Backtracking-combinationsum-expressionsoperations

[sadabala30]

No description provided.

[super30admin]

Solution 1: Combination Sum

• Correctness: The solution correctly implements backtracking for combination sum with repetition allowed. The approach of using a pivot index and allowing the same element to be chosen again (passing i instead of i+1) is correct. Base cases handle target==0, target<0, and exhausted candidates properly.
• Time Complexity: O(N^M) where N is the number of candidates and M is the target/min element ratio. In worst case, this is exponential.
• Space Complexity: O(M) for the recursion depth plus O(number of combinations) for storing results.
• Code Quality: Good use of helper function, clear comments explaining the backtracking pattern. The code is readable and well-structured.

Solution 2: Expression Add Operators

• Correctness: The solution correctly handles the expression formation problem. The key insight of tracking calc_val (running total) and tail (last operand for undoing multiplication) is properly implemented. Edge case for leading zeros is handled correctly.
• Time Complexity: O(4^N) where N is the length of the string, as each position can have +, -, *, or be part of a multi-digit number.
• Space Complexity: O(N) for recursion depth plus O(number of valid expressions) for results.
• Code Quality: The comment about "* operation and use tail*curr condition" shows good understanding. The code is well-structured with clear base case and recursive logic.

Areas for Improvement (both solutions):

1. Could add type hints for better code documentation
2. Could use from typing import List import for Python best practices
3. Could add docstrings explaining the approach
4. In combination sum, consider adding early termination if smallest candidate > target

Strengths:

• Both solutions demonstrate solid understanding of backtracking patterns
• Clear separation of action/recurse/backtrack phases
• Proper handling of edge cases (negative targets, leading zeros)
• Good use of deep copies to avoid mutation issues