Function malachite_base::vecs::exhaustive::shortlex_vecs_from_length_iterator

pub const fn shortlex_vecs_from_length_iterator<T: Clone, I: Iterator<Item = u64>, J: Clone + Iterator<Item = T>>(
    xs: I,
    ys: J,
) -> ShortlexVecs<T, I, J> 

Generates all Vecs with elements from a specified iterator and with lengths from another iterator.

The length-generating iterator is xs, and the element-generating iterator is ys.

If the provided lengths are $\ell_0, \ell_1, \ell_2, \ldots$, then first all Vecs with length $\ell_0$ will be generated, in lexicographic order; then all Vecs with length $\ell_2$, and so on. If the lengths iterator has repetitions, then the generated Vecs will be repeated too.

ys must be finite; if it’s infinite, the output will never get past the first nonzero $\ell$.

There’s one quirk if ys is empty: then the iterator will stop as soon as it encounters a nonzero $\ell$, even if there are zeros later on. This prevents the iterator hanging when given an empty ys and lengths $0, 1, 2, \ldots$.

If ys is empty, the output length is the amount of zeros generated by xs before the first nonzero length. If ys is nonempty and xs is infinite, the output is infinite. Finally, if ys is nonempty and xs is finite, the output length is $$ \sum_{k=0}^{m-1} n^{\ell_k}, $$ where $n$ is ys.count() and $m$ is xs.count().

Examples

use itertools::Itertools;
use malachite_base::bools::exhaustive::exhaustive_bools;
use malachite_base::nevers::nevers;
use malachite_base::vecs::exhaustive::shortlex_vecs_from_length_iterator;

let xss = shortlex_vecs_from_length_iterator([2, 1, 2].iter().cloned(), exhaustive_bools())
    .collect_vec();
assert_eq!(
    xss.iter().map(Vec::as_slice).collect_vec().as_slice(),
    &[
        &[false, false][..],
        &[false, true],
        &[true, false],
        &[true, true],
        &[false],
        &[true],
        &[false, false],
        &[false, true],
        &[true, false],
        &[true, true]
    ]
);

let xss =
    shortlex_vecs_from_length_iterator([0, 0, 1, 0].iter().cloned(), nevers()).collect_vec();
// Stops after first empty ys
assert_eq!(
    xss.iter().map(Vec::as_slice).collect_vec().as_slice(),
    &[&[], &[]]
);