CustomCC0-1.0#cp-tp3-0171725
Sumset Subsequence Counting
Summary
- •Phase 3 / subsequence-enumeration
- •Reasoning-first competitive programming drill
Problem Description
Given an array of n integers, count the number of non-empty subsequences where the sum of the subsequence equals the sum of some (possibly different) contiguous subarray. Output the count modulo 1e9+7.
How to read this problem in plain language:
- This is a Phase 3 reasoning drill focused on subsequence-enumeration.
- Typical lenses to test first: combinatorics, dp, subsequence.
- Constraints reminder: 1 ≤ ≤ 1e3
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 ≤ ≤ 1e3
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.
combinatoricsdpsubsequenceset