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Also includes a summary verdict, explanatory reasons, the configured ops-per-second and budget, and any disclaimer about approximation for very large numbers.","failureModes":["n out of range (must be 1 to 1e12) returns a validation error","missing required query parameter n returns a 400-level error","opsPerSecond or budgetSeconds set to zero or negative may cause undefined behavior","very large n values for 2^n and n! return approximated powers of ten rather than exact counts","payment of 0.02 USDC not provided results in 402 Payment Required response"],"whenToPreferThis":"Choose this endpoint when you need a quick, structured comparison of multiple algorithmic complexity classes at a specific input size — especially for capacity planning, algorithm selection, or educational illustration. 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