Completed Backtracking-1

[rahulpulluri]

No description provided.

[super30admin]

1. Correctness: The solution appears to correctly solve both problems (combination sum and expression add operators) using standard backtracking approaches. The provided test cases cover various scenarios including edge cases like empty results and single-element inputs.

2. Time Complexity:

   • For combinationSum: The analysis of O(2^t) is reasonable, where t is the target value. This accounts for the worst-case scenario where candidates can be repeatedly used.
   • For addOperators: The analysis of O(4^n) is accurate, considering the branching factor of 3 operators plus the no-operator case at each digit.

3. Space Complexity:

   • For combinationSum: The O(t) analysis is correct for the recursion stack and current combination storage.
   • For addOperators: The O(n) analysis for recursion depth and expression space is appropriate.

4. Code Quality:

   • The code is well-structured and readable with clear function definitions and comments.
   • The use of type hints (List, int, str) enhances code clarity.
   • The commented-out alternative implementations provide useful insights into different approaches.
   • The main blocks are properly guarded with if __name__ == "__main__":.

5. Efficiency:

   • The combinationSum solution efficiently uses backtracking with a single list mutation (append/pop) rather than creating new copies at each step.
   • The addOperators solution handles leading zeros correctly and efficiently computes values during the recursion.
   • One potential optimization could be to pre-filter candidates in combinationSum that are larger than the target, though this might not significantly impact performance in most cases.

Areas for Improvement:

• While the time complexity analyses are correct, it might be helpful to explain why the complexities are what they are (e.g., why 2^t for combinationSum).
• The addOperators solution could benefit from a brief explanation of how the multiplication case works (value - prev + prev * curr_num).