I need help implementing sorting algorithms.

I. Here, you will implement Insertion Sort, Quicksort, and Mergesort in C$++.$ These algorithms should be able to successfully sort all $9$ of the datasets provided for you $($not necessarily at the same time though!$).$ Sorting should be in descending order. Details: You may not use a high$-$level function for implementing these sorts $($generally$,$ anything that simply solves the problem for you$).$

Please include instructions for how to compile and run the code, and explain any implementation choices you had to make.

II$.$ Try to estimate how fast each of these algorithms is on each dataset. To do this, modify your sorting algorithms so that they can keep track of the number of comparisons made in each algorithm. Remember, every sorting algorithm must, at some point, compare one value to another to determine where it goes in the list.

These are the operations I want you to keep track of:

For each algorithm on each dataset, report, visualize, or otherwise present the number of comparisons made. Does this align with what you would expect to happen given the big$-$O runtimes of each algorithm?

Details:

You can choose how you want to present the data. It could be as a table containing all of the values. It could also be a graph if you'd like. You can use any tool you'd like

to represent the data. Be sure to include a discussion of whether this behavior seems normal given what you know about how each algorithm works and the best and worst$-$case runtime complexities of each algorithm. All of this information should be included in comments.

The datasets include a small dataset $($only $100$ entries$),$ a medium dataset $($only containing $250$ entries$),$ and a large dataset $($containing all $500$ entries$).$ Each of these also comes in a sorted, reverse sorted, and random variety.