> but there is also Counting Sort, Radix Sort, and other forms of distribution sorting that are of high utility in real-world applications.

These algorithms are all limited to elements of fixed length (which is the case), but Sundial suggested unix sort which knows nothing about the nature of the input.

And did you try to look into the space complexity of your suggestions?

Counting Sort requires 4**21 buckets. Seriously ???

Radix Sort is still the best in this respect, but has O(l*n) with l length of alphabet (here 21). Even worse identical elements are in worst case only identified in the last step, requiring to be able to hold all elements in memory, while shifting them all l times from bucket to bucket.

A hash count can go thru different files without keeping them all in memory, because identical elements collapse into one count.

Last but not least, a hash count is much easier implemented.

Cheers Rolf
(addicted to the Perl Programming Language and ☆☆☆☆ :)
Wikisyntax for the Monastery

In reply to Re^4: Out of Memory when generating large matrix (space complexity) by LanX
in thread Out of Memory when generating large matrix by cathyyihao

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.