Write both insertion sort and merge sort programs in Python and follow the instructions below to test the programs with all data sets provided below. You may reuse any existing insertion and recursive merge sorting algorithms available out there without specifying the references.

$2-1)$ Using your time efficiency function from HW$1,$ Measure the execution times of both insertion and merge sorting algorithms using the $6$ data files.

$2-2)$ Count the total number of comparisons for the completion of each sorting algorithm.

Here are the set pdf data files you should use for your testing:

$1,000,000$ integers are in rand$1000000.$txt $($the largest$)$

Download rand$1000000.$txt $($the largest$)$

$1,000$ integers are in rand$1000.$txt

Download rand$1000.$txt $($for the initial testing purpose$)$

Other data sets.

rand$10000.$txt

Download rand$10000.$txt

rand$100000.$txt

Download rand$100000.$txt

rand$250000.$txt

Download rand$250000.$txt

rand$500000.$txt

Download rand$500000.$txt

$2-3)$ Record the execution time with each data size and display the results in a graph using any Python data visualization library. $($matplotlib$,$ plotly, $...).$

NOTE $1$: For counting the number of comparisons in a mergesort that employs recursive function calls, using a global variable might be more practical, and one of those cases where using a global variable makes more sense.

NOTE $2$: Ensure you read the data as integers, not as strings.

NOTE $3$: Ensure the second algorithm works with the initial unsorted dataset, not the result dataset sorted by the other algorithm.

NOTE $4$: You may add the following lines to test all the data sizes in one test run

fileNames $=["$rand$1000.$txt$",$ "rand$10000.$txt$",$ "rand$100000.$txt$",$ "rand$250000.$txt$",$ "rand$500000.$txt$",$ "rand$1000000.$txt$"]$

for name in fileNames :

$[$your codes $...]$