1use alloc::vec::Vec;
2use core::cmp::Ordering;
3
4/// Consumes a given iterator, returning the minimum elements in **ascending** order.
5pub(crate) fn k_smallest_general<I, F>(iter: I, k: usize, mut comparator: F) -> Vec<I::Item>
6where
7 I: Iterator,
8 F: FnMut(&I::Item, &I::Item) -> Ordering,
9{
10 /// Sift the element currently at `origin` away from the root until it is properly ordered.
11 ///
12 /// This will leave **larger** elements closer to the root of the heap.
13 fn sift_down<T, F>(heap: &mut [T], is_less_than: &mut F, mut origin: usize)
14 where
15 F: FnMut(&T, &T) -> bool,
16 {
17 #[inline]
18 fn children_of(n: usize) -> (usize, usize) {
19 (2 * n + 1, 2 * n + 2)
20 }
21
22 while origin < heap.len() {
23 let (left_idx, right_idx) = children_of(origin);
24 if left_idx >= heap.len() {
25 return;
26 }
27
28 let replacement_idx =
29 if right_idx < heap.len() && is_less_than(&heap[left_idx], &heap[right_idx]) {
30 right_idx
31 } else {
32 left_idx
33 };
34
35 if is_less_than(&heap[origin], &heap[replacement_idx]) {
36 heap.swap(origin, replacement_idx);
37 origin = replacement_idx;
38 } else {
39 return;
40 }
41 }
42 }
43
44 if k == 0 {
45 iter.last();
46 return Vec::new();
47 }
48 if k == 1 {
49 return iter.min_by(comparator).into_iter().collect();
50 }
51 let mut iter = iter.fuse();
52 let mut storage: Vec<I::Item> = iter.by_ref().take(k).collect();
53
54 let mut is_less_than = move |a: &_, b: &_| comparator(a, b) == Ordering::Less;
55
56 // Rearrange the storage into a valid heap by reordering from the second-bottom-most layer up to the root.
57 // Slightly faster than ordering on each insert, but only by a factor of lg(k).
58 // The resulting heap has the **largest** item on top.
59 for i in (0..=(storage.len() / 2)).rev() {
60 sift_down(&mut storage, &mut is_less_than, i);
61 }
62
63 iter.for_each(|val| {
64 debug_assert_eq!(storage.len(), k);
65 if is_less_than(&val, &storage[0]) {
66 // Treating this as an push-and-pop saves having to write a sift-up implementation.
67 // https://en.wikipedia.org/wiki/Binary_heap#Insert_then_extract
68 storage[0] = val;
69 // We retain the smallest items we've seen so far, but ordered largest first so we can drop the largest efficiently.
70 sift_down(&mut storage, &mut is_less_than, 0);
71 }
72 });
73
74 // Ultimately the items need to be in least-first, strict order, but the heap is currently largest-first.
75 // To achieve this, repeatedly,
76 // 1) "pop" the largest item off the heap into the tail slot of the underlying storage,
77 // 2) shrink the logical size of the heap by 1,
78 // 3) restore the heap property over the remaining items.
79 let mut heap = &mut storage[..];
80 while heap.len() > 1 {
81 let last_idx = heap.len() - 1;
82 heap.swap(0, last_idx);
83 // Sifting over a truncated slice means that the sifting will not disturb already popped elements.
84 heap = &mut heap[..last_idx];
85 sift_down(heap, &mut is_less_than, 0);
86 }
87
88 storage
89}
90
91#[inline]
92pub(crate) fn key_to_cmp<T, K, F>(mut key: F) -> impl FnMut(&T, &T) -> Ordering
93where
94 F: FnMut(&T) -> K,
95 K: Ord,
96{
97 move |a: &T, b: &T| key(a).cmp(&key(b))
98}
99