Objectives:

Apply time and space complexity concepts to algorithm analysis.

Implement and compare fundamental algorithms covered in class.

Explore the effect of input size on algorithm performance.

Requirements:

Algorithm Implementation: Write code to implement each algorithm.

Complexity Analysis: Analyze the time and space complexity of each algorithm and explain how they behave with different input sizes.

Empirical Analysis: Test the algorithms on datasets of varying sizes and provide runtime measurements $($small$,$ medium, large$).$

Report: A $2-3$ page$($without cover$)$ report that includes:

Problem description

Algorithms used

Complexity analysis

Empirical results with graphs to visualize performance.

Deliverables:

Source Code: Code for each algorithm, with comments explaining key sections.

Report: A structured report as outlined above.

Evaluation Criteria:

Correctness of the implementations $(25\%)$

Depth of complexity analysis $(25\%)$

Quality of empirical performance analysis $(25\%)$

Clarity of report $(25\%)$

QUESTIONS

Problem $1$: Sorting Customer Orders for a Sales Dashboard

You work on the back$-$end system for a retail platform that processes daily customer orders. Sales managers need to see the highest$-$value orders at the top of their dashboard to prioritize shipment, and during major sales events like Black Friday, the number of orders increases significantly.

Task:

Implement two sorting algorithms of your choice.

Test and compare their performance on datasets representing a typical day's orders $($small dataset$)$ and during peak sales periods $($large dataset$).$

Decide which sorting algorithm is better suited for each situation based on time and space complexity.

Problem $2$: Product Search in an Online Store

The product search function on an e$-$commerce website must find products quickly, whether the customer provides the exact product name or a partial match $($e$.$g$.,$ "sneaker" might match "running sneaker" or "sneaker shoe"$).$

Task:

Implement two search algorithms: one for exact match and one for partial match

Compare their performance on product catalogs of varying sizes $($small$,$ medium, and large$).$

Decide which algorithm performs best for each situation and explain how search times vary depending on dataset size and search type.