Completed

[shantanujoshi25]

Completed

[super30admin]

Your solution is well-implemented and correct. Here are some points for improvement:

1. Time Complexity Comment: The comment for time complexity is not accurate. The worst-case time complexity is actually exponential. A better way to describe it might be O(k * 2^t), where k is the average length of combinations, but it's complex. You could say it's exponential in the target value.

2. Space Complexity Comment: The space complexity is O(t) for the recursion stack, but note that the output storage (the result list) requires additional space, which is O(n * number_of_combinations). So the overall space complexity is higher. However, the recursion stack space is O(t), which is correct.

3. Sorting and Early Break: Sorting the candidates and breaking early when the candidate exceeds the target is an excellent optimization. This reduces unnecessary recursion.

4. Code Readability: The code is clean and easy to understand. Using a for-loop with index tracking is a standard approach for combination problems. The use of path.copy() ensures that we store a snapshot of the current path, which is correct.

5. Efficiency: The solution is efficient. However, note that the reference solution uses a different approach (choose/not choose) which might be less efficient in terms of space because it creates new lists at each step. Your approach uses backtracking with a single list that is modified in place, which is more space-efficient.

6. Minor Suggestion: Consider adding a docstring to the helper function to explain its parameters, as it improves readability.

Overall, great job! The solution is optimal and follows best practices.

[super30admin]

Strengths:

• The solution correctly implements the backtracking approach with a for-loop, which is efficient and avoids duplicate combinations by using the index.
• The code is clean and readable, with good variable names and structure.
• The student has included time and space complexity analysis, which shows understanding of the algorithm's efficiency.

Areas for Improvement:

1. Time Complexity Analysis: The student's time complexity of O(n^t) is a bit vague. A more precise analysis would note that the worst-case time complexity is exponential, specifically O(n^(target/min_candidate)), which is standard for backtracking in combination sum problems. However, the provided O(n^t) is acceptable as a high-level estimate.
2. Space Complexity: The student states O(t), which refers to the depth of the recursion stack (which is at most target/min_candidate). However, the space complexity should also account for the storage of the result, which can be significant. The reference solution notes O(n^2) for space due to deep copies, but in this solution, the backtracking uses a single path list that is modified in-place, so the space for the recursion stack is O(t), but the result storage is O(n * number_of_combinations). It's important to mention both.
3. Unnecessary Sorting: The solution sorts the candidates, which is not strictly required for correctness but can help in optimization (to break early when candidates exceed the target). This is a good optimization, but it adds O(n log n) time, which is acceptable given the constraints.
4. Deep Copies: The solution uses path.copy() when adding to the result, which is efficient because it only copies when a valid combination is found. This is better than creating deep copies at every recursive call (as in the reference solution), so the student's approach is more space-efficient.

Suggestions:

• Consider adding a comment explaining why the sorting is done (to enable the break condition).
• The space complexity comment could be expanded to note that the recursion stack depth is O(t) and the result storage is O(n * k) where k is the number of combinations.

Overall, the solution is well-implemented and efficient.