1-A: Construct large datasets taking random numbers from uniform distribution (UD)

1-B: Construct large datasets taking random numbers from normal distribution (ND)

2-A: Implement Merge Sort (MS) and check for correctness

2-B: Implement Quick Sort (QS) and check for correctness

3: Count the operations performed, like comparisons and swaps with problem size increasing in powers of 2, for both MS and QS with both UD and ND as input data.

4: Experiment with randomized QS (RQS) with both UD and ND as input data to arrive at the average complexity (count of operations performed) with both input datasets.

5: Now normalize both the datasets in the range from 0 to 1 and implement bucket sort (BS) algorithm and check for correctness.

6: Experiment with BS to arrive at its average complexity for both UD and ND data sets and infer.

7: Implement the worst case linear median selection algorithm by taking the median of medians (MoM) as the pivotal element and check for correctness.

8: Take different sizes for each trivial partition (3/5/7 ...) and see how the time taken is changing.

9: Perform experiments by rearranging the elements of the datasets (both UD and ND) and comment on the partition or split obtained using the pivotal element chosen as MoM.