## Description

- Implement Shellsort which reverts to insertion sort. (Use the increment

sequence 7, 3, 1). Create a plot for the total number of comparisons made

in the sorting the data for both cases (insertion sort phase and shell sort

phase).why Shellshort is more effective than Insertion sort in**Explain**

this case. Also,results for the relative (physical wall clock)**discuss**

time taken when using (i) Shellsort that reverts to insertions sort, (ii)

Shellsort all the way.2. The Kendall Tau distance is a variant of the “number of inversions”. It is

defined as the number of pairs that are in different order in two

permutations. Write an efficient program that computes the Kendall Tau

distance in less than quadratic time on average. Plot your results and

discuss.[Use the dataset linked after Q4. Note: data0.* for convenience is an

ordered set of numbers (in powers of two). data1.* are shuffled data sets

of sizes (as given by “*”).]3. Implement the two versions of MergeSort that we discussed in class. Create

a table or a plot for the total number of comparisons to sort the data

(using data set here) for both cases. Discuss (i) relative number of

operations, (ii) relative (physical wall clock) time taken.4. Create a data set of 8192 entries which has in the following order: 1024

repeats of 1, 2048 repeats of 11, 4096 repeats of 111 and 1024 repeats of

1111. Write a sort algorithm that you think will sort this set “most”

effectively. Explain why you think so.Data Set for Questions above:

https://drive.google.com/file/d/0B4xMi5S-VFVRVWh0YzV6bmFLMjQ/view?usp=sharing5. Implement Quicksort using median-of-three to determine the partition

element. Compare the performance of Quicksort with the Mergesort

implementation and dataset from Q3. Is there any noticable difference when

you use N=7 as the cut-off to insertion sort. Experiment if there is any

value of “cut-off to insertion” at which the performance inverts.6. Extra Points: View the following Data Set here. The column on the left is

the original input of strings to be sorted or shuffled; the column on the

extreme right are the string in sorted order; the other columns are the

contents at some intermediate step during one of the 8 algorithms listed

below. Match up each algorithm under the corresponding column. Use each

algorithm exactly once: (1) Knuth shuffle (2) Selection sort(3) Insertion

sort (4) Mergesort(top-down)(5) Mergesort (bottom-up) (6) Quicksort

(standard, no shuffle) (7) Quicksort (3-way, no shuffle) (8) Heapsort.Location of data for Q6: https://drive.google.com/file/d/1tQgg5IKLzS3OiVEznu2rrnW83Qw1lwHO/view?usp=sharing

*Please note: Your explanations to any question should be 2-4 sentences, and*

*no more. Save Electrons**! 🙂*