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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::num::arithmetic::traits::{
BinomialCoefficient, CheckedBinomialCoefficient, UnsignedAbs,
};
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::OverflowingFrom;
use crate::num::exhaustive::primitive_int_increasing_inclusive_range;
use core::cmp::min;
fn checked_binomial_coefficient_unsigned<T: PrimitiveUnsigned>(n: T, mut k: T) -> Option<T> {
if k > n {
return Some(T::ZERO);
}
k = min(k, n - k);
if k == T::ZERO {
Some(T::ONE)
} else if k == T::ONE {
Some(n)
} else if k == T::TWO {
(if n.even() { n - T::ONE } else { n }).checked_mul(n >> 1)
} else {
// Some binomial coefficient algorithms have intermediate results greater than the final
// result, risking overflow. This one does not.
let mut product = n - k + T::ONE;
let mut numerator = product;
for i in primitive_int_increasing_inclusive_range(T::TWO, k) {
numerator += T::ONE;
let gcd = numerator.gcd(i);
product /= i / gcd;
product = product.checked_mul(numerator / gcd)?;
}
Some(product)
}
}
fn checked_binomial_coefficient_signed<
U: PrimitiveUnsigned,
S: OverflowingFrom<U> + PrimitiveSigned + TryFrom<U> + UnsignedAbs<Output = U>,
>(
n: S,
k: S,
) -> Option<S> {
if k < S::ZERO {
return None;
}
if n >= S::ZERO {
S::try_from(U::checked_binomial_coefficient(
n.unsigned_abs(),
k.unsigned_abs(),
)?)
.ok()
} else {
let k = k.unsigned_abs();
let b = U::checked_binomial_coefficient(n.unsigned_abs() + k - U::ONE, k)?;
if k.even() {
S::try_from(b).ok()
} else {
let (b, overflow) = S::overflowing_from(b);
if overflow {
if b == S::MIN { Some(S::MIN) } else { None }
} else {
Some(-b)
}
}
}
}
macro_rules! impl_binomial_coefficient_unsigned {
($t:ident) => {
impl CheckedBinomialCoefficient for $t {
/// Computes the binomial coefficient of two numbers. If the inputs are too large, the
/// function returns `None`.
///
/// $$
/// f(n, k) = \\begin{cases}
/// \operatorname{Some}(\binom{n}{k}) & \text{if} \\quad \binom{n}{k} < 2^W, \\\\
/// \operatorname{None} & \text{if} \\quad \binom{n}{k} \geq 2^W,
/// \\end{cases}
/// $$
/// where $W$ is `Self::WIDTH`.
///
/// # Worst-case complexity
/// $T(k) = O(k)$
///
/// $M(k) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $k$ is `k`.
///
/// # Examples
/// See [here](super::binomial_coefficient#checked_binomial_coefficient).
#[inline]
fn checked_binomial_coefficient(n: $t, k: $t) -> Option<$t> {
checked_binomial_coefficient_unsigned(n, k)
}
}
};
}
apply_to_unsigneds!(impl_binomial_coefficient_unsigned);
macro_rules! impl_binomial_coefficient_signed {
($t:ident) => {
impl CheckedBinomialCoefficient for $t {
/// Computes the binomial coefficient of two numbers. If the inputs are too large, the
/// function returns `None`.
///
/// 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.
///
/// $$
/// f(n, k) = \\begin{cases}
/// \operatorname{Some}(\binom{n}{k}) & \text{if} \\quad n \geq 0 \\ \text{and}
/// \\ -2^{W-1} \leq \binom{n}{k} < 2^{W-1}, \\\\
/// \operatorname{Some}((-1)^k \binom{-n+k-1}{k}) & \text{if} \\quad n < 0
/// \\ \text{and} \\ -2^{W-1} \leq \binom{n}{k} < 2^{W-1}, \\\\
/// \operatorname{None} & \\quad \\text{otherwise},
/// \\end{cases}
/// $$
/// where $W$ is `Self::WIDTH`.
///
/// # Worst-case complexity
/// $T(k) = O(k)$
///
/// $M(k) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $k$ is `k.abs()`.
///
/// # Examples
/// See [here](super::binomial_coefficient#checked_binomial_coefficient).
#[inline]
fn checked_binomial_coefficient(n: $t, k: $t) -> Option<$t> {
checked_binomial_coefficient_signed(n, k)
}
}
};
}
apply_to_signeds!(impl_binomial_coefficient_signed);
macro_rules! impl_binomial_coefficient_primitive_int {
($t:ident) => {
impl BinomialCoefficient for $t {
/// Computes the binomial coefficient of two numbers. If the inputs are too large, the
/// function panics.
///
/// 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
/// $T(k) = O(k)$
///
/// $M(k) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $k$ is `k.abs()`.
///
/// # Panics
/// Panics if the result is not representable by this type, or if $k$ is negative.
///
/// # Examples
/// See [here](super::binomial_coefficient#binomial_coefficient).
#[inline]
fn binomial_coefficient(n: $t, k: $t) -> $t {
$t::checked_binomial_coefficient(n, k).unwrap()
}
}
};
}
apply_to_primitive_ints!(impl_binomial_coefficient_primitive_int);