use rand::random;

const SAMPLE_SIZE: usize = 5_000;

fn simpson_from_uniform(m: i32, a: i32, r: f32) -> f32 {
    if r <= 0.5 {
        let d = (2f32 * r).sqrt() / 0.2;
        (m - a) as f32 + d
    } else {
        let d = (2f32 * (1f32 - r)).sqrt() / 0.2;
        (m + a) as f32 - d
    }
}

fn mean(distribution: &[f32]) -> f32 {
    distribution.iter().sum::<f32>() / distribution.len() as f32
}

fn dispersion(mean: f32, distribution: &[f32]) -> f32 {
    distribution
        .iter()
        .map(|x| (*x - mean).powi(2))
        .sum::<f32>()
        / distribution.len() as f32
}

fn standard_deviation(mean: f32, distribution: &[f32]) -> f32 {
    dispersion(mean, distribution).sqrt()
}

fn probability_in_limits(lower: f32, upper: f32, distribution: &[f32]) -> f32 {
    distribution
        .iter()
        .filter(|x| **x > lower && **x < upper)
        .count() as f32
        / distribution.len() as f32
}

fn main() {
    let set_m = 20;
    let set_a = 5;
    let simpson_numbers: Vec<f32> = (0..=SAMPLE_SIZE)
        .map(|_| simpson_from_uniform(set_m, set_a, random::<f32>()))
        .collect();

    let m = mean(&simpson_numbers);
    let std_dev = standard_deviation(m, &simpson_numbers);
    let probability = probability_in_limits(17f32, 24f32, &simpson_numbers);

    println!("Математичне очікування розподілу: {m}");
    println!("Середньоквадратичне відхилення розподілу: {std_dev}");
    println!("Ймовірність потрапляння у проміжок [17; 24]: {probability}");
}