In this project you need to compare the effectiveness of the merge sort, quick sort, and heap sort algorithms against randomly generated arrays. Please implement all three methods and execute them for different values of N (the array size). Notice the runtime for N=100,000, 200,000, 300,000, 400,000. Also notice how doubling the size of the array affects the runtime for the methods.
Make your predictions about the time each of these methods require for N=200,000,000. Be detailed explaining your reasons.