Struct malachite_base::rational_sequences::RationalSequence

pub struct RationalSequence<T: Eq> { /* private fields */ }

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.

Implementations

impl<T: Eq> RationalSequence<T>

pub fn get(&self, i: usize) -> Option<&T>

Gets a reference to an element of a RationalSequence at an index.

If the index is greater than or equal to the length of the sequence, None is returned.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(RationalSequence::from_slices(&[1, 2], &[3, 4]).get(1), Some(&2));
assert_eq!(RationalSequence::from_slices(&[1, 2], &[3, 4]).get(10), Some(&3));

impl<T: Clone + Eq> RationalSequence<T>

pub fn mutate<F: FnOnce(&mut T) -> U, U>(&mut self, i: usize, f: F) -> U

Mutates an element of a RationalSequence at an index using a provided closure, and then returns whatever the closure returns.

If the index is greater than or equal to the length of the sequence, this function panics.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is index.

Panics

Panics if index is greater than or equal to the length of this sequence.

Examples

use malachite_base::rational_sequences::RationalSequence;

let mut xs = RationalSequence::from_slices(&[1, 2], &[3, 4]);
assert_eq!(xs.mutate(1, |x| { *x = 100; 25 }), 25);
assert_eq!(xs, RationalSequence::from_slices(&[1, 100], &[3, 4]));

let mut xs = RationalSequence::from_slices(&[1, 2], &[3, 4]);
assert_eq!(xs.mutate(6, |x| { *x = 100; 25 }), 25);
assert_eq!(xs, RationalSequence::from_slices(&[1, 2, 3, 4, 3, 4, 100], &[4, 3]));

impl<T: Eq> RationalSequence<T>

pub fn from_vec(non_repeating: Vec<T>) -> RationalSequence<T>

Converts a Vec to a finite RationalSequence.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(RationalSequence::<u8>::from_vec(vec![]).to_string(), "[]");
assert_eq!(RationalSequence::<u8>::from_vec(vec![1, 2]).to_string(), "[1, 2]");

pub fn from_vecs(
    non_repeating: Vec<T>,
    repeating: Vec<T>
) -> RationalSequence<T>

Converts two Vecs to a finite RationalSequence. The first Vec is the nonrepeating part and the second is the repeating part.

Worst-case complexity

$T(n, m) = O(n + m^{1+\epsilon})$ for all $\epsilon > 0$

$M(n, m) = O(1)$

where $T$ is time, $M$ is additional memory, $n$ is non_repeating.len(), and $m$ is repeating.len().

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(RationalSequence::<u8>::from_vecs(vec![], vec![]).to_string(), "[]");
assert_eq!(RationalSequence::<u8>::from_vecs(vec![], vec![1, 2]).to_string(), "[[1, 2]]");
assert_eq!(RationalSequence::<u8>::from_vecs(vec![1, 2], vec![]).to_string(), "[1, 2]");
assert_eq!(
    RationalSequence::<u8>::from_vecs(vec![1, 2], vec![3, 4]).to_string(),
    "[1, 2, [3, 4]]"
);
assert_eq!(
    RationalSequence::<u8>::from_vecs(vec![1, 2, 3], vec![4, 3]).to_string(),
    "[1, 2, [3, 4]]"
);

pub fn into_vecs(self) -> (Vec<T>, Vec<T>)

Converts a RationalSequence to a pair of Vecs containing the non-repeating and repeating parts, taking the RationalSequence by value.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(
    RationalSequence::from_slices(&[1, 2], &[3, 4]).into_vecs(),
    (vec![1, 2], vec![3, 4])
);

pub fn slices_ref(&self) -> (&[T], &[T])

Returns references to the non-repeating and repeating parts of a RationalSequence.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(
    RationalSequence::from_slices(&[1u8, 2], &[3, 4]).slices_ref(),
    (&[1u8, 2][..], &[3u8, 4][..])
);

impl<T: Clone + Eq> RationalSequence<T>

pub fn from_slice(non_repeating: &[T]) -> RationalSequence<T>

Converts a slice to a finite RationalSequence.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is xs.len().

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(RationalSequence::<u8>::from_slice(&[]).to_string(), "[]");
assert_eq!(RationalSequence::<u8>::from_slice(&[1, 2]).to_string(), "[1, 2]");

pub fn from_slices(non_repeating: &[T], repeating: &[T]) -> RationalSequence<T>

Converts two slices to a finite RationalSequence. The first slice is the nonrepeating part and the second is the repeating part.

Worst-case complexity

$T(n, m) = O(n + m^{1+\epsilon})$ for all $\epsilon > 0$

$M(n, m) = O(n + m)$

where $T$ is time, $M$ is additional memory, $n$ is non_repeating.len(), and $m$ is repeating.len().

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(RationalSequence::<u8>::from_slices(&[], &[]).to_string(), "[]");
assert_eq!(RationalSequence::<u8>::from_slices(&[], &[1, 2]).to_string(), "[[1, 2]]");
assert_eq!(RationalSequence::<u8>::from_slices(&[1, 2], &[]).to_string(), "[1, 2]");
assert_eq!(
    RationalSequence::<u8>::from_slices(&[1, 2], &[3, 4]).to_string(),
    "[1, 2, [3, 4]]"
);
assert_eq!(
    RationalSequence::<u8>::from_slices(&[1, 2, 3], &[4, 3]).to_string(),
    "[1, 2, [3, 4]]"
);

pub fn to_vecs(&self) -> (Vec<T>, Vec<T>)

Converts a RationalSequence to a pair of Vecs containing the non-repeating and repeating parts, taking the RationalSequence by reference.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is xs.component_len().

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(
    RationalSequence::from_slices(&[1, 2], &[3, 4]).to_vecs(),
    (vec![1, 2], vec![3, 4])
);

impl<T: Eq> RationalSequence<T>

pub fn is_empty(&self) -> bool

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_finite(&self) -> bool

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 len(&self) -> Option<usize>

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.

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 component_len(&self) -> usize

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.

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 iter(&self) -> Chain<Iter<'_, T>, Cycle<Iter<'_, T>>>

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]
);

Trait Implementations

impl<T: Clone + Eq> Clone for RationalSequence<T>

fn clone(&self) -> RationalSequence<T>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Display + Eq> Debug for RationalSequence<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Converts a RationalSequence to a String.

This is the same implementation as for Display.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is self.component_len().

Examples

use malachite_base::rational_sequences::RationalSequence;
use malachite_base::strings::ToDebugString;

assert_eq!(RationalSequence::<u8>::from_vecs(vec![], vec![]).to_debug_string(), "[]");
assert_eq!(
    RationalSequence::<u8>::from_vecs(vec![], vec![1, 2]).to_debug_string(),
    "[[1, 2]]"
);
assert_eq!(
    RationalSequence::<u8>::from_vecs(vec![1, 2], vec![]).to_debug_string(),
    "[1, 2]"
);
assert_eq!(
    RationalSequence::<u8>::from_vecs(vec![1, 2], vec![3, 4]).to_string(),
    "[1, 2, [3, 4]]"
);

impl<T: Default + Eq> Default for RationalSequence<T>

fn default() -> RationalSequence<T>

Returns the “default value” for a type.

impl<T: Display + Eq> Display for RationalSequence<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Converts a RationalSequence to a String.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is self.component_len().

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(RationalSequence::<u8>::from_vecs(vec![], vec![]).to_string(), "[]");
assert_eq!(RationalSequence::<u8>::from_vecs(vec![], vec![1, 2]).to_string(), "[[1, 2]]");
assert_eq!(RationalSequence::<u8>::from_vecs(vec![1, 2], vec![]).to_string(), "[1, 2]");
assert_eq!(
    RationalSequence::<u8>::from_vecs(vec![1, 2], vec![3, 4]).to_string(),
    "[1, 2, [3, 4]]"
);

impl<T: Hash + Eq> Hash for RationalSequence<T>

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl<T: Eq> Index<usize> for RationalSequence<T>

fn index(&self, i: usize) -> &T

Gets a reference to an element of a RationalSequence at an index.

If the index is greater than or equal to the length of the sequence, this function panics.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if index is greater than or equal to the length of this sequence.

Examples

use malachite_base::rational_sequences::RationalSequence;

assert_eq!(RationalSequence::from_slices(&[1, 2], &[3, 4])[1], 2);
assert_eq!(RationalSequence::from_slices(&[1, 2], &[3, 4])[10], 3);

type Output = T

The returned type after indexing.

impl<T: Eq + Ord> Ord for RationalSequence<T>

fn cmp(&self, other: &RationalSequence<T>) -> Ordering

Compares a RationalSequence to another RationalSequence.

The comparison is made lexicographically with respect to the element type’s ordering.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is self.component_len().

Examples

use malachite_base::rational_sequences::RationalSequence;

assert!(
    RationalSequence::from_slice(&[1, 2]) <
        RationalSequence::from_slices(&[1, 2], &[1])
);
assert!(
    RationalSequence::from_slice(&[1, 2, 3]) <
        RationalSequence::from_slices(&[1, 2], &[3, 4])
);

fn max(self, other: Self) -> Self

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

Restrict a value to a certain interval.

impl<T: PartialEq + Eq> PartialEq<RationalSequence<T>> for RationalSequence<T>

fn eq(&self, other: &RationalSequence<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &RationalSequence<T>) -> bool

This method tests for !=.

impl<T: Eq + Ord> PartialOrd<RationalSequence<T>> for RationalSequence<T>

fn partial_cmp(&self, other: &RationalSequence<T>) -> Option<Ordering>

Compares a RationalSequence to another RationalSequence.

See here for more information.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<T: Eq + Eq> Eq for RationalSequence<T>

impl<T: Eq> StructuralEq for RationalSequence<T>

impl<T: Eq> StructuralPartialEq for RationalSequence<T>