CustomCC0-1.0#cp018-772300
Divisor Sum Path in DAG
Summary
- •Phase 5 / DAG, DP, modular arithmetic
- •Reasoning-first competitive programming drill
Problem Description
Given a directed acyclic graph (DAG) with n nodes and m edges, each node has a value. A path is valid if the sum of its node values is divisible by a fixed integer d. Count the number of distinct valid paths from node 1 to node n.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on DAG, DP, modular arithmetic.
- Typical lenses to test first: DAG, DP, modulo.
- Constraints reminder: 2 <= n <= 2*10^5, 1 <= m <= 3*10^5, 1 <= vi <= 10^9, 1 <= d <= 1000
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
- •2 <= n <= 2*10^5, 1 <= m <= 3*10^5, 1 <= vi <= 10^9, 1 <= d <= 1000
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
DAGDPmodulo