Target Problem Specification
Empirical Dynamic Range: N=100 → N=5,000
Task: Given an array of intervals [start, end], merge all overlapping intervals and return non-overlapping intervals in sorted order.
Evaluating Model Alpha (Naïve in-place quadratic merger) against Model Beta (Linearithmic pre-sorted sweep).
■ Model Alpha (Naïve Quadratic)
Inefficient O(N²)
Intended Complexity: O(N²) worst-case due to repeated in-place nested splicing inside while loop.
■ Model Beta (Optimal Sorting)
Optimal O(N log N)
Intended Complexity: O(N log N) pre-sort + single O(N) sweep; space complexity O(N).
Empirical Asymptotic Complexity Benchmark (Live Browser Execution)
Status: Ready (Default Fixture Loaded)
Model Alpha @ N=5,000
134.2 ms
Model Beta @ N=5,000
2.4 ms
Alpha Scaling Curve
Steep Quadratic O(N²)
Beta Scaling Curve
Linearithmic O(N log N)
Throughput Delta
55.9x Faster
Boundary & Edge-Case Stress Suite
Pass Rate: 100% Boundary Logic
| Test Case Name | Input Fixture | Model Alpha | Model Beta |
|---|
Both pass boundary correctness tests, but Model Alpha fails on throughput limits at large N.
Reviewer Rubric & Comparative Verdict
Standard RLHF Dimension Rubric