Struct normalize_interval::interval::Interval

pub struct Interval<T>(_);

A contiguous interval of the type T.

Intervals are Normalized when created. For Finite types, open bounds will be converted to the nearest contained closed bound.

Implementations

impl<T> Interval<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

pub fn new(left: Bound<T>, right: Bound<T>) -> Self

Constructs a new Interval from the given Bounds.

Examples

let interval: Interval<i32> = Interval::new(Include(3), Exclude(7));

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::new(Exclude(-3), Exclude(7));

assert_eq!(interval, Interval::new(Include(-2), Include(6)));

If the bounds are out of order, and empty Interval will be returned.

let interval: Interval<i32> = Interval::new(Exclude(7), Exclude(-7));

assert_eq!(interval, Interval::empty());

pub fn empty() -> Self

Constructs an empty Interval.

Example

let interval: Interval<i32> = Interval::empty();

pub fn point(point: T) -> Self

Constructs a new degenerate Interval containing the given point.

Example

let interval: Interval<i32> = Interval::point(3);

pub fn open(left: T, right: T) -> Self

Constructs a new bounded open Interval from the given points.

Examples

let interval: Interval<i32> = Interval::open(3, 7);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::open(-3, 7);

assert_eq!(interval, Interval::new(Include(-2), Include(6)));

If the bounds are out of order, and empty Interval will be returned.

let interval: Interval<i32> = Interval::open(7, -7);

assert_eq!(interval, Interval::empty());

pub fn left_open(left: T, right: T) -> Self

Constructs a new bounded left-open Interval from the given points.

Examples

let interval: Interval<i32> = Interval::left_open(3, 7);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::left_open(-3, 7);

assert_eq!(interval, Interval::new(Include(-2), Include(7)));

If the bounds are out of order, and empty Interval will be returned.

let interval: Interval<i32> = Interval::left_open(7, -7);

assert_eq!(interval, Interval::empty());

If the bounds are identical, a point Interval will be returned.

let interval: Interval<i32> = Interval::left_open(5, 5);

assert_eq!(interval, Interval::point(5));

pub fn right_open(left: T, right: T) -> Self

Constructs a new bounded right-open Interval from the given points.

Examples

let interval: Interval<i32> = Interval::right_open(3, 7);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::right_open(-3, 7);

assert_eq!(interval, Interval::new(Include(-3), Include(6)));

If the bounds are out of order, and empty Interval will be returned.

let interval: Interval<i32> = Interval::right_open(7, -7);

assert_eq!(interval, Interval::empty());

If the bounds are identical, a point Interval will be returned.

let interval: Interval<i32> = Interval::right_open(5, 5);

assert_eq!(interval, Interval::point(5));

pub fn closed(left: T, right: T) -> Self

Constructs a new bounded closed Interval from the given points.

Examples

let interval: Interval<i32> = Interval::closed(3, 7);

If the bounds are out of order, and empty Interval will be returned.

let interval: Interval<i32> = Interval::closed(7, -7);

assert_eq!(interval, Interval::empty());

If the bounds are identical, a point Interval will be returned.

let interval: Interval<i32> = Interval::closed(5, 5);

assert_eq!(interval, Interval::point(5));

pub fn left_closed(left: T, right: T) -> Self

Constructs a new bounded left-closed Interval from the given points.

Examples

let interval: Interval<i32> = Interval::left_closed(3, 7);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::left_closed(-3, 7);

assert_eq!(interval, Interval::new(Include(-3), Include(6)));

If the bounds are out of order, and empty Interval will be returned.

let interval: Interval<i32> = Interval::left_closed(7, -7);

assert_eq!(interval, Interval::empty());

If the bounds are identical, a point Interval will be returned.

let interval: Interval<i32> = Interval::left_closed(5, 5);

assert_eq!(interval, Interval::point(5));

pub fn right_closed(left: T, right: T) -> Self

Constructs a new bounded right-closed Interval from the given points.

Examples

let interval: Interval<i32> = Interval::right_closed(3, 7);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::right_closed(-3, 7);

assert_eq!(interval, Interval::new(Include(-2), Include(7)));

If the bounds are out of order, and empty Interval will be returned.

let interval: Interval<i32> = Interval::right_closed(7, -7);

assert_eq!(interval, Interval::empty());

If the bounds are identical, a point Interval will be returned.

let interval: Interval<i32> = Interval::right_closed(5, 5);

assert_eq!(interval, Interval::point(5));

pub fn unbounded_from(point: T) -> Self

Constructs a new right-unbounded Interval from (and including) the given point.

Examples

let interval: Interval<i32> = Interval::unbounded_from(3);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::unbounded_from(7);

assert_eq!(interval, Interval::new(Include(7), Include(i32::MAX)));

pub fn unbounded_to(point: T) -> Self

Constructs a new left-unbounded Interval to (and including) the given point.

Examples

let interval: Interval<i32> = Interval::unbounded_to(3);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::unbounded_to(7);

assert_eq!(interval, Interval::new(Include(i32::MIN), Include(7)));

pub fn unbounded_up_from(point: T) -> Self

Constructs a new right-unbounded Interval from (but excluding) the given point.

Examples

let interval: Interval<i32> = Interval::unbounded_up_from(3);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::unbounded_up_from(7);

assert_eq!(interval, Interval::new(Include(8), Include(i32::MAX)));

pub fn unbounded_up_to(point: T) -> Self

Constructs a new left-unbounded Interval to (but excluding) the given point.

Examples

let interval: Interval<i32> = Interval::unbounded_up_to(3);

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::unbounded_up_to(7);

assert_eq!(interval, Interval::new(Include(i32::MIN), Include(6)));

pub fn full() -> Self

Constructs a new unbounded Interval containing all points.

Examples

let interval: Interval<i32> = Interval::full();

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::full();

assert_eq!(interval, Interval::new(Include(i32::MIN), Include(i32::MAX)));

pub fn into_non_empty(self) -> Option<Self>

Converts the Interval into an Option, returning None if it is empty.

let interval: Interval<i32> = Interval::closed(0, 4);
assert_eq!(interval.into_non_empty(), Some(Interval::closed(0, 4)));

let interval: Interval<i32> = Interval::empty();
assert_eq!(interval.into_non_empty(), None);

pub fn lower_bound(&self) -> Option<Bound<T>>

Returns the lower Bound of the Interval, or None if the Interval is empty.

Examples

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.lower_bound(), Some(Include(-3)));

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::open(-3, 5);
 
assert_eq!(interval.lower_bound(), Some(Include(-2)));

pub fn upper_bound(&self) -> Option<Bound<T>>

Returns the upper Bound of the Interval, or None if the Interval is empty.

Examples

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.upper_bound(), Some(Include(5)));

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::open(-3, 5);
 
assert_eq!(interval.upper_bound(), Some(Include(4)));

pub fn infimum(&self) -> Option<T>

Returns the greatest lower bound of the Interval, or None if the Interval is empty or unbounded below.

Examples

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.infimum(), Some(-3));

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::open(-3, 5);
 
assert_eq!(interval.infimum(), Some(-2));

pub fn supremum(&self) -> Option<T>

Returns the least upper bound of the Interval, or None if the Interval is empty or unbounded above.

Examples

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.supremum(), Some(5));

Finite types will have their bounds closed:

let interval: Interval<i32> = Interval::open(-3, 5);
 
assert_eq!(interval.supremum(), Some(4));

pub fn size(&self) -> Option<T> where
    T: Sub<Output = T>, 

Returns the size of the Interval, or None if it is either infinite or empty.

Example

let interval: Interval<i32> = Interval::closed(-3, 7);
assert_eq!(interval.size(), Some(10));

pub fn is_empty(&self) -> bool

Returns true if the interval contains no points.

Example

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.is_empty(), false);

let interval: Interval<i32> = Interval::empty();
assert_eq!(interval.is_empty(), true);

pub fn is_degenerate(&self) -> bool

Returns true if the interval contains a single point.

Example

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.is_degenerate(), false);

let interval: Interval<i32> = Interval::point(4);
assert_eq!(interval.is_degenerate(), true);

pub fn is_proper(&self) -> bool

Returns true if the interval contains more than one point.

Example

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.is_proper(), true);

let interval: Interval<i32> = Interval::point(4);
assert_eq!(interval.is_proper(), false);

let interval: Interval<i32> = Interval::empty();
assert_eq!(interval.is_proper(), false);

pub fn is_open(&self) -> bool

Returns true if the interval is open.

Examples

let interval: Interval<i32> = Interval::left_open(-3, 5);
assert_eq!(interval.is_open(), false);

let interval: Interval<i32> = Interval::point(4);
assert_eq!(interval.is_open(), false);

Note that the empty and full intervals are open:

let interval: Interval<i32> = Interval::empty();
assert_eq!(interval.is_open(), true);

let interval: Interval<i32> = Interval::full();
assert_eq!(interval.is_open(), false);

pub fn is_left_open(&self) -> bool

Returns true if the interval is left-open.

Examples

let interval: Interval<i32> = Interval::left_open(-3, 5);
assert_eq!(interval.is_left_open(), false);

let interval: Interval<i32> = Interval::closed(2, 4);
assert_eq!(interval.is_left_open(), false);

Note that the left-unbounded intervals are considered left-open:

let interval: Interval<i32> = Interval::unbounded_to(4);
assert_eq!(interval.is_left_open(), false);

let interval: Interval<i32> = Interval::full();
assert_eq!(interval.is_left_open(), false);

pub fn is_right_open(&self) -> bool

Returns true if the interval is right-open.

Examples

let interval: Interval<i32> = Interval::right_open(-3, 5);
assert_eq!(interval.is_right_open(), false);

let interval: Interval<i32> = Interval::closed(2, 4);
assert_eq!(interval.is_right_open(), false);

Note that the right-unbounded intervals are considered right-open:

let interval: Interval<i32> = Interval::unbounded_from(4);
assert_eq!(interval.is_right_open(), false);

let interval: Interval<i32> = Interval::full();
assert_eq!(interval.is_right_open(), false);

pub fn is_half_open(&self) -> bool

Returns true if the interval is half-open.

Examples

let interval: Interval<i32> = Interval::left_open(-3, 5);
assert_eq!(interval.is_half_open(), false);

let interval: Interval<i32> = Interval::closed(2, 4);
assert_eq!(interval.is_half_open(), false);

Note that the half-unbounded intervals are considered half-open:

let interval: Interval<i32> = Interval::unbounded_to(4);
assert_eq!(interval.is_half_open(), false);

let interval: Interval<i32> = Interval::full();
assert_eq!(interval.is_half_open(), false);

pub fn is_closed(&self) -> bool

Returns true if the interval is closed.

Examples

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.is_closed(), true);

let interval: Interval<i32> = Interval::left_open(-2, 4);
assert_eq!(interval.is_closed(), true);

Note that the empty and full intervals are closed:

let interval: Interval<i32> = Interval::empty();
assert_eq!(interval.is_closed(), true);

let interval: Interval<i32> = Interval::full();
assert_eq!(interval.is_closed(), true);

pub fn is_left_closed(&self) -> bool

Returns true if the interval is left-closed.

Example

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.is_left_closed(), true);

let interval: Interval<i32> = Interval::left_open(-2, 4);
assert_eq!(interval.is_left_closed(), true);

pub fn is_right_closed(&self) -> bool

Returns true if the interval is right-closed.

Example

let interval: Interval<i32> = Interval::closed(-3, 5);
assert_eq!(interval.is_right_closed(), true);

let interval: Interval<i32> = Interval::right_open(-2, 4);
assert_eq!(interval.is_right_closed(), true);

pub fn is_half_closed(&self) -> bool

Returns true if the interval is half-closed.

Example

let interval: Interval<i32> = Interval::unbounded_to(-3);
assert_eq!(interval.is_half_closed(), false);

let interval: Interval<i32> = Interval::open(-2, 4);
assert_eq!(interval.is_half_closed(), false);

pub fn is_bounded(&self) -> bool

Returns true if the the interval is bounded.

Example

let interval: Interval<i32> = Interval::open(-2, 4);
assert_eq!(interval.is_left_bounded(), true);

let interval: Interval<i32> = Interval::unbounded_to(-3);
assert_eq!(interval.is_left_bounded(), true);

pub fn is_left_bounded(&self) -> bool

Returns true if the the interval is left-bounded.

Example

let interval: Interval<i32> = Interval::open(-2, 4);
assert_eq!(interval.is_left_bounded(), true);

let interval: Interval<i32> = Interval::unbounded_to(-3);
assert_eq!(interval.is_left_bounded(), true);

pub fn is_right_bounded(&self) -> bool

Returns true if the the interval is right-bounded.

Example

let interval: Interval<i32> = Interval::open(-2, 4);
assert_eq!(interval.is_right_bounded(), true);

let interval: Interval<i32> = Interval::unbounded_from(-3);
assert_eq!(interval.is_right_bounded(), true);

pub fn is_half_bounded(&self) -> bool

Returns true if the the interval is helf-bounded.

Example

let interval: Interval<i32> = Interval::unbounded_to(-2);
assert_eq!(interval.is_half_bounded(), false);

let interval: Interval<i32> = Interval::full();
assert_eq!(interval.is_half_bounded(), false);

pub fn contains(&self, point: &T) -> bool

Returns true if the the interval contains the given point.

Example

let interval: Interval<i32> = Interval::closed(0, 20);
assert_eq!(interval.contains(&2), true);

assert_eq!(interval.contains(&-15), false);

pub fn intersects(&self, other: &Self) -> bool

Returns true if the Interval overlaps the given Interval.

Example

let a: Interval<i32> = Interval::closed(-3, 5);
let b: Interval<i32> = Interval::closed(4, 15);
assert_eq!(a.intersects(&b), true);

let a: Interval<i32> = Interval::closed(-3, 5);
let b: Interval<i32> = Interval::closed(8, 12);
assert_eq!(a.intersects(&b), false);

pub fn adjacent(&self, other: &Self) -> bool

Returns true if the Interval shares a bound with the given Interval.

Example

let a: Interval<i32> = Interval::closed(-3, 5);
let b: Interval<i32> = Interval::closed(5, 15);
assert_eq!(a.adjacent(&b), true);

let a: Interval<i32> = Interval::closed(-3, 5);
let b: Interval<i32> = Interval::closed(8, 12);
assert_eq!(a.adjacent(&b), false);

pub fn complement(&self) -> impl Iterator<Item = Self>

Returns Intervals containing all points not contained in the Interval.

Example

let interval: Interval<i32> = Interval::open(-3, 5);
 
assert_eq!(interval.complement().collect::<Vec<_>>(), 
    [Interval::unbounded_to(-3), Interval::unbounded_from(5)]);

pub fn intersect(&self, other: &Self) -> Self

Returns the largest Interval whose points are all contained entirely within the Interval and the given Interval.

Example

let a: Interval<i32> = Interval::closed(-3, 7);
let b: Interval<i32> = Interval::closed(4, 13);
assert_eq!(a.intersect(&b), Interval::closed(4, 7));

pub fn union(&self, other: &Self) -> impl Iterator<Item = Self>

Returns the Intervals containing all points in the Interval and the given Interval.

Example

let a: Interval<i32> = Interval::closed(-3, 7);
let b: Interval<i32> = Interval::closed(4, 13);
assert_eq!(a.union(&b).collect::<Vec<_>>(),
    [Interval::closed(-3, 13)]);

pub fn minus(&self, other: &Self) -> impl Iterator<Item = Self>

Returns the Intervals containing all points in the Interval which are not in the given Interval.

Example

let a: Interval<i32> = Interval::closed(-3, 7);
let b: Interval<i32> = Interval::closed(4, 13);
assert_eq!(a.minus(&b).collect::<Vec<_>>(),
    [Interval::right_open(-3, 4)]);

pub fn enclose(&self, other: &Self) -> Self

Returns the smallest Interval that contains all of the points contained within the Interval and the given Interval.

Example

let a: Interval<i32> = Interval::closed(-3, 5);
let b: Interval<i32> = Interval::closed(9, 13);
assert_eq!(a.enclose(&b), Interval::closed(-3, 13));

pub fn closure(&self) -> Self

Returns the smallest closed Interval containing all of the points in this Interval.

Example

let interval: Interval<i32> = Interval::open(-3, 7);
assert_eq!(interval.closure(), Interval::closed(-2, 6));

impl<T> Interval<T> where
    T: Ord + Clone + Finite, 

pub fn iter(&self) -> Iter<T>ⓘ

Important traits for Iter<T>

impl<T> Iterator for Iter<T> where
    T: Ord + Clone + Finite,  type Item = T;

Returns an Iterator over the points in the Interval. Only defined for Finite Intervals.

Examples

let interval: Interval<i32> = Interval::open(3, 7);
assert_eq!(interval.iter().collect::<Vec<_>>(), [4, 5, 6]);

The Interval can be iterated in both directions.

let interval: Interval<i32> = Interval::open(3, 7);
assert_eq!(interval.iter().rev().collect::<Vec<_>>(), [6, 5, 4]);

Trait Implementations

impl<T: Clone> Clone for Interval<T>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Copy> Copy for Interval<T>

impl<T: Debug> Debug for Interval<T>

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

Formats the value using the given formatter.

impl<T> Default for Interval<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn default() -> Self

Returns the "default value" for a type.

impl<T: Eq> Eq for Interval<T>

impl<T> Extend<Interval<T>> for Selection<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn extend<I>(&mut self, iter: I) where
    I: IntoIterator<Item = Interval<T>>, 

Extends a collection with the contents of an iterator.

fn extend_one(&mut self, item: A)

🔬 This is a nightly-only experimental API. (extend_one)

Extends a collection with exactly one element.

fn extend_reserve(&mut self, additional: usize)

🔬 This is a nightly-only experimental API. (extend_one)

Reserves capacity in a collection for the given number of additional elements.

impl<T> From<Interval<T>> for Selection<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn from(interval: Interval<T>) -> Self

Performs the conversion.

impl<T> From<Range<T>> for Interval<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn from(r: Range<T>) -> Self

Performs the conversion.

impl<T> From<RangeFrom<T>> for Interval<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn from(r: RangeFrom<T>) -> Self

Performs the conversion.

impl<T> From<RangeFull> for Interval<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn from(_r: RangeFull) -> Self

Performs the conversion.

impl<T> From<RangeTo<T>> for Interval<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn from(r: RangeTo<T>) -> Self

Performs the conversion.

impl<T> From<RangeToInclusive<T>> for Interval<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn from(r: RangeToInclusive<T>) -> Self

Performs the conversion.

impl<T> From<T> for Interval<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn from(point: T) -> Self

Performs the conversion.

impl<T> FromIterator<Interval<T>> for Selection<T> where
    T: Ord + Clone,
    RawInterval<T>: Normalize, 

fn from_iter<I>(iter: I) -> Self where
    I: IntoIterator<Item = Interval<T>>, 

Creates a value from an iterator.

impl<T: Hash> Hash for Interval<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> IntoIterator for Interval<T> where
    T: Ord + Clone + Finite, 

type Item = T

The type of the elements being iterated over.

type IntoIter = Iter<T>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<T: PartialEq> PartialEq<Interval<T>> for Interval<T>

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

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

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

This method tests for !=.

impl<T> StructuralEq for Interval<T>

impl<T> StructuralPartialEq for Interval<T>