Heap comparison based sorting 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 $m &gt;$
  $\sqrt{n}$, 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 $m&gt;\sqrt{n}$?
Hint: Convert the input into $n/m &lt; m$ chunks of length $m$ and sort the chunks. Then use your heap idea. Note that you're using the assumption $m &gt; \sqrt{n}$ so that the heap fits in memory.