Every night, Verizon has to update its database of every customers telephone number. To enable fast lookups, the database includes an index that is a sorted list of all its phone numbers. This index must be rebuilt each night by re-sorting the contents of the database. Verizon has hired you as a consultant to analyze their computing needs for the nightly sorting run. After carefully checking GitHub, you have found three sorting algorithms A, B, and C that can sort n phone numbers in 2 10⁷n², 10⁵n log₂ n, and 1.5 10⁴n seconds respectively on a single processor.

QUESTION: Describe how to construct a sorting algorithm that always achieves the best running time of any of algorithms A, B, or C for a given n.