Implement the following algorithms in Java: The pseudocode for QUICKSORT introduced in (slide 14), including procedure PARTITION implementing right-most element pivot selection (slide 13). Slide 13: PARTITION(A,p,r)   x := A[r]   i := p – 1   for j = p to r - 1     if A[j]  x       i := i + 1       SWAP(A[i],A[j])   SWAP(A[i+1],A[r])    return i + 1 Slide 14: QUICKSORT(A,p,r)   if p < r     q := PARTITION(A,p,r)     QUICKSORT(A,p,q-1)     QUICKSORT(A,q+1,r)

Make and implement a mergesort variation that gives an int[] array perm, where perm[i] is the index of the array's i th smallest element, rather than rearranges the array's elements.

Implement MERGE-SORT() algorithm that reads from a file named “inputHW02.txt” a list of double numbers (max =3,000,000 numbers), sorts those numbers and indicates time consumption. This programming question will address theadvantage of using iteration loops over recursive calls as well as using INSERTION-SORT() as a procedure in MERGESORT().Your program must perform the following actions:1. Opens the given file name and reads all double numbers. For simplicity, we assume this file only containsnumbers and nothing else.2. Implements the function INSERTION-SORT() that only sort an array of maximum 25 numbers. The idea is thatINSERTION-SORT() will be used as a sub-procedure to sort any sub-array when its size is small enough.3. Four versions of MERGE-SORT() namelya. MERGE-SORT-A(): Using recursive calls and NO INSERTION-SORT() as a sub-procedureb. MERGE-SORT-B(): Using ITERATIVE loops (i.e, NO recursion) and NO INSERTION-SORT() as a subprocedure.c. MERGE-SORT-C(): Using recursive calls…

Draw the state of the array after a first pass of a shellsort with gap size 5, and then again after a second pass with gap size 3.