You are required to choose two sorting algorithms from a specified list: the first algorithm can be either Sequential $($Linear$)$ Search, Binary Search, or Bubble Sort, while the second algorithm can be either Merge Sort or Heap Sort.

a$)$ Write a C$++$ program where you implement the two sorting algorithms you have chosen $-$ ensure that they are part of the same program and can be called using methods, functions and$/$or procedures.

b$)$ Continue in this C$++$ program and generate random input arrays of different sizes, specifically $100,1000,$ and $5000$ elements.

c$)$ Utilize the implemented TWO sorting algorithms to sort these randomly generated arrays.

d$)$ Generate a report to indicate:

$-$ The input size $($number of elements$).$

$-$ The execution time for the two different sorting algorithms.

$-$ The time complexity formulas for the two different sorting algorithms.