+', '-', and '*' separately, emphasizing how multiplication requires undoing the previous addition/subtraction before applying the new product.
5. Validate and prune: Explain checking if the final sum equals the target only when reaching the end of the string, and mention pruning branches where the remaining digits cannot possibly reach the target.
Key Points to Cover
- Explicitly handling the 'last operand' variable to correctly resolve multiplication precedence during backtracking
- Demonstrating awareness of edge cases involving leading zeros in multi-digit numbers
- Proactively discussing integer overflow prevention strategies for large inputs
- Clearly articulating the recursive state transitions and base conditions
- Structuring the solution to prioritize readability and maintainability under interview pressure
Sample Answer
To solve the Expression Add Operators problem, I would use a depth-first search approach with backtracking. First, I'd define a helper function that tracks four key states: the current index in the string, the cumulative result so far, the value of the last operand added (crucial for multiplication), and the current expression string being built.
I would iterate through the string from the current index, extracting substrings to form potential numbers. A critical check here is ensuring we don't treat '05' as valid unless it's just '0'; any number starting with '0' and having more than one digit must be skipped. For each valid number, I'd branch into three scenarios: adding it with '+', subtracting it with '-', or multiplying it with '*'. The multiplication case is tricky; unlike addition or subtraction, we cannot simply add the new number. Instead, we must subtract the last operand from our running total, multiply that last operand by the new number, and then add the result back. This ensures correct operator precedence without needing a full parser.
Once we reach the end of the string, we check if the cumulative result matches the target. If it does, we add the current expression to our results list. Throughout this process, I would ensure robust error handling for potential integer overflows, which is particularly relevant given Stripe's focus on financial precision and reliability in their systems.
Common Mistakes to Avoid
- Failing to handle multiplication precedence correctly by simply adding the new number instead of adjusting the previous term
- Ignoring leading zero constraints, which leads to accepting invalid numbers like '01' or '00'
- Not accounting for integer overflow when the input string represents very large numbers
- Missing the base case check, resulting in expressions being added prematurely before the string is fully traversed
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