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//! A priority queue implemented with a binary heap.
//!
//! Insertion and popping the largest element have `O(log n)` time complexity. Checking the largest
//! / smallest element is `O(1)`.
// TODO not yet implemented
// Converting a vector to a binary heap can be done in-place, and has `O(n)` complexity. A binary
// heap can also be converted to a sorted vector in-place, allowing it to be used for an `O(n log
// n)` in-place heapsort.
use core::{
cmp::Ordering,
fmt,
marker::PhantomData,
mem::{self, ManuallyDrop},
ops::{Deref, DerefMut},
ptr, slice,
};
use crate::vec::Vec;
/// Min-heap
pub enum Min {}
/// Max-heap
pub enum Max {}
/// The binary heap kind: min-heap or max-heap
pub trait Kind: private::Sealed {
#[doc(hidden)]
fn ordering() -> Ordering;
}
impl Kind for Min {
fn ordering() -> Ordering {
Ordering::Less
}
}
impl Kind for Max {
fn ordering() -> Ordering {
Ordering::Greater
}
}
/// Sealed traits
mod private {
pub trait Sealed {}
}
impl private::Sealed for Max {}
impl private::Sealed for Min {}
/// A priority queue implemented with a binary heap.
///
/// This can be either a min-heap or a max-heap.
///
/// It is a logic error for an item to be modified in such a way that the item's ordering relative
/// to any other item, as determined by the `Ord` trait, changes while it is in the heap. This is
/// normally only possible through `Cell`, `RefCell`, global state, I/O, or unsafe code.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
///
/// // We can use peek to look at the next item in the heap. In this case,
/// // there's no items in there yet so we get None.
/// assert_eq!(heap.peek(), None);
///
/// // Let's add some scores...
/// heap.push(1).unwrap();
/// heap.push(5).unwrap();
/// heap.push(2).unwrap();
///
/// // Now peek shows the most important item in the heap.
/// assert_eq!(heap.peek(), Some(&5));
///
/// // We can check the length of a heap.
/// assert_eq!(heap.len(), 3);
///
/// // We can iterate over the items in the heap, although they are returned in
/// // a random order.
/// for x in &heap {
/// println!("{}", x);
/// }
///
/// // If we instead pop these scores, they should come back in order.
/// assert_eq!(heap.pop(), Some(5));
/// assert_eq!(heap.pop(), Some(2));
/// assert_eq!(heap.pop(), Some(1));
/// assert_eq!(heap.pop(), None);
///
/// // We can clear the heap of any remaining items.
/// heap.clear();
///
/// // The heap should now be empty.
/// assert!(heap.is_empty())
/// ```
pub struct BinaryHeap<T, K, const N: usize> {
pub(crate) _kind: PhantomData<K>,
pub(crate) data: Vec<T, N>,
}
impl<T, K, const N: usize> BinaryHeap<T, K, N> {
/* Constructors */
/// Creates an empty BinaryHeap as a $K-heap.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// // allocate the binary heap on the stack
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
/// heap.push(4).unwrap();
///
/// // allocate the binary heap in a static variable
/// static mut HEAP: BinaryHeap<i32, Max, 8> = BinaryHeap::new();
/// ```
pub const fn new() -> Self {
Self {
_kind: PhantomData,
data: Vec::new(),
}
}
}
impl<T, K, const N: usize> BinaryHeap<T, K, N>
where
T: Ord,
K: Kind,
{
/* Public API */
/// Returns the capacity of the binary heap.
pub fn capacity(&self) -> usize {
self.data.capacity()
}
/// Drops all items from the binary heap.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
/// heap.push(1).unwrap();
/// heap.push(3).unwrap();
///
/// assert!(!heap.is_empty());
///
/// heap.clear();
///
/// assert!(heap.is_empty());
/// ```
pub fn clear(&mut self) {
self.data.clear()
}
/// Returns the length of the binary heap.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
/// heap.push(1).unwrap();
/// heap.push(3).unwrap();
///
/// assert_eq!(heap.len(), 2);
/// ```
pub fn len(&self) -> usize {
self.data.len()
}
/// Checks if the binary heap is empty.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
///
/// assert!(heap.is_empty());
///
/// heap.push(3).unwrap();
/// heap.push(5).unwrap();
/// heap.push(1).unwrap();
///
/// assert!(!heap.is_empty());
/// ```
pub fn is_empty(&self) -> bool {
self.len() == 0
}
/// Returns an iterator visiting all values in the underlying vector, in arbitrary order.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
/// heap.push(1).unwrap();
/// heap.push(2).unwrap();
/// heap.push(3).unwrap();
/// heap.push(4).unwrap();
///
/// // Print 1, 2, 3, 4 in arbitrary order
/// for x in heap.iter() {
/// println!("{}", x);
///
/// }
/// ```
pub fn iter(&self) -> slice::Iter<'_, T> {
self.data.as_slice().iter()
}
/// Returns a mutable iterator visiting all values in the underlying vector, in arbitrary order.
///
/// **WARNING** Mutating the items in the binary heap can leave the heap in an inconsistent
/// state.
pub fn iter_mut(&mut self) -> slice::IterMut<'_, T> {
self.data.as_mut_slice().iter_mut()
}
/// Returns the *top* (greatest if max-heap, smallest if min-heap) item in the binary heap, or
/// None if it is empty.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
/// assert_eq!(heap.peek(), None);
///
/// heap.push(1).unwrap();
/// heap.push(5).unwrap();
/// heap.push(2).unwrap();
/// assert_eq!(heap.peek(), Some(&5));
/// ```
pub fn peek(&self) -> Option<&T> {
self.data.as_slice().get(0)
}
/// Returns a mutable reference to the greatest item in the binary heap, or
/// `None` if it is empty.
///
/// Note: If the `PeekMut` value is leaked, the heap may be in an
/// inconsistent state.
///
/// # Examples
///
/// Basic usage:
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
/// assert!(heap.peek_mut().is_none());
///
/// heap.push(1);
/// heap.push(5);
/// heap.push(2);
/// {
/// let mut val = heap.peek_mut().unwrap();
/// *val = 0;
/// }
///
/// assert_eq!(heap.peek(), Some(&2));
/// ```
pub fn peek_mut(&mut self) -> Option<PeekMut<'_, T, K, N>> {
if self.is_empty() {
None
} else {
Some(PeekMut {
heap: self,
sift: true,
})
}
}
/// Removes the *top* (greatest if max-heap, smallest if min-heap) item from the binary heap and
/// returns it, or None if it is empty.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
/// heap.push(1).unwrap();
/// heap.push(3).unwrap();
///
/// assert_eq!(heap.pop(), Some(3));
/// assert_eq!(heap.pop(), Some(1));
/// assert_eq!(heap.pop(), None);
/// ```
pub fn pop(&mut self) -> Option<T> {
if self.is_empty() {
None
} else {
Some(unsafe { self.pop_unchecked() })
}
}
/// Removes the *top* (greatest if max-heap, smallest if min-heap) item from the binary heap and
/// returns it, without checking if the binary heap is empty.
pub unsafe fn pop_unchecked(&mut self) -> T {
let mut item = self.data.pop_unchecked();
if !self.is_empty() {
mem::swap(&mut item, self.data.as_mut_slice().get_unchecked_mut(0));
self.sift_down_to_bottom(0);
}
item
}
/// Pushes an item onto the binary heap.
///
/// ```
/// use heapless::binary_heap::{BinaryHeap, Max};
///
/// let mut heap: BinaryHeap<_, Max, 8> = BinaryHeap::new();
/// heap.push(3).unwrap();
/// heap.push(5).unwrap();
/// heap.push(1).unwrap();
///
/// assert_eq!(heap.len(), 3);
/// assert_eq!(heap.peek(), Some(&5));
/// ```
pub fn push(&mut self, item: T) -> Result<(), T> {
if self.data.is_full() {
return Err(item);
}
unsafe { self.push_unchecked(item) }
Ok(())
}
/// Pushes an item onto the binary heap without first checking if it's full.
pub unsafe fn push_unchecked(&mut self, item: T) {
let old_len = self.len();
self.data.push_unchecked(item);
self.sift_up(0, old_len);
}
/// Returns the underlying ```Vec<T,N>```. Order is arbitrary and time is O(1).
pub fn into_vec(self) -> Vec<T, N> {
self.data
}
/* Private API */
fn sift_down_to_bottom(&mut self, mut pos: usize) {
let end = self.len();
let start = pos;
unsafe {
let mut hole = Hole::new(self.data.as_mut_slice(), pos);
let mut child = 2 * pos + 1;
while child < end {
let right = child + 1;
// compare with the greater of the two children
if right < end && hole.get(child).cmp(hole.get(right)) != K::ordering() {
child = right;
}
hole.move_to(child);
child = 2 * hole.pos() + 1;
}
pos = hole.pos;
}
self.sift_up(start, pos);
}
fn sift_up(&mut self, start: usize, pos: usize) -> usize {
unsafe {
// Take out the value at `pos` and create a hole.
let mut hole = Hole::new(self.data.as_mut_slice(), pos);
while hole.pos() > start {
let parent = (hole.pos() - 1) / 2;
if hole.element().cmp(hole.get(parent)) != K::ordering() {
break;
}
hole.move_to(parent);
}
hole.pos()
}
}
}
/// Hole represents a hole in a slice i.e. an index without valid value
/// (because it was moved from or duplicated).
/// In drop, `Hole` will restore the slice by filling the hole
/// position with the value that was originally removed.
struct Hole<'a, T> {
data: &'a mut [T],
/// `elt` is always `Some` from new until drop.
elt: ManuallyDrop<T>,
pos: usize,
}
impl<'a, T> Hole<'a, T> {
/// Create a new Hole at index `pos`.
///
/// Unsafe because pos must be within the data slice.
#[inline]
unsafe fn new(data: &'a mut [T], pos: usize) -> Self {
debug_assert!(pos < data.len());
let elt = ptr::read(data.get_unchecked(pos));
Hole {
data,
elt: ManuallyDrop::new(elt),
pos,
}
}
#[inline]
fn pos(&self) -> usize {
self.pos
}
/// Returns a reference to the element removed.
#[inline]
fn element(&self) -> &T {
&self.elt
}
/// Returns a reference to the element at `index`.
///
/// Unsafe because index must be within the data slice and not equal to pos.
#[inline]
unsafe fn get(&self, index: usize) -> &T {
debug_assert!(index != self.pos);
debug_assert!(index < self.data.len());
self.data.get_unchecked(index)
}
/// Move hole to new location
///
/// Unsafe because index must be within the data slice and not equal to pos.
#[inline]
unsafe fn move_to(&mut self, index: usize) {
debug_assert!(index != self.pos);
debug_assert!(index < self.data.len());
let ptr = self.data.as_mut_ptr();
let index_ptr: *const _ = ptr.add(index);
let hole_ptr = ptr.add(self.pos);
ptr::copy_nonoverlapping(index_ptr, hole_ptr, 1);
self.pos = index;
}
}
/// Structure wrapping a mutable reference to the greatest item on a
/// `BinaryHeap`.
///
/// This `struct` is created by [`BinaryHeap::peek_mut`].
/// See its documentation for more.
pub struct PeekMut<'a, T, K, const N: usize>
where
T: Ord,
K: Kind,
{
heap: &'a mut BinaryHeap<T, K, N>,
sift: bool,
}
impl<T, K, const N: usize> Drop for PeekMut<'_, T, K, N>
where
T: Ord,
K: Kind,
{
fn drop(&mut self) {
if self.sift {
self.heap.sift_down_to_bottom(0);
}
}
}
impl<T, K, const N: usize> Deref for PeekMut<'_, T, K, N>
where
T: Ord,
K: Kind,
{
type Target = T;
fn deref(&self) -> &T {
debug_assert!(!self.heap.is_empty());
// SAFE: PeekMut is only instantiated for non-empty heaps
unsafe { self.heap.data.as_slice().get_unchecked(0) }
}
}
impl<T, K, const N: usize> DerefMut for PeekMut<'_, T, K, N>
where
T: Ord,
K: Kind,
{
fn deref_mut(&mut self) -> &mut T {
debug_assert!(!self.heap.is_empty());
// SAFE: PeekMut is only instantiated for non-empty heaps
unsafe { self.heap.data.as_mut_slice().get_unchecked_mut(0) }
}
}
impl<'a, T, K, const N: usize> PeekMut<'a, T, K, N>
where
T: Ord,
K: Kind,
{
/// Removes the peeked value from the heap and returns it.
pub fn pop(mut this: PeekMut<'a, T, K, N>) -> T {
let value = this.heap.pop().unwrap();
this.sift = false;
value
}
}
impl<'a, T> Drop for Hole<'a, T> {
#[inline]
fn drop(&mut self) {
// fill the hole again
unsafe {
let pos = self.pos;
ptr::write(self.data.get_unchecked_mut(pos), ptr::read(&*self.elt));
}
}
}
impl<T, K, const N: usize> Default for BinaryHeap<T, K, N>
where
T: Ord,
K: Kind,
{
fn default() -> Self {
Self::new()
}
}
impl<T, K, const N: usize> Clone for BinaryHeap<T, K, N>
where
K: Kind,
T: Ord + Clone,
{
fn clone(&self) -> Self {
Self {
_kind: self._kind,
data: self.data.clone(),
}
}
}
impl<T, K, const N: usize> fmt::Debug for BinaryHeap<T, K, N>
where
K: Kind,
T: Ord + fmt::Debug,
{
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.debug_list().entries(self.iter()).finish()
}
}
impl<'a, T, K, const N: usize> IntoIterator for &'a BinaryHeap<T, K, N>
where
K: Kind,
T: Ord,
{
type Item = &'a T;
type IntoIter = slice::Iter<'a, T>;
fn into_iter(self) -> Self::IntoIter {
self.iter()
}
}
#[cfg(test)]
mod tests {
use std::vec::Vec;
use crate::binary_heap::{BinaryHeap, Max, Min};
#[test]
fn static_new() {
static mut _B: BinaryHeap<i32, Min, 16> = BinaryHeap::new();
}
#[test]
fn drop() {
droppable!();
{
let mut v: BinaryHeap<Droppable, Max, 2> = BinaryHeap::new();
v.push(Droppable::new()).ok().unwrap();
v.push(Droppable::new()).ok().unwrap();
v.pop().unwrap();
}
assert_eq!(Droppable::count(), 0);
{
let mut v: BinaryHeap<Droppable, Max, 2> = BinaryHeap::new();
v.push(Droppable::new()).ok().unwrap();
v.push(Droppable::new()).ok().unwrap();
}
assert_eq!(Droppable::count(), 0);
{
let mut v: BinaryHeap<Droppable, Min, 2> = BinaryHeap::new();
v.push(Droppable::new()).ok().unwrap();
v.push(Droppable::new()).ok().unwrap();
v.pop().unwrap();
}
assert_eq!(Droppable::count(), 0);
{
let mut v: BinaryHeap<Droppable, Min, 2> = BinaryHeap::new();
v.push(Droppable::new()).ok().unwrap();
v.push(Droppable::new()).ok().unwrap();
}
assert_eq!(Droppable::count(), 0);
}
#[test]
fn into_vec() {
droppable!();
let mut h: BinaryHeap<Droppable, Max, 2> = BinaryHeap::new();
h.push(Droppable::new()).ok().unwrap();
h.push(Droppable::new()).ok().unwrap();
h.pop().unwrap();
assert_eq!(Droppable::count(), 1);
let v = h.into_vec();
assert_eq!(Droppable::count(), 1);
core::mem::drop(v);
assert_eq!(Droppable::count(), 0);
}
#[test]
fn min() {
let mut heap = BinaryHeap::<_, Min, 16>::new();
heap.push(1).unwrap();
heap.push(2).unwrap();
heap.push(3).unwrap();
heap.push(17).unwrap();
heap.push(19).unwrap();
heap.push(36).unwrap();
heap.push(7).unwrap();
heap.push(25).unwrap();
heap.push(100).unwrap();
assert_eq!(
heap.iter().cloned().collect::<Vec<_>>(),
[1, 2, 3, 17, 19, 36, 7, 25, 100]
);
assert_eq!(heap.pop(), Some(1));
assert_eq!(
heap.iter().cloned().collect::<Vec<_>>(),
[2, 17, 3, 25, 19, 36, 7, 100]
);
assert_eq!(heap.pop(), Some(2));
assert_eq!(heap.pop(), Some(3));
assert_eq!(heap.pop(), Some(7));
assert_eq!(heap.pop(), Some(17));
assert_eq!(heap.pop(), Some(19));
assert_eq!(heap.pop(), Some(25));
assert_eq!(heap.pop(), Some(36));
assert_eq!(heap.pop(), Some(100));
assert_eq!(heap.pop(), None);
assert!(heap.peek_mut().is_none());
heap.push(1).unwrap();
heap.push(2).unwrap();
heap.push(10).unwrap();
{
let mut val = heap.peek_mut().unwrap();
*val = 7;
}
assert_eq!(heap.pop(), Some(2));
assert_eq!(heap.pop(), Some(7));
assert_eq!(heap.pop(), Some(10));
assert_eq!(heap.pop(), None);
}
#[test]
fn max() {
let mut heap = BinaryHeap::<_, Max, 16>::new();
heap.push(1).unwrap();
heap.push(2).unwrap();
heap.push(3).unwrap();
heap.push(17).unwrap();
heap.push(19).unwrap();
heap.push(36).unwrap();
heap.push(7).unwrap();
heap.push(25).unwrap();
heap.push(100).unwrap();
assert_eq!(
heap.iter().cloned().collect::<Vec<_>>(),
[100, 36, 19, 25, 3, 2, 7, 1, 17]
);
assert_eq!(heap.pop(), Some(100));
assert_eq!(
heap.iter().cloned().collect::<Vec<_>>(),
[36, 25, 19, 17, 3, 2, 7, 1]
);
assert_eq!(heap.pop(), Some(36));
assert_eq!(heap.pop(), Some(25));
assert_eq!(heap.pop(), Some(19));
assert_eq!(heap.pop(), Some(17));
assert_eq!(heap.pop(), Some(7));
assert_eq!(heap.pop(), Some(3));
assert_eq!(heap.pop(), Some(2));
assert_eq!(heap.pop(), Some(1));
assert_eq!(heap.pop(), None);
assert!(heap.peek_mut().is_none());
heap.push(1).unwrap();
heap.push(9).unwrap();
heap.push(10).unwrap();
{
let mut val = heap.peek_mut().unwrap();
*val = 7;
}
assert_eq!(heap.pop(), Some(9));
assert_eq!(heap.pop(), Some(7));
assert_eq!(heap.pop(), Some(1));
assert_eq!(heap.pop(), None);
}
}