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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::integer::Integer;
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{BinomialCoefficient, Parity};
use malachite_base::num::basic::traits::One;
impl BinomialCoefficient for Integer {
/// Computes the binomial coefficient of two [`Integer`]s, taking both by value.
///
/// The second argument must be non-negative, but the first may be negative. If it is, the
/// identity $\binom{-n}{k} = (-1)^k \binom{n+k-1}{k}$ is used.
///
/// $$
/// f(n, k) = \\begin{cases}
/// \binom{n}{k} & \text{if} \\quad n \geq 0, \\\\
/// (-1)^k \binom{-n+k-1}{k} & \text{if} \\quad n < 0.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// TODO
///
/// # Panics
/// Panics if $k$ is negative.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::BinomialCoefficient;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(4), Integer::from(0)),
/// 1
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(4), Integer::from(1)),
/// 4
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(4), Integer::from(2)),
/// 6
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(4), Integer::from(3)),
/// 4
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(4), Integer::from(4)),
/// 1
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(10), Integer::from(5)),
/// 252
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(100), Integer::from(50)).to_string(),
/// "100891344545564193334812497256"
/// );
///
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(-3), Integer::from(0)),
/// 1
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(-3), Integer::from(1)),
/// -3
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(-3), Integer::from(2)),
/// 6
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(Integer::from(-3), Integer::from(3)),
/// -10
/// );
/// ```
fn binomial_coefficient(n: Self, k: Self) -> Self {
assert!(k.sign);
if n.sign {
Self::from(Natural::binomial_coefficient(n.abs, k.abs))
} else {
let k_abs = k.abs;
Self {
sign: k_abs.even(),
abs: Natural::binomial_coefficient(n.abs + &k_abs - Natural::ONE, k_abs),
}
}
}
}
impl<'a> BinomialCoefficient<&'a Self> for Integer {
/// Computes the binomial coefficient of two [`Integer`]s, taking both by reference.
///
/// The second argument must be non-negative, but the first may be negative. If it is, the
/// identity $\binom{-n}{k} = (-1)^k \binom{n+k-1}{k}$ is used.
///
/// $$
/// f(n, k) = \\begin{cases}
/// \binom{n}{k} & \text{if} \\quad n \geq 0, \\\\
/// (-1)^k \binom{-n+k-1}{k} & \text{if} \\quad n < 0.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// TODO
///
/// # Panics
/// Panics if $k$ is negative.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::BinomialCoefficient;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(4), &Integer::from(0)),
/// 1
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(4), &Integer::from(1)),
/// 4
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(4), &Integer::from(2)),
/// 6
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(4), &Integer::from(3)),
/// 4
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(4), &Integer::from(4)),
/// 1
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(10), &Integer::from(5)),
/// 252
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(100), &Integer::from(50)).to_string(),
/// "100891344545564193334812497256"
/// );
///
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(-3), &Integer::from(0)),
/// 1
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(-3), &Integer::from(1)),
/// -3
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(-3), &Integer::from(2)),
/// 6
/// );
/// assert_eq!(
/// Integer::binomial_coefficient(&Integer::from(-3), &Integer::from(3)),
/// -10
/// );
/// ```
fn binomial_coefficient(n: &'a Self, k: &'a Self) -> Self {
assert!(k.sign);
if n.sign {
Self::from(Natural::binomial_coefficient(&n.abs, &k.abs))
} else {
let k_abs = &k.abs;
Self {
sign: k_abs.even(),
abs: Natural::binomial_coefficient(&(&n.abs + k_abs - Natural::ONE), k_abs),
}
}
}
}