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

comment on

( [id://3333] : superdoc . print w/replies, xml ) Need Help??
A mapping of the form
f(x) = (a*x + b) % m
is 1-to-1 (restricted to 0 <= x < m) as long as gcd(a,m)==1, since that's the only time you can find an inverse to a mod m, and invert the function.

I would suggest splitting your "seed" value into the a & b coefficients in the following way:

  • a = largest number less than seed satisfying gcd(a,m)=1
  • b = seed - a
sub gcd { $_[1] ? gcd($_[1], $_[0] % $_[1]) : $_[0] } sub shuffle { my ($seed, $max, $i) = @_; my $ca = $seed; $ca-- until gcd($ca, $max) == 1; my $cb = $seed - $ca; ($ca * $i + $cb) % $max; } for my $seed (1 .. 10) { my @result = map shuffle($seed, 15, $_), 0 .. 14; print "seed=$seed ==> @result\n"; }
But take this approach for what it's worth -- The only kinds of mapping you'll get by this process are simple linear (affine) mappings, which may not "look random enough":
seed=1 ==> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 seed=2 ==> 0 2 4 6 8 10 12 14 1 3 5 7 9 11 13 seed=3 ==> 1 3 5 7 9 11 13 0 2 4 6 8 10 12 14 seed=4 ==> 0 4 8 12 1 5 9 13 2 6 10 14 3 7 11 seed=5 ==> 1 5 9 13 2 6 10 14 3 7 11 0 4 8 12 seed=6 ==> 2 6 10 14 3 7 11 0 4 8 12 1 5 9 13 seed=7 ==> 0 7 14 6 13 5 12 4 11 3 10 2 9 1 8 seed=8 ==> 0 8 1 9 2 10 3 11 4 12 5 13 6 14 7 seed=9 ==> 1 9 2 10 3 11 4 12 5 13 6 14 7 0 8 seed=10 ==> 2 10 3 11 4 12 5 13 6 14 7 0 8 1 9
For more "unpredictable" orders, you could have more tools at your disposal if $max is always a prime. Then you take one of the linear sequences above and use it as a sequence of powers of a generator element for the field mod $max.

blokhead


In reply to Re^3: Random 1-1 mapping by blokhead
in thread Random 1-1 mapping by tomazos

Title:
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 How to display code and escape characters are good places to start.