nodit

This crate provides Discrete Interval Tree Data-Structures, which are based off BTreeMap.

no_std is supported and should work with the default features.

Several Discrete Interval Tree data-structures have been implemented, here is a brief summary of each of them and why you might use them:

Struct	Abbreviation	Use-Case
NoditMap	Non-Overlapping Discrete Interval Tree Map	General purpose way of associating data with intervals that do not overlap
NoditSet	Non-Overlapping Discrete Interval Tree Set	Useful for when you want to store intervals but don't want/need to associate data with each interval
ZosditMap	Zero-Overlap Sequential Discrete Interval Tree Map	Useful for time-graph traversal algorithms and possibly other things
Gqdit	Gap-Query Discrete Interval Tree	Useful for when you have a set of different non-overlapping intervals and want to perform efficient gap-query searches over all the sets of intervals

Copy is partially required

Due to implementation complications with non-Copy types the data-structures currently require both the interval type and the points the intervals are over to be Copy. However, the value type used when using the NoditMap does not have to be Copy. In fact the only required traits on the value type are sometimes Clone or Eq but only for some methods so if in doubt check a methods trait bounds.

Example using an Inclusive-Exclusive interval

use nodit::interval::ie;
use nodit::NoditMap;

let mut map = NoditMap::new();

map.insert_strict(ie(0, 5), true);
map.insert_strict(ie(5, 10), false);

assert_eq!(map.overlaps(ie(-2, 12)), true);
assert_eq!(map.contains_point(20), false);
assert_eq!(map.contains_point(5), true);

Example using a custom interval type

use std::ops::{Bound, RangeBounds};

use nodit::interval::ie;
use nodit::{
	DiscreteFinite, InclusiveInterval, Interval, NoditMap,
};

#[derive(Debug, Copy, Clone)]
enum Reservation {
	// Start, End (Inclusive-Inclusive)
	Finite(i8, i8),
	// Start (Inclusive-Infinity)
	Infinite(i8),
}

// First, we need to implement InclusiveInterval
impl InclusiveInterval<i8> for Reservation {
	fn start(&self) -> i8 {
		match self {
			Reservation::Finite(start, _) => *start,
			Reservation::Infinite(start) => *start,
		}
	}
	fn end(&self) -> i8 {
		match self {
			Reservation::Finite(_, end) => *end,
			Reservation::Infinite(_) => i8::MAX,
		}
	}
}

// Second, we need to implement From<Interval<i8>>
impl From<Interval<i8>> for Reservation {
	fn from(value: Interval<i8>) -> Self {
		if value.end() == i8::MAX {
			Reservation::Infinite(value.start())
		} else {
			Reservation::Finite(
				value.start(),
				value.end().up().unwrap(),
			)
		}
	}
}

// Next we can create a custom typed NoditMap
let reservation_map = NoditMap::from_slice_strict([
	(Reservation::Finite(10, 20), "Ferris".to_string()),
	(Reservation::Infinite(21), "Corro".to_string()),
])
.unwrap();

for (reservation, name) in reservation_map.overlapping(ie(16, 17))
{
	println!(
		"{name} has reserved {reservation:?} inside the interval 16..17"
	);
}

for (reservation, name) in reservation_map.iter() {
	println!("{name} has reserved {reservation:?}");
}

assert_eq!(
	reservation_map.overlaps(Reservation::Infinite(0)),
	true
);

Key Understandings and Philosophies

Discrete-ness

This crate is designed to work with Discrete types as compared to Continuous types. For example, u8 is a Discrete type, but String is a Continuous if you try to parse it as a decimal value.

The reason for this is that common interval-Mathematics operations differ depending on whether the underlying type is Discrete or Continuous. For example 5..=6 touches 7..=8 since integers are Discrete but 5.0..=6.0 does not touch 7.0..=8.0 since the value 6.5 exists.

Importantly, this also makes Inclusive/Exclusive ended intervals really easy to work with as they can be losslessly converted between one another. For example, 3..6 is equivalent to 3..=5.

Finite-ness

At the moment this crate is also designed to work only with Finite types such as u8 or i128, but not with Infinite types such as BigInt from the num_bigint crate. This is because the get_key_value_at_point() method would not be able to return anything from an empty map if the type was an infinite type such as BigInt since it has no maximum value.

A handy trick you can use to pretend to have infinite types when you don't expect to reach to top end of your type is to use Actual Infinity to pretend you have an Infinity. For example, if you were using u8 as your point type then you could create a wrapper type such as this:

use std::cmp::Ordering;

use nodit::DiscreteFinite;

#[derive(Debug, Clone, Copy, PartialEq, Eq)]
enum WithInfinity<T> {
	Finite(T),
	Infinity,
}

impl<T> Ord for WithInfinity<T>
where
	T: Ord,
{
	fn cmp(&self, other: &Self) -> Ordering {
		match (self, other) {
			(
				WithInfinity::Finite(x),
				WithInfinity::Finite(y),
			) => x.cmp(y),
			(WithInfinity::Finite(_), WithInfinity::Infinity) => {
				Ordering::Less
			}
			(WithInfinity::Infinity, WithInfinity::Finite(_)) => {
				Ordering::Greater
			}
			(WithInfinity::Infinity, WithInfinity::Infinity) => {
				Ordering::Equal
			}
		}
	}
}

impl<T> PartialOrd for WithInfinity<T>
where
	T: Ord,
{
	fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
		Some(self.cmp(other))
	}
}

impl<T> DiscreteFinite for WithInfinity<T>
where
	T: DiscreteFinite,
{
	const MIN: Self = WithInfinity::Finite(T::MIN);
	const MAX: Self = WithInfinity::Infinity;

	fn up(self) -> Option<Self>
	where
		Self: Sized,
	{
		match self {
			WithInfinity::Finite(x) => match x.up() {
				Some(y) => Some(WithInfinity::Finite(y)),
				None => Some(WithInfinity::Infinity),
			},
			WithInfinity::Infinity => None,
		}
	}
	fn down(self) -> Option<Self>
	where
		Self: Sized,
	{
		match self {
			WithInfinity::Finite(x) => {
				Some(WithInfinity::Finite(x.down()?))
			}
			WithInfinity::Infinity => {
				Some(WithInfinity::Finite(T::MAX))
			}
		}
	}
}

// And then you this means you can be explicit with when
// Infinity is encountered such as when it might be
// returned by `get_key_value_at_point()`, for example:

use nodit::interval::uu;
use nodit::{Interval, NoditMap};

let map: NoditMap<
	WithInfinity<u8>,
	Interval<WithInfinity<u8>>,
	bool,
> = NoditMap::new();

let mut gap = map.get_key_value_at_point(WithInfinity::Finite(4));

assert_eq!(gap, Err(uu()));

Invalid Intervals

Within this crate, not all intervals are considered valid intervals. The definition of the validity of a interval used within this crate is that a interval is only valid if it contains at least one value of the underlying domain.

For example, 4..6 is considered valid as it contains the values 4 and 5, however, 4..4 is considered invalid as it contains no values. Another example of invalid interval are those whose start values are greater than their end values. such as 5..2 or 100..=40.

Here are a few examples of intervals and whether they are valid:

interval	valid
0..=0	YES
0..0	NO
0..1	YES
9..8	NO
(Bound::Excluded(3), Bound::Excluded(4))	NO
400..=400	YES

Overlap

Two intervals are "overlapping" if there exists a point that is contained within both intervals. For example, 2..4 and 2..6 overlap but 2..4 and 4..8 do not.

Touching

Two intervals are "touching" if they do not overlap and there exists no value between them. For example, 2..4 and 4..6 are touching but 2..4 and 6..8 are not, neither are 2..6 and 4..8.

Further Reading

See Wikipedia's article on mathematical Intervals: https://en.wikipedia.org/wiki/Interval_(mathematics)

Features

Feature Name	Description
default	The implicit default feature enabled by default which currently does not activate any other features
serde	Enables the optional serde dependency and implements serde::Serialize and serde::Deserialize on all the types in this crate

Credit

Lots of my inspiration came from the rangemap crate.

The BTreeMap implementation (btree_monstrousity) used under the hood was inspired and forked from the copse crate.

Name Changes

This crate was previously named range_bounds_map it was renamed around about 2023-04-24 to discrete_range_map due to it no longer being an accurate name.

This crate was renamed again on 2023-01-02 from discrete_range_map to nodit for a similar reason, hopefully given the abstractness of the new name it will never need to change again.

Similar Crates

Here are some relevant crates I found whilst searching around the topic area, beware my biases when reading:

• https://docs.rs/rangemap Very similar to this crate but can only use std Ranges and RangeInclusives as keys in it's map and set structs (separately).
• https://docs.rs/btree-range-map
• https://docs.rs/ranges Cool library for fully-generic ranges (unlike std::ops ranges), along with a Ranges data-structure for storing them (Vec-based unfortunately)
• https://docs.rs/intervaltree Allows overlapping intervals but is immutable unfortunately
• https://docs.rs/nonoverlapping_interval_tree Very similar to rangemap except without a gaps() function and only for Ranges and not RangeInclusives. And also no fancy merging functions.
• https://docs.rs/unbounded-interval-tree A data structure based off of a 2007 published paper! It supports any range as keys, unfortunately, it is implemented with a non-balancing Box<Node> based tree, however it also supports overlapping ranges which my library does not.
• https://docs.rs/rangetree I'm not entirely sure what this library is or isn't, but it looks like a custom red-black tree/BTree implementation used specifically for a Range Tree. Interesting but also quite old (5 years) and uses unsafe.
• https://docs.rs/rust-lapper Another sort-of immutable (can insert but its very expensive) interval data-structure optimised for lots of intervals of the same size such as their staple use-case of genomic datasets.
• https://docs.rs/store-interval-tree An interval tree very similar to this crate and rangemap with many of the same methods (and lots of doc examples!) except using a custom in-house self-balancing tree implementation. It is not exactly clear from my reading of the docs whether they support overlapping intervals or not. On the one hand their examples show overlapping intervals but then their insert() method says "if interval already exists, interval will be ignored", so perhaps it allows overlapping but not duplicate intervals? A bit of an odd choice in my opinion.
• https://docs.rs/bio and https://docs.rs/rudac Both essentially identical to store-interval-tree as it looks like store-interval-tree is a fork of rudac's interval tree. bio in particular seems targeted at bio-infographics.