1 // Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! A priority queue implemented with a binary heap.
13 //! Insertion and popping the largest element have `O(log n)` time complexity.
14 //! Checking the largest element is `O(1)`. Converting a vector to a binary heap
15 //! can be done in-place, and has `O(n)` complexity. A binary heap can also be
16 //! converted to a sorted vector in-place, allowing it to be used for an `O(n
17 //! log n)` in-place heapsort.
21 //! This is a larger example that implements [Dijkstra's algorithm][dijkstra]
22 //! to solve the [shortest path problem][sssp] on a [directed graph][dir_graph].
23 //! It shows how to use `BinaryHeap` with custom types.
25 //! [dijkstra]: http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
26 //! [sssp]: http://en.wikipedia.org/wiki/Shortest_path_problem
27 //! [dir_graph]: http://en.wikipedia.org/wiki/Directed_graph
30 //! use std::cmp::Ordering;
31 //! use std::collections::BinaryHeap;
34 //! #[derive(Copy, Clone, Eq, PartialEq)]
40 //! // The priority queue depends on `Ord`.
41 //! // Explicitly implement the trait so the queue becomes a min-heap
42 //! // instead of a max-heap.
43 //! impl Ord for State {
44 //! fn cmp(&self, other: &State) -> Ordering {
45 //! // Notice that the we flip the ordering here
46 //! other.cost.cmp(&self.cost)
50 //! // `PartialOrd` needs to be implemented as well.
51 //! impl PartialOrd for State {
52 //! fn partial_cmp(&self, other: &State) -> Option<Ordering> {
53 //! Some(self.cmp(other))
57 //! // Each node is represented as an `usize`, for a shorter implementation.
63 //! // Dijkstra's shortest path algorithm.
65 //! // Start at `start` and use `dist` to track the current shortest distance
66 //! // to each node. This implementation isn't memory-efficient as it may leave duplicate
67 //! // nodes in the queue. It also uses `usize::MAX` as a sentinel value,
68 //! // for a simpler implementation.
69 //! fn shortest_path(adj_list: &Vec<Vec<Edge>>, start: usize, goal: usize) -> usize {
70 //! // dist[node] = current shortest distance from `start` to `node`
71 //! let mut dist: Vec<_> = (0..adj_list.len()).map(|_| usize::MAX).collect();
73 //! let mut heap = BinaryHeap::new();
75 //! // We're at `start`, with a zero cost
77 //! heap.push(State { cost: 0, position: start });
79 //! // Examine the frontier with lower cost nodes first (min-heap)
80 //! while let Some(State { cost, position }) = heap.pop() {
81 //! // Alternatively we could have continued to find all shortest paths
82 //! if position == goal { return cost; }
84 //! // Important as we may have already found a better way
85 //! if cost > dist[position] { continue; }
87 //! // For each node we can reach, see if we can find a way with
88 //! // a lower cost going through this node
89 //! for edge in &adj_list[position] {
90 //! let next = State { cost: cost + edge.cost, position: edge.node };
92 //! // If so, add it to the frontier and continue
93 //! if next.cost < dist[next.position] {
95 //! // Relaxation, we have now found a better way
96 //! dist[next.position] = next.cost;
101 //! // Goal not reachable
106 //! // This is the directed graph we're going to use.
107 //! // The node numbers correspond to the different states,
108 //! // and the edge weights symbolize the cost of moving
109 //! // from one node to another.
110 //! // Note that the edges are one-way.
113 //! // +-----------------+
116 //! // 0 -----> 1 -----> 3 ---> 4
120 //! // +------> 2 -------+ |
122 //! // +---------------+
124 //! // The graph is represented as an adjacency list where each index,
125 //! // corresponding to a node value, has a list of outgoing edges.
126 //! // Chosen for its efficiency.
127 //! let graph = vec![
129 //! vec![Edge { node: 2, cost: 10 },
130 //! Edge { node: 1, cost: 1 }],
132 //! vec![Edge { node: 3, cost: 2 }],
134 //! vec![Edge { node: 1, cost: 1 },
135 //! Edge { node: 3, cost: 3 },
136 //! Edge { node: 4, cost: 1 }],
138 //! vec![Edge { node: 0, cost: 7 },
139 //! Edge { node: 4, cost: 2 }],
143 //! assert_eq!(shortest_path(&graph, 0, 1), 1);
144 //! assert_eq!(shortest_path(&graph, 0, 3), 3);
145 //! assert_eq!(shortest_path(&graph, 3, 0), 7);
146 //! assert_eq!(shortest_path(&graph, 0, 4), 5);
147 //! assert_eq!(shortest_path(&graph, 4, 0), usize::MAX);
151 #![allow(missing_docs)]
152 #![stable(feature = "rust1", since = "1.0.0")]
155 use core::prelude::v1::*;
157 use core::iter::{FromIterator};
162 use vec::{self, Vec};
164 /// A priority queue implemented with a binary heap.
166 /// This will be a max-heap.
168 /// It is a logic error for an item to be modified in such a way that the
169 /// item's ordering relative to any other item, as determined by the `Ord`
170 /// trait, changes while it is in the heap. This is normally only possible
171 /// through `Cell`, `RefCell`, global state, I/O, or unsafe code.
173 #[stable(feature = "rust1", since = "1.0.0")]
174 pub struct BinaryHeap<T> {
178 #[stable(feature = "rust1", since = "1.0.0")]
179 impl<T: Ord> Default for BinaryHeap<T> {
181 fn default() -> BinaryHeap<T> { BinaryHeap::new() }
184 impl<T: Ord> BinaryHeap<T> {
185 /// Creates an empty `BinaryHeap` as a max-heap.
190 /// use std::collections::BinaryHeap;
191 /// let mut heap = BinaryHeap::new();
194 #[stable(feature = "rust1", since = "1.0.0")]
195 pub fn new() -> BinaryHeap<T> { BinaryHeap { data: vec![] } }
197 /// Creates an empty `BinaryHeap` with a specific capacity.
198 /// This preallocates enough memory for `capacity` elements,
199 /// so that the `BinaryHeap` does not have to be reallocated
200 /// until it contains at least that many values.
205 /// use std::collections::BinaryHeap;
206 /// let mut heap = BinaryHeap::with_capacity(10);
209 #[stable(feature = "rust1", since = "1.0.0")]
210 pub fn with_capacity(capacity: usize) -> BinaryHeap<T> {
211 BinaryHeap { data: Vec::with_capacity(capacity) }
214 /// Creates a `BinaryHeap` from a vector. This is sometimes called
215 /// `heapifying` the vector.
220 /// #![feature(collections)]
222 /// use std::collections::BinaryHeap;
223 /// let heap = BinaryHeap::from_vec(vec![9, 1, 2, 7, 3, 2]);
225 pub fn from_vec(vec: Vec<T>) -> BinaryHeap<T> {
226 let mut heap = BinaryHeap { data: vec };
227 let mut n = heap.len() / 2;
235 /// Returns an iterator visiting all values in the underlying vector, in
241 /// #![feature(collections)]
243 /// use std::collections::BinaryHeap;
244 /// let heap = BinaryHeap::from_vec(vec![1, 2, 3, 4]);
246 /// // Print 1, 2, 3, 4 in arbitrary order
247 /// for x in heap.iter() {
248 /// println!("{}", x);
251 #[stable(feature = "rust1", since = "1.0.0")]
252 pub fn iter(&self) -> Iter<T> {
253 Iter { iter: self.data.iter() }
256 /// Returns the greatest item in the binary heap, or `None` if it is empty.
261 /// use std::collections::BinaryHeap;
262 /// let mut heap = BinaryHeap::new();
263 /// assert_eq!(heap.peek(), None);
268 /// assert_eq!(heap.peek(), Some(&5));
271 #[stable(feature = "rust1", since = "1.0.0")]
272 pub fn peek(&self) -> Option<&T> {
276 /// Returns the number of elements the binary heap can hold without reallocating.
281 /// use std::collections::BinaryHeap;
282 /// let mut heap = BinaryHeap::with_capacity(100);
283 /// assert!(heap.capacity() >= 100);
286 #[stable(feature = "rust1", since = "1.0.0")]
287 pub fn capacity(&self) -> usize { self.data.capacity() }
289 /// Reserves the minimum capacity for exactly `additional` more elements to be inserted in the
290 /// given `BinaryHeap`. Does nothing if the capacity is already sufficient.
292 /// Note that the allocator may give the collection more space than it requests. Therefore
293 /// capacity can not be relied upon to be precisely minimal. Prefer `reserve` if future
294 /// insertions are expected.
298 /// Panics if the new capacity overflows `usize`.
303 /// use std::collections::BinaryHeap;
304 /// let mut heap = BinaryHeap::new();
305 /// heap.reserve_exact(100);
306 /// assert!(heap.capacity() >= 100);
309 #[stable(feature = "rust1", since = "1.0.0")]
310 pub fn reserve_exact(&mut self, additional: usize) {
311 self.data.reserve_exact(additional);
314 /// Reserves capacity for at least `additional` more elements to be inserted in the
315 /// `BinaryHeap`. The collection may reserve more space to avoid frequent reallocations.
319 /// Panics if the new capacity overflows `usize`.
324 /// use std::collections::BinaryHeap;
325 /// let mut heap = BinaryHeap::new();
326 /// heap.reserve(100);
327 /// assert!(heap.capacity() >= 100);
330 #[stable(feature = "rust1", since = "1.0.0")]
331 pub fn reserve(&mut self, additional: usize) {
332 self.data.reserve(additional);
335 /// Discards as much additional capacity as possible.
336 #[stable(feature = "rust1", since = "1.0.0")]
337 pub fn shrink_to_fit(&mut self) {
338 self.data.shrink_to_fit();
341 /// Removes the greatest item from the binary heap and returns it, or `None` if it
347 /// #![feature(collections)]
349 /// use std::collections::BinaryHeap;
350 /// let mut heap = BinaryHeap::from_vec(vec![1, 3]);
352 /// assert_eq!(heap.pop(), Some(3));
353 /// assert_eq!(heap.pop(), Some(1));
354 /// assert_eq!(heap.pop(), None);
356 #[stable(feature = "rust1", since = "1.0.0")]
357 pub fn pop(&mut self) -> Option<T> {
358 self.data.pop().map(|mut item| {
359 if !self.is_empty() {
360 swap(&mut item, &mut self.data[0]);
367 /// Pushes an item onto the binary heap.
372 /// use std::collections::BinaryHeap;
373 /// let mut heap = BinaryHeap::new();
378 /// assert_eq!(heap.len(), 3);
379 /// assert_eq!(heap.peek(), Some(&5));
381 #[stable(feature = "rust1", since = "1.0.0")]
382 pub fn push(&mut self, item: T) {
383 let old_len = self.len();
384 self.data.push(item);
385 self.sift_up(0, old_len);
388 /// Pushes an item onto the binary heap, then pops the greatest item off the queue in
389 /// an optimized fashion.
394 /// #![feature(collections)]
396 /// use std::collections::BinaryHeap;
397 /// let mut heap = BinaryHeap::new();
401 /// assert_eq!(heap.push_pop(3), 5);
402 /// assert_eq!(heap.push_pop(9), 9);
403 /// assert_eq!(heap.len(), 2);
404 /// assert_eq!(heap.peek(), Some(&3));
406 pub fn push_pop(&mut self, mut item: T) -> T {
407 match self.data.get_mut(0) {
409 Some(top) => if *top > item {
410 swap(&mut item, top);
420 /// Pops the greatest item off the binary heap, then pushes an item onto the queue in
421 /// an optimized fashion. The push is done regardless of whether the binary heap
427 /// #![feature(collections)]
429 /// use std::collections::BinaryHeap;
430 /// let mut heap = BinaryHeap::new();
432 /// assert_eq!(heap.replace(1), None);
433 /// assert_eq!(heap.replace(3), Some(1));
434 /// assert_eq!(heap.len(), 1);
435 /// assert_eq!(heap.peek(), Some(&3));
437 pub fn replace(&mut self, mut item: T) -> Option<T> {
438 if !self.is_empty() {
439 swap(&mut item, &mut self.data[0]);
448 /// Consumes the `BinaryHeap` and returns the underlying vector
449 /// in arbitrary order.
454 /// #![feature(collections)]
456 /// use std::collections::BinaryHeap;
457 /// let heap = BinaryHeap::from_vec(vec![1, 2, 3, 4, 5, 6, 7]);
458 /// let vec = heap.into_vec();
460 /// // Will print in some order
462 /// println!("{}", x);
465 pub fn into_vec(self) -> Vec<T> { self.data }
467 /// Consumes the `BinaryHeap` and returns a vector in sorted
468 /// (ascending) order.
473 /// #![feature(collections)]
475 /// use std::collections::BinaryHeap;
477 /// let mut heap = BinaryHeap::from_vec(vec![1, 2, 4, 5, 7]);
481 /// let vec = heap.into_sorted_vec();
482 /// assert_eq!(vec, [1, 2, 3, 4, 5, 6, 7]);
484 pub fn into_sorted_vec(mut self) -> Vec<T> {
485 let mut end = self.len();
488 self.data.swap(0, end);
489 self.sift_down_range(0, end);
494 // The implementations of sift_up and sift_down use unsafe blocks in
495 // order to move an element out of the vector (leaving behind a
496 // hole), shift along the others and move the removed element back into the
497 // vector at the final location of the hole.
498 // The `Hole` type is used to represent this, and make sure
499 // the hole is filled back at the end of its scope, even on panic.
500 // Using a hole reduces the constant factor compared to using swaps,
501 // which involves twice as many moves.
502 fn sift_up(&mut self, start: usize, pos: usize) {
504 // Take out the value at `pos` and create a hole.
505 let mut hole = Hole::new(&mut self.data, pos);
507 while hole.pos() > start {
508 let parent = (hole.pos() - 1) / 2;
509 if hole.removed() <= hole.get(parent) { break }
510 hole.move_to(parent);
515 fn sift_down_range(&mut self, mut pos: usize, end: usize) {
518 let mut hole = Hole::new(&mut self.data, pos);
519 let mut child = 2 * pos + 1;
521 let right = child + 1;
522 if right < end && !(hole.get(child) > hole.get(right)) {
526 child = 2 * hole.pos() + 1;
531 self.sift_up(start, pos);
534 fn sift_down(&mut self, pos: usize) {
535 let len = self.len();
536 self.sift_down_range(pos, len);
539 /// Returns the length of the binary heap.
540 #[stable(feature = "rust1", since = "1.0.0")]
541 pub fn len(&self) -> usize { self.data.len() }
543 /// Checks if the binary heap is empty.
544 #[stable(feature = "rust1", since = "1.0.0")]
545 pub fn is_empty(&self) -> bool { self.len() == 0 }
547 /// Clears the binary heap, returning an iterator over the removed elements.
549 /// The elements are removed in arbitrary order.
551 #[unstable(feature = "drain",
552 reason = "matches collection reform specification, \
553 waiting for dust to settle")]
554 pub fn drain(&mut self) -> Drain<T> {
555 Drain { iter: self.data.drain(..) }
558 /// Drops all items from the binary heap.
559 #[stable(feature = "rust1", since = "1.0.0")]
560 pub fn clear(&mut self) { self.drain(); }
563 /// Hole represents a hole in a slice i.e. an index without valid value
564 /// (because it was moved from or duplicated).
565 /// In drop, `Hole` will restore the slice by filling the hole
566 /// position with the value that was originally removed.
567 struct Hole<'a, T: 'a> {
569 /// `elt` is always `Some` from new until drop.
574 impl<'a, T> Hole<'a, T> {
575 /// Create a new Hole at index `pos`.
576 fn new(data: &'a mut [T], pos: usize) -> Self {
578 let elt = ptr::read(&data[pos]);
588 fn pos(&self) -> usize { self.pos }
590 /// Return a reference to the element removed
592 fn removed(&self) -> &T {
593 self.elt.as_ref().unwrap()
596 /// Return a reference to the element at `index`.
598 /// Panics if the index is out of bounds.
600 /// Unsafe because index must not equal pos.
602 unsafe fn get(&self, index: usize) -> &T {
603 debug_assert!(index != self.pos);
607 /// Move hole to new location
609 /// Unsafe because index must not equal pos.
611 unsafe fn move_to(&mut self, index: usize) {
612 debug_assert!(index != self.pos);
613 let index_ptr: *const _ = &self.data[index];
614 let hole_ptr = &mut self.data[self.pos];
615 ptr::copy_nonoverlapping(index_ptr, hole_ptr, 1);
620 impl<'a, T> Drop for Hole<'a, T> {
622 // fill the hole again
625 ptr::write(&mut self.data[pos], self.elt.take().unwrap());
630 /// `BinaryHeap` iterator.
631 #[stable(feature = "rust1", since = "1.0.0")]
632 pub struct Iter <'a, T: 'a> {
633 iter: slice::Iter<'a, T>,
636 // FIXME(#19839) Remove in favor of `#[derive(Clone)]`
637 #[stable(feature = "rust1", since = "1.0.0")]
638 impl<'a, T> Clone for Iter<'a, T> {
639 fn clone(&self) -> Iter<'a, T> {
640 Iter { iter: self.iter.clone() }
644 #[stable(feature = "rust1", since = "1.0.0")]
645 impl<'a, T> Iterator for Iter<'a, T> {
649 fn next(&mut self) -> Option<&'a T> { self.iter.next() }
652 fn size_hint(&self) -> (usize, Option<usize>) { self.iter.size_hint() }
655 #[stable(feature = "rust1", since = "1.0.0")]
656 impl<'a, T> DoubleEndedIterator for Iter<'a, T> {
658 fn next_back(&mut self) -> Option<&'a T> { self.iter.next_back() }
661 #[stable(feature = "rust1", since = "1.0.0")]
662 impl<'a, T> ExactSizeIterator for Iter<'a, T> {}
664 /// An iterator that moves out of a `BinaryHeap`.
665 #[stable(feature = "rust1", since = "1.0.0")]
666 pub struct IntoIter<T> {
667 iter: vec::IntoIter<T>,
670 #[stable(feature = "rust1", since = "1.0.0")]
671 impl<T> Iterator for IntoIter<T> {
675 fn next(&mut self) -> Option<T> { self.iter.next() }
678 fn size_hint(&self) -> (usize, Option<usize>) { self.iter.size_hint() }
681 #[stable(feature = "rust1", since = "1.0.0")]
682 impl<T> DoubleEndedIterator for IntoIter<T> {
684 fn next_back(&mut self) -> Option<T> { self.iter.next_back() }
687 #[stable(feature = "rust1", since = "1.0.0")]
688 impl<T> ExactSizeIterator for IntoIter<T> {}
690 /// An iterator that drains a `BinaryHeap`.
691 #[unstable(feature = "drain", reason = "recent addition")]
692 pub struct Drain<'a, T: 'a> {
693 iter: vec::Drain<'a, T>,
696 #[stable(feature = "rust1", since = "1.0.0")]
697 impl<'a, T: 'a> Iterator for Drain<'a, T> {
701 fn next(&mut self) -> Option<T> { self.iter.next() }
704 fn size_hint(&self) -> (usize, Option<usize>) { self.iter.size_hint() }
707 #[stable(feature = "rust1", since = "1.0.0")]
708 impl<'a, T: 'a> DoubleEndedIterator for Drain<'a, T> {
710 fn next_back(&mut self) -> Option<T> { self.iter.next_back() }
713 #[stable(feature = "rust1", since = "1.0.0")]
714 impl<'a, T: 'a> ExactSizeIterator for Drain<'a, T> {}
716 #[stable(feature = "rust1", since = "1.0.0")]
717 impl<T: Ord> FromIterator<T> for BinaryHeap<T> {
718 fn from_iter<I: IntoIterator<Item=T>>(iter: I) -> BinaryHeap<T> {
719 BinaryHeap::from_vec(iter.into_iter().collect())
723 #[stable(feature = "rust1", since = "1.0.0")]
724 impl<T: Ord> IntoIterator for BinaryHeap<T> {
726 type IntoIter = IntoIter<T>;
728 /// Creates a consuming iterator, that is, one that moves each value out of
729 /// the binary heap in arbitrary order. The binary heap cannot be used
730 /// after calling this.
735 /// #![feature(collections)]
737 /// use std::collections::BinaryHeap;
738 /// let heap = BinaryHeap::from_vec(vec![1, 2, 3, 4]);
740 /// // Print 1, 2, 3, 4 in arbitrary order
741 /// for x in heap.into_iter() {
742 /// // x has type i32, not &i32
743 /// println!("{}", x);
746 fn into_iter(self) -> IntoIter<T> {
747 IntoIter { iter: self.data.into_iter() }
751 #[stable(feature = "rust1", since = "1.0.0")]
752 impl<'a, T> IntoIterator for &'a BinaryHeap<T> where T: Ord {
754 type IntoIter = Iter<'a, T>;
756 fn into_iter(self) -> Iter<'a, T> {
761 #[stable(feature = "rust1", since = "1.0.0")]
762 impl<T: Ord> Extend<T> for BinaryHeap<T> {
763 fn extend<I: IntoIterator<Item=T>>(&mut self, iterable: I) {
764 let iter = iterable.into_iter();
765 let (lower, _) = iter.size_hint();
775 #[stable(feature = "extend_ref", since = "1.2.0")]
776 impl<'a, T: 'a + Ord + Copy> Extend<&'a T> for BinaryHeap<T> {
777 fn extend<I: IntoIterator<Item=&'a T>>(&mut self, iter: I) {
778 self.extend(iter.into_iter().cloned());