$1.$In java Implement a method to sort a given array using the merge sort algorithm. You can use the

algorithm provided $($see Page $2)$ instead of the algorithm from the textbook.

$2.$ Write a driver program to test the merge sort algorithm for the arrays of varying lengths provided

in Canvas.

$3.$ Compare the execution time of merge sort with insertion sort implemented in Lab$-2.$ Make sure

you use the same array to compare the performance. Use a table or plot to summarize the results

and document your observations and analysis in the report.

$4.$ Based on the performance results obtained in Problem$-3,$ modify the merge sort algorithm such

that when the array size gets small enough, you would invoke insertion sort instead of invoking

merge sort $($hint: you have to change the base condition in the recursion$).$ Instead of hardcoding

the array size make it a variable that you can pass as an argument to the merge sort method and

test this cutoff value with at least four different values.

$5.$ Test the program for the same array sizes and values. Compare the performance with the original

merge sort implementation, plot the execution times, and document the analysis in your lab

report