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use alloc::boxed::Box;
use std::fmt;
use std::iter::FusedIterator;
use super::lazy_buffer::LazyBuffer;
use crate::adaptors::checked_binomial;
use crate::combinations::PoolIndex;
/// An iterator to iterate through all the `n`-length combinations in an iterator, with replacement.
///
/// See [`.combinations_with_replacement()`](crate::Itertools::combinations_with_replacement)
/// for more information.
#[derive(Clone)]
#[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
pub struct CombinationsWithReplacementGeneric<I, Idx>
where
I: Iterator,
I::Item: Clone,
{
indices: Idx,
pool: LazyBuffer<I>,
first: bool,
}
/// Iterator for `Box<[I]>` valued combinations_with_replacement returned by [`.combinations_with_replacement()`](crate::Itertools::combinations_with_replacement)
pub type CombinationsWithReplacement<I> = CombinationsWithReplacementGeneric<I, Box<[usize]>>;
/// Iterator for const generic combinations_with_replacement returned by [`.array_combinations_with_replacement()`](crate::Itertools::array_combinations_with_replacement)
pub type ArrayCombinationsWithReplacement<I, const K: usize> =
CombinationsWithReplacementGeneric<I, [usize; K]>;
impl<I, Idx> fmt::Debug for CombinationsWithReplacementGeneric<I, Idx>
where
I: Iterator + fmt::Debug,
I::Item: fmt::Debug + Clone,
Idx: fmt::Debug,
{
debug_fmt_fields!(CombinationsWithReplacementGeneric, indices, pool, first);
}
/// Create a new `ArrayCombinationsWithReplacement`` from a cloneable iterator.
pub fn array_combinations_with_replacement<I: Iterator, const K: usize>(
iter: I,
) -> ArrayCombinationsWithReplacement<I, K>
where
I::Item: Clone,
{
ArrayCombinationsWithReplacement::new(iter, [0; K])
}
/// Create a new `CombinationsWithReplacement` from a cloneable iterator.
pub fn combinations_with_replacement<I>(iter: I, k: usize) -> CombinationsWithReplacement<I>
where
I: Iterator,
I::Item: Clone,
{
let indices = alloc::vec![0; k].into_boxed_slice();
CombinationsWithReplacementGeneric::new(iter, indices)
}
impl<I: Iterator, Idx: PoolIndex<I::Item>> CombinationsWithReplacementGeneric<I, Idx>
where
I: Iterator,
I::Item: Clone,
{
/// Increments indices representing the combination to advance to the next
/// (in lexicographic order by increasing sequence) combination.
///
/// Returns true if we've run out of combinations, false otherwise.
fn increment_indices(&mut self) -> bool {
// Check if we need to consume more from the iterator
// This will run while we increment our first index digit
self.pool.get_next();
// Work out where we need to update our indices
let mut increment = None;
let indices: &mut [usize] = self.indices.borrow_mut();
for (i, indices_int) in indices.iter().enumerate().rev() {
if *indices_int < self.pool.len() - 1 {
increment = Some((i, indices_int + 1));
break;
}
}
match increment {
// If we can update the indices further
Some((increment_from, increment_value)) => {
// We need to update the rightmost non-max value
// and all those to the right
indices[increment_from..].fill(increment_value);
false
}
// Otherwise, we're done
None => true,
}
}
/// Constructor with arguments the inner iterator and the initial state for the indices.
fn new(iter: I, indices: Idx) -> Self {
Self {
indices,
pool: LazyBuffer::new(iter),
first: true,
}
}
}
impl<I, Idx> Iterator for CombinationsWithReplacementGeneric<I, Idx>
where
I: Iterator,
I::Item: Clone,
Idx: PoolIndex<I::Item>,
{
type Item = Idx::Item;
fn next(&mut self) -> Option<Self::Item> {
if self.first {
// In empty edge cases, stop iterating immediately
if !(self.indices.borrow().is_empty() || self.pool.get_next()) {
return None;
}
self.first = false;
} else if self.increment_indices() {
return None;
}
Some(self.indices.extract_item(&self.pool))
}
fn nth(&mut self, n: usize) -> Option<Self::Item> {
if self.first {
// In empty edge cases, stop iterating immediately
if !(self.indices.borrow().is_empty() || self.pool.get_next()) {
return None;
}
self.first = false;
} else if self.increment_indices() {
return None;
}
for _ in 0..n {
if self.increment_indices() {
return None;
}
}
Some(self.indices.extract_item(&self.pool))
}
fn size_hint(&self) -> (usize, Option<usize>) {
let (mut low, mut upp) = self.pool.size_hint();
low = remaining_for(low, self.first, self.indices.borrow()).unwrap_or(usize::MAX);
upp = upp.and_then(|upp| remaining_for(upp, self.first, self.indices.borrow()));
(low, upp)
}
fn count(self) -> usize {
let Self {
indices,
pool,
first,
} = self;
let n = pool.count();
remaining_for(n, first, indices.borrow()).unwrap()
}
}
impl<I, Idx> FusedIterator for CombinationsWithReplacementGeneric<I, Idx>
where
I: Iterator,
I::Item: Clone,
Idx: PoolIndex<I::Item>,
{
}
/// For a given size `n`, return the count of remaining combinations with replacement or None if it would overflow.
fn remaining_for(n: usize, first: bool, indices: &[usize]) -> Option<usize> {
// With a "stars and bars" representation, choose k values with replacement from n values is
// like choosing k out of k + n − 1 positions (hence binomial(k + n - 1, k) possibilities)
// to place k stars and therefore n - 1 bars.
// Example (n=4, k=6): ***|*||** represents [0,0,0,1,3,3].
let count = |n: usize, k: usize| {
let positions = if n == 0 {
k.saturating_sub(1)
} else {
(n - 1).checked_add(k)?
};
checked_binomial(positions, k)
};
let k = indices.len();
if first {
count(n, k)
} else {
// The algorithm is similar to the one for combinations *without replacement*,
// except we choose values *with replacement* and indices are *non-strictly* monotonically sorted.
// The combinations generated after the current one can be counted by counting as follows:
// - The subsequent combinations that differ in indices[0]:
// If subsequent combinations differ in indices[0], then their value for indices[0]
// must be at least 1 greater than the current indices[0].
// As indices is monotonically sorted, this means we can effectively choose k values with
// replacement from (n - 1 - indices[0]), leading to count(n - 1 - indices[0], k) possibilities.
// - The subsequent combinations with same indices[0], but differing indices[1]:
// Here we can choose k - 1 values with replacement from (n - 1 - indices[1]) values,
// leading to count(n - 1 - indices[1], k - 1) possibilities.
// - (...)
// - The subsequent combinations with same indices[0..=i], but differing indices[i]:
// Here we can choose k - i values with replacement from (n - 1 - indices[i]) values: count(n - 1 - indices[i], k - i).
// Since subsequent combinations can in any index, we must sum up the aforementioned binomial coefficients.
// Below, `n0` resembles indices[i].
indices.iter().enumerate().try_fold(0usize, |sum, (i, n0)| {
sum.checked_add(count(n - 1 - *n0, k - i)?)
})
}
}