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// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT // file at the top-level directory of this distribution and at // http://rust-lang.org/COPYRIGHT. // // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your // option. This file may not be copied, modified, or distributed // except according to those terms. //! A priority queue implemented with a binary heap. //! //! Insertion and popping the largest element have `O(log n)` time complexity. Checking the largest //! element is `O(1)`. 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. //! //! # Examples //! //! This is a larger example that implements [Dijkstra's algorithm][dijkstra] //! to solve the [shortest path problem][sssp] on a [directed graph][dir_graph]. //! It shows how to use `BinaryHeap` with custom types. //! //! [dijkstra]: http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm //! [sssp]: http://en.wikipedia.org/wiki/Shortest_path_problem //! [dir_graph]: http://en.wikipedia.org/wiki/Directed_graph //! //! ``` //! use std::cmp::Ordering; //! use std::collections::BinaryHeap; //! use std::usize; //! //! #[derive(Copy, Clone, Eq, PartialEq)] //! struct State { //! cost: usize, //! position: usize, //! } //! //! // The priority queue depends on `Ord`. //! // Explicitly implement the trait so the queue becomes a min-heap //! // instead of a max-heap. //! impl Ord for State { //! fn cmp(&self, other: &State) -> Ordering { //! // Notice that the we flip the ordering here //! other.cost.cmp(&self.cost) //! } //! } //! //! // `PartialOrd` needs to be implemented as well. //! impl PartialOrd for State { //! fn partial_cmp(&self, other: &State) -> Option<Ordering> { //! Some(self.cmp(other)) //! } //! } //! //! // Each node is represented as an `usize`, for a shorter implementation. //! struct Edge { //! node: usize, //! cost: usize, //! } //! //! // Dijkstra's shortest path algorithm. //! //! // Start at `start` and use `dist` to track the current shortest distance //! // to each node. This implementation isn't memory-efficient as it may leave duplicate //! // nodes in the queue. It also uses `usize::MAX` as a sentinel value, //! // for a simpler implementation. //! fn shortest_path(adj_list: &Vec<Vec<Edge>>, start: usize, goal: usize) -> usize { //! // dist[node] = current shortest distance from `start` to `node` //! let mut dist: Vec<_> = (0..adj_list.len()).map(|_| usize::MAX).collect(); //! //! let mut heap = BinaryHeap::new(); //! //! // We're at `start`, with a zero cost //! dist[start] = 0; //! heap.push(State { cost: 0, position: start }); //! //! // Examine the frontier with lower cost nodes first (min-heap) //! while let Some(State { cost, position }) = heap.pop() { //! // Alternatively we could have continued to find all shortest paths //! if position == goal { return cost; } //! //! // Important as we may have already found a better way //! if cost > dist[position] { continue; } //! //! // For each node we can reach, see if we can find a way with //! // a lower cost going through this node //! for edge in adj_list[position].iter() { //! let next = State { cost: cost + edge.cost, position: edge.node }; //! //! // If so, add it to the frontier and continue //! if next.cost < dist[next.position] { //! heap.push(next); //! // Relaxation, we have now found a better way //! dist[next.position] = next.cost; //! } //! } //! } //! //! // Goal not reachable //! usize::MAX //! } //! //! fn main() { //! // This is the directed graph we're going to use. //! // The node numbers correspond to the different states, //! // and the edge weights symbolize the cost of moving //! // from one node to another. //! // Note that the edges are one-way. //! // //! // 7 //! // +-----------------+ //! // | | //! // v 1 2 | //! // 0 -----> 1 -----> 3 ---> 4 //! // | ^ ^ ^ //! // | | 1 | | //! // | | | 3 | 1 //! // +------> 2 -------+ | //! // 10 | | //! // +---------------+ //! // //! // The graph is represented as an adjacency list where each index, //! // corresponding to a node value, has a list of outgoing edges. //! // Chosen for its efficiency. //! let graph = vec![ //! // Node 0 //! vec![Edge { node: 2, cost: 10 }, //! Edge { node: 1, cost: 1 }], //! // Node 1 //! vec![Edge { node: 3, cost: 2 }], //! // Node 2 //! vec![Edge { node: 1, cost: 1 }, //! Edge { node: 3, cost: 3 }, //! Edge { node: 4, cost: 1 }], //! // Node 3 //! vec![Edge { node: 0, cost: 7 }, //! Edge { node: 4, cost: 2 }], //! // Node 4 //! vec![]]; //! //! assert_eq!(shortest_path(&graph, 0, 1), 1); //! assert_eq!(shortest_path(&graph, 0, 3), 3); //! assert_eq!(shortest_path(&graph, 3, 0), 7); //! assert_eq!(shortest_path(&graph, 0, 4), 5); //! assert_eq!(shortest_path(&graph, 4, 0), usize::MAX); //! } //! ``` #![allow(missing_docs)] #![stable(feature = "rust1", since = "1.0.0")] use core::prelude::*; use core::iter::{FromIterator}; use core::mem::swap; use core::ptr; use slice; use vec::{self, Vec}; /// A priority queue implemented with a binary heap. /// /// This will be 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. #[derive(Clone)] #[stable(feature = "rust1", since = "1.0.0")] pub struct BinaryHeap<T> { data: Vec<T>, } #[stable(feature = "rust1", since = "1.0.0")] impl<T: Ord> Default for BinaryHeap<T> { #[inline] fn default() -> BinaryHeap<T> { BinaryHeap::new() } } impl<T: Ord> BinaryHeap<T> { /// Creates an empty `BinaryHeap` as a max-heap. /// /// # Examples /// /// ``` /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::new(); /// heap.push(4); /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn new() -> BinaryHeap<T> { BinaryHeap { data: vec![] } } /// Creates an empty `BinaryHeap` with a specific capacity. /// This preallocates enough memory for `capacity` elements, /// so that the `BinaryHeap` does not have to be reallocated /// until it contains at least that many values. /// /// # Examples /// /// ``` /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::with_capacity(10); /// heap.push(4); /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn with_capacity(capacity: usize) -> BinaryHeap<T> { BinaryHeap { data: Vec::with_capacity(capacity) } } /// Creates a `BinaryHeap` from a vector. This is sometimes called /// `heapifying` the vector. /// /// # Examples /// /// ``` /// # #![feature(collections)] /// use std::collections::BinaryHeap; /// let heap = BinaryHeap::from_vec(vec![9, 1, 2, 7, 3, 2]); /// ``` pub fn from_vec(vec: Vec<T>) -> BinaryHeap<T> { let mut heap = BinaryHeap { data: vec }; let mut n = heap.len() / 2; while n > 0 { n -= 1; heap.sift_down(n); } heap } /// Returns an iterator visiting all values in the underlying vector, in /// arbitrary order. /// /// # Examples /// /// ``` /// # #![feature(collections)] /// use std::collections::BinaryHeap; /// let heap = BinaryHeap::from_vec(vec![1, 2, 3, 4]); /// /// // Print 1, 2, 3, 4 in arbitrary order /// for x in heap.iter() { /// println!("{}", x); /// } /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn iter(&self) -> Iter<T> { Iter { iter: self.data.iter() } } /// Returns the greatest item in the binary heap, or `None` if it is empty. /// /// # Examples /// /// ``` /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::new(); /// assert_eq!(heap.peek(), None); /// /// heap.push(1); /// heap.push(5); /// heap.push(2); /// assert_eq!(heap.peek(), Some(&5)); /// /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn peek(&self) -> Option<&T> { self.data.get(0) } /// Returns the number of elements the binary heap can hold without reallocating. /// /// # Examples /// /// ``` /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::with_capacity(100); /// assert!(heap.capacity() >= 100); /// heap.push(4); /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn capacity(&self) -> usize { self.data.capacity() } /// Reserves the minimum capacity for exactly `additional` more elements to be inserted in the /// given `BinaryHeap`. Does nothing if the capacity is already sufficient. /// /// Note that the allocator may give the collection more space than it requests. Therefore /// capacity can not be relied upon to be precisely minimal. Prefer `reserve` if future /// insertions are expected. /// /// # Panics /// /// Panics if the new capacity overflows `usize`. /// /// # Examples /// /// ``` /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::new(); /// heap.reserve_exact(100); /// assert!(heap.capacity() >= 100); /// heap.push(4); /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn reserve_exact(&mut self, additional: usize) { self.data.reserve_exact(additional); } /// Reserves capacity for at least `additional` more elements to be inserted in the /// `BinaryHeap`. The collection may reserve more space to avoid frequent reallocations. /// /// # Panics /// /// Panics if the new capacity overflows `usize`. /// /// # Examples /// /// ``` /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::new(); /// heap.reserve(100); /// assert!(heap.capacity() >= 100); /// heap.push(4); /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn reserve(&mut self, additional: usize) { self.data.reserve(additional); } /// Discards as much additional capacity as possible. #[stable(feature = "rust1", since = "1.0.0")] pub fn shrink_to_fit(&mut self) { self.data.shrink_to_fit(); } /// Removes the greatest item from the binary heap and returns it, or `None` if it /// is empty. /// /// # Examples /// /// ``` /// # #![feature(collections)] /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::from_vec(vec![1, 3]); /// /// assert_eq!(heap.pop(), Some(3)); /// assert_eq!(heap.pop(), Some(1)); /// assert_eq!(heap.pop(), None); /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn pop(&mut self) -> Option<T> { self.data.pop().map(|mut item| { if !self.is_empty() { swap(&mut item, &mut self.data[0]); self.sift_down(0); } item }) } /// Pushes an item onto the binary heap. /// /// # Examples /// /// ``` /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::new(); /// heap.push(3); /// heap.push(5); /// heap.push(1); /// /// assert_eq!(heap.len(), 3); /// assert_eq!(heap.peek(), Some(&5)); /// ``` #[stable(feature = "rust1", since = "1.0.0")] pub fn push(&mut self, item: T) { let old_len = self.len(); self.data.push(item); self.sift_up(0, old_len); } /// Pushes an item onto the binary heap, then pops the greatest item off the queue in /// an optimized fashion. /// /// # Examples /// /// ``` /// # #![feature(collections)] /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::new(); /// heap.push(1); /// heap.push(5); /// /// assert_eq!(heap.push_pop(3), 5); /// assert_eq!(heap.push_pop(9), 9); /// assert_eq!(heap.len(), 2); /// assert_eq!(heap.peek(), Some(&3)); /// ``` pub fn push_pop(&mut self, mut item: T) -> T { match self.data.get_mut(0) { None => return item, Some(top) => if *top > item { swap(&mut item, top); } else { return item; }, } self.sift_down(0); item } /// Pops the greatest item off the binary heap, then pushes an item onto the queue in /// an optimized fashion. The push is done regardless of whether the binary heap /// was empty. /// /// # Examples /// /// ``` /// # #![feature(collections)] /// use std::collections::BinaryHeap; /// let mut heap = BinaryHeap::new(); /// /// assert_eq!(heap.replace(1), None); /// assert_eq!(heap.replace(3), Some(1)); /// assert_eq!(heap.len(), 1); /// assert_eq!(heap.peek(), Some(&3)); /// ``` pub fn replace(&mut self, mut item: T) -> Option<T> { if !self.is_empty() { swap(&mut item, &mut self.data[0]); self.sift_down(0); Some(item) } else { self.push(item); None } } /// Consumes the `BinaryHeap` and returns the underlying vector /// in arbitrary order. /// /// # Examples /// /// ``` /// # #![feature(collections)] /// use std::collections::BinaryHeap; /// let heap = BinaryHeap::from_vec(vec![1, 2, 3, 4, 5, 6, 7]); /// let vec = heap.into_vec(); /// /// // Will print in some order /// for x in vec.iter() { /// println!("{}", x); /// } /// ``` pub fn into_vec(self) -> Vec<T> { self.data } /// Consumes the `BinaryHeap` and returns a vector in sorted /// (ascending) order. /// /// # Examples /// /// ``` /// # #![feature(collections)] /// use std::collections::BinaryHeap; /// /// let mut heap = BinaryHeap::from_vec(vec![1, 2, 4, 5, 7]); /// heap.push(6); /// heap.push(3); /// /// let vec = heap.into_sorted_vec(); /// assert_eq!(vec, [1, 2, 3, 4, 5, 6, 7]); /// ``` pub fn into_sorted_vec(mut self) -> Vec<T> { let mut end = self.len(); while end > 1 { end -= 1; self.data.swap(0, end); self.sift_down_range(0, end); } self.into_vec() } // The implementations of sift_up and sift_down use unsafe blocks in // order to move an element out of the vector (leaving behind a // hole), shift along the others and move the removed element back into the // vector at the final location of the hole. // The `Hole` type is used to represent this, and make sure // the hole is filled back at the end of its scope, even on panic. // Using a hole reduces the constant factor compared to using swaps, // which involves twice as many moves. fn sift_up(&mut self, start: usize, pos: usize) { unsafe { // Take out the value at `pos` and create a hole. let mut hole = Hole::new(&mut self.data, pos); while hole.pos() > start { let parent = (hole.pos() - 1) / 2; if hole.removed() <= hole.get(parent) { break } hole.move_to(parent); } } } fn sift_down_range(&mut self, mut pos: usize, end: usize) { let start = pos; unsafe { let mut hole = Hole::new(&mut self.data, pos); let mut child = 2 * pos + 1; while child < end { let right = child + 1; if right < end && !(hole.get(child) > hole.get(right)) { child = right; } hole.move_to(child); child = 2 * hole.pos() + 1; } pos = hole.pos; } self.sift_up(start, pos); } fn sift_down(&mut self, pos: usize) { let len = self.len(); self.sift_down_range(pos, len); } /// Returns the length of the binary heap. #[stable(feature = "rust1", since = "1.0.0")] pub fn len(&self) -> usize { self.data.len() } /// Checks if the binary heap is empty. #[stable(feature = "rust1", since = "1.0.0")] pub fn is_empty(&self) -> bool { self.len() == 0 } /// Clears the binary heap, returning an iterator over the removed elements. /// /// The elements are removed in arbitrary order. #[inline] #[unstable(feature = "collections", reason = "matches collection reform specification, waiting for dust to settle")] pub fn drain(&mut self) -> Drain<T> { Drain { iter: self.data.drain(..) } } /// Drops all items from the binary heap. #[stable(feature = "rust1", since = "1.0.0")] pub fn clear(&mut self) { self.drain(); } } /// 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: 'a> { data: &'a mut [T], /// `elt` is always `Some` from new until drop. elt: Option<T>, pos: usize, } impl<'a, T> Hole<'a, T> { /// Create a new Hole at index `pos`. fn new(data: &'a mut [T], pos: usize) -> Self { unsafe { let elt = ptr::read(&data[pos]); Hole { data: data, elt: Some(elt), pos: pos, } } } #[inline(always)] fn pos(&self) -> usize { self.pos } /// Return a reference to the element removed #[inline(always)] fn removed(&self) -> &T { self.elt.as_ref().unwrap() } /// Return a reference to the element at `index`. /// /// Panics if the index is out of bounds. /// /// Unsafe because index must not equal pos. #[inline(always)] unsafe fn get(&self, index: usize) -> &T { debug_assert!(index != self.pos); &self.data[index] } /// Move hole to new location /// /// Unsafe because index must not equal pos. #[inline(always)] unsafe fn move_to(&mut self, index: usize) { debug_assert!(index != self.pos); let index_ptr: *const _ = &self.data[index]; let hole_ptr = &mut self.data[self.pos]; ptr::copy_nonoverlapping(index_ptr, hole_ptr, 1); self.pos = index; } } impl<'a, T> Drop for Hole<'a, T> { fn drop(&mut self) { // fill the hole again unsafe { let pos = self.pos; ptr::write(&mut self.data[pos], self.elt.take().unwrap()); } } } /// `BinaryHeap` iterator. #[stable(feature = "rust1", since = "1.0.0")] pub struct Iter <'a, T: 'a> { iter: slice::Iter<'a, T>, } // FIXME(#19839) Remove in favor of `#[derive(Clone)]` #[stable(feature = "rust1", since = "1.0.0")] impl<'a, T> Clone for Iter<'a, T> { fn clone(&self) -> Iter<'a, T> { Iter { iter: self.iter.clone() } } } #[stable(feature = "rust1", since = "1.0.0")] impl<'a, T> Iterator for Iter<'a, T> { type Item = &'a T; #[inline] fn next(&mut self) -> Option<&'a T> { self.iter.next() } #[inline] fn size_hint(&self) -> (usize, Option<usize>) { self.iter.size_hint() } } #[stable(feature = "rust1", since = "1.0.0")] impl<'a, T> DoubleEndedIterator for Iter<'a, T> { #[inline] fn next_back(&mut self) -> Option<&'a T> { self.iter.next_back() } } #[stable(feature = "rust1", since = "1.0.0")] impl<'a, T> ExactSizeIterator for Iter<'a, T> {} /// An iterator that moves out of a `BinaryHeap`. #[stable(feature = "rust1", since = "1.0.0")] pub struct IntoIter<T> { iter: vec::IntoIter<T>, } #[stable(feature = "rust1", since = "1.0.0")] impl<T> Iterator for IntoIter<T> { type Item = T; #[inline] fn next(&mut self) -> Option<T> { self.iter.next() } #[inline] fn size_hint(&self) -> (usize, Option<usize>) { self.iter.size_hint() } } #[stable(feature = "rust1", since = "1.0.0")] impl<T> DoubleEndedIterator for IntoIter<T> { #[inline] fn next_back(&mut self) -> Option<T> { self.iter.next_back() } } #[stable(feature = "rust1", since = "1.0.0")] impl<T> ExactSizeIterator for IntoIter<T> {} /// An iterator that drains a `BinaryHeap`. #[unstable(feature = "collections", reason = "recent addition")] pub struct Drain<'a, T: 'a> { iter: vec::Drain<'a, T>, } #[stable(feature = "rust1", since = "1.0.0")] impl<'a, T: 'a> Iterator for Drain<'a, T> { type Item = T; #[inline] fn next(&mut self) -> Option<T> { self.iter.next() } #[inline] fn size_hint(&self) -> (usize, Option<usize>) { self.iter.size_hint() } } #[stable(feature = "rust1", since = "1.0.0")] impl<'a, T: 'a> DoubleEndedIterator for Drain<'a, T> { #[inline] fn next_back(&mut self) -> Option<T> { self.iter.next_back() } } #[stable(feature = "rust1", since = "1.0.0")] impl<'a, T: 'a> ExactSizeIterator for Drain<'a, T> {} #[stable(feature = "rust1", since = "1.0.0")] impl<T: Ord> FromIterator<T> for BinaryHeap<T> { fn from_iter<I: IntoIterator<Item=T>>(iter: I) -> BinaryHeap<T> { BinaryHeap::from_vec(iter.into_iter().collect()) } } #[stable(feature = "rust1", since = "1.0.0")] impl<T: Ord> IntoIterator for BinaryHeap<T> { type Item = T; type IntoIter = IntoIter<T>; /// Creates a consuming iterator, that is, one that moves each value out of /// the binary heap in arbitrary order. The binary heap cannot be used /// after calling this. /// /// # Examples /// /// ``` /// # #![feature(collections)] /// use std::collections::BinaryHeap; /// let heap = BinaryHeap::from_vec(vec![1, 2, 3, 4]); /// /// // Print 1, 2, 3, 4 in arbitrary order /// for x in heap.into_iter() { /// // x has type i32, not &i32 /// println!("{}", x); /// } /// ``` fn into_iter(self) -> IntoIter<T> { IntoIter { iter: self.data.into_iter() } } } #[stable(feature = "rust1", since = "1.0.0")] impl<'a, T> IntoIterator for &'a BinaryHeap<T> where T: Ord { type Item = &'a T; type IntoIter = Iter<'a, T>; fn into_iter(self) -> Iter<'a, T> { self.iter() } } #[stable(feature = "rust1", since = "1.0.0")] impl<T: Ord> Extend<T> for BinaryHeap<T> { fn extend<I: IntoIterator<Item=T>>(&mut self, iterable: I) { let iter = iterable.into_iter(); let (lower, _) = iter.size_hint(); self.reserve(lower); for elem in iter { self.push(elem); } } }