Suppose You Have Two Different Algorithms for Solving a Problem $n \sqrt { n }$

question 11

Essay

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:

ATC

Average total cost (ATC) is the total cost of production divided by the quantity of output produced, representing the cost per unit of output.

Marginal Cost

The supplementary expense involved in creating an additional unit of a product or service.

Marginal Revenue

The extra revenue a company earns by selling an additional unit of a product or service.

Competitive Market

A market structure characterized by many buyers and sellers where no single entity can dictate or significantly alter the market price.