CustomCC0-1.0#ct-p3-021850
Bounded Jumps Maximum Score
Summary
- •Phase 3 / monotone-queue-dp
- •Reasoning-first competitive programming drill
Problem Description
From index 1 to n, you may jump up to k steps forward. Maximize sum of visited values.
How to read this problem in plain language:
- This is a Phase 3 reasoning drill focused on monotone-queue-dp.
- Typical lenses to test first: dp, deque, optimization.
- Constraints reminder: 1 <= n <= 2e5
Mini examples for mental simulation:
1) Boundary example: Only linear path. Explain expected behavior and why naive logic may fail.
2) Adversarial example: Can jump almost anywhere. 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
- •1 <= n <= 2e5
Analysis
Key Insight
Maintain decreasing dp order. This step should reduce search space or formalize correctness. State why this insight changes your algorithm choice.
dpdequeoptimization