Function malachite_base::vecs::exhaustive::shortlex_unique_vecs

pub fn shortlex_unique_vecs<I: Clone + Iterator>(xs: I) -> ShortlexUniqueVecs<I> 
where
    I::Item: Clone,

Generates Vecs with elements from a single iterator, such that each Vec has no repeated elements.

The Vecs are generated in order of increasing length, and within each length they are ordered lexicographically with respect to the order of the element iterator.

The source iterator should not repeat any elements, but this is not enforced.

The iterator should be finite; if it is infinite, Vecs of length 2 and above will never be generated.

If the input iterator is infinite, the output length is also infinite.

If the input iterator length is $n$, the output length is $$ \sum_ {k=0}^n \frac{n!}{k!} $$ $$ = \begin{cases} 1 & \text{if} \quad n = 0, \\ 2 & \text{if} \quad n = 1, \\ \operatorname{round}(en!) & \text{otherwise}. \end{cases} $$

See https://oeis.org/A000522.

If xs is empty, the output consists of a single empty Vec.

Examples

use itertools::Itertools;
use malachite_base::vecs::exhaustive::shortlex_unique_vecs;

let xss = shortlex_unique_vecs(1..=4).take(20).collect_vec();
assert_eq!(
    xss.iter().map(Vec::as_slice).collect_vec().as_slice(),
    &[
        &[][..],
        &[1],
        &[2],
        &[3],
        &[4],
        &[1, 2],
        &[1, 3],
        &[1, 4],
        &[2, 1],
        &[2, 3],
        &[2, 4],
        &[3, 1],
        &[3, 2],
        &[3, 4],
        &[4, 1],
        &[4, 2],
        &[4, 3],
        &[1, 2, 3],
        &[1, 2, 4],
        &[1, 3, 2]
    ]
);