### 12 releases

0.1.11 | May 16, 2023 |
---|---|

0.1.10 | Mar 29, 2023 |

0.1.8 | Nov 15, 2021 |

0.1.7 | Sep 9, 2020 |

0.1.5 | Nov 14, 2019 |

#**117** in Cryptography

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# Sorted Iter

# About

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``,` `13``u64` `}``.``into_iter``(``)``;`
`let` fibs `=` `btreeset!` `{` `1``,` `2``,` `3``,` `5``,` `8``,` `13``u64` `}``.``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`"``,`
`3``u8` `=>` `"`Berlin`"`
`}``.``into_iter``(``)``;`
`let` countries `=` `btreemap!` `{`
`1` `=>` `"`USA`"``,`
`2` `=>` `"`Japan`"``,`
`3``u8` `=>` `"`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``,``7``u8``]``.``into_iter``(``)``.``assume_sorted_by_item``(``)``;`
`let` even `=` `vec!``[``2``,``4``,``6``,``8``u8``]``.``into_iter``(``)``.``assume_sorted_by_item``(``)``;`
`let` all `=` odd`.``union``(`even`)``;`
`let` cities `=` `vec!``[``(``1``u8``,` `"`New York`"``)``]``.``into_iter``(``)``.``assume_sorted_by_key``(``)``;`
`let` countries `=` `vec!``[``(``1``u8``,` `"`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.