Completed Backtracking-1

[samikshm]

No description provided.

[super30admin]

Combination Sum (combination_sum.java):

• Correctness: The solution correctly implements the classic combination sum problem using backtracking. It explores both "don't choose" and "choose" paths, handles the base cases properly (target < 0 or index out of bounds), and adds a deep copy of the path when target equals 0. The backtracking step correctly removes the last element after recursion.
• Time Complexity: The stated complexity O(2^(m+n)) is not accurate. A more precise bound would be O(N^M) where N is the number of candidates and M is the target/min candidate value, as each position can be chosen multiple times. The exponential nature is correct but the formula is imprecise.
• Space Complexity: O(n) is stated, but this only accounts for the recursion stack depth and current path. The result storage is not included in this analysis.
• Code Quality: The code is clean and well-structured with clear comments explaining the approach. The three-sentence explanation requirement is met.

Expression Add Operators (expression_add_operator.java):

• Correctness: The solution correctly handles the expression add operators problem. It properly manages multiplication precedence using the tail variable, skips numbers with leading zeros, and correctly backtracks the StringBuilder. The three operators (+, -, *) are handled appropriately.
• Time Complexity: O(4^n) is a reasonable upper bound for this problem since at each position there are up to 4 choices (no operator at top level, or +, -, * at subsequent levels).
• Space Complexity: O(n) correctly accounts for the recursion depth and StringBuilder path length.
• Code Quality: The code is well-structured with clear separation of logic. However, there's a minor issue: the le variable is set before the loop but used inside the loop for backtracking, which works correctly. The code could benefit from more descriptive variable names (e.g., pivot could be index or startPos).

Areas for Improvement:

1. In combination_sum.java, consider adding early termination when candidates[index] > target to prune branches.
2. In expression_add_operator.java, the StringBuilder length restoration pattern is correct but could be extracted into a helper method for better readability.
3. Both solutions could benefit from input validation (e.g., checking for null/empty arrays in combination_sum).