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// Copyright © 2024 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 core::iter::{once, Chain, Once, Rev};
use itertools::{Interleave, Itertools};
use malachite_base::num::basic::traits::{NegativeOne, One, Zero};
/// Generates all [`Integer`]s in a finite interval, in ascending order.
///
/// This `struct` is created by the [`integer_increasing_range`] and
/// [`integer_increasing_inclusive_range`]; see their documentation for more.
#[derive(Clone, Debug, Eq, Hash, PartialEq)]
pub struct IntegerIncreasingRange {
a: Integer,
b: Integer,
}
impl Iterator for IntegerIncreasingRange {
type Item = Integer;
fn next(&mut self) -> Option<Integer> {
if self.a == self.b {
None
} else {
let result = self.a.clone();
self.a += Integer::ONE;
Some(result)
}
}
}
impl DoubleEndedIterator for IntegerIncreasingRange {
fn next_back(&mut self) -> Option<Integer> {
if self.a == self.b {
None
} else {
self.b -= Integer::ONE;
Some(self.b.clone())
}
}
}
/// Generates all [`Integer`]s greater than or equal to some [`Integer`], in ascending order.
///
/// This `struct` is created by [`integer_increasing_range_to_infinity`]; see its documentation for
/// more.
#[derive(Clone, Debug, Eq, Hash, PartialEq)]
pub struct IntegerIncreasingRangeToInfinity {
a: Integer,
}
impl Iterator for IntegerIncreasingRangeToInfinity {
type Item = Integer;
fn next(&mut self) -> Option<Integer> {
let result = self.a.clone();
self.a += Integer::ONE;
Some(result)
}
}
/// Generates all [`Integer`]s less than or equal to some [`Integer`], in ascending order.
///
/// This `struct` is created by [`integer_decreasing_range_to_negative_infinity`]; see its
/// documentation for more.
#[derive(Clone, Debug, Eq, Hash, PartialEq)]
pub struct IntegerDecreasingRangeToNegativeInfinity {
a: Integer,
}
impl Iterator for IntegerDecreasingRangeToNegativeInfinity {
type Item = Integer;
fn next(&mut self) -> Option<Integer> {
let result = self.a.clone();
self.a -= Integer::ONE;
Some(result)
}
}
/// Generates all [`Integer`]s in a finite interval, in order of increasing absolute value.
///
/// This `struct` is created [`exhaustive_integer_range`] and
/// [`exhaustive_integer_inclusive_range`]; see their documentation for more.
#[derive(Clone, Debug)]
pub enum ExhaustiveIntegerRange {
NonNegative(IntegerIncreasingRange),
NonPositive(Rev<IntegerIncreasingRange>),
BothSigns(
Chain<Once<Integer>, Interleave<IntegerIncreasingRange, Rev<IntegerIncreasingRange>>>,
),
}
impl Iterator for ExhaustiveIntegerRange {
type Item = Integer;
fn next(&mut self) -> Option<Integer> {
match self {
ExhaustiveIntegerRange::NonNegative(ref mut xs) => xs.next(),
ExhaustiveIntegerRange::NonPositive(ref mut xs) => xs.next(),
ExhaustiveIntegerRange::BothSigns(ref mut xs) => xs.next(),
}
}
}
/// Generates all [`Integer`]s greater than or equal to some [`Integer`], in order of increasing
/// absolute value.
///
/// This `struct` is created by [`exhaustive_integer_range_to_infinity`]; see its documentation for
/// more.
#[derive(Clone, Debug)]
pub enum ExhaustiveIntegerRangeToInfinity {
NonNegative(IntegerIncreasingRangeToInfinity),
BothSigns(
Chain<
Once<Integer>,
Interleave<IntegerIncreasingRangeToInfinity, Rev<IntegerIncreasingRange>>,
>,
),
}
impl Iterator for ExhaustiveIntegerRangeToInfinity {
type Item = Integer;
fn next(&mut self) -> Option<Integer> {
match self {
ExhaustiveIntegerRangeToInfinity::NonNegative(ref mut xs) => xs.next(),
ExhaustiveIntegerRangeToInfinity::BothSigns(ref mut xs) => xs.next(),
}
}
}
/// Generates all [`Integer`]s less than or equal to some [`Integer`], in order of increasing
/// absolute value.
///
/// This `struct` is created by [`exhaustive_integer_range_to_negative_infinity`]; see its
/// documentation for more.
#[derive(Clone, Debug)]
pub enum ExhaustiveIntegerRangeToNegativeInfinity {
NonPositive(IntegerDecreasingRangeToNegativeInfinity),
BothSigns(
Chain<
Once<Integer>,
Interleave<IntegerIncreasingRange, IntegerDecreasingRangeToNegativeInfinity>,
>,
),
}
impl Iterator for ExhaustiveIntegerRangeToNegativeInfinity {
type Item = Integer;
fn next(&mut self) -> Option<Integer> {
match self {
ExhaustiveIntegerRangeToNegativeInfinity::NonPositive(ref mut xs) => xs.next(),
ExhaustiveIntegerRangeToNegativeInfinity::BothSigns(ref mut xs) => xs.next(),
}
}
}
#[doc(hidden)]
pub type IntegerUpDown =
Interleave<IntegerIncreasingRangeToInfinity, IntegerDecreasingRangeToNegativeInfinity>;
/// Generates all [`Integer`]s, in order of increasing absolute value. When two [`Integer`]s have
/// the same absolute value, the positive one comes first.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(1)$, amortized.
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::exhaustive_integers;
///
/// assert_eq!(
/// prefix_to_string(exhaustive_integers(), 10),
/// "[0, 1, -1, 2, -2, 3, -3, 4, -4, 5, ...]"
/// )
/// ```
#[inline]
pub fn exhaustive_integers() -> Chain<Once<Integer>, IntegerUpDown> {
once(Integer::ZERO).chain(exhaustive_nonzero_integers())
}
/// Generates all natural [`Integer`]s in ascending order.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(1)$, amortized.
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::exhaustive_natural_integers;
///
/// assert_eq!(
/// prefix_to_string(exhaustive_natural_integers(), 10),
/// "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...]"
/// )
/// ```
#[inline]
pub const fn exhaustive_natural_integers() -> IntegerIncreasingRangeToInfinity {
integer_increasing_range_to_infinity(Integer::ZERO)
}
/// Generates all positive [`Integer`]s in ascending order.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(1)$, amortized.
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::exhaustive_positive_integers;
///
/// assert_eq!(
/// prefix_to_string(exhaustive_positive_integers(), 10),
/// "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...]"
/// )
/// ```
#[inline]
pub const fn exhaustive_positive_integers() -> IntegerIncreasingRangeToInfinity {
integer_increasing_range_to_infinity(Integer::ONE)
}
/// Generates all negative [`Integer`]s in descending order.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(1)$, amortized.
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::exhaustive_negative_integers;
///
/// assert_eq!(
/// prefix_to_string(exhaustive_negative_integers(), 10),
/// "[-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, ...]"
/// )
/// ```
#[inline]
pub const fn exhaustive_negative_integers() -> IntegerDecreasingRangeToNegativeInfinity {
integer_decreasing_range_to_negative_infinity(Integer::NEGATIVE_ONE)
}
/// Generates all nonzero [`Integer`]s, in order of increasing absolute value. When two [`Integer`]s
/// have the same absolute value, the positive one comes first.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(1)$, amortized.
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::exhaustive_nonzero_integers;
///
/// assert_eq!(
/// prefix_to_string(exhaustive_nonzero_integers(), 10),
/// "[1, -1, 2, -2, 3, -3, 4, -4, 5, -5, ...]"
/// )
/// ```
#[inline]
pub fn exhaustive_nonzero_integers() -> IntegerUpDown {
exhaustive_positive_integers().interleave(exhaustive_negative_integers())
}
/// Generates all [`Integer`]s in the half-open interval $[a, b)$, in ascending order.
///
/// $a$ must be less than or equal to $b$. If $a$ and $b$ are equal, the range is empty. To generate
/// all [`Integer`]s in an infinite interval in ascending or descending order, use
/// [`integer_increasing_range_to_infinity`] or [`integer_decreasing_range_to_negative_infinity`].
///
/// The output is $(k)_{k=a}^{b-1}$.
///
/// The output length is $b - a$.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// Although the time and space complexities are worst-case linear, the worst case is very rare. If
/// we exclude the cases where the the previously-generated value is positive and its
/// least-significant limb is `Limb::MAX`, the worst case space and time complexities are constant.
///
/// # Panics
/// Panics if $a > b$.
///
/// # Examples
/// ```
/// use itertools::Itertools;
/// use malachite_base::strings::ToDebugString;
/// use malachite_nz::integer::exhaustive::integer_increasing_range;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// integer_increasing_range(Integer::from(-4), Integer::from(4))
/// .collect_vec()
/// .to_debug_string(),
/// "[-4, -3, -2, -1, 0, 1, 2, 3]"
/// )
/// ```
#[inline]
pub fn integer_increasing_range(a: Integer, b: Integer) -> IntegerIncreasingRange {
assert!(a <= b, "a must be less than or equal to b. a: {a}, b: {b}");
IntegerIncreasingRange { a, b }
}
/// Generates all [`Integer`]s in the closed interval $[a, b]$, in ascending order.
///
/// $a$ must be less than or equal to $b$. If $a$ and $b$ are equal, the range contains a single
/// element. To generate all [`Integer`]s in an infinite interval in ascending or descending order,
/// use [`integer_increasing_range_to_infinity`] or
/// [`integer_decreasing_range_to_negative_infinity`].
///
/// The output is $(k)_{k=a}^{b}$.
///
/// The output length is $b - a + 1$.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// Although the time and space complexities are worst-case linear, the worst case is very rare. If
/// we exclude the cases where the the previously-generated value is positive and its
/// least-significant limb is `Limb::MAX`, the worst case space and time complexities are constant.
///
/// # Panics
/// Panics if $a > b$.
///
/// # Examples
/// ```
/// use itertools::Itertools;
/// use malachite_base::strings::ToDebugString;
/// use malachite_nz::integer::exhaustive::integer_increasing_inclusive_range;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// integer_increasing_inclusive_range(Integer::from(-4), Integer::from(4))
/// .collect_vec()
/// .to_debug_string(),
/// "[-4, -3, -2, -1, 0, 1, 2, 3, 4]"
/// )
/// ```
#[inline]
pub fn integer_increasing_inclusive_range(a: Integer, b: Integer) -> IntegerIncreasingRange {
assert!(a <= b, "a must be less than or equal to b. a: {a}, b: {b}");
IntegerIncreasingRange {
a,
b: b + Integer::ONE,
}
}
/// Generates all [`Integer`]s greater than or equal to some number $a$, in ascending order.
///
/// The output is $(k)_{k=a}^{\infty}$.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// Although the time and space complexities are worst-case linear, the worst case is very rare. If
/// we exclude the cases where the the previously-generated value is positive and its
/// least-significant limb is `Limb::MAX`, the worst case space and time complexities are constant.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::integer_increasing_range_to_infinity;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// prefix_to_string(integer_increasing_range_to_infinity(Integer::from(-4)), 10),
/// "[-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...]"
/// )
/// ```
#[inline]
pub const fn integer_increasing_range_to_infinity(a: Integer) -> IntegerIncreasingRangeToInfinity {
IntegerIncreasingRangeToInfinity { a }
}
/// Generates all [`Integer`]s less than or equal to some number $a$, in descending order.
///
/// The output is $(-k)_{k=-a}^{\infty}$.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// Although the time and space complexities are worst-case linear, the worst case is very rare. If
/// we exclude the cases where the the previously-generated value is negative and the
/// least-significant limb of its absolute value is `Limb::MAX`, the worst case space and time
/// complexities are constant.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::integer_decreasing_range_to_negative_infinity;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// prefix_to_string(
/// integer_decreasing_range_to_negative_infinity(Integer::from(4)),
/// 10
/// ),
/// "[4, 3, 2, 1, 0, -1, -2, -3, -4, -5, ...]"
/// )
/// ```
#[inline]
pub const fn integer_decreasing_range_to_negative_infinity(
a: Integer,
) -> IntegerDecreasingRangeToNegativeInfinity {
IntegerDecreasingRangeToNegativeInfinity { a }
}
/// Generates all [`Integer`]s in the half-open interval $[a, b)$, in order of increasing absolute
/// value.
///
/// When two [`Integer`]s have the same absolute value, the positive one comes first. $a$ must be
/// less than or equal to $b$. If $a$ and $b$ are equal, the range is empty.
///
/// The output satisfies $(|x_i|, \operatorname{sgn}(-x_i)) <_\mathrm{lex} (|x_j|,
/// \operatorname{sgn}(-x_j))$ whenever $i, j \\in [0, b - a)$ and $i < j$.
///
/// The output length is $b - a$.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// Although the time and space complexities are worst-case linear, the worst case is very rare. If
/// we exclude the cases where the the least-significant limb of the absolute value of the
/// previously-generated value is `Limb::MAX`, the worst case space and time complexities are
/// constant.
///
/// # Panics
/// Panics if $a > b$.
///
/// # Examples
/// ```
/// use itertools::Itertools;
/// use malachite_base::strings::ToDebugString;
/// use malachite_nz::integer::exhaustive::exhaustive_integer_range;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// exhaustive_integer_range(Integer::from(-4), Integer::from(4))
/// .collect_vec()
/// .to_debug_string(),
/// "[0, 1, -1, 2, -2, 3, -3, -4]"
/// )
/// ```
pub fn exhaustive_integer_range(a: Integer, b: Integer) -> ExhaustiveIntegerRange {
assert!(a <= b, "a must be less than or equal to b. a: {a}, b: {b}");
if a >= 0 {
ExhaustiveIntegerRange::NonNegative(integer_increasing_range(a, b))
} else if b <= 0 {
ExhaustiveIntegerRange::NonPositive(integer_increasing_range(a, b).rev())
} else {
ExhaustiveIntegerRange::BothSigns(
once(Integer::ZERO).chain(
integer_increasing_range(Integer::ONE, b)
.interleave(integer_increasing_range(a, Integer::ZERO).rev()),
),
)
}
}
/// Generates all [`Integer`]s in the closed interval $[a, b]$, in order of increasing absolute
/// value.
///
/// When two [`Integer`]s have the same absolute value, the positive one comes first. $a$ must be
/// less than or equal to $b$. If $a$ and $b$ are equal, the range contains a single element.
///
/// The output satisfies $(|x_i|, \operatorname{sgn}(-x_i)) <_\mathrm{lex} (|x_j|,
/// \operatorname{sgn}(-x_j))$ whenever $i, j \\in [0, b - a]$ and $i < j$.
///
/// The output length is $b - a + 1$.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// Although the time and space complexities are worst-case linear, the worst case is very rare. If
/// we exclude the cases where the the least-significant limb of the absolute value of the
/// previously-generated value is `Limb::MAX`, the worst case space and time complexities are
/// constant.
///
/// # Panics
/// Panics if $a > b$.
///
/// # Examples
/// ```
/// use itertools::Itertools;
/// use malachite_base::strings::ToDebugString;
/// use malachite_nz::integer::exhaustive::exhaustive_integer_inclusive_range;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// exhaustive_integer_inclusive_range(Integer::from(-4), Integer::from(4))
/// .collect_vec()
/// .to_debug_string(),
/// "[0, 1, -1, 2, -2, 3, -3, 4, -4]"
/// )
/// ```
pub fn exhaustive_integer_inclusive_range(a: Integer, b: Integer) -> ExhaustiveIntegerRange {
assert!(a <= b, "a must be less than or equal to b. a: {a}, b: {b}");
if a >= 0 {
ExhaustiveIntegerRange::NonNegative(integer_increasing_inclusive_range(a, b))
} else if b <= 0 {
ExhaustiveIntegerRange::NonPositive(integer_increasing_inclusive_range(a, b).rev())
} else {
ExhaustiveIntegerRange::BothSigns(
once(Integer::ZERO).chain(
integer_increasing_inclusive_range(Integer::ONE, b)
.interleave(integer_increasing_inclusive_range(a, Integer::NEGATIVE_ONE).rev()),
),
)
}
}
/// Generates all [`Integer`]s greater than or equal to some number $a$, in order of increasing
/// absolute value.
///
/// When two [`Integer`]s have the same absolute value, the positive one comes first.
///
/// The output satisfies $(|x_i|, \operatorname{sgn}(-x_i)) <_\mathrm{lex} (|x_j|,
/// \operatorname{sgn}(-x_j))$ whenever $i < j$.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// Although the time and space complexities are worst-case linear, the worst case is very rare. If
/// we exclude the cases where the the previously-generated value is positive and its
/// least-significant limb is `Limb::MAX`, the worst case space and time complexities are constant.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::exhaustive_integer_range_to_infinity;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// prefix_to_string(exhaustive_integer_range_to_infinity(Integer::from(-2)), 10),
/// "[0, 1, -1, 2, -2, 3, 4, 5, 6, 7, ...]"
/// )
/// ```
#[inline]
pub fn exhaustive_integer_range_to_infinity(a: Integer) -> ExhaustiveIntegerRangeToInfinity {
if a >= 0 {
ExhaustiveIntegerRangeToInfinity::NonNegative(integer_increasing_range_to_infinity(a))
} else {
ExhaustiveIntegerRangeToInfinity::BothSigns(
once(Integer::ZERO).chain(
integer_increasing_range_to_infinity(Integer::ONE)
.interleave(integer_increasing_range(a, Integer::ZERO).rev()),
),
)
}
}
/// Generates all [`Integer`]s less than or equal to some number $a$, in order of increasing
/// absolute value.
///
/// When two [`Integer`]s have the same absolute value, the positive one comes first.
///
/// The output satisfies $(|x_i|, \operatorname{sgn}(-x_i)) <_\mathrm{lex} (|x_j|,
/// \operatorname{sgn}(-x_j))$ whenever $i < j$.
///
/// The output length is infinite.
///
/// # Worst-case complexity per iteration
/// $T(i) = O(i)$
///
/// $M(i) = O(i)$
///
/// where $T$ is time, $M$ is additional memory, and $i$ is the iteration number.
///
/// Although the time and space complexities are worst-case linear, the worst case is very rare. If
/// we exclude the cases where the the previously-generated value is positive and its
/// least-significant limb is `Limb::MAX`, the worst case space and time complexities are constant.
///
/// # Examples
/// ```
/// use malachite_base::iterators::prefix_to_string;
/// use malachite_nz::integer::exhaustive::exhaustive_integer_range_to_negative_infinity;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(
/// prefix_to_string(
/// exhaustive_integer_range_to_negative_infinity(Integer::from(2)),
/// 10
/// ),
/// "[0, 1, -1, 2, -2, -3, -4, -5, -6, -7, ...]"
/// )
/// ```
#[inline]
pub fn exhaustive_integer_range_to_negative_infinity(
a: Integer,
) -> ExhaustiveIntegerRangeToNegativeInfinity {
if a <= 0 {
ExhaustiveIntegerRangeToNegativeInfinity::NonPositive(
integer_decreasing_range_to_negative_infinity(a),
)
} else {
ExhaustiveIntegerRangeToNegativeInfinity::BothSigns(once(Integer::ZERO).chain(
integer_increasing_range(Integer::ONE, a + Integer::ONE).interleave(
integer_decreasing_range_to_negative_infinity(Integer::NEGATIVE_ONE),
),
))
}
}