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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_vector::IntegerVector;
use crate::natural::Natural;
use crate::natural_vector::NaturalVector;
use malachite_base::num::arithmetic::traits::BalancedMod;
impl BalancedMod<Natural> for NaturalVector {
type Output = IntegerVector;
/// Reduces every element of a [`NaturalVector`] modulo a [`Natural`] to the representative
/// closest to zero, returning an [`IntegerVector`], taking the vector by value and the modulus
/// by value.
///
/// Each element $w_i$ of the result satisfies $-m/2 < w_i \leq m/2$ and $w_i \equiv v_i \bmod
/// m$, which determine it uniquely, as with [`BalancedMod`] for [`Natural`]s. A remainder of
/// exactly $m/2$ is positive. Remainders above $m/2$ become negative, which is why the result
/// is an [`IntegerVector`]. The dimension is unchanged.
///
/// Applied to a vector of residues modulo $m$, this gives their balanced representatives. An
/// [`UnsignedVector`](malachite_base::unsigned_vector::UnsignedVector) of residues can be
/// converted to a [`NaturalVector`] with [`From`] first.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits in the
/// vector's elements.
///
/// # Panics
/// Panics if `m` is zero.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedMod;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// // Each element goes to the representative closest to zero, and half the modulus stays
/// // positive.
/// let v = NaturalVector::from_str("(1, 27, 23, 5, 10)").unwrap();
/// assert_eq!(
/// v.clone().balanced_mod(Natural::from(10u32)).to_string(),
/// "(1, -3, 3, 5, 0)"
/// );
/// ```
///
/// This is equivalent to `_fmpz_vec_set_nmod_vec` from `fmpz_vec/set_nmod_vec.c`, FLINT 3.6.0,
/// for elements less than the modulus.
#[inline]
fn balanced_mod(self, m: Natural) -> IntegerVector {
(&self).balanced_mod(&m)
}
}
impl<'a> BalancedMod<&'a Natural> for NaturalVector {
type Output = IntegerVector;
/// Reduces every element of a [`NaturalVector`] modulo a [`Natural`] to the representative
/// closest to zero, returning an [`IntegerVector`], taking the vector by value and the modulus
/// by reference.
///
/// See the documentation for the [`BalancedMod`] implementation on [`NaturalVector`] that takes
/// both arguments by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits in the
/// vector's elements.
///
/// # Panics
/// Panics if `m` is zero.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedMod;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// // Each element goes to the representative closest to zero, and half the modulus stays
/// // positive.
/// let v = NaturalVector::from_str("(1, 27, 23, 5, 10)").unwrap();
/// assert_eq!(
/// v.clone().balanced_mod(&Natural::from(10u32)).to_string(),
/// "(1, -3, 3, 5, 0)"
/// );
/// ```
#[inline]
fn balanced_mod(self, m: &'a Natural) -> IntegerVector {
(&self).balanced_mod(m)
}
}
impl BalancedMod<Natural> for &NaturalVector {
type Output = IntegerVector;
/// Reduces every element of a [`NaturalVector`] modulo a [`Natural`] to the representative
/// closest to zero, returning an [`IntegerVector`], taking the vector by reference and the
/// modulus by value.
///
/// See the documentation for the [`BalancedMod`] implementation on [`NaturalVector`] that takes
/// both arguments by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits in the
/// vector's elements.
///
/// # Panics
/// Panics if `m` is zero.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedMod;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// // Each element goes to the representative closest to zero, and half the modulus stays
/// // positive.
/// let v = NaturalVector::from_str("(1, 27, 23, 5, 10)").unwrap();
/// assert_eq!(
/// (&v).balanced_mod(Natural::from(10u32)).to_string(),
/// "(1, -3, 3, 5, 0)"
/// );
/// ```
#[inline]
fn balanced_mod(self, m: Natural) -> IntegerVector {
self.balanced_mod(&m)
}
}
impl<'a> BalancedMod<&'a Natural> for &NaturalVector {
type Output = IntegerVector;
/// Reduces every element of a [`NaturalVector`] modulo a [`Natural`] to the representative
/// closest to zero, returning an [`IntegerVector`], taking the vector by reference and the
/// modulus by reference.
///
/// See the documentation for the [`BalancedMod`] implementation on [`NaturalVector`] that takes
/// both arguments by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits in the
/// vector's elements.
///
/// # Panics
/// Panics if `m` is zero.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedMod;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// // Each element goes to the representative closest to zero, and half the modulus stays
/// // positive.
/// let v = NaturalVector::from_str("(1, 27, 23, 5, 10)").unwrap();
/// assert_eq!(
/// (&v).balanced_mod(&Natural::from(10u32)).to_string(),
/// "(1, -3, 3, 5, 0)"
/// );
/// ```
fn balanced_mod(self, m: &'a Natural) -> IntegerVector {
assert_ne!(*m, 0u32, "division by zero");
IntegerVector {
elements: self.elements.iter().map(|x| x.balanced_mod(m)).collect(),
}
}
}