binomial.rs

binomial.rs

//use std::cmp::min;

/// Calculates the binomial coefficient (n choose k).
///
/// # Arguments
///
/// * `n`: The total number of items.
/// * `k`: The number of items to choose.
///
/// # Returns
///
/// The binomial coefficient as a usize.
fn binomial_coefficient(n: usize, k: usize) -> usize {
    if k > n {
        return 0;
    }

    let mut result = 1;
    for i in 0..k {
        result = result * (n - i) / (i + 1);
    }

    result
}

/// Calculates the binomial expansion of (x + y)^n.
///
/// # Arguments
///
/// * `n`: The exponent.
/// * `x`: The first term.
/// * `y`: The second term.
///
/// # Returns
///
/// A vector containing the coefficients of the expansion.
fn binomial_expansion(n: usize, x: i32, y: i32) -> Vec<i32> {
    let mut coefficients = Vec::with_capacity(n + 1);

    for k in 0..=n {
		let coefficient = binomial_coefficient(n, k) as i32 * x.pow((n - k).try_into().unwrap()) * y.pow(k.try_into().unwrap());
        coefficients.push(coefficient);
    }

    coefficients
}

fn main() {
    let n = 5;
    let x = 2;
    let y = 3;

    let coefficients = binomial_expansion(n, x, y);

    println!("Binomial expansion of ({x} + {y})^n:");
    for (i, coefficient) in coefficients.iter().enumerate() {
        if *coefficient != 0 {
            print!("{coefficient}");
            if i < n {
                print!("*x^{{{}}}{} ", n - i, if i > 0 { " + " } else { "" });
            }
        }
    }
    println!();
}