Exercises 4–5 explore the fact that for relatively small

Chapter 11, Problem 4E

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Problem 4E

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.

Suppose that when run with an input of size n, algorithm A requires 2n2 operations and algorithm B requires 80n3/2 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?

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