Algorithm Problem Solver

The AI would provide a solution template:

Problem: [Given problem statement]

1. Category: Dynamic Programming / Graph / Greedy
2. Constraints Analysis: n ≤ 10^5 → O(n log n) required
3. Brute Force: O(n²) — try all pairs
4. Optimization Insight: Sort + two pointers
5. Optimized Solution (with proof):
   def solve(nums, target):
       nums.sort()
       left, right = 0, len(nums) - 1
       while left < right:
           s = nums[left] + nums[right]
           ...
6. Edge Cases: empty input, single element, duplicates
7. Complexity: Time O(n log n), Space O(1)