1. Implement external sort: for sort phase use normal sort,   for merge phase use two way merge to merge n sorted files (merge2way(n)), for array sort use heapsort. Also write merge(f1, f2, f3) to merge two sorted files f1 and f2 into f3.. Write mergenway(n) method and print execution time of both merges for initial input file over 10MB data.  A sample input is as follow:Note:Fist input is max array size for sort           10   84   82   52   80   96   85   75   75   82   87  92   89   57   94   93   92   63   99   87  72   73   56   74   50   84   62   72   55   86   75  74  100   83   60   53   68   89   67  66  65   72   94   73   54   98   96   85   75   75   82   87  92   89

Shell sort is an in-place comparison-based sorting algorithm which is based on insertion sort algorithm. It works as follow : It breaks the original list into a number of smaller sublists, each of which is sorted using an insertion sort. The unique way that these sublists are chosen is the key to the shell sort. Instead of breaking the list into sublists of contiguous items, the shell sort uses an increment i, sometimes called the gap, to create a sublist by choosing all items that are i items apart. n a) We say that the our initial gap is floor: when we divide our sequence into 2k n sublists where 2k k>0 be the number of passes that can be increment until the denominator not greater than n, n and then sorting the elements which are position away with insertion sort. We have three 2k passes for an array size of 8 to 15. Demonstrate the Shell algorithm on the input array A = [35,33,42,10,14,19,27,44] showing how even- %3D п tually the algorithm outputs the sorted array…

Select true or false for the statements below. Explain your answers if you like to receive partial credit 9) Which of the following is true about the Mergesort algorithm applied to an array ofnumbers that are all different?a. Memory usage is efficient because all swaps take place within the same arrayb. Performance is consistently at O(n log n) for all array scenariosc. When the partition function completes on the array, the pivot element willalways be in the exact center of the array

Write a program that allows the user to sort using the  Heap Sort and Bin/Radix Sort. The program should be able to read in data from a binary file.  The first element of the binary file will be used to tell how many elements to read in.  Once all the data has been read in, the program should sort the data.  The user should be able to choose which algorithm to use to sort the data.  The program should print the time before and after the sort.  The last part of the program should prompt the user for a lower and upper bound.  These two values should then be used to decide how much and which part of the array will be display.     Note: The binary files may have duplicate numbers in them. Make sure your sorts are able to handle these cases.       Reminder: The implementation of your algorithms must follow the format we cover in class. Bin sort must be constructed yourself using pointers. No vectors, queues, etc..