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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::Rational;
use crate::arithmetic::traits::{DenominatorsInClosedInterval, SimplestRationalInInterval};
use crate::exhaustive::{
exhaustive_rationals_with_denominator_inclusive_range,
exhaustive_rationals_with_denominator_range,
};
use alloc::collections::BTreeSet;
use malachite_base::num::arithmetic::traits::{Ceiling, Reciprocal, UnsignedAbs};
use malachite_base::num::basic::traits::{One, Two, Zero};
use malachite_base::num::factorization::traits::Primes;
use malachite_nz::natural::Natural;
use malachite_nz::platform::Limb;
// Returns a k such that for all n >= k, any closed interval with the given diameter is guaranteed
// to contain rationals with (reduced) denominator n.
fn smallest_guaranteed_denominator(interval_diameter: &Rational) -> Natural {
if *interval_diameter >= 1u32 {
return Natural::ONE;
}
let mut primorial = Natural::TWO;
let mut pow = Natural::TWO;
for p in Limb::primes().skip(1) {
primorial *= Natural::from(p);
pow <<= 1;
let limit = Rational::from_naturals_ref(&pow, &primorial);
if *interval_diameter >= limit {
return primorial;
}
}
panic!();
}
fn smallest_likely_denominator(interval_diameter: &Rational) -> Natural {
interval_diameter.reciprocal().ceiling().unsigned_abs()
}
/// Returns an iterator of all denominators that appear in the [`Rational`]s contained in a closed
/// interval.
///
/// This `struct` is created by [`DenominatorsInClosedInterval::denominators_in_closed_interval`];
/// see its documentation for more.
#[derive(Clone, Debug)]
pub struct DenominatorsInClosedRationalInterval {
a: Rational,
b: Rational,
low_threshold: Natural,
high_threshold: Natural,
current: Natural,
points: BTreeSet<Rational>,
}
impl Iterator for DenominatorsInClosedRationalInterval {
type Item = Natural;
fn next(&mut self) -> Option<Natural> {
if self.current >= self.high_threshold {
self.points.clear();
self.current += Natural::ONE;
Some(self.current.clone())
} else if self.current >= self.low_threshold {
self.points.clear();
loop {
self.current += Natural::ONE;
if exhaustive_rationals_with_denominator_inclusive_range(
self.current.clone(),
self.a.clone(),
self.b.clone(),
)
.next()
.is_some()
{
return Some(self.current.clone());
}
}
} else if self.points.is_empty() {
assert_eq!(self.current, 0u32);
self.points.insert(self.a.clone());
self.points.insert(self.b.clone());
self.points
.insert(Rational::simplest_rational_in_open_interval(
&self.a, &self.b,
));
let mut min_denominator = self.a.denominator_ref();
for p in &self.points {
let pd = p.denominator_ref();
if pd < min_denominator {
min_denominator = pd;
}
}
self.current = min_denominator.clone();
for p in exhaustive_rationals_with_denominator_range(
self.current.clone(),
self.a.clone(),
self.b.clone(),
) {
self.points.insert(p);
}
Some(self.current.clone())
} else {
let mut previous_point = None;
let mut min_interior_denominator = None;
for p in &self.points {
if let Some(previous) = previous_point {
let interior_denominator =
Rational::simplest_rational_in_open_interval(previous, p)
.into_denominator();
if let Some(previous_min) = min_interior_denominator.as_ref() {
if interior_denominator < *previous_min {
min_interior_denominator = Some(interior_denominator);
}
} else {
min_interior_denominator = Some(interior_denominator);
}
}
previous_point = Some(p);
}
let min_interior_denominator = min_interior_denominator.unwrap();
assert!(min_interior_denominator > self.current);
let mut min_denominator = min_interior_denominator;
for p in &self.points {
let pd = p.denominator_ref();
if *pd > self.current && *pd < min_denominator {
min_denominator = pd.clone();
}
}
self.current = min_denominator;
for p in exhaustive_rationals_with_denominator_range(
self.current.clone(),
self.a.clone(),
self.b.clone(),
) {
self.points.insert(p);
}
Some(self.current.clone())
}
}
}
impl DenominatorsInClosedInterval for Rational {
type Denominators = DenominatorsInClosedRationalInterval;
/// Returns an iterator of all denominators that appear in the [`Rational`]s contained in a
/// closed interval.
///
/// For example, consider the interval $[1/3, 1/2]$. It contains no integers, so no
/// [`Rational`]s with denominator 1. It does contain [`Rational`]s with denominators 2 and 3
/// (the endpoints). It contains none with denominator 4, but it does contain $2/5$. It contains
/// none with denominator 6 (though $1/3$ and $1/2$ are $2/6$ and $3/6$, those representations
/// are not reduced). It contains $3/7$, $3/8$, and $4/9$ but none with denominator 10 ($0.4$
/// does not count because it is $2/5$). It contains all denominators greater than 10, so the
/// complete list is $2, 3, 5, 7, 8, 9, 11, 12, 13, \ldots$.
///
/// # Worst-case complexity per iteration
/// $T(n, i) = O(n + \log i)$
///
/// $M(n, i) = O(n + \log i)$
///
/// where $T$ is time, $M$ is additional memory, $i$ is the iteration number, and $n$ is
/// `max(a.significant_bits(), b.significant_bits())`.
///
/// # Panics
/// Panics if $a \geq b$.
///
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_base::num::basic::traits::{One, Two};
/// use malachite_q::arithmetic::traits::DenominatorsInClosedInterval;
/// use malachite_q::Rational;
///
/// assert_eq!(
/// prefix_to_string(
/// Rational::denominators_in_closed_interval(Rational::ONE, Rational::TWO),
/// 20
/// ),
/// "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ...]"
/// );
/// assert_eq!(
/// prefix_to_string(
/// Rational::denominators_in_closed_interval(
/// Rational::from_signeds(1, 3),
/// Rational::from_signeds(1, 2)
/// ),
/// 20
/// ),
/// "[2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, ...]"
/// );
/// assert_eq!(
/// prefix_to_string(
/// Rational::denominators_in_closed_interval(
/// Rational::from_signeds(1, 1000001),
/// Rational::from_signeds(1, 1000000)
/// ),
/// 20
/// ),
/// "[1000000, 1000001, 2000001, 3000001, 3000002, 4000001, 4000003, 5000001, 5000002, \
/// 5000003, 5000004, 6000001, 6000005, 7000001, 7000002, 7000003, 7000004, 7000005, \
/// 7000006, 8000001, ...]"
/// );
/// ```
fn denominators_in_closed_interval(
a: Rational,
b: Rational,
) -> DenominatorsInClosedRationalInterval {
assert!(a < b);
let diameter = &b - &a;
let (mut low_threshold, high_threshold) = if diameter >= 1u32 {
(Natural::ZERO, Natural::ZERO)
} else {
(
smallest_likely_denominator(&diameter),
smallest_guaranteed_denominator(&diameter),
)
};
if low_threshold < 100u32 {
low_threshold = Natural::ZERO;
}
DenominatorsInClosedRationalInterval {
a,
b,
low_threshold,
high_threshold,
current: Natural::ZERO,
points: BTreeSet::new(),
}
}
}