Backtracking-1 Homework Solution

[richapatil]

No description provided.

[super30admin]

Combination Sum (39. Combination Sum/Solution.java)

Evaluation

1. Correctness

The student's solution correctly solves the Combination Sum problem. It uses backtracking with a pivot index to allow reuse of the same element, and properly handles all base cases. The solution correctly adds a copy of the path when a valid combination is found and backtracks properly after recursion.

2. Time Complexity

• Student's solution: O(2^(m+n)) - stated in comments
• Reference solution: O(n * 2^(m+n))

The student's solution is actually more efficient in practice because it uses a for-loop approach with backtracking, which prunes branches earlier when elements don't lead to valid combinations. The reference solution creates new ArrayList copies at every recursive call (both choose and no-choose paths), which is more expensive.

3. Space Complexity

• Student's solution: O(n²) - stated in comments
• Reference solution: O(n²)

Both solutions have similar space complexity. The student's solution uses O(h) recursion depth where h is the height of the tree, and the path list grows to at most target/min_candidate elements.

4. Code Quality

The code is well-structured and readable:

• Clear method names and parameter ordering
• Proper base case handling
• Good use of backtracking pattern
• Comments explaining the approach

5. Efficiency

The student's solution is more efficient than the reference because:

1. It uses backtracking with in-place modification (add/remove) rather than creating deep copies at every step
2. The for-loop with pivot index naturally prunes branches that won't lead to valid solutions
3. Only creates a new ArrayList copy when adding to result (when a valid combination is found)

Feedback

Strengths:

• Excellent use of backtracking pattern with proper cleanup (remove at end)
• Clean, readable code with appropriate comments
• Efficient use of pivot index to allow element reuse while avoiding duplicates
• Only creates copies when necessary (when adding to result)

Areas for Improvement:

• The time complexity comment (2^(m+n)) is imprecise. A more accurate bound would be O(n * 2^t) where t is the target, or O(C) where C is the number of valid combinations (at most 150 per constraints).
• Consider adding a check to skip candidates[i] > target early to prune branches, though this is a minor optimization.

The student's solution is correct, more efficient than the reference (due to proper backtracking without unnecessary copies), and well-structured. It demonstrates a solid understanding of the backtracking pattern.

VERDICT: PASS

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Operations and expressions (282. Expression Add Operators/Solution.java)

Strengths:

• Correct implementation of the core backtracking algorithm
• Proper handling of multiplication precedence using the tail variable
• Good use of StringBuilder for efficient string manipulation
• Clean code structure with appropriate comments
• Correctly handles edge cases like leading zeros

Areas for Improvement:

• The time complexity comment "4n" is incorrect - it should be O(4^n) or O(N4^N)
• Consider adding type parameters to List: List<String> result = new ArrayList<>() for better type safety
• Could add early termination optimization for very large numbers that exceed target bounds

The solution is functionally correct and follows good coding practices. The only issue is the incorrect time complexity notation.

VERDICT: PASS