Computational Complexity Explorer

This simulator makes the abstract notation of computational complexity theory concrete. The growth-rate chart plots six standard complexity classes — O(1), O(log n), O(n), O(n log n), O(n²) and O(2^n) — on a shared logarithmic axis and converts each one's operation count at the current problem size into an actual duration at one billion operations per second, so the gap between "fast" and "intractable" is measured in real milliseconds, seconds and minutes rather than abstract symbols. The second panel demonstrates the P vs NP distinction directly through the Travelling Salesman Problem: verifying a proposed tour's length is linear-time and instant, while finding the guaranteed-shortest tour by exhaustive brute force requires trying every permutation of the remaining cities — a factorial search space that visibly explodes as the city count grows from 5 to 8.