CustomCC0-1.0#cpq014-7081600
Interval Longest Arithmetic Progression
Summary
- •Phase 2 / dp, range-query
- •Reasoning-first competitive programming drill
Problem Description
Given an array A of N integers and Q queries (L, R), for each, output the length of the longest contiguous arithmetic progression (AP) within A[L..R].
How to read this problem in plain language:
- This is a Phase 2 reasoning drill focused on dp, range-query.
- Typical lenses to test first: dp, range-query, arithmetic-progression.
- Constraints reminder: 1 <= N, Q <= 1e5; <= 1e9; 1 <= L <= R <= N
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 <= N, Q <= 1e5; <= 1e9; 1 <= L <= R <= N
Analysis
Key Insight
Use this hint to refine your reasoning. This step should reduce search space or formalize correctness. State why this insight changes your algorithm choice.
dprange-queryarithmetic-progression