CustomCC0-1.0#ct-p5-042280
Aliens Trick Budget DP
Summary
- •Phase 5 / advanced-dp
- •Reasoning-first competitive programming drill
Problem Description
Choose segments maximizing gain with at most k picks. Large n requires Lagrangian optimization.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on advanced-dp.
- Typical lenses to test first: dp, parametric-search, optimization.
- Constraints reminder: n <= 2e5
Mini examples for mental simulation:
1) Boundary example: Answer should be 0. Explain expected behavior and why naive logic may fail.
2) Adversarial example: Best may choose fewer segments. Explain expected behavior and why naive logic may fail.
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
- •n <= 2e5
Analysis
Key Insight
Quantifying complexity against constraints is mandatory for selecting the final approach and rejecting brute force formally.
dpparametric-searchoptimization