Function malachite_base::sets::exhaustive::shortlex_hash_sets_min_length

pub fn shortlex_hash_sets_min_length<I: Clone + Iterator>(
    min_length: u64,
    xs: I,
) -> ShortlexOrderedUniqueCollections<I, HashSet<I::Item>> 
where
    I::Item: Clone + Eq + Hash,

Generates HashSets with a mininum length, with elements from a single iterator.

The HashSets 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, HashSets of length \max(2, \ell + 1) and above will never be generated.

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

If the input iterator length is $n$ and the min_length is $\ell$, the output length is $$ \sum_{i=\ell}^n \binom{n}{i}. $$

Examples

use itertools::Itertools;
use malachite_base::sets::exhaustive::shortlex_hash_sets_min_length;
use maplit::hashset;

let xss = shortlex_hash_sets_min_length(2, 1..=4).collect_vec();
assert_eq!(
    xss,
    &[
        hashset! {1, 2},
        hashset! {1, 3},
        hashset! {1, 4},
        hashset! {2, 3},
        hashset! {2, 4},
        hashset! {3, 4},
        hashset! {1, 2, 3},
        hashset! {1, 2, 4},
        hashset! {1, 3, 4},
        hashset! {2, 3, 4},
        hashset! {1, 2, 3, 4}
    ]
);