Beefy Boxes and Bandwidth Generously Provided by pair Networks
laziness, impatience, and hubris

comment on

( #3333=superdoc: print w/replies, xml ) Need Help??
my @order = sort { $Costs[$a]+$Trims[$a]*$Costs[$b] <=> $Costs[$b]+$Trims[$b]*$Costs[ +$a] } 0..$#Costs;

I'm pretty sure that this is the optimal solution, but I'm too lazy to write down the complete mathematical proof.

The basic idea is that the terms represent the general cost difference of swapping the first and the second filter╣!

So by sorting you get a solution which can't be improved by a pairwise swapping and any permutation can be represented by a sequence of pairwise swaps.

Cheers Rolf

╣) see restructured formula for c in Re^2: Evolving a faster filter? (combinatorics) and you will notice that these are the first elements and the rest is fix.


basic transformations lead to a simpler solution:

my @order = sort { $Costs[$a]/(1-$Trims[$a]) <=> $Costs[$b]/(1-$Trims[$b]) } 0..$#Costs;

which can be precalculated to save calculation time

my @order = sort { $weight[$a] <=> $weight[$b] } 0..$#Costs;

(the edge case of a division by zero must be handled as practically infinity)

In reply to Re^3: Evolving a faster filter? (optimal solution?) by LanX
in thread Evolving a faster filter? by Ovid

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

  • Are you posting in the right place? Check out Where do I post X? to know for sure.
  • Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
    <code> <a> <b> <big> <blockquote> <br /> <dd> <dl> <dt> <em> <font> <h1> <h2> <h3> <h4> <h5> <h6> <hr /> <i> <li> <nbsp> <ol> <p> <small> <strike> <strong> <sub> <sup> <table> <td> <th> <tr> <tt> <u> <ul>
  • Snippets of code should be wrapped in <code> tags not <pre> tags. In fact, <pre> tags should generally be avoided. If they must be used, extreme care should be taken to ensure that their contents do not have long lines (<70 chars), in order to prevent horizontal scrolling (and possible janitor intervention).
  • Want more info? How to link or or How to display code and escape characters are good places to start.
Log In?

What's my password?
Create A New User
Domain Nodelet?
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others cooling their heels in the Monastery: (4)
As of 2021-10-20 07:41 GMT
Find Nodes?
    Voting Booth?
    My first memorable Perl project was:

    Results (79 votes). Check out past polls.