CustomCC0-1.0#cptp0091500
Minimum Cost Non-Adjacent
Summary
- •Phase 4 / dp, house_robber_variant
- •Reasoning-first competitive programming drill
Problem Description
Given an array of n integers, select a subset of elements such that no two chosen elements are adjacent, maximizing the sum. Additionally, each selection incurs a fixed cost c. Output the maximal achievable value.
How to read this problem in plain language:
- This is a Phase 4 reasoning drill focused on dp, hous_variant.
- Typical lenses to test first: dp, arrays, greedy.
- Constraints reminder: 1 ≤ , ≤ 1e9, ≤ 1e9
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 ≤ , ≤ 1e9, ≤ 1e9
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
dparraysgreedy