Implement three sorting algorithms – mergesort, quicksort, and heapsort in the language of your choice and investigate their performance on arrays of sizes n = 10 2 , 10 3 , 10 4 , 10 5 , and 10 6 ....

Implement three sorting algorithms – mergesort, quicksort, and heapsort in the language of your choice and investigate their performance on arrays of sizes
n
= 10², 10³, 10⁴, 10⁵, and 10⁶. For each of these sizes consider:

1. randomly generated files of integers in the range [1..n].


2. increasing files of integers 1, 2, ..., n.


3. decreasing files of integers n, n − 1, ..., 1.