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use slices::min_repeating_len;
use std::iter::{Chain, Cycle};
fn rational_sequence_reduce<T: Eq>(non_repeating: &mut Vec<T>, repeating: &mut Vec<T>) {
if repeating.is_empty() {
return;
}
repeating.truncate(min_repeating_len(repeating));
if non_repeating.is_empty() {
return;
}
let extra_non_repeating = non_repeating
.iter()
.rev()
.zip(repeating.iter().rev().cycle())
.take_while(|(x, y)| x == y)
.count();
if extra_non_repeating != 0 {
non_repeating.truncate(non_repeating.len() - extra_non_repeating);
let len = repeating.len();
repeating.rotate_right(extra_non_repeating % len);
}
}
pub_test! {rational_sequence_is_reduced<T: Eq>(non_repeating: &[T], repeating: &[T]) -> bool {
if repeating.is_empty() {
return true;
}
if min_repeating_len(repeating) != repeating.len() {
return false;
}
if non_repeating.is_empty() {
return true;
}
non_repeating
.iter()
.rev()
.zip(repeating.iter().rev().cycle())
.take_while(|(x, y)| x == y)
.count()
== 0
}}
/// A `RationalSequence` is a sequence that is either finite or eventually repeating, just like
/// the digits of a rational number.
///
/// In testing, the set of rational sequences may be used as a proxy for the set of all sequences,
/// which is too large to work with.
#[derive(Clone, Default, Eq, Hash, PartialEq)]
pub struct RationalSequence<T: Eq> {
non_repeating: Vec<T>,
repeating: Vec<T>,
}
impl<T: Eq> RationalSequence<T> {
/// Returns whether this `RationalSequence` is empty.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::rational_sequences::RationalSequence;
///
/// assert_eq!(RationalSequence::<u8>::from_slice(&[]).is_empty(), true);
/// assert_eq!(RationalSequence::<u8>::from_slice(&[1, 2, 3]).is_empty(), false);
/// assert_eq!(RationalSequence::<u8>::from_slices(&[], &[3, 4]).is_empty(), false);
/// assert_eq!(RationalSequence::<u8>::from_slices(&[1, 2], &[3, 4]).is_empty(), false);
/// ```
pub fn is_empty(&self) -> bool {
self.non_repeating.is_empty() && self.repeating.is_empty()
}
/// Returns whether this `RationalSequence` is finite (has no repeating part).
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::rational_sequences::RationalSequence;
///
/// assert_eq!(RationalSequence::<u8>::from_slice(&[]).is_finite(), true);
/// assert_eq!(RationalSequence::<u8>::from_slice(&[1, 2, 3]).is_finite(), true);
/// assert_eq!(RationalSequence::<u8>::from_slices(&[], &[3, 4]).is_finite(), false);
/// assert_eq!(RationalSequence::<u8>::from_slices(&[1, 2], &[3, 4]).is_finite(), false);
/// ```
pub fn is_finite(&self) -> bool {
self.repeating.is_empty()
}
/// Returns the length of this `RationalSequence`. If the sequence is infinite, `None` is
/// returned.
///
/// For a measure of length that always exists, try [`component_len`](Self::component_len).
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::rational_sequences::RationalSequence;
///
/// assert_eq!(RationalSequence::<u8>::from_slice(&[]).len(), Some(0));
/// assert_eq!(RationalSequence::<u8>::from_slice(&[1, 2, 3]).len(), Some(3));
/// assert_eq!(RationalSequence::<u8>::from_slices(&[], &[3, 4]).len(), None);
/// assert_eq!(RationalSequence::<u8>::from_slices(&[1, 2], &[3, 4]).len(), None);
/// ```
pub fn len(&self) -> Option<usize> {
if self.repeating.is_empty() {
Some(self.non_repeating.len())
} else {
None
}
}
/// Returns the sum of the lengths of the non-repeating and repeating parts of this
/// `RationalSequence`.
///
/// This is often a more useful way of measuring the complexity of a sequence than
/// [`len`](Self::len).
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::rational_sequences::RationalSequence;
///
/// assert_eq!(RationalSequence::<u8>::from_slice(&[]).component_len(), 0);
/// assert_eq!(RationalSequence::<u8>::from_slice(&[1, 2, 3]).component_len(), 3);
/// assert_eq!(RationalSequence::<u8>::from_slices(&[], &[3, 4]).component_len(), 2);
/// assert_eq!(RationalSequence::<u8>::from_slices(&[1, 2], &[3, 4]).component_len(), 4);
/// ```
pub fn component_len(&self) -> usize {
self.non_repeating.len() + self.repeating.len()
}
/// Returns an iterator of references to the elements of this sequence.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// extern crate itertools;
///
/// use itertools::Itertools;
/// use malachite_base::rational_sequences::RationalSequence;
///
/// let empty: &[u8] = &[];
/// assert_eq!(RationalSequence::<u8>::from_slice(empty).iter().cloned().collect_vec(), empty);
/// assert_eq!(
/// RationalSequence::<u8>::from_slice(&[1, 2, 3]).iter().cloned().collect_vec(),
/// &[1, 2, 3]
/// );
/// assert_eq!(
/// RationalSequence::<u8>::from_slices(&[], &[3, 4]).iter().cloned().take(10)
/// .collect_vec(),
/// &[3, 4, 3, 4, 3, 4, 3, 4, 3, 4]
/// );
/// assert_eq!(
/// RationalSequence::<u8>::from_slices(&[1, 2], &[3, 4]).iter().cloned().take(10)
/// .collect_vec(),
/// &[1, 2, 3, 4, 3, 4, 3, 4, 3, 4]
/// );
/// ```
pub fn iter(&self) -> Chain<std::slice::Iter<T>, Cycle<std::slice::Iter<T>>> {
(&self.non_repeating)
.iter()
.chain((&self.repeating).iter().cycle())
}
}
impl<T: Clone + Eq> RationalSequence<T> {
// Returns true iff `self` is valid.
//
// To be valid, the non-repeating and repeating parts must be reduced. For example, `[1, 2]`
// and `[3, 4]` is a reduced pair. On the other hand, `[1, 2]` and `[3, 4, 3, 4]` is a
// non-reduced pair representing the same sequence, as is `[1, 2, 3]` and `[4, 3]`. All
// `RationalSequence`s must be valid.
#[cfg(feature = "test_build")]
pub fn is_valid(&self) -> bool {
rational_sequence_is_reduced(&self.non_repeating, &self.repeating)
}
}
/// Functions for getting and setting elements in a [`RationalSequence`].
pub mod access;
/// Functions for comparing [`RationalSequence`]s.
pub mod cmp;
/// Functions for converting a [`RationalSequence`]s to and from a [`Vec`] or a slice.
pub mod conversion;
/// Functions for generating all [`RationalSequence`]s over a set of elements.
pub mod exhaustive;
/// Functions for generating random [`RationalSequence`]s from a set of elements.
pub mod random;
/// Functions for displaying a [`RationalSequence`].
pub mod to_string;