Part A: Critical Analysis of Algorithm Efficiency

Choose two fundamental sorting algorithms that you have studied this semester$$Bubble Sort and Quick Sort. Compare and contrast these algorithms based on the following criteria:

Time Complexity:

Discuss the best, average, and worst$-$case scenarios for each algorithm.

Explain why these cases occur, citing the nature of the input data that leads to each scenario.

Space Complexity:

Evaluate the memory usage of each algorithm during execution.

Discuss the importance of in$-$place sorting in the context of the algorithms chosen.

Stability and Adaptability:

Define what makes an algorithm stable and assess if either of the algorithms meets this criterion.

Discuss the adaptability of each algorithm to nearly sorted input data.

Part B: Application Scenarios

Given the characteristics you have discussed in Part A:

Recommend which algorithm would be more suitable for an application requiring the sorting of large datasets with a high frequency of duplicate values. Justify your recommendation based on the analysis provided in Part A$.$

Propose an application scenario where it would be advantageous to use an unstable sorting algorithm. Explain your choice and discuss the benefits over stable sorting algorithms in this specific context.

Part C: Theoretical Implications

Reflect on the significance of algorithm analysis in real$-$world applications:

Discuss the impact of theoretical knowledge of algorithms, like those studied, on practical application development. Provide examples of how misjudgments in algorithm selection can affect application performance.

Evaluate the role of algorithm analysis in the broader context of software development. Discuss how this understanding influences decisions in system architecture and user experience design.