INSERTION SORT, MERGE SORT and ALGORITHM ANALYSIS

1. Using Insertion Sort algorithm Implement a Program in any language you desire (preferably C++ , java, or Python ) to sort an array of Real Numbers of size N.

1. Input at least 10 or more sets of randomized unsorted data with at least N elements in each set. For example, N= 12, 29, 30, 35, 49, 52, 65, and 76
2. Display the Unsorted data input and sorted data output for each array of N elements. Plot a graph to compare the worst case (average case) algorithm and the actual count putting counters in strategic points of your programs by assuming the cost ci = 1 for all statements.
3. Display a table of N, Actual count and the worst case T(N).
4. Plot a graph to compare the Worst Case Complexity of the algorithm and actual count putting counters in strategic points of your programs. Input data must be good for Worst Case Insertion Sort or average case insertion sort.

Notes: The axis of the graph should be the theoretic total cost T(N) or the actual count vs. the N value.

2. Using Merge sort algorithm Implement a Program in any language you desire (preferably C++ or java) to sort an array of Real numbers of size N.

Do (1), (2), (3) and (4) same as in problem (a) using general case for Merge Sort.

You may combine (a) and (b) in one program, or in two separate programs.

You may need to move function curve by multiplying a constant for easy comparison.