CustomCC0-1.0#P0031500
Modulo K Longest Increasing Subsequence
Summary
- •Phase 2 / DP, Number Theory
- •Reasoning-first competitive programming drill
Problem Description
Given a sequence of N integers and an integer K, find the length of the longest strictly increasing subsequence such that adjacent elements in the subsequence differ by a value divisible by K.
How to read this problem in plain language:
- This is a Phase 2 reasoning drill focused on DP, Number Theory.
- Typical lenses to test first: dp, number theory, subsequence.
- Constraints reminder: 1 ≤ , 1 ≤ , 1 ≤ A[i] ≤ 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 ≤ , 1 ≤ , 1 ≤ A[i] ≤ 1e9
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.
dpnumber theorysubsequence