Completed combination Sum

[swatisharma27]

No description provided.

[super30admin]

The student has provided multiple implementations (combinationSum, combinationSum1, combinationSum2, combinationSum3, combinationSum4) for solving the combination sum problem using backtracking. Here's an evaluation of their solution:

Strengths:

1. The student demonstrates a good understanding of backtracking approaches, showing both for-loop and 0-1 matrix methods.
2. The solutions are generally correct and cover different variations of the backtracking approach.
3. The student has included time and space complexity analysis for each method.
4. The code is well-structured with clear function definitions and comments explaining each approach.

Areas for Improvement:

1. The deepcopy operations in combinationSum1, combinationSum3, and combinationSum4 are inefficient and unnecessary in most cases. The backtracking approach (using pop()) is more efficient.
2. Some of the implementations are redundant (combinationSum3 and combinationSum4 are very similar with just order of operations changed).
3. The docstrings could be more descriptive about what each method does differently.
4. The base case checks could be consolidated in some implementations (like checking target < 0 before the recursive calls).
5. The variable names could be more descriptive (e.g., 'path' could be 'current_combination').

Edge Cases to Consider:

1. Empty candidates list
2. Target smaller than all candidates
3. Candidates with duplicate values (though the problem likely assumes unique candidates)
4. Candidates with zero values

General Best Practices:

1. Prefer backtracking with pop() over deepcopy for better performance.
2. Consider adding input validation.
3. For production code, consider using type hints more consistently.
4. The multiple implementations are good for learning but in practice, one clean implementation would suffice.