Part $1.$ External Merge Sort

Exercise $1(60$ points$)$

Answer the following questions for each of these scenarios, assuming that our most general external sorting algorithm is used:

$($a$)$ A file with $10,000$ pages and three available buffer pages.

$($b$)$ A file with $20,000$ pages and five available buffer pages

$($c$)$ A file with $2,000,000$ pages and $17$ available buffer pages.

$1.$ How many sorted runs will you produce in the first pass?

$2.$ How many passes will it take to sort the file completely?

$3.$ What is the total I$/$O cost of sorting the file?

$4.$ How many buffer pages do you need to sort the file completely in just two passes?