How to resolve the algorithm Pythagorean quadruples step by step in the Perl programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Pythagorean quadruples step by step in the Perl programming language

Table of Contents

Problem Statement

One form of   Pythagorean quadruples   is   (for positive integers   a,   b,   c,   and   d):

An example:

For positive integers up   2,200   (inclusive),   for all values of   a,   b,   c,   and   d, find   (and show here)   those values of   d   that   can't   be represented. Show the values of   d   on one line of output   (optionally with a title).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Pythagorean quadruples step by step in the Perl programming language

Source code in the perl programming language

my $N = 2200;
push @sq, $_**2 for 0 .. $N;
my @not = (0) x $N;
@not[0] = 1;


for my $d (1 .. $N) {
    my $last = 0;
    for my $a (reverse ceiling($d/3) .. $d) {
        for my $b (1 .. ceiling($a/2)) {
            my $ab = $sq[$a] + $sq[$b];
            last if $ab > $sq[$d];
            my $x = sqrt($sq[$d] - $ab);
            if ($x == int $x) {
                $not[$d] = 1;
                $last = 1;
                last
            }
        }
        last if $last;
    }
}

sub ceiling { int $_[0] + 1 - 1e-15 }

for (0 .. $#not) {
    $result .= "$_ " unless $not[$_]
}
print "$result\n"


  

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