Recursive Function and Merge Sort - Computer Science Assignment Help

Assignment Task

Question 1
Write a class with methods for each of the below. Test your methods from the main method.
Write a recursive function that prints a given positive integer value as its binary equivalent. For example, if the value is 11 the output should be 1011.
Given below is a recursive function sum(a,b) that calculates the summation of the numbers:   a + (a+1) + (a+2) +  .. + b. Write a tail recursive function that provides the same functionality.
 

Question 2
MergeSort continuously divides the data into segments until segments of size 1 are reached. It then begins the merging phase. This is the expensive part. Improvements could be made if we could reduce the cost of merging. It turns out that InsertionSort is very efficient for small data sequences (say sequences of 32 or 64 values) where the data is partially ordered in the correct order and the displacement is small.
The idea is to combine MergeSort & InsertionSort to reduce the overhead of merging. To do this we terminate the MergeSort when segments of a given size are reached (here we will use array length is <= 100) & use InsertionSort to sort the segments and then do the merging as before.
You will be given some skeleton code (Question2.java) which will create and test your mergeInsertSort using the following various arrays:

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