Your solutions for Combination Sum are excellent. You have implemented multiple approaches, which shows a strong grasp of backtracking and recursion. Here are some points to consider:

1. For Solution 1 and Solution 3, you correctly use backtracking by appending and then popping. This is efficient in terms of space because it avoids creating multiple copies of the path.

2. In Solution 2, you use deepcopy to create new lists. While this is correct, it is less efficient in terms of both time and space. However, it is a valid approach and easier to reason about for some.

3. You have correctly analyzed the time and space complexities for each solution. However, for the time complexity of Solution 1 and Solution 3, a more precise expression might be O(2^(target/min_candidate)), but your notation is acceptable.

4. The code is clean and well-commented. It's great that you have included comments about the logic and base cases.

5. One suggestion: In Solution 1, the base case checks if i >= len(candidates) or target < 0. Actually, the condition target < 0 can be checked at the beginning of the function to avoid unnecessary recursion. However, your current implementation is correct.

6. For Solution 3, the for-loop based recursion is a common pattern for combination problems. It is efficient and avoids duplicate combinations by using the pivot.

Overall, your solutions are correct, efficient, and well-written. Keep up the good work!

Your solutions for Combination Sum are well-implemented and cover different approaches. Here are some points to consider:

Strengths:

• You provided multiple solutions, showing a deep understanding of the problem and different techniques (backtracking, deep copy, for-loop recursion).
• The code is clean, well-commented, and easy to read.
• You correctly analyzed the time and space complexities for each solution.

Areas for Improvement:

• For Solution 1 and Solution 3, you use a mutable list (path) that is modified and then backtracked. This is efficient, but you should be cautious about passing the same list reference in recursive calls. In Solution 1, you are passing the same list and then popping, which is correct. However, in Solution 3, you are also using backtracking correctly.
• In Solution 2, creating deep copies for each call increases the time and space complexity. While it is correct, it is less efficient. It's good that you are aware of the trade-offs.
• You included solutions for Expression Add Operators, which was not part of the problem. While it shows your enthusiasm, make sure to focus on the problem at hand when submitting solutions.

Overall, your work is excellent. Keep up the good practice!