Heap comparison based sorting question

Question

I need some help with this question from my problem set. I do not want a solution but some $\textbf{hints}$ on how to proceed.

Given $n$ records in a file that are so numerous, that just storing the $n$ keys alone would require more RAM than is available on your computer. Let $m$ be the maximum number of records that you can store in RAM at once. Assuming that $m >$ $\sqrt{n}$, produce a $\mathcal{O}(n \log n)$ time algorithm for sorting the $n$ records. The sorted records would then be written to a file, since it will not be possible for them to all fit in memory at once.

$\textbf{My approach:}$ I figure I should use a heap based approach. Try to create a type of online algorithm to read $m$ records at a time, and then use heapsort or a type of comparison based algorithm to solve it?

$\textbf{Related Questions:}$

1) I don't understand the underlying assumption of letting $m>\sqrt{n}$?

Answer 1

Hint: Convert the input into $n/m < m$ chunks of length $m$ and sort the chunks. Then use your heap idea. Note that you're using the assumption $m > \sqrt{n}$ so that the heap fits in memory.