#!/usr/bin/perl
#
# @(#)$Id: cs402calc.txt,v 1.1 2020/08/07 16:48:31 william Exp $
#
# This is a kernel utility program.  Do this first:
#     chmod 755 ./cs402calc.txt
#
# Usage: cs402calc.txt grade p1 p2 ...
#
# Please see the Grading for Group Projects section of the Projects web page about this program.

$debug = 1;

$num_args = $#ARGV + 1;
if ($num_args < 3) {
    print "usage: cs402calc.txt grade p1 p2 ...\n";
    exit(-1);
}
$grade = $ARGV[0];
$num_members = $num_args - 1;
@percentages = ( );
@fractions = ( );
$dsum = 0.0;
$dsum_of_squares = 0.0;
$total = 0;
for ($i = 0; $i < $num_members; $i++) {
    $percentages[$i] = $ARGV[$i+1];
    $total = $total + $percentages[$i];
    $frac = $percentages[$i] / 100.0;
    $fractions[$i] = $frac;
    $dsum = $dsum + $frac;
    $dsum_of_squares = $dsum_of_squares + ($frac * $frac);
}
if ($total != 100) {
    print "ERROR: percentages do not add up to be 100.\n";
    exit(-1);
}

$avg = $dsum / ($num_members * 1.0);
$var = ($dsum_of_squares / ($num_members * 1.0)) - ($avg * $avg);
$std = sqrt($var);
$max_std = sqrt((($num_members-1)*1.0) / ($num_members*$num_members*1.0));

if ($debug) {
    print "grade = $grade\n";
    for ($i = 0; $i < $num_members; $i++) {
        print "percentages[$i] = $percentages[$i]\n";
    }
    print "avg = $avg\n";
    print "std = $std\n";
    print "max_std = $max_std\n";
}

$frac = $std / $max_std;
$scale = (($num_members-1)*1.0) * $frac + 1.0;
$base = $grade / 2.0;
$points_to_distr = $base * ($num_members * 1.0) / $scale;

print "                                                STD = $std\n";
print "                                   Max possible STD = $max_std\n";
print "    Number of points to distribute (before scaling) = $points_to_distr\n";
print "                                     Scaling factor = $scale\n";
print "     Number of points to distribute (after scaling) = $points_to_distr\n";
print "                                Base (50% of grade) = $base\n";
print "                                    Assigned points =";

for ($i = 0; $i < $num_members; $i++) {
    $f = $base + $fractions[$i] * $points_to_distr;
    print sprintf(" %.6g", $f);
}
print "\n";