CustomCC0-1.0#cptp0142300
Longest Sum-Free Subsequence
Summary
- •Phase 5 / set_theory, greedy
- •Reasoning-first competitive programming drill
Problem Description
Given an array of n positive integers, find the length of the longest subsequence with no two elements summing to another element present in the array.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on se, greedy.
- Typical lenses to test first: greedy, set, construction.
- Constraints reminder: 1 ≤ , 1 ≤
Mini examples for mental simulation:
1) Boundary example: Describe why this case is tricky. Explain expected behavior and why naive logic may fail.
2) Adversarial example: Adversarial case where naive greedy/local decision looks correct but fails globally.
Lite-mode writing target:
- Write 1~2 observations that shrink the search space.
- Name one final algorithm and state target complexity explicitly.
- Validate with at least 2 edge cases and one hand simulation.
Constraints
- •1 ≤ , 1 ≤
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
greedysetconstruction