CustomCC0-1.0#P003-1951550
Range-Query Increasing Triplet Count
Summary
- •Phase 4 / combinatorics/range_query/increasing_triplets
- •Reasoning-first competitive programming drill
Problem Description
You have an array of N integers. For Q queries, each query gives indices (L, R), count the number of triplets (i, j, k) with < such that A[i] < A[j] < A[k].
How to read this problem in plain language:
- This is a Phase 4 reasoning drill focused on combinatorics/rang/increasin.
- Typical lenses to test first: range query, triplets, combinatorics.
- Constraints reminder: 1 ≤ 1 ≤ ,000; 1 ≤ A[i] ≤ 10^6
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 ≤ ,000; 1 ≤ A[i] ≤ 10^6
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.
range querytripletscombinatorics