Textbook Problem

Exercises 4—5 explore the fact that for relatively small values of n, algorithms with larger orders can be more efficient than algorithms with smaller orders.

5. Suppose that when run with an input of size n, algorithm A requires ${10}^6{n}^2$ operations and algorithm B requires $n^3$ operations.

a. What are orders for algorithms A and B from among the set of power functions?
b. For what values of n is algorithm A more efficient than algorithm B? c. For what values of n is algorithm B at least 100 times more efficient than algorithm A?