Beefy Boxes and Bandwidth Generously Provided by pair Networks
Syntactic Confectionery Delight

Comment on

( #3333=superdoc: print w/replies, xml ) Need Help??

The general form of the Schwartzian Transform is this:

my @sorted = map { $_->[0] } sort { $a->[1] cmp $b->[1] } # or <=>, or $b before $a map { [$_, f($_)] } @unsorted;

... where f($foo) is a comparatively expensive function.

For the purposes of this discussion, let's suppose that @unsorted is qw(8 11 9 4 3) and f($n) is a function that converts a number into Roman numerals. So we're sorting the numbers alphabetically by Roman numeral. We want the result qw(3 4 9 8 11) because 3 is "iii" and 11 is "xi".

Reading from bottom to top, the first transform map { [$_, f($_)] } converts each number to an arrayref where the first element is the original number, and the second is the Roman numeral for it:

# the first map does this qw(8 11 9 4 3) --> ( [ 8, "viii"], [11, "xi"], [ 9, "ix"], [ 4, "vi"], [ 3, "iii"], )

Now we sort the transformed list alphabetically by $_->[1]:

# the sort does this: ( [ 8, "viii"], [11, "xi"], [ 9, "ix"], [ 4, "vi"], [ 3, "iii"], ) --> ( [ 3, "iii"], [ 9, "ix"], [ 4, "vi"], [ 8, "viii"], [11, "xi"], )

And the second transform map { $_->[0] }, just pulls out the original number from each arrayref:

( [ 3, "iii"], [ 9, "ix"], [ 4, "vi"], [ 8, "viii"], [11, "xi"], ) --> qw( 3 9 4 8 11 )

Let's see all that in action:

use strict; use warnings; use Roman (); my @unsorted = qw(8 11 9 4 3); *f = \&Roman::roman; my @sorted = map { $_->[0] } sort { $a->[1] cmp $b->[1] } # or <=>, or $b before $a map { [$_, f($_)] } @unsorted; print "@sorted\n"; __END__ # output shown below 3 4 9 8 11

The sharp-eyed may have spotted that there's a simpler way to do the same sort:

my @sorted = sort { f($a) cmp f($b) } @unsorted;

So why the transform? Well, it enables you to call f() fewer times; the function is called just once for each item on the list. Using the simpler version it's called twice for each pair of items that is compared, and there are typically more comparisons performed than items on the list. Let's have f() log how many times it was called. We'll define it like this:

*f = sub { $::count++; END { print "f() called $::count times\n" }; goto \&Roman::roman; };

Running this on my computer (and this may vary depending on the sorting algorithm that your version of Perl uses - it's changed once or twice), f() is called 10 times. With the transform it's called 5 times.

If we extend the original unsorted list to 100 items; e.g.:

use List::Util "shuffle"; my @unsorted = shuffle(1..100);

... then f() gets called typically over 1000 times, compared to exactly 100 for the version with the transform. If f() takes 0.01 seconds to run, that's a 10 seconds without the transform versus 1 second with the transform. If the unsorted list were 1000 items long, it would be about 3 minutes without the transform, versus 10 seconds with the transform.

(PS: Roman is available on CPAN; published by our fellow monk chorny.)

package Cow { use Moo; has name => (is => 'lazy', default => sub { 'Mooington' }) } say Cow->new->name

In reply to Re: Understanding the Schwartzian transform. by tobyink
in thread Understanding the Schwartzian transform. by Anonymous Monk

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, 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, 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.
  • Log In?

    What's my password?
    Create A New User
    and all is quiet...

    How do I use this? | Other CB clients
    Other Users?
    Others avoiding work at the Monastery: (4)
    As of 2018-04-23 23:52 GMT
    Find Nodes?
      Voting Booth?