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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::integer_polynomial::{IntegerPolynomial, ZERO};
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{Height, HeightRef, UnsignedAbs};
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_base::polynomial::Polynomial;
// The coefficient of largest magnitude, or a reference to zero if there are no coefficients. The
// `Integer` is returned rather than its magnitude so that both the borrowing and the consuming
// forms can start here.
fn largest_coefficient(p: &IntegerPolynomial) -> &Integer {
p.coefficients_asc()
.iter()
.max_by(|x, y| x.unsigned_abs_ref().cmp(y.unsigned_abs_ref()))
.unwrap_or(&ZERO)
}
impl Height for IntegerPolynomial {
type Output = Natural;
/// Returns the height of an [`IntegerPolynomial`]: the largest of the absolute values of its
/// coefficients, taking the polynomial by reference and cloning.
///
/// The zero polynomial has no coefficients, and its height is 0.
///
/// $$
/// f(p) = H(p) = \max_i |p_i|.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of bits of the
/// coefficients, and $m$ is the number of bits of the height.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Height;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// assert_eq!(
/// IntegerPolynomial::from_str("x^2-3*x+2")
/// .unwrap()
/// .to_height(),
/// 3
/// );
/// assert_eq!(
/// IntegerPolynomial::from_str("-x^100").unwrap().to_height(),
/// 1
/// );
/// assert_eq!(IntegerPolynomial::from_str("0").unwrap().to_height(), 0);
/// ```
///
/// This is `fmpz_poly_height` from `fmpz_poly/norms.c`, FLINT 3.6.0.
#[inline]
fn to_height(&self) -> Natural {
self.height_ref().clone()
}
/// Returns the height of an [`IntegerPolynomial`]: the largest of the absolute values of its
/// coefficients, taking the polynomial by value.
///
/// The coefficient of largest magnitude is moved out of the polynomial rather than cloned.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Height;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// assert_eq!(
/// IntegerPolynomial::from_str("x^2-3*x+2")
/// .unwrap()
/// .into_height(),
/// 3
/// );
/// assert_eq!(IntegerPolynomial::from_str("0").unwrap().into_height(), 0);
/// ```
#[inline]
fn into_height(self) -> Natural {
self.into_coefficients_asc()
.into_iter()
.map(Integer::unsigned_abs)
.max()
.unwrap_or(Natural::ZERO)
}
/// Returns the number of significant bits of the height of an [`IntegerPolynomial`].
///
/// Since bit length is monotone, this is the largest of the coefficients' bit lengths, without
/// materializing the height.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Height;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// assert_eq!(
/// IntegerPolynomial::from_str("x^2-3*x+2")
/// .unwrap()
/// .height_significant_bits(),
/// 2
/// );
/// assert_eq!(
/// IntegerPolynomial::from_str("0")
/// .unwrap()
/// .height_significant_bits(),
/// 0
/// );
/// ```
#[inline]
fn height_significant_bits(&self) -> u64 {
self.coefficients_asc()
.iter()
.map(SignificantBits::significant_bits)
.max()
.unwrap_or(0)
}
}
impl HeightRef for IntegerPolynomial {
/// Returns a reference to the height of an [`IntegerPolynomial`]: the largest of the absolute
/// values of its coefficients.
///
/// An [`Integer`] holds its magnitude as a [`Natural`], so the height is already there to be
/// lent and nothing needs to be built. The zero polynomial has no coefficients, and a reference
/// to zero is returned for it.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::HeightRef;
/// use malachite_nz::integer_polynomial::IntegerPolynomial;
///
/// assert_eq!(
/// *IntegerPolynomial::from_str("x^2-3*x+2")
/// .unwrap()
/// .height_ref(),
/// 3
/// );
/// assert_eq!(*IntegerPolynomial::from_str("0").unwrap().height_ref(), 0);
/// ```
#[inline]
fn height_ref(&self) -> &Natural {
largest_coefficient(self).unsigned_abs_ref()
}
}