CIS 120:

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The two algorithms to Joe’s Diner are the sameas they both get you to the same destination, but they contrast in howeffective they are. The highway path is faster and is thus shorter in code, butthe winding road path is more natural at the cost of more coding. Criteria liketime and fuel efficiency are much more helping in determining which path isbetter suited as being able to get to Joe’s Diner in a reasonable time withfuel to spare is absolutely necessary with determining the optimal efficiency.

The Big-O Notation is the only part of the problem that is measured because thebiggest value of N has dominion over the function. The other values are leftout because they are irrelevant to N as it gets bigger. Just like in theproblem N⁴ + 8N + 40, N⁴ is the biggest N value, and because of how dominant it isin the order of magnitude, the 8N + 40 become irrelevant.

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The two algorithms inthe scenario are similar in that both routes are effective in getting you toJoes Diner. However, they differ because the first route is simplistic andtakes less time while the other is a slightly longer drive with a more scenicpath. One approach may be preferable to the other if the request for directionsincluded distinctive conditions. For instance, the best course of action forsomeone in a hurry would be the first route because it is the shortest of thetwo algorithms.

According to thetextbook, when it comes to assessing algorithms, the term that grows thefastest in relation to the size of the problem dominates the function,essentially pushing the others to the “noise” level. We may ignorethe other terms because N4 is so much greater than 50, 10N, or even 100N2 forlarge values of N. This isn’t to say that the other terms aren’t important inour approximation when N is “big,” but it does mean that they aren’trelevant in our approximation when N is large (Dale and Lewis 2019).