How to resolve the algorithm Heronian triangles step by step in the Raku programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Heronian triangles step by step in the Raku programming language

Table of Contents

Problem Statement

Hero's formula for the area of a triangle given the length of its three sides   a,   b,   and   c   is given by: where   s   is half the perimeter of the triangle; that is,

Heronian triangles are triangles whose sides and area are all integers.

Note that any triangle whose sides are all an integer multiple of   3, 4, 5;   such as   6, 8, 10,   will also be a Heronian triangle. Define a Primitive Heronian triangle as a Heronian triangle where the greatest common divisor of all three sides is   1   (unity). This will exclude, for example, triangle   6, 8, 10.

Show all output here. Note: when generating triangles it may help to restrict

a <= b <= c

{\displaystyle a<=b<=c}

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Heronian triangles step by step in the Raku programming language

Source code in the raku programming language

sub hero($a, $b, $c) {
    my $s = ($a + $b + $c) / 2;
    ($s * ($s - $a) * ($s - $b) * ($s - $c)).sqrt;
}
 
sub heronian-area($a, $b, $c) {
    $_ when Int given hero($a, $b, $c).narrow;
} 

sub primitive-heronian-area($a, $b, $c) {
    heronian-area $a, $b, $c
        if 1 == [gcd] $a, $b, $c;
}

sub show(@measures) {
    say "   Area Perimeter   Sides";
    for @measures -> [$area, $perim, $c, $b, $a] {
	printf "%6d %6d %12s\n", $area, $perim, "$a×$b×$c";
    }
}
 
sub MAIN ($maxside = 200, $first = 10, $witharea = 210) {
    my @hh[1000];
    my atomicint $i;
    (1 .. $maxside).race(:12batch).map: -> $c {
        for 1 .. $c -> $b {
            for $c - $b + 1 .. $b -> $a {
                if primitive-heronian-area($a,$b,$c) -> $area {
                    @hh[$i⚛++] = [$area, $a+$b+$c, $c, $b, $a];
                }
            }
        }
    }

    my @h = (@hh.grep: so *).sort;
    say "Primitive Heronian triangles with sides up to $maxside: ", +@h;

    say "\nFirst $first:";
    show @h[^$first];

    say "\nArea $witharea:";
    show @h.grep: *[0] == $witharea;
}


  

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