Suppose You Have Two Different Algorithms for Solving a Problem $n _ { , }$

question 33

Short Answer

Suppose you have two different algorithms for solving a problem. To solve a problem of size $n _ { , }$ the first algorithm uses exactly $n \sqrt { n }$ operations and the second algorithm uses exactly $n ^ { 2 }$ log $n$ operations. As $n$ grows, which algorithm uses fewer operations?

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Definitions:

Gear Restrictions

Regulations or limits set on the range of gears that can be used in certain vehicles or machinery to ensure safety or efficiency.

Marginal Social Cost

The cumulative expense to the community for creating an extra unit of a product or service.

Private Cost

The cost incurred by a person or a firm directly involved in a transaction, excluding any external or social costs.

Efficient Outcome

A situation where resources are allocated in the most effective way possible, maximizing benefits without wasting resources.