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use std::fmt;
use std::iter::FusedIterator;
use super::lazy_buffer::LazyBuffer;
use alloc::vec::Vec;
use crate::adaptors::checked_binomial;
/// An iterator to iterate through all the `k`-length combinations in an iterator.
///
/// See [`.combinations()`](crate::Itertools::combinations) for more information.
#[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
pub struct Combinations<I: Iterator> {
indices: Vec<usize>,
pool: LazyBuffer<I>,
first: bool,
}
impl<I> Clone for Combinations<I>
where
I: Clone + Iterator,
I::Item: Clone,
{
clone_fields!(indices, pool, first);
}
impl<I> fmt::Debug for Combinations<I>
where
I: Iterator + fmt::Debug,
I::Item: fmt::Debug,
{
debug_fmt_fields!(Combinations, indices, pool, first);
}
/// Create a new `Combinations` from a clonable iterator.
pub fn combinations<I>(iter: I, k: usize) -> Combinations<I>
where
I: Iterator,
{
Combinations {
indices: (0..k).collect(),
pool: LazyBuffer::new(iter),
first: true,
}
}
impl<I: Iterator> Combinations<I> {
/// Returns the length of a combination produced by this iterator.
#[inline]
pub fn k(&self) -> usize {
self.indices.len()
}
/// Returns the (current) length of the pool from which combination elements are
/// selected. This value can change between invocations of [`next`](Combinations::next).
#[inline]
pub fn n(&self) -> usize {
self.pool.len()
}
/// Returns a reference to the source pool.
#[inline]
pub(crate) fn src(&self) -> &LazyBuffer<I> {
&self.pool
}
/// Resets this `Combinations` back to an initial state for combinations of length
/// `k` over the same pool data source. If `k` is larger than the current length
/// of the data pool an attempt is made to prefill the pool so that it holds `k`
/// elements.
pub(crate) fn reset(&mut self, k: usize) {
self.first = true;
if k < self.indices.len() {
self.indices.truncate(k);
for i in 0..k {
self.indices[i] = i;
}
} else {
for i in 0..self.indices.len() {
self.indices[i] = i;
}
self.indices.extend(self.indices.len()..k);
self.pool.prefill(k);
}
}
pub(crate) fn n_and_count(self) -> (usize, usize) {
let Self {
indices,
pool,
first,
} = self;
let n = pool.count();
(n, remaining_for(n, first, &indices).unwrap())
}
}
impl<I> Iterator for Combinations<I>
where
I: Iterator,
I::Item: Clone,
{
type Item = Vec<I::Item>;
fn next(&mut self) -> Option<Self::Item> {
if self.first {
self.pool.prefill(self.k());
if self.k() > self.n() {
return None;
}
self.first = false;
} else if self.indices.is_empty() {
return None;
} else {
// Scan from the end, looking for an index to increment
let mut i: usize = self.indices.len() - 1;
// Check if we need to consume more from the iterator
if self.indices[i] == self.pool.len() - 1 {
self.pool.get_next(); // may change pool size
}
while self.indices[i] == i + self.pool.len() - self.indices.len() {
if i > 0 {
i -= 1;
} else {
// Reached the last combination
return None;
}
}
// Increment index, and reset the ones to its right
self.indices[i] += 1;
for j in i + 1..self.indices.len() {
self.indices[j] = self.indices[j - 1] + 1;
}
}
// Create result vector based on the indices
Some(self.indices.iter().map(|i| self.pool[*i].clone()).collect())
}
fn size_hint(&self) -> (usize, Option<usize>) {
let (mut low, mut upp) = self.pool.size_hint();
low = remaining_for(low, self.first, &self.indices).unwrap_or(usize::MAX);
upp = upp.and_then(|upp| remaining_for(upp, self.first, &self.indices));
(low, upp)
}
#[inline]
fn count(self) -> usize {
self.n_and_count().1
}
}
impl<I> FusedIterator for Combinations<I>
where
I: Iterator,
I::Item: Clone,
{
}
/// For a given size `n`, return the count of remaining combinations or None if it would overflow.
fn remaining_for(n: usize, first: bool, indices: &[usize]) -> Option<usize> {
let k = indices.len();
if n < k {
Some(0)
} else if first {
checked_binomial(n, k)
} else {
// https://en.wikipedia.org/wiki/Combinatorial_number_system
// http://www.site.uottawa.ca/~lucia/courses/5165-09/GenCombObj.pdf
// 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 strictly monotonically sorted, this means we can effectively choose k values
// from (n - 1 - indices[0]), leading to binomial(n - 1 - indices[0], k) possibilities.
// - The subsequent combinations with same indices[0], but differing indices[1]:
// Here we can choose k - 1 values from (n - 1 - indices[1]) values,
// leading to binomial(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 from (n - 1 - indices[i]) values: binomial(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(checked_binomial(n - 1 - *n0, k - i)?)
})
}
}