d36a8f3f9c
Implement for Vec, DList, RingBuf. Add MutableSeq to the prelude. Since the collections traits are in the prelude most consumers of these methods will continue to work without change. [breaking-change]
545 lines
17 KiB
Rust
545 lines
17 KiB
Rust
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! A priority queue implemented with a binary heap.
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//!
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//! # Example
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//!
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//! This is a larger example which implements [Dijkstra's algorithm][dijkstra]
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//! to solve the [shortest path problem][sssp] on a [directed graph][dir_graph].
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//! It showcases how to use the `PriorityQueue` with custom types.
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//!
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//! [dijkstra]: http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
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//! [sssp]: http://en.wikipedia.org/wiki/Shortest_path_problem
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//! [dir_graph]: http://en.wikipedia.org/wiki/Directed_graph
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//!
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//! ```
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//! use std::collections::PriorityQueue;
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//! use std::uint;
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//!
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//! #[deriving(Eq, PartialEq)]
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//! struct State {
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//! cost: uint,
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//! position: uint
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//! }
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//!
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//! // The priority queue depends on `Ord`.
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//! // Explicitly implement the trait so the queue becomes a min-heap
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//! // instead of a max-heap.
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//! impl Ord for State {
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//! fn cmp(&self, other: &State) -> Ordering {
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//! // Notice that the we flip the ordering here
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//! other.cost.cmp(&self.cost)
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//! }
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//! }
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//!
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//! // `PartialOrd` needs to be implemented as well.
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//! impl PartialOrd for State {
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//! fn partial_cmp(&self, other: &State) -> Option<Ordering> {
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//! Some(self.cmp(other))
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//! }
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//! }
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//!
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//! // Each node is represented as an `uint`, for a shorter implementation.
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//! struct Edge {
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//! node: uint,
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//! cost: uint
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//! }
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//!
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//! // Dijkstra's shortest path algorithm.
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//!
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//! // Start at `start` and use `dist` to track the current shortest distance
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//! // to each node. This implementation isn't memory efficient as it may leave duplicate
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//! // nodes in the queue. It also uses `uint::MAX` as a sentinel value,
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//! // for a simpler implementation.
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//! fn shortest_path(adj_list: &Vec<Vec<Edge>>, start: uint, goal: uint) -> uint {
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//! // dist[node] = current shortest distance from `start` to `node`
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//! let mut dist = Vec::from_elem(adj_list.len(), uint::MAX);
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//!
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//! let mut pq = PriorityQueue::new();
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//!
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//! // We're at `start`, with a zero cost
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//! *dist.get_mut(start) = 0u;
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//! pq.push(State { cost: 0u, position: start });
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//!
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//! // Examine the frontier with lower cost nodes first (min-heap)
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//! loop {
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//! let State { cost, position } = match pq.pop() {
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//! None => break, // empty
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//! Some(s) => s
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//! };
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//!
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//! // Alternatively we could have continued to find all shortest paths
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//! if position == goal { return cost }
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//!
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//! // Important as we may have already found a better way
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//! if cost > dist[position] { continue }
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//!
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//! // For each node we can reach, see if we can find a way with
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//! // a lower cost going through this node
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//! for edge in adj_list[position].iter() {
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//! let next = State { cost: cost + edge.cost, position: edge.node };
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//!
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//! // If so, add it to the frontier and continue
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//! if next.cost < dist[next.position] {
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//! pq.push(next);
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//! // Relaxation, we have now found a better way
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//! *dist.get_mut(next.position) = next.cost;
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//! }
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//! }
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//! }
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//!
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//! // Goal not reachable
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//! uint::MAX
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//! }
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//!
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//! fn main() {
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//! // This is the directed graph we're going to use.
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//! // The node numbers correspond to the different states,
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//! // and the edge weights symbolises the cost of moving
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//! // from one node to another.
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//! // Note that the edges are one-way.
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//! //
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//! // 7
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//! // +-----------------+
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//! // | |
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//! // v 1 2 |
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//! // 0 -----> 1 -----> 3 ---> 4
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//! // | ^ ^ ^
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//! // | | 1 | |
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//! // | | | 3 | 1
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//! // +------> 2 -------+ |
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//! // 10 | |
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//! // +---------------+
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//! //
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//! // The graph is represented as an adjecency list where each index,
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//! // corresponding to a node value, has a list of outgoing edges.
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//! // Chosen for it's efficiency.
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//! let graph = vec![
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//! // Node 0
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//! vec![Edge { node: 2, cost: 10 },
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//! Edge { node: 1, cost: 1 }],
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//! // Node 1
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//! vec![Edge { node: 3, cost: 2 }],
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//! // Node 2
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//! vec![Edge { node: 1, cost: 1 },
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//! Edge { node: 3, cost: 3 },
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//! Edge { node: 4, cost: 1 }],
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//! // Node 3
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//! vec![Edge { node: 0, cost: 7 },
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//! Edge { node: 4, cost: 2 }],
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//! // Node 4
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//! vec![]];
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//!
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//! assert_eq!(shortest_path(&graph, 0, 1), 1);
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//! assert_eq!(shortest_path(&graph, 0, 3), 3);
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//! assert_eq!(shortest_path(&graph, 3, 0), 7);
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//! assert_eq!(shortest_path(&graph, 0, 4), 5);
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//! assert_eq!(shortest_path(&graph, 4, 0), uint::MAX);
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//! }
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//! ```
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#![allow(missing_doc)]
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use core::prelude::*;
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use core::default::Default;
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use core::mem::{zeroed, replace, swap};
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use core::ptr;
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use {Collection, Mutable, MutableSeq};
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use slice;
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use vec::Vec;
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/// A priority queue implemented with a binary heap
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#[deriving(Clone)]
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pub struct PriorityQueue<T> {
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data: Vec<T>,
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}
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impl<T: Ord> Collection for PriorityQueue<T> {
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/// Returns the length of the queue
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fn len(&self) -> uint { self.data.len() }
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}
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impl<T: Ord> Mutable for PriorityQueue<T> {
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/// Drop all items from the queue
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fn clear(&mut self) { self.data.truncate(0) }
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}
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impl<T: Ord> Default for PriorityQueue<T> {
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#[inline]
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fn default() -> PriorityQueue<T> { PriorityQueue::new() }
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}
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impl<T: Ord> PriorityQueue<T> {
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/// An iterator visiting all values in underlying vector, in
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/// arbitrary order.
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pub fn iter<'a>(&'a self) -> Items<'a, T> {
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Items { iter: self.data.iter() }
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}
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/// Returns the greatest item in a queue or None if it is empty
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pub fn top<'a>(&'a self) -> Option<&'a T> {
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if self.is_empty() { None } else { Some(self.data.get(0)) }
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}
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#[deprecated="renamed to `top`"]
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pub fn maybe_top<'a>(&'a self) -> Option<&'a T> { self.top() }
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/// Returns the number of elements the queue can hold without reallocating
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pub fn capacity(&self) -> uint { self.data.capacity() }
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/// Reserve capacity for exactly n elements in the PriorityQueue.
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/// Do nothing if the capacity is already sufficient.
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pub fn reserve_exact(&mut self, n: uint) { self.data.reserve_exact(n) }
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/// Reserve capacity for at least n elements in the PriorityQueue.
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/// Do nothing if the capacity is already sufficient.
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pub fn reserve(&mut self, n: uint) {
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self.data.reserve(n)
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}
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/// Remove the greatest item from a queue and return it, or `None` if it is
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/// empty.
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pub fn pop(&mut self) -> Option<T> {
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match self.data.pop() {
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None => { None }
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Some(mut item) => {
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if !self.is_empty() {
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swap(&mut item, self.data.get_mut(0));
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self.siftdown(0);
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}
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Some(item)
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}
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}
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}
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#[deprecated="renamed to `pop`"]
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pub fn maybe_pop(&mut self) -> Option<T> { self.pop() }
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/// Push an item onto the queue
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pub fn push(&mut self, item: T) {
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self.data.push(item);
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let new_len = self.len() - 1;
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self.siftup(0, new_len);
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}
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/// Optimized version of a push followed by a pop
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pub fn push_pop(&mut self, mut item: T) -> T {
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if !self.is_empty() && *self.top().unwrap() > item {
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swap(&mut item, self.data.get_mut(0));
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self.siftdown(0);
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}
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item
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}
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/// Optimized version of a pop followed by a push. The push is done
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/// regardless of whether the queue is empty.
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pub fn replace(&mut self, mut item: T) -> Option<T> {
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if !self.is_empty() {
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swap(&mut item, self.data.get_mut(0));
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self.siftdown(0);
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Some(item)
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} else {
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self.push(item);
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None
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}
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}
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#[allow(dead_code)]
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#[deprecated="renamed to `into_vec`"]
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fn to_vec(self) -> Vec<T> { self.into_vec() }
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#[allow(dead_code)]
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#[deprecated="renamed to `into_sorted_vec`"]
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fn to_sorted_vec(self) -> Vec<T> { self.into_sorted_vec() }
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/// Consume the PriorityQueue and return the underlying vector
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pub fn into_vec(self) -> Vec<T> { let PriorityQueue{data: v} = self; v }
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/// Consume the PriorityQueue and return a vector in sorted
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/// (ascending) order
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pub fn into_sorted_vec(self) -> Vec<T> {
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let mut q = self;
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let mut end = q.len();
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while end > 1 {
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end -= 1;
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q.data.as_mut_slice().swap(0, end);
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q.siftdown_range(0, end)
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}
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q.into_vec()
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}
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/// Create an empty PriorityQueue
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pub fn new() -> PriorityQueue<T> { PriorityQueue{data: vec!(),} }
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/// Create an empty PriorityQueue with capacity `capacity`
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pub fn with_capacity(capacity: uint) -> PriorityQueue<T> {
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PriorityQueue { data: Vec::with_capacity(capacity) }
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}
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/// Create a PriorityQueue from a vector (heapify)
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pub fn from_vec(xs: Vec<T>) -> PriorityQueue<T> {
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let mut q = PriorityQueue{data: xs,};
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let mut n = q.len() / 2;
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while n > 0 {
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n -= 1;
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q.siftdown(n)
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}
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q
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}
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// The implementations of siftup and siftdown use unsafe blocks in
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// order to move an element out of the vector (leaving behind a
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// zeroed element), shift along the others and move it back into the
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// vector over the junk element. This reduces the constant factor
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// compared to using swaps, which involves twice as many moves.
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fn siftup(&mut self, start: uint, mut pos: uint) {
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unsafe {
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let new = replace(self.data.get_mut(pos), zeroed());
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while pos > start {
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let parent = (pos - 1) >> 1;
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if new > *self.data.get(parent) {
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let x = replace(self.data.get_mut(parent), zeroed());
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ptr::write(self.data.get_mut(pos), x);
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pos = parent;
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continue
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}
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break
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}
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ptr::write(self.data.get_mut(pos), new);
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}
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}
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fn siftdown_range(&mut self, mut pos: uint, end: uint) {
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unsafe {
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let start = pos;
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let new = replace(self.data.get_mut(pos), zeroed());
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let mut child = 2 * pos + 1;
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while child < end {
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let right = child + 1;
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if right < end && !(*self.data.get(child) > *self.data.get(right)) {
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child = right;
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}
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let x = replace(self.data.get_mut(child), zeroed());
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ptr::write(self.data.get_mut(pos), x);
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pos = child;
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child = 2 * pos + 1;
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}
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ptr::write(self.data.get_mut(pos), new);
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self.siftup(start, pos);
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}
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}
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fn siftdown(&mut self, pos: uint) {
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let len = self.len();
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self.siftdown_range(pos, len);
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}
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}
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/// PriorityQueue iterator
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pub struct Items <'a, T> {
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iter: slice::Items<'a, T>,
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}
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impl<'a, T> Iterator<&'a T> for Items<'a, T> {
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#[inline]
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fn next(&mut self) -> Option<(&'a T)> { self.iter.next() }
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#[inline]
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fn size_hint(&self) -> (uint, Option<uint>) { self.iter.size_hint() }
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}
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impl<T: Ord> FromIterator<T> for PriorityQueue<T> {
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fn from_iter<Iter: Iterator<T>>(iter: Iter) -> PriorityQueue<T> {
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let mut q = PriorityQueue::new();
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q.extend(iter);
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q
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}
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}
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impl<T: Ord> Extendable<T> for PriorityQueue<T> {
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fn extend<Iter: Iterator<T>>(&mut self, mut iter: Iter) {
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let (lower, _) = iter.size_hint();
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let len = self.capacity();
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self.reserve(len + lower);
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for elem in iter {
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self.push(elem);
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}
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}
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}
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#[cfg(test)]
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mod tests {
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use std::prelude::*;
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use priority_queue::PriorityQueue;
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use vec::Vec;
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use MutableSeq;
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#[test]
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fn test_iterator() {
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let data = vec!(5i, 9, 3);
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let iterout = [9i, 5, 3];
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let pq = PriorityQueue::from_vec(data);
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let mut i = 0;
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for el in pq.iter() {
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assert_eq!(*el, iterout[i]);
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i += 1;
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}
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}
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#[test]
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fn test_top_and_pop() {
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let data = vec!(2u, 4, 6, 2, 1, 8, 10, 3, 5, 7, 0, 9, 1);
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let mut sorted = data.clone();
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sorted.sort();
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let mut heap = PriorityQueue::from_vec(data);
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while !heap.is_empty() {
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assert_eq!(heap.top().unwrap(), sorted.last().unwrap());
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assert_eq!(heap.pop().unwrap(), sorted.pop().unwrap());
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}
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}
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#[test]
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fn test_push() {
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let mut heap = PriorityQueue::from_vec(vec!(2i, 4, 9));
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assert_eq!(heap.len(), 3);
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assert!(*heap.top().unwrap() == 9);
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heap.push(11);
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assert_eq!(heap.len(), 4);
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assert!(*heap.top().unwrap() == 11);
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heap.push(5);
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assert_eq!(heap.len(), 5);
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assert!(*heap.top().unwrap() == 11);
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heap.push(27);
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assert_eq!(heap.len(), 6);
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assert!(*heap.top().unwrap() == 27);
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heap.push(3);
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assert_eq!(heap.len(), 7);
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assert!(*heap.top().unwrap() == 27);
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heap.push(103);
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assert_eq!(heap.len(), 8);
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assert!(*heap.top().unwrap() == 103);
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}
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#[test]
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fn test_push_unique() {
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let mut heap = PriorityQueue::from_vec(vec!(box 2i, box 4, box 9));
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assert_eq!(heap.len(), 3);
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assert!(*heap.top().unwrap() == box 9);
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heap.push(box 11);
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assert_eq!(heap.len(), 4);
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assert!(*heap.top().unwrap() == box 11);
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heap.push(box 5);
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assert_eq!(heap.len(), 5);
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assert!(*heap.top().unwrap() == box 11);
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heap.push(box 27);
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assert_eq!(heap.len(), 6);
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assert!(*heap.top().unwrap() == box 27);
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heap.push(box 3);
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assert_eq!(heap.len(), 7);
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assert!(*heap.top().unwrap() == box 27);
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heap.push(box 103);
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assert_eq!(heap.len(), 8);
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assert!(*heap.top().unwrap() == box 103);
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}
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#[test]
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fn test_push_pop() {
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let mut heap = PriorityQueue::from_vec(vec!(5i, 5, 2, 1, 3));
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assert_eq!(heap.len(), 5);
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assert_eq!(heap.push_pop(6), 6);
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assert_eq!(heap.len(), 5);
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assert_eq!(heap.push_pop(0), 5);
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assert_eq!(heap.len(), 5);
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assert_eq!(heap.push_pop(4), 5);
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assert_eq!(heap.len(), 5);
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assert_eq!(heap.push_pop(1), 4);
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assert_eq!(heap.len(), 5);
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}
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#[test]
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fn test_replace() {
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let mut heap = PriorityQueue::from_vec(vec!(5i, 5, 2, 1, 3));
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assert_eq!(heap.len(), 5);
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assert_eq!(heap.replace(6).unwrap(), 5);
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assert_eq!(heap.len(), 5);
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assert_eq!(heap.replace(0).unwrap(), 6);
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assert_eq!(heap.len(), 5);
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assert_eq!(heap.replace(4).unwrap(), 5);
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assert_eq!(heap.len(), 5);
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assert_eq!(heap.replace(1).unwrap(), 4);
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assert_eq!(heap.len(), 5);
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}
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fn check_to_vec(mut data: Vec<int>) {
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let heap = PriorityQueue::from_vec(data.clone());
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let mut v = heap.clone().into_vec();
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v.sort();
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data.sort();
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assert_eq!(v.as_slice(), data.as_slice());
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assert_eq!(heap.into_sorted_vec().as_slice(), data.as_slice());
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}
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#[test]
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fn test_to_vec() {
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check_to_vec(vec!());
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check_to_vec(vec!(5i));
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check_to_vec(vec!(3i, 2));
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|
check_to_vec(vec!(2i, 3));
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|
check_to_vec(vec!(5i, 1, 2));
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|
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));
|
|
}
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|
|
|
#[test]
|
|
fn test_empty_pop() {
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|
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);
|
|
}
|
|
}
|
|
}
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