## Question

* When I ask you to use your own words, I expect you to study the topic and develop a good understanding of it to the point where you can answer the questions with a mature interpretation of it, possibly extending into your own personal experience, etc. If you find yourself paraphrasing some text, a person, or an internet source, you are not showing mature understanding of the content of this course, and will be performing below expectations for a grad-school program in software engineering/computer science.

1) What are the different factors that allow for sorting algorithms to run in O(n)?

2) In a software design meeting in your company, your manager says that one of the most important engines of the Record Keeping System you are developing is the Index Sorting Engine. Your coworker quickly jumps in and says that Quicksort should do the job. You have only been in the company for a few months but know that that are many factors to be considered before choosing a sorting algorithm for a problem. Describe your participation in this meeting.

## Solution Preview

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1).
We first recall that any comparison-based sorting algorithm has a lower bound for the worst case complexity of Big-Omega(nlogn). More than this, based on the analysis of the average case, this is either Big-Theta(nlogn) or quadratic (O(n2)). On the other hand, we recall that some of them run in O(n) only in best case scenario (e.g. Bubble Sort, Insertion Sort, TimSort). So, the starting point for identifying the factors that allow some of these running in O(n) time is to identify under which conditions this outcome is made possible. For instance, BubbleSort runs in O(n) time only when the array is already sorted; Insertion Sort exhibits its best case in the same situation. As for TimSort, it makes ~ O(n) comparisons when the list is either already sorted or sorted in reversed order....

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