Please help with this assignment. I dont understand what it wants and what i am suppose to do$.$

a$.$ Explain the meaning of stability in a sorting algorithm and discuss why stability in sorting is desired. Using merge sort and quick sort as an example, determine which sorting algorithm is stable. Explain in detail your justification.

b$.$ Quick sort and merge sort are $2$ popular sorting algorithms. Implement both algorithms. Evaluate the space and time complexity of each algorithm.

c$.$ Recommend a way to improve the quick sort algorithm in terms of its time complexity as compared to the algorithm shown in the lecture slide. Implement this algorithm and prove its efficiency with some experiment and complexity analysis.

Required Documentation:

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Requirements$/$Specification: a paragraph giving a detailed account of what the program is supposed to do$.$ State any assumptions or conditions on the format of input and expected output.

User Guide: instructions on how to compile, run and use the program.

Design and analysis: Outline the design of your program by describing your approach. Give a written description. Use diagrams or pseudo code, if required. Provide a detail space or$/$and time complexity analysis $($big$-$oh$)$ of the implemented algorithm.

Limitations: Describe program shortfalls $($if any$).$ For example, the features asked for but not implemented, the situations it cannot handle etc.

Testing: Describe your testing strategy $($the more systematic, the better$)$ and any errors noticed. Provide a copy of all your results of testing in this section.

Listings: Your source code must be included in this section.