discreterangemap

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This crate provides [DiscreteRangeMap] and [DiscreteRangeSet], Data Structures for storing non-overlapping discrete intervals based off [BTreeMap].

You must implement Copy

Due to implementation complications with non-Copy types the datastructures currently require both the range type and the points the ranges are over to be Copy.

Example using an Inclusive-Exclusive range

```rust use discreterangemap::testranges::ie; use discreterange_map::DiscreteRangeMap;

let mut map = DiscreteRangeMap::new();

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

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

Example using a custom range type

```rust use discreterangemap::testranges::ie; use discreterange_map::{ DiscreteFinite, DiscreteFiniteBounds, DiscreteRangeMap, FiniteRange, };

[derive(Debug, Copy, Clone)]

enum Reservation { // Start, End (Inclusive-Exclusive) Finite(i8, i8), // Start (Inclusive-Forever) Infinite(i8), }

// First, we need to implement FiniteRange impl FiniteRange for Reservation { fn start(&self) -> i8 { match self { Reservation::Finite(start, ) => *start, Reservation::Infinite(start) => *start, } } fn end(&self) -> i8 { match self { //the end is exclusive so we take off 1 with checking //for compile time error overflow detection Reservation::Finite(, end) => end.down().unwrap(), Reservation::Infinite(_) => i8::MAX, } } }

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

// Next we can create a custom typed DiscreteRangeMap let reservationmap = DiscreteRangeMap::fromslicestrict([ (Reservation::Finite(10, 20), "Ferris".tostring()), (Reservation::Infinite(20), "Corro".to_string()), ]) .unwrap();

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

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

asserteq!( reservationmap.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 wether 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.

Finite-ness

This crate is also designed to work with [Finite] types since it is much easier to implement and it is not restrictive to users since you can still represent Infinite numbers in Finite types paradoxically using the concept of [Actual Infinity].

For example you could define Infinite for u8 as u8::MAX or if you still want to use u8::MAX as a Finite number you could define a wrapper type for u8 that adds an [Actual Infinity] value to the u8 set.

Invalid Ranges

Within this crate, not all ranges are considered valid ranges. The definition of the validity of a range used within this crate is that a range 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 range are those whose start values are greater than their end values. such as 5..2 or 100..=40.

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

| range | valid | | -------------------------------------- | ----- | | 0..=0 | YES | | 0..0 | NO | | 0..1 | YES | | 9..8 | NO | | (Bound::Exluded(3), Bound::Exluded(4)) | NO | | 400..=400 | YES |

Overlap

Two ranges are "overlapping" if there exists a point that is contained within both ranges.

Touching

Two ranges 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.

Merging

When a range "merges" other ranges it absorbs them to become larger.

Further Reading

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

Credit

I originally came up with the StartBound: [Ord] bodge on my own, however, I later stumbled across [rangemap] which also used a StartBound: [Ord] bodge. [rangemap] then became my main source of inspiration.

Later I then undid the [Ord] bodge and switched to my own full-code port of [BTreeMap], inspired and forked from [copse], for it's increased flexibility.

Origin

The aim for this library was to become a more generic superset of [rangemap], following from this issue and this pull request in which I changed [rangemap]'s [RangeMap] to use [RangeBounds]s as keys before I realized it might be easier and simpler to just write it all from scratch.

It is however worth noting the library eventually expanded and evolved from it's origins.

This crate was previously named [range_bounds_map].

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