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Heronian triangles: Difference between revisions
Add Rust implementation
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7x65x68 140 210.0
3x148x149 300 210.0
</pre>
=={{header|Rust}}==
<lang rust>
use num_integer::Integer;
use std::{f64, usize};
const MAXSIZE: usize = 200;
#[derive(Debug)]
struct HerionanTriangle {
a: usize,
b: usize,
c: usize,
area: usize,
perimeter: usize,
}
fn get_area(a: &usize, b: &usize, c: &usize) -> f64 {
let s = (a + b + c) as f64 / 2.;
(s * (s - *a as f64) * (s - *b as f64) * (s - *c as f64)).sqrt()
}
fn is_heronian(a: &usize, b: &usize, c: &usize) -> bool {
let area = get_area(a, b, c);
// Heronian if the area is an integer number
area != 0. && area.fract() == 0.
}
fn main() {
let mut heronians: Vec<HerionanTriangle> = vec![];
(1..=MAXSIZE).into_iter().for_each(|a| {
(a..=MAXSIZE).into_iter().for_each(|b| {
(b..=MAXSIZE).into_iter().for_each(|c| {
if a + b > c && a.gcd(&b).gcd(&c) == 1 && is_heronian(&a, &b, &c) {
heronians.push(HerionanTriangle {
a,
b,
c,
perimeter: a + b + c,
area: get_area(&a, &b, &c) as usize,
})
}
})
})
});
// sort by area then by perimeter, then by maximum side
heronians.sort_unstable_by(|x, y| {
x.area
.cmp(&y.area)
.then(x.perimeter.cmp(&y.perimeter))
.then((x.a.max(x.b).max(x.c)).cmp(&y.a.max(y.b).max(y.c)))
});
println!(
"Primitive Heronian triangles with sides up to 200: {}",
heronians.len()
);
println!("\nFirst ten when ordered by increasing area, then perimeter,then maximum sides:");
heronians.iter().take(10).for_each(|h| println!("{:?}", h));
println!("\nAll with area 210 subject to the previous ordering:");
heronians
.iter()
.filter(|h| h.area == 210)
.for_each(|h| println!("{:?}", h));
}
</lang>
{{out}}
<pre>
Primitive Heronian triangles with sides up to 200: 517
First ten when ordered by increasing area, then perimeter,then maximum sides:
HerionanTriangle { a: 3, b: 4, c: 5, area: 6, perimeter: 12 }
HerionanTriangle { a: 5, b: 5, c: 6, area: 12, perimeter: 16 }
HerionanTriangle { a: 5, b: 5, c: 8, area: 12, perimeter: 18 }
HerionanTriangle { a: 4, b: 13, c: 15, area: 24, perimeter: 32 }
HerionanTriangle { a: 5, b: 12, c: 13, area: 30, perimeter: 30 }
HerionanTriangle { a: 9, b: 10, c: 17, area: 36, perimeter: 36 }
HerionanTriangle { a: 3, b: 25, c: 26, area: 36, perimeter: 54 }
HerionanTriangle { a: 7, b: 15, c: 20, area: 42, perimeter: 42 }
HerionanTriangle { a: 10, b: 13, c: 13, area: 60, perimeter: 36 }
HerionanTriangle { a: 8, b: 15, c: 17, area: 60, perimeter: 40 }
All with area 210 subject to the previous ordering:
HerionanTriangle { a: 17, b: 25, c: 28, area: 210, perimeter: 70 }
HerionanTriangle { a: 20, b: 21, c: 29, area: 210, perimeter: 70 }
HerionanTriangle { a: 12, b: 35, c: 37, area: 210, perimeter: 84 }
HerionanTriangle { a: 17, b: 28, c: 39, area: 210, perimeter: 84 }
HerionanTriangle { a: 7, b: 65, c: 68, area: 210, perimeter: 140 }
HerionanTriangle { a: 3, b: 148, c: 149, area: 210, perimeter: 300 }
</pre>
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