rust/src/libcollections/priority_queue.rs
2014-09-13 15:05:56 -04:00

716 lines
22 KiB
Rust

// 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.
//!
//! Insertions have `O(log n)` time complexity and checking or popping the largest element is
//! `O(1)`. Converting a vector to a priority queue can be done in-place, and has `O(n)`
//! complexity. A priority queue can also be converted to a sorted vector in-place, allowing it to
//! be used for an `O(n log n)` in-place heapsort.
//!
//! # Example
//!
//! This is a larger example which implements [Dijkstra's algorithm][dijkstra]
//! to solve the [shortest path problem][sssp] on a [directed graph][dir_graph].
//! It showcases how to use the `PriorityQueue` 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::collections::PriorityQueue;
//! use std::uint;
//!
//! #[deriving(Eq, PartialEq)]
//! struct State {
//! cost: uint,
//! position: uint
//! }
//!
//! // 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 `uint`, for a shorter implementation.
//! struct Edge {
//! node: uint,
//! cost: uint
//! }
//!
//! // 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 `uint::MAX` as a sentinel value,
//! // for a simpler implementation.
//! fn shortest_path(adj_list: &Vec<Vec<Edge>>, start: uint, goal: uint) -> uint {
//! // dist[node] = current shortest distance from `start` to `node`
//! let mut dist = Vec::from_elem(adj_list.len(), uint::MAX);
//!
//! let mut pq = PriorityQueue::new();
//!
//! // We're at `start`, with a zero cost
//! *dist.get_mut(start) = 0u;
//! pq.push(State { cost: 0u, position: start });
//!
//! // Examine the frontier with lower cost nodes first (min-heap)
//! loop {
//! let State { cost, position } = match pq.pop() {
//! None => break, // empty
//! Some(s) => s
//! };
//!
//! // 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] {
//! pq.push(next);
//! // Relaxation, we have now found a better way
//! *dist.get_mut(next.position) = next.cost;
//! }
//! }
//! }
//!
//! // Goal not reachable
//! uint::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 symbolises 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 it's 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), uint::MAX);
//! }
//! ```
#![allow(missing_doc)]
use core::prelude::*;
use core::default::Default;
use core::mem::{zeroed, replace, swap};
use core::ptr;
use {Mutable, MutableSeq};
use slice;
use vec::Vec;
/// A priority queue implemented with a binary heap.
///
/// This will be a max-heap.
#[deriving(Clone)]
pub struct PriorityQueue<T> {
data: Vec<T>,
}
impl<T: Ord> Collection for PriorityQueue<T> {
/// Returns the length of the queue.
fn len(&self) -> uint { self.data.len() }
}
impl<T: Ord> Mutable for PriorityQueue<T> {
/// Drops all items from the queue.
fn clear(&mut self) { self.data.truncate(0) }
}
impl<T: Ord> Default for PriorityQueue<T> {
#[inline]
fn default() -> PriorityQueue<T> { PriorityQueue::new() }
}
impl<T: Ord> PriorityQueue<T> {
/// Creates an empty `PriorityQueue` as a max-heap.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
/// let pq: PriorityQueue<uint> = PriorityQueue::new();
/// ```
pub fn new() -> PriorityQueue<T> { PriorityQueue{data: vec!(),} }
/// Creates an empty `PriorityQueue` with a specific capacity.
/// This preallocates enough memory for `capacity` elements,
/// so that the `PriorityQueue` does not have to be reallocated
/// until it contains at least that many values.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
/// let pq: PriorityQueue<uint> = PriorityQueue::with_capacity(10u);
/// ```
pub fn with_capacity(capacity: uint) -> PriorityQueue<T> {
PriorityQueue { data: Vec::with_capacity(capacity) }
}
/// Creates a `PriorityQueue` from a vector. This is sometimes called
/// `heapifying` the vector.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
/// let pq = PriorityQueue::from_vec(vec![9i, 1, 2, 7, 3, 2]);
/// ```
pub fn from_vec(xs: Vec<T>) -> PriorityQueue<T> {
let mut q = PriorityQueue{data: xs,};
let mut n = q.len() / 2;
while n > 0 {
n -= 1;
q.siftdown(n)
}
q
}
/// An iterator visiting all values in underlying vector, in
/// arbitrary order.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
/// let pq = PriorityQueue::from_vec(vec![1i, 2, 3, 4]);
///
/// // Print 1, 2, 3, 4 in arbitrary order
/// for x in pq.iter() {
/// println!("{}", x);
/// }
/// ```
pub fn iter<'a>(&'a self) -> Items<'a, T> {
Items { iter: self.data.iter() }
}
/// Returns the greatest item in a queue, or `None` if it is empty.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let mut pq = PriorityQueue::new();
/// assert_eq!(pq.top(), None);
///
/// pq.push(1i);
/// pq.push(5i);
/// pq.push(2i);
/// assert_eq!(pq.top(), Some(&5i));
///
/// ```
pub fn top<'a>(&'a self) -> Option<&'a T> {
if self.is_empty() { None } else { Some(&self.data[0]) }
}
#[deprecated="renamed to `top`"]
pub fn maybe_top<'a>(&'a self) -> Option<&'a T> { self.top() }
/// Returns the number of elements the queue can hold without reallocating.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let pq: PriorityQueue<uint> = PriorityQueue::with_capacity(100u);
/// assert!(pq.capacity() >= 100u);
/// ```
pub fn capacity(&self) -> uint { self.data.capacity() }
/// Reserves capacity for exactly `n` elements in the `PriorityQueue`.
/// Do nothing if the capacity is already sufficient.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let mut pq: PriorityQueue<uint> = PriorityQueue::new();
/// pq.reserve_exact(100u);
/// assert!(pq.capacity() == 100u);
/// ```
pub fn reserve_exact(&mut self, n: uint) { self.data.reserve_exact(n) }
/// Reserves capacity for at least `n` elements in the `PriorityQueue`.
/// Do nothing if the capacity is already sufficient.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let mut pq: PriorityQueue<uint> = PriorityQueue::new();
/// pq.reserve(100u);
/// assert!(pq.capacity() >= 100u);
/// ```
pub fn reserve(&mut self, n: uint) {
self.data.reserve(n)
}
/// Removes the greatest item from a queue and returns it, or `None` if it
/// is empty.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let mut pq = PriorityQueue::from_vec(vec![1i, 3]);
///
/// assert_eq!(pq.pop(), Some(3i));
/// assert_eq!(pq.pop(), Some(1i));
/// assert_eq!(pq.pop(), None);
/// ```
pub fn pop(&mut self) -> Option<T> {
match self.data.pop() {
None => { None }
Some(mut item) => {
if !self.is_empty() {
swap(&mut item, self.data.get_mut(0));
self.siftdown(0);
}
Some(item)
}
}
}
#[deprecated="renamed to `pop`"]
pub fn maybe_pop(&mut self) -> Option<T> { self.pop() }
/// Pushes an item onto the queue.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let mut pq = PriorityQueue::new();
/// pq.push(3i);
/// pq.push(5i);
/// pq.push(1i);
///
/// assert_eq!(pq.len(), 3);
/// assert_eq!(pq.top(), Some(&5i));
/// ```
pub fn push(&mut self, item: T) {
self.data.push(item);
let new_len = self.len() - 1;
self.siftup(0, new_len);
}
/// Pushes an item onto a queue then pops the greatest item off the queue in
/// an optimized fashion.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let mut pq = PriorityQueue::new();
/// pq.push(1i);
/// pq.push(5i);
///
/// assert_eq!(pq.push_pop(3i), 5);
/// assert_eq!(pq.push_pop(9i), 9);
/// assert_eq!(pq.len(), 2);
/// assert_eq!(pq.top(), Some(&3i));
/// ```
pub fn push_pop(&mut self, mut item: T) -> T {
if !self.is_empty() && *self.top().unwrap() > item {
swap(&mut item, self.data.get_mut(0));
self.siftdown(0);
}
item
}
/// Pops the greatest item off a queue then pushes an item onto the queue in
/// an optimized fashion. The push is done regardless of whether the queue
/// was empty.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let mut pq = PriorityQueue::new();
///
/// assert_eq!(pq.replace(1i), None);
/// assert_eq!(pq.replace(3i), Some(1i));
/// assert_eq!(pq.len(), 1);
/// assert_eq!(pq.top(), Some(&3i));
/// ```
pub fn replace(&mut self, mut item: T) -> Option<T> {
if !self.is_empty() {
swap(&mut item, self.data.get_mut(0));
self.siftdown(0);
Some(item)
} else {
self.push(item);
None
}
}
#[allow(dead_code)]
#[deprecated="renamed to `into_vec`"]
fn to_vec(self) -> Vec<T> { self.into_vec() }
#[allow(dead_code)]
#[deprecated="renamed to `into_sorted_vec`"]
fn to_sorted_vec(self) -> Vec<T> { self.into_sorted_vec() }
/// Consumes the `PriorityQueue` and returns the underlying vector
/// in arbitrary order.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let pq = PriorityQueue::from_vec(vec![1i, 2, 3, 4, 5, 6, 7]);
/// let vec = pq.into_vec();
///
/// // Will print in some order
/// for x in vec.iter() {
/// println!("{}", x);
/// }
/// ```
pub fn into_vec(self) -> Vec<T> { let PriorityQueue{data: v} = self; v }
/// Consumes the `PriorityQueue` and returns a vector in sorted
/// (ascending) order.
///
/// # Example
///
/// ```
/// use std::collections::PriorityQueue;
///
/// let mut pq = PriorityQueue::from_vec(vec![1i, 2, 4, 5, 7]);
/// pq.push(6);
/// pq.push(3);
///
/// let vec = pq.into_sorted_vec();
/// assert_eq!(vec, vec![1i, 2, 3, 4, 5, 6, 7]);
/// ```
pub fn into_sorted_vec(self) -> Vec<T> {
let mut q = self;
let mut end = q.len();
while end > 1 {
end -= 1;
q.data.as_mut_slice().swap(0, end);
q.siftdown_range(0, end)
}
q.into_vec()
}
// The implementations of siftup and siftdown use unsafe blocks in
// order to move an element out of the vector (leaving behind a
// zeroed element), shift along the others and move it back into the
// vector over the junk element. This reduces the constant factor
// compared to using swaps, which involves twice as many moves.
fn siftup(&mut self, start: uint, mut pos: uint) {
unsafe {
let new = replace(self.data.get_mut(pos), zeroed());
while pos > start {
let parent = (pos - 1) >> 1;
if new > self.data[parent] {
let x = replace(self.data.get_mut(parent), zeroed());
ptr::write(self.data.get_mut(pos), x);
pos = parent;
continue
}
break
}
ptr::write(self.data.get_mut(pos), new);
}
}
fn siftdown_range(&mut self, mut pos: uint, end: uint) {
unsafe {
let start = pos;
let new = replace(self.data.get_mut(pos), zeroed());
let mut child = 2 * pos + 1;
while child < end {
let right = child + 1;
if right < end && !(self.data[child] > self.data[right]) {
child = right;
}
let x = replace(self.data.get_mut(child), zeroed());
ptr::write(self.data.get_mut(pos), x);
pos = child;
child = 2 * pos + 1;
}
ptr::write(self.data.get_mut(pos), new);
self.siftup(start, pos);
}
}
fn siftdown(&mut self, pos: uint) {
let len = self.len();
self.siftdown_range(pos, len);
}
}
/// `PriorityQueue` iterator.
pub struct Items <'a, T:'a> {
iter: slice::Items<'a, T>,
}
impl<'a, T> Iterator<&'a T> for Items<'a, T> {
#[inline]
fn next(&mut self) -> Option<(&'a T)> { self.iter.next() }
#[inline]
fn size_hint(&self) -> (uint, Option<uint>) { self.iter.size_hint() }
}
impl<T: Ord> FromIterator<T> for PriorityQueue<T> {
fn from_iter<Iter: Iterator<T>>(mut iter: Iter) -> PriorityQueue<T> {
let vec: Vec<T> = iter.collect();
PriorityQueue::from_vec(vec)
}
}
impl<T: Ord> Extendable<T> for PriorityQueue<T> {
fn extend<Iter: Iterator<T>>(&mut self, mut iter: Iter) {
let (lower, _) = iter.size_hint();
let len = self.capacity();
self.reserve(len + lower);
for elem in iter {
self.push(elem);
}
}
}
#[cfg(test)]
mod tests {
use std::prelude::*;
use priority_queue::PriorityQueue;
use vec::Vec;
use MutableSeq;
#[test]
fn test_iterator() {
let data = vec!(5i, 9, 3);
let iterout = [9i, 5, 3];
let pq = PriorityQueue::from_vec(data);
let mut i = 0;
for el in pq.iter() {
assert_eq!(*el, iterout[i]);
i += 1;
}
}
#[test]
fn test_top_and_pop() {
let data = vec!(2u, 4, 6, 2, 1, 8, 10, 3, 5, 7, 0, 9, 1);
let mut sorted = data.clone();
sorted.sort();
let mut heap = PriorityQueue::from_vec(data);
while !heap.is_empty() {
assert_eq!(heap.top().unwrap(), sorted.last().unwrap());
assert_eq!(heap.pop().unwrap(), sorted.pop().unwrap());
}
}
#[test]
fn test_push() {
let mut heap = PriorityQueue::from_vec(vec!(2i, 4, 9));
assert_eq!(heap.len(), 3);
assert!(*heap.top().unwrap() == 9);
heap.push(11);
assert_eq!(heap.len(), 4);
assert!(*heap.top().unwrap() == 11);
heap.push(5);
assert_eq!(heap.len(), 5);
assert!(*heap.top().unwrap() == 11);
heap.push(27);
assert_eq!(heap.len(), 6);
assert!(*heap.top().unwrap() == 27);
heap.push(3);
assert_eq!(heap.len(), 7);
assert!(*heap.top().unwrap() == 27);
heap.push(103);
assert_eq!(heap.len(), 8);
assert!(*heap.top().unwrap() == 103);
}
#[test]
fn test_push_unique() {
let mut heap = PriorityQueue::from_vec(vec!(box 2i, box 4, box 9));
assert_eq!(heap.len(), 3);
assert!(*heap.top().unwrap() == box 9);
heap.push(box 11);
assert_eq!(heap.len(), 4);
assert!(*heap.top().unwrap() == box 11);
heap.push(box 5);
assert_eq!(heap.len(), 5);
assert!(*heap.top().unwrap() == box 11);
heap.push(box 27);
assert_eq!(heap.len(), 6);
assert!(*heap.top().unwrap() == box 27);
heap.push(box 3);
assert_eq!(heap.len(), 7);
assert!(*heap.top().unwrap() == box 27);
heap.push(box 103);
assert_eq!(heap.len(), 8);
assert!(*heap.top().unwrap() == box 103);
}
#[test]
fn test_push_pop() {
let mut heap = PriorityQueue::from_vec(vec!(5i, 5, 2, 1, 3));
assert_eq!(heap.len(), 5);
assert_eq!(heap.push_pop(6), 6);
assert_eq!(heap.len(), 5);
assert_eq!(heap.push_pop(0), 5);
assert_eq!(heap.len(), 5);
assert_eq!(heap.push_pop(4), 5);
assert_eq!(heap.len(), 5);
assert_eq!(heap.push_pop(1), 4);
assert_eq!(heap.len(), 5);
}
#[test]
fn test_replace() {
let mut heap = PriorityQueue::from_vec(vec!(5i, 5, 2, 1, 3));
assert_eq!(heap.len(), 5);
assert_eq!(heap.replace(6).unwrap(), 5);
assert_eq!(heap.len(), 5);
assert_eq!(heap.replace(0).unwrap(), 6);
assert_eq!(heap.len(), 5);
assert_eq!(heap.replace(4).unwrap(), 5);
assert_eq!(heap.len(), 5);
assert_eq!(heap.replace(1).unwrap(), 4);
assert_eq!(heap.len(), 5);
}
fn check_to_vec(mut data: Vec<int>) {
let heap = PriorityQueue::from_vec(data.clone());
let mut v = heap.clone().into_vec();
v.sort();
data.sort();
assert_eq!(v.as_slice(), data.as_slice());
assert_eq!(heap.into_sorted_vec().as_slice(), data.as_slice());
}
#[test]
fn test_to_vec() {
check_to_vec(vec!());
check_to_vec(vec!(5i));
check_to_vec(vec!(3i, 2));
check_to_vec(vec!(2i, 3));
check_to_vec(vec!(5i, 1, 2));
check_to_vec(vec!(1i, 100, 2, 3));
check_to_vec(vec!(1i, 3, 5, 7, 9, 2, 4, 6, 8, 0));
check_to_vec(vec!(2i, 4, 6, 2, 1, 8, 10, 3, 5, 7, 0, 9, 1));
check_to_vec(vec!(9i, 11, 9, 9, 9, 9, 11, 2, 3, 4, 11, 9, 0, 0, 0, 0));
check_to_vec(vec!(0i, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10));
check_to_vec(vec!(10i, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0));
check_to_vec(vec!(0i, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 1, 2));
check_to_vec(vec!(5i, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1));
}
#[test]
fn test_empty_pop() {
let mut heap: PriorityQueue<int> = PriorityQueue::new();
assert!(heap.pop().is_none());
}
#[test]
fn test_empty_top() {
let empty: PriorityQueue<int> = PriorityQueue::new();
assert!(empty.top().is_none());
}
#[test]
fn test_empty_replace() {
let mut heap: PriorityQueue<int> = PriorityQueue::new();
heap.replace(5).is_none();
}
#[test]
fn test_from_iter() {
let xs = vec!(9u, 8, 7, 6, 5, 4, 3, 2, 1);
let mut q: PriorityQueue<uint> = xs.as_slice().iter().rev().map(|&x| x).collect();
for &x in xs.iter() {
assert_eq!(q.pop().unwrap(), x);
}
}
}