   Chapter 11.3, Problem 4ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# 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.4. Suppose that when run with an input of size n, algorithm A requires 2 n 2 operations and algorithm B requires 80 n 3 / 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?

To determine

(a)

What are orders for algorithms AandB from among the set of power functions?

Explanation

Given information:

Algorithm A and Algorithm B

Concept used:

The order of algorithm is the power of variable.

Calculation:

Algorithm A has the order of n2 (since A requires 2n2 operations)

Algorithm B has order n

To determine

(b)

For what values of n is algorithm A more efficient than algorithm B ?

To determine

(c)

For what values of n is algorithm B at least 100 times more efficient than algorithm A ?

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