I want an efficient subroutine that inserts $elt into @x and returns
the percentile of $elt in @x.
For example, if @x is (2,2,3,3,3,4,5,6,7,8) and $elt is 3, the
subroutine returns .363636... and @x is now
(2,2,3,3,3,3,4,5,6,7,8). Why .363636...?:
% After insertion, @x has 11 elements. $elt (3) beats 2 of those
elements and ties 4 (including itself). Ties count as half-wins, so
the new element beats 2+(4/2) or 4 elements, and 4/11 is .3636...
Below is one way to do it. I'd turn it into a subroutine if I wanted
to use it, but it's really inefficient. If I insert 100 elements and
want the percentile of each as its inserted, it has to do something
like 50K comparisons. The subroutine's also ugly, but ignore that.
I'm guessing a subroutine that maintained a sorted list would work
much better.
My ugly inefficient solution:
@mylist = (2,2,3,3,3,4,5,6,7,8);
$elt = 3;
push(@mylist,$elt); #insert the element first
for $i (@mylist) {
if ($elt>$i) {$win++; next} # how many times does $elt beat list values
if ($elt<$i) {$lose++; next} # how many times does $elt lose to list value
$tie++; # ties count as half-wins, including the element I just inserted
}
print "WIN: $win, TIE: $tie, LOSE: $lose\n";
# could use $#mylist+1 for denominator below; 1. is to force floating point
print 1.*($win+$tie/2)/($win+$lose+$tie);
print "\n";
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