Create a simple sorting application that uses the mergesort algorithm to sort a large collection $($e$.$g$.,107)$ of $32-$bit integers. The input data and output results should be stored in files, and the I$/$O operations should be considered a sequential part of the application. Mergesort is an algorithm that is considered appropriate for parallel execution, although it cannot be equally divided between an arbitrary number of processors, as Amdahl$$s and Gustafson$-$Barsis$$ laws require.

Assuming that this equal division is possible, estimate $\backslash$alpha $,$ i$.$e$.,$ the part of the program that can be parallelized, by using a profiler like gprof or valgrind to measure the duration of mergesort$$s execution relative to the overall execution time. Use this number to estimate the predicted speedup for your program.

Does $\backslash$alpha depend on the size of the input? If it does, how should you modify your predictions and their graphical illustration?