SPUG: FW: Help..Any Math GENIUS out there?

[Jim Flanagan]

--On Thursday, July 25, 2002 10:50 AM -0700 "Orr, Chuck  (NOC)" 
<chuck.orr at attws.com> wrote:

     >> I am hoping to use Perl to solve an equation like the below:
     >>
     >> A + (36*B) + (360*C) + (3600*D) + (129600*E) = 2,307,012
     >>
     >> I know that each of the variables A - E is a whole number in the
     >> range 1-36.
     >>
     >> Could I load those numbers (1 -36) in an array and substitute each
     >> number for each variable until this is solved?

  I'm no genius, but here's a possible way to do it. It may not work for
  all equations, but seems to work for this one. The strategy is to take as
  many multiples (not exceeding the maximum, in this case 36) of the
  largest number out first, then subtract that from the total, then work on
  the next largest, and so on. The first step is to subtract at least 1
  times each of the "factors" from the total, since none of the variables
  can be 0.

  The answer in this case is:

  24 + 3*36 + 8*360 + 28*3600 + 17*129600 = 2307012

  Here's a quick and dirty:

        my @factors = (1,36,360,3600,129600);
        my $target = 2307012;

        my @multipliers = ();

        my $max = 36;
        my $min = 1;

        # Assume each factor is multiplied by at least $min

        map {$target -= $min * $_} @factors;

        for my $factor (sort {$b <=> $a} @factors) {
          $mult = int($target/$factor);
          $mult = ($mult <= $max) ? $mult : $max;
          $target -= $mult * $factor;
          unshift @multipliers, $min + $mult;
        }

        # Show the list of multipliers

        @tmp = @multipliers;
        print join(' + ', (map {shift(@tmp) . "*$_"} @factors));
        print "\n";

        # Check our work
        my $foo = 0;
        map {$foo += $_ * shift @multipliers} @factors;
        print $foo;
~


-- 
Flanagan::Jim

  http://jimfl.tensegrity.net
  mailto:jimfl%40t%65ns%65gr%69ty.n%65t


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