binary_heap.rs

// 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::{zeroed, replace, 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
    // 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 sift_up(&mut self, start: usize, mut pos: usize) {
        unsafe {
            let new = replace(&mut self.data[pos], zeroed());

            while pos > start {
                let parent = (pos - 1) >> 1;

                if new <= self.data[parent] { break; }

                let x = replace(&mut self.data[parent], zeroed());
                ptr::write(&mut self.data[pos], x);
                pos = parent;
            }
            ptr::write(&mut self.data[pos], new);
        }
    }

    fn sift_down_range(&mut self, mut pos: usize, end: usize) {
        unsafe {
            let start = pos;
            let new = replace(&mut self.data[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(&mut self.data[child], zeroed());
                ptr::write(&mut self.data[pos], x);
                pos = child;
                child = 2 * pos + 1;
            }

            ptr::write(&mut self.data[pos], new);
            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(); }
}

/// `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);
        }
    }
}