CustomCC0-1.0#cp009-9751600
Smallest Covering Rectangle After Removal
Summary
- •Phase 5 / geometry, brute-force min-max
- •Reasoning-first competitive programming drill
Problem Description
Given n distinct points in the 2D integer plane, you may remove one point. Find the minimal area of the axis-aligned rectangle covering the remaining points.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on geometry, brute-force min-max.
- Typical lenses to test first: geometry, brute-force, sorting.
- Constraints reminder: 3 <= n <= 2*10^5, 0 <= xi,yi <= 10^9, points distinct
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
- •3 <= n <= 2*10^5, 0 <= xi,yi <= 10^9, points distinct
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
geometrybrute-forcesorting