Project Euler #9: Special Pythogorean triplet

This article is part of a series where I'll be diving head first into the Project Euler puzzles. I want to document the challenge of solving such a puzzle and how I got to the answer. I want to prefix this by stating that I can't cheat for any of these challenges; with that I mean I can't look up any other implementations online. After the implementation, I will validate the answer by using this document or a similar sheet.

In this article I'll be solving: Project Euler #9.

This article features only an answer, because I’ve started writing from problem 14.

fn is_triplet(x: i32, y: i32, z: i32) -> bool {
    if y < x || z < y {
        return false
    }

    let powers = (x.pow(2) + y.pow(2)) as f32;
    let result = powers.sqrt();

    result == z as f32
}

fn find_triplet(total: i32) -> (i32, i32, i32) {
    let (mut x, mut y, mut z) = (1, 2, total - 3);

    'x: loop {
        while (z - y) > 1 {
            z -= 1;
            y += 1;

            if is_triplet(x, y, z) {
                break 'x;
            }
        }
        x += 1;
        y = x + 1;
        z = total - x - y;

        if is_triplet(x, y, z) {
            break;
        }
    }

    (x, y, z)
}

#[test]
fn pythagorean_triplet() {
    assert_eq!(is_triplet(3,4,5), true);
    assert_eq!(is_triplet(3,4,6), false);
    assert_eq!(is_triplet(6,8,10), true);
    assert_eq!(is_triplet(48,55,73), true);
    assert_eq!(is_triplet(17,144,145), true);
}

#[test]
fn find_triplet_test() {
    assert_eq!(find_triplet(12), (3, 4, 5));
    assert_eq!(find_triplet(24), (6, 8, 10));
    assert_eq!(find_triplet(176), (48, 55, 73));
    assert_eq!(find_triplet(1000), (200, 375, 425));
}

The full solution is available on GitHub.

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