Crate sorted_iter

This crate provides set and relational operations for all iterators in the standard library that are known at compile time to be sorted.

Set operations

use sorted_iter::SortedIterator;

let primes = btreeset! { 2, 3, 5, 7, 11, 13u64 }.into_iter();
let fibs = btreeset! { 1, 2, 3, 5, 8, 13u64 }.into_iter();
let fib_primes = primes.intersection(fibs);

It is possible to efficiently define set operations on sorted iterators. Sorted iterators are very common in the standard library. E.g. the elements of a BTreeSet or the keys of a BTreeMap are guaranteed to be sorted according to the element order, as are iterable ranges like 0..100.

There are also a number of operations on iterators that preserve the sort order. E.g. if an iterator is sorted, take, take_while etc. are going to result in a sorted iterator as well.

Since the complete types of iterators are typically visible in rust, it is possible to encode these rules at type level. This is what this crate does.

For available set operations, see SortedIterator. For sorted iterators in the std lib, see instances the for SortedByItem marker trait.

Relational operations

use sorted_iter::SortedPairIterator;

let cities = btreemap! {
  1 => "New York",
  2 => "Tokyo",
  3u8 => "Berlin"
}.into_iter();
let countries = btreemap! {
  1 => "USA",
  2 => "Japan",
  3u8 => "Germany"
}.into_iter();
let cities_and_countries = cities.join(countries);

Iterators of pairs that are sorted according to the first element / key are also very common in the standard library and elsewhere. E.g. the elements of a BTreeMap are guaranteed to be sorted according to the key order.

The same rules as for sorted iterators apply for preservation of the sort order, except that there are some additional operations that preserve sort order. Anything that only operates on the value, like e.g. map or filter_map on the value, is guaranteed to preserve the sort order.

The operations that can be defined on sorted pair operations are the relational operations known from relational algebra / SQL, namely join, left_join, right_join and outer_join.

For available relational operations, see SortedPairIterator. For sorted iterators in the std lib, see instances the for SortedByKey marker trait.

Transformations that retain order are allowed

use sorted_iter::*;

let odd = (1..31).step_by(2);
let multiples_of_3 = (3..30).step_by(3);
let either = odd.union(multiples_of_3);

Transformations that can change the order lose the sorted property

use sorted_iter::*;

// we have no idea what map does to the order. could be anything!
let a = (1..31).map(|x| -x);
let b = (3..30).step_by(3);
let either = a.union(b); // does not compile!

Assuming sort ordering

For most std lib iterators, this library already provides instances. But there will occasionally be an iterator from a third party library where you know that it is properly sorted.

For this case, there is an escape hatch:

// the assume_ extensions have to be implicitly imported
use sorted_iter::*;
use sorted_iter::assume::*;
let odd = vec![1,3,5,7u8].into_iter().assume_sorted_by_item();
let even = vec![2,4,6,8u8].into_iter().assume_sorted_by_item();
let all = odd.union(even);

let cities = vec![(1u8, "New York")].into_iter().assume_sorted_by_key();
let countries = vec![(1u8, "USA")].into_iter().assume_sorted_by_key();
let cities_and_countries = cities.join(countries);

Marking your own iterators

If you have a library and want to mark some iterators as sorted, this is possible by implementing the appropriate marker trait, SortedByItem or SortedByKey.

// marker traits are not at top level, since usually you don't need them
use sorted_iter::sorted_iterator::SortedByItem;
use sorted_iter::sorted_pair_iterator::SortedByKey;

pub struct MySortedIter<T> { whatever: T }
pub struct MySortedPairIter<K, V> { whatever: (K, V) }

impl<T> SortedByItem for MySortedIter<T> {}
impl<K, V> SortedByKey for MySortedPairIter<K, V> {}

By reexporting the extension traits, you get a seamless experience for people using your library.

extern crate sorted_iter;
pub use sorted_iter::{SortedIterator, SortedPairIterator};

Tests

Tests are done using the fantastic quickcheck crate, by comparing against the operations defined on BTreeSet and BTreeMap.

Modules

assume	extension traits for unchecked conversions from iterators to sorted iterators
sorted_iterator	implementation of the sorted_iterator set operations
sorted_pair_iterator	implementation of the sorted_pair_iterator relational operations

Traits

SortedIterator	set operations for iterators where the items are sorted according to the natural order
SortedPairIterator	relational operations for iterators of pairs where the items are sorted according to the key

Functions

multiway_union

Union of multiple sorted iterators.