binary_heap.rs.html -- source
Description: Source to the Rust file `src/liballoc/collections/binary_heap.rs`.
Keywords: rust, rustlang, rust-lang

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    //! 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
    //! [`BinaryHeap`]: struct.BinaryHeap.html
    //!
    //! ```
    //! 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 on costs.
    //!         // In case of a tie we compare positions - this step is necessary
    //!         // to make implementations of `PartialEq` and `Ord` consistent.
    //!         other.cost.cmp(&self.cost)
    //!             .then_with(|| self.position.cmp(&other.position))
    //!     }
    //! }
    //!
    //! // `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) -> Option<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 Some(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] {
    //!             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
    //!     None
    //! }
    //!
    //! 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    |  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), Some(1));
    //!     assert_eq!(shortest_path(&graph, 0, 3), Some(3));
    //!     assert_eq!(shortest_path(&graph, 3, 0), Some(7));
    //!     assert_eq!(shortest_path(&graph, 0, 4), Some(5));
    //!     assert_eq!(shortest_path(&graph, 4, 0), None);
    //! }
    //! ```

    #![allow(missing_docs)]
    #![stable(feature = "rust1", since = "1.0.0")]

    use core::ops::{Deref, DerefMut};
    use core::iter::{FromIterator, FusedIterator};
    use core::mem::{swap, size_of, ManuallyDrop};
    use core::ptr;
    use core::fmt;

    use crate::slice;
    use crate::vec::{self, Vec};

    use super::SpecExtend;

    /// 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.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BinaryHeap;
    ///
    /// // Type inference lets us omit an explicit type signature (which
    /// // would be `BinaryHeap<i32>` in this example).
    /// let mut heap = BinaryHeap::new();
    ///
    /// // We can use peek to look at the next item in the heap. In this case,
    /// // there's no items in there yet so we get None.
    /// assert_eq!(heap.peek(), None);
    ///
    /// // Let's add some scores...
    /// heap.push(1);
    /// heap.push(5);
    /// heap.push(2);
    ///
    /// // Now peek shows the most important item in the heap.
    /// assert_eq!(heap.peek(), Some(&5));
    ///
    /// // We can check the length of a heap.
    /// assert_eq!(heap.len(), 3);
    ///
    /// // We can iterate over the items in the heap, although they are returned in
    /// // a random order.
    /// for x in &heap {
    ///     println!("{}", x);
    /// }
    ///
    /// // If we instead pop these scores, they should come back in order.
    /// assert_eq!(heap.pop(), Some(5));
    /// assert_eq!(heap.pop(), Some(2));
    /// assert_eq!(heap.pop(), Some(1));
    /// assert_eq!(heap.pop(), None);
    ///
    /// // We can clear the heap of any remaining items.
    /// heap.clear();
    ///
    /// // The heap should now be empty.
    /// assert!(heap.is_empty())
    /// ```
    ///
    /// ## Min-heap
    ///
    /// Either `std::cmp::Reverse` or a custom `Ord` implementation can be used to
    /// make `BinaryHeap` a min-heap. This makes `heap.pop()` return the smallest
    /// value instead of the greatest one.
    ///
    /// ```
    /// use std::collections::BinaryHeap;
    /// use std::cmp::Reverse;
    ///
    /// let mut heap = BinaryHeap::new();
    ///
    /// // Wrap values in `Reverse`
    /// heap.push(Reverse(1));
    /// heap.push(Reverse(5));
    /// heap.push(Reverse(2));
    ///
    /// // If we pop these scores now, they should come back in the reverse order.
    /// assert_eq!(heap.pop(), Some(Reverse(1)));
    /// assert_eq!(heap.pop(), Some(Reverse(2)));
    /// assert_eq!(heap.pop(), Some(Reverse(5)));
    /// assert_eq!(heap.pop(), None);
    /// ```
    ///
    /// # Time complexity
    ///
    /// | [push] | [pop]    | [peek]/[peek\_mut] |
    /// |--------|----------|--------------------|
    /// | O(1)~  | O(log n) | O(1)               |
    ///
    /// The value for `push` is an expected cost; the method documentation gives a
    /// more detailed analysis.
    ///
    /// [push]: #method.push
    /// [pop]: #method.pop
    /// [peek]: #method.peek
    /// [peek\_mut]: #method.peek_mut
    #[stable(feature = "rust1", since = "1.0.0")]
    pub struct BinaryHeap<T> {
        data: Vec<T>,
    }

    /// Structure wrapping a mutable reference to the greatest item on a
    /// `BinaryHeap`.
    ///
    /// This `struct` is created by the [`peek_mut`] method on [`BinaryHeap`]. See
    /// its documentation for more.
    ///
    /// [`peek_mut`]: struct.BinaryHeap.html#method.peek_mut
    /// [`BinaryHeap`]: struct.BinaryHeap.html
    #[stable(feature = "binary_heap_peek_mut", since = "1.12.0")]
    pub struct PeekMut<'a, T: 'a + Ord> {
        heap: &'a mut BinaryHeap<T>,
        sift: bool,
    }

    #[stable(feature = "collection_debug", since = "1.17.0")]
    impl<T: Ord + fmt::Debug> fmt::Debug for PeekMut<'_, T> {
        fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
            f.debug_tuple("PeekMut")
             .field(&self.heap.data[0])
             .finish()
        }
    }

    #[stable(feature = "binary_heap_peek_mut", since = "1.12.0")]
    impl<T: Ord> Drop for PeekMut<'_, T> {
        fn drop(&mut self) {
            if self.sift {
                self.heap.sift_down(0);
            }
        }
    }

    #[stable(feature = "binary_heap_peek_mut", since = "1.12.0")]
    impl<T: Ord> Deref for PeekMut<'_, T> {
        type Target = T;
        fn deref(&self) -> &T {
            debug_assert!(!self.heap.is_empty());
            // SAFE: PeekMut is only instantiated for non-empty heaps
            unsafe { self.heap.data.get_unchecked(0) }
        }
    }

    #[stable(feature = "binary_heap_peek_mut", since = "1.12.0")]
    impl<T: Ord> DerefMut for PeekMut<'_, T> {
        fn deref_mut(&mut self) -> &mut T {
            debug_assert!(!self.heap.is_empty());
            // SAFE: PeekMut is only instantiated for non-empty heaps
            unsafe { self.heap.data.get_unchecked_mut(0) }
        }
    }

    impl<'a, T: Ord> PeekMut<'a, T> {
        /// Removes the peeked value from the heap and returns it.
        #[stable(feature = "binary_heap_peek_mut_pop", since = "1.18.0")]
        pub fn pop(mut this: PeekMut<'a, T>) -> T {
            let value = this.heap.pop().unwrap();
            this.sift = false;
            value
        }
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<T: Clone> Clone for BinaryHeap<T> {
        fn clone(&self) -> Self {
            BinaryHeap { data: self.data.clone() }
        }

        fn clone_from(&mut self, source: &Self) {
            self.data.clone_from(&source.data);
        }
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<T: Ord> Default for BinaryHeap<T> {
        /// Creates an empty `BinaryHeap<T>`.
        #[inline]
        fn default() -> BinaryHeap<T> {
            BinaryHeap::new()
        }
    }

    #[stable(feature = "binaryheap_debug", since = "1.4.0")]
    impl<T: fmt::Debug> fmt::Debug for BinaryHeap<T> {
        fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
            f.debug_list().entries(self.iter()).finish()
        }
    }

    impl<T: Ord> BinaryHeap<T> {
        /// Creates an empty `BinaryHeap` as a max-heap.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// 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
        ///
        /// Basic usage:
        ///
        /// ```
        /// 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) }
        }

        /// Returns a mutable reference to the greatest item in the binary heap, or
        /// `None` if it is empty.
        ///
        /// Note: If the `PeekMut` value is leaked, the heap may be in an
        /// inconsistent state.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let mut heap = BinaryHeap::new();
        /// assert!(heap.peek_mut().is_none());
        ///
        /// heap.push(1);
        /// heap.push(5);
        /// heap.push(2);
        /// {
        ///     let mut val = heap.peek_mut().unwrap();
        ///     *val = 0;
        /// }
        /// assert_eq!(heap.peek(), Some(&2));
        /// ```
        ///
        /// # Time complexity
        ///
        /// Cost is O(1) in the worst case.
        #[stable(feature = "binary_heap_peek_mut", since = "1.12.0")]
        pub fn peek_mut(&mut self) -> Option<PeekMut<'_, T>> {
            if self.is_empty() {
                None
            } else {
                Some(PeekMut {
                    heap: self,
                    sift: true,
                })
            }
        }

        /// Removes the greatest item from the binary heap and returns it, or `None` if it
        /// is empty.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let mut heap = BinaryHeap::from(vec![1, 3]);
        ///
        /// assert_eq!(heap.pop(), Some(3));
        /// assert_eq!(heap.pop(), Some(1));
        /// assert_eq!(heap.pop(), None);
        /// ```
        ///
        /// # Time complexity
        ///
        /// The worst case cost of `pop` on a heap containing *n* elements is O(log
        /// n).
        #[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_to_bottom(0);
                }
                item
            })
        }

        /// Pushes an item onto the binary heap.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// 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));
        /// ```
        ///
        /// # Time complexity
        ///
        /// The expected cost of `push`, averaged over every possible ordering of
        /// the elements being pushed, and over a sufficiently large number of
        /// pushes, is O(1). This is the most meaningful cost metric when pushing
        /// elements that are *not* already in any sorted pattern.
        ///
        /// The time complexity degrades if elements are pushed in predominantly
        /// ascending order. In the worst case, elements are pushed in ascending
        /// sorted order and the amortized cost per push is O(log n) against a heap
        /// containing *n* elements.
        ///
        /// The worst case cost of a *single* call to `push` is O(n). The worst case
        /// occurs when capacity is exhausted and needs a resize. The resize cost
        /// has been amortized in the previous figures.
        #[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);
        }

        /// Consumes the `BinaryHeap` and returns a vector in sorted
        /// (ascending) order.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        ///
        /// let mut heap = BinaryHeap::from(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]);
        /// ```
        #[stable(feature = "binary_heap_extras_15", since = "1.5.0")]
        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) -> 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.element() <= hole.get(parent) {
                        break;
                    }
                    hole.move_to(parent);
                }
                hole.pos()
            }
        }

        /// Take an element at `pos` and move it down the heap,
        /// while its children are larger.
        fn sift_down_range(&mut self, pos: usize, end: usize) {
            unsafe {
                let mut hole = Hole::new(&mut self.data, pos);
                let mut child = 2 * pos + 1;
                while child < end {
                    let right = child + 1;
                    // compare with the greater of the two children
                    if right < end && !(hole.get(child) > hole.get(right)) {
                        child = right;
                    }
                    // if we are already in order, stop.
                    if hole.element() >= hole.get(child) {
                        break;
                    }
                    hole.move_to(child);
                    child = 2 * hole.pos() + 1;
                }
            }
        }

        fn sift_down(&mut self, pos: usize) {
            let len = self.len();
            self.sift_down_range(pos, len);
        }

        /// Take an element at `pos` and move it all the way down the heap,
        /// then sift it up to its position.
        ///
        /// Note: This is faster when the element is known to be large / should
        /// be closer to the bottom.
        fn sift_down_to_bottom(&mut self, mut pos: usize) {
            let end = self.len();
            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;
                    // compare with the greater of the two children
                    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 rebuild(&mut self) {
            let mut n = self.len() / 2;
            while n > 0 {
                n -= 1;
                self.sift_down(n);
            }
        }

        /// Moves all the elements of `other` into `self`, leaving `other` empty.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        ///
        /// let v = vec![-10, 1, 2, 3, 3];
        /// let mut a = BinaryHeap::from(v);
        ///
        /// let v = vec![-20, 5, 43];
        /// let mut b = BinaryHeap::from(v);
        ///
        /// a.append(&mut b);
        ///
        /// assert_eq!(a.into_sorted_vec(), [-20, -10, 1, 2, 3, 3, 5, 43]);
        /// assert!(b.is_empty());
        /// ```
        #[stable(feature = "binary_heap_append", since = "1.11.0")]
        pub fn append(&mut self, other: &mut Self) {
            if self.len() < other.len() {
                swap(self, other);
            }

            if other.is_empty() {
                return;
            }

            #[inline(always)]
            fn log2_fast(x: usize) -> usize {
                8 * size_of::<usize>() - (x.leading_zeros() as usize) - 1
            }

            // `rebuild` takes O(len1 + len2) operations
            // and about 2 * (len1 + len2) comparisons in the worst case
            // while `extend` takes O(len2 * log_2(len1)) operations
            // and about 1 * len2 * log_2(len1) comparisons in the worst case,
            // assuming len1 >= len2.
            #[inline]
            fn better_to_rebuild(len1: usize, len2: usize) -> bool {
                2 * (len1 + len2) < len2 * log2_fast(len1)
            }

            if better_to_rebuild(self.len(), other.len()) {
                self.data.append(&mut other.data);
                self.rebuild();
            } else {
                self.extend(other.drain());
            }
        }
    }

    impl<T> BinaryHeap<T> {
        /// Returns an iterator visiting all values in the underlying vector, in
        /// arbitrary order.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let heap = BinaryHeap::from(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
        ///
        /// Basic usage:
        ///
        /// ```
        /// 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));
        ///
        /// ```
        ///
        /// # Time complexity
        ///
        /// Cost is O(1) in the worst case.
        #[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
        ///
        /// Basic usage:
        ///
        /// ```
        /// 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
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let mut heap = BinaryHeap::new();
        /// heap.reserve_exact(100);
        /// assert!(heap.capacity() >= 100);
        /// heap.push(4);
        /// ```
        ///
        /// [`reserve`]: #method.reserve
        #[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
        ///
        /// Basic usage:
        ///
        /// ```
        /// 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.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let mut heap: BinaryHeap<i32> = BinaryHeap::with_capacity(100);
        ///
        /// assert!(heap.capacity() >= 100);
        /// heap.shrink_to_fit();
        /// assert!(heap.capacity() == 0);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        pub fn shrink_to_fit(&mut self) {
            self.data.shrink_to_fit();
        }

        /// Discards capacity with a lower bound.
        ///
        /// The capacity will remain at least as large as both the length
        /// and the supplied value.
        ///
        /// Panics if the current capacity is smaller than the supplied
        /// minimum capacity.
        ///
        /// # Examples
        ///
        /// ```
        /// #![feature(shrink_to)]
        /// use std::collections::BinaryHeap;
        /// let mut heap: BinaryHeap<i32> = BinaryHeap::with_capacity(100);
        ///
        /// assert!(heap.capacity() >= 100);
        /// heap.shrink_to(10);
        /// assert!(heap.capacity() >= 10);
        /// ```
        #[inline]
        #[unstable(feature = "shrink_to", reason = "new API", issue="56431")]
        pub fn shrink_to(&mut self, min_capacity: usize) {
            self.data.shrink_to(min_capacity)
        }

        /// Consumes the `BinaryHeap` and returns the underlying vector
        /// in arbitrary order.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let heap = BinaryHeap::from(vec![1, 2, 3, 4, 5, 6, 7]);
        /// let vec = heap.into_vec();
        ///
        /// // Will print in some order
        /// for x in vec {
        ///     println!("{}", x);
        /// }
        /// ```
        #[stable(feature = "binary_heap_extras_15", since = "1.5.0")]
        pub fn into_vec(self) -> Vec<T> {
            self.into()
        }

        /// Returns the length of the binary heap.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let heap = BinaryHeap::from(vec![1, 3]);
        ///
        /// assert_eq!(heap.len(), 2);
        /// ```
        #[stable(feature = "rust1", since = "1.0.0")]
        pub fn len(&self) -> usize {
            self.data.len()
        }

        /// Checks if the binary heap is empty.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let mut heap = BinaryHeap::new();
        ///
        /// assert!(heap.is_empty());
        ///
        /// heap.push(3);
        /// heap.push(5);
        /// heap.push(1);
        ///
        /// assert!(!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.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let mut heap = BinaryHeap::from(vec![1, 3]);
        ///
        /// assert!(!heap.is_empty());
        ///
        /// for x in heap.drain() {
        ///     println!("{}", x);
        /// }
        ///
        /// assert!(heap.is_empty());
        /// ```
        #[inline]
        #[stable(feature = "drain", since = "1.6.0")]
        pub fn drain(&mut self) -> Drain<'_, T> {
            Drain { iter: self.data.drain(..) }
        }

        /// Drops all items from the binary heap.
        ///
        /// # Examples
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let mut heap = BinaryHeap::from(vec![1, 3]);
        ///
        /// assert!(!heap.is_empty());
        ///
        /// heap.clear();
        ///
        /// assert!(heap.is_empty());
        /// ```
        #[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: ManuallyDrop<T>,
        pos: usize,
    }

    impl<'a, T> Hole<'a, T> {
        /// Create a new `Hole` at index `pos`.
        ///
        /// Unsafe because pos must be within the data slice.
        #[inline]
        unsafe fn new(data: &'a mut [T], pos: usize) -> Self {
            debug_assert!(pos < data.len());
            // SAFE: pos should be inside the slice
            let elt = ptr::read(data.get_unchecked(pos));
            Hole {
                data,
                elt: ManuallyDrop::new(elt),
                pos,
            }
        }

        #[inline]
        fn pos(&self) -> usize {
            self.pos
        }

        /// Returns a reference to the element removed.
        #[inline]
        fn element(&self) -> &T {
            &self.elt
        }

        /// Returns a reference to the element at `index`.
        ///
        /// Unsafe because index must be within the data slice and not equal to pos.
        #[inline]
        unsafe fn get(&self, index: usize) -> &T {
            debug_assert!(index != self.pos);
            debug_assert!(index < self.data.len());
            self.data.get_unchecked(index)
        }

        /// Move hole to new location
        ///
        /// Unsafe because index must be within the data slice and not equal to pos.
        #[inline]
        unsafe fn move_to(&mut self, index: usize) {
            debug_assert!(index != self.pos);
            debug_assert!(index < self.data.len());
            let index_ptr: *const _ = self.data.get_unchecked(index);
            let hole_ptr = self.data.get_unchecked_mut(self.pos);
            ptr::copy_nonoverlapping(index_ptr, hole_ptr, 1);
            self.pos = index;
        }
    }

    impl<T> Drop for Hole<'_, T> {
        #[inline]
        fn drop(&mut self) {
            // fill the hole again
            unsafe {
                let pos = self.pos;
                ptr::copy_nonoverlapping(&*self.elt, self.data.get_unchecked_mut(pos), 1);
            }
        }
    }

    /// An iterator over the elements of a `BinaryHeap`.
    ///
    /// This `struct` is created by the [`iter`] method on [`BinaryHeap`]. See its
    /// documentation for more.
    ///
    /// [`iter`]: struct.BinaryHeap.html#method.iter
    /// [`BinaryHeap`]: struct.BinaryHeap.html
    #[stable(feature = "rust1", since = "1.0.0")]
    pub struct Iter<'a, T: 'a> {
        iter: slice::Iter<'a, T>,
    }

    #[stable(feature = "collection_debug", since = "1.17.0")]
    impl<T: fmt::Debug> fmt::Debug for Iter<'_, T> {
        fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
            f.debug_tuple("Iter")
             .field(&self.iter.as_slice())
             .finish()
        }
    }

    // FIXME(#26925) Remove in favor of `#[derive(Clone)]`
    #[stable(feature = "rust1", since = "1.0.0")]
    impl<T> Clone for Iter<'_, T> {
        fn clone(&self) -> Self {
            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()
        }

        #[inline]
        fn last(self) -> Option<&'a T> {
            self.iter.last()
        }
    }

    #[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<T> ExactSizeIterator for Iter<'_, T> {
        fn is_empty(&self) -> bool {
            self.iter.is_empty()
        }
    }

    #[stable(feature = "fused", since = "1.26.0")]
    impl<T> FusedIterator for Iter<'_, T> {}

    /// An owning iterator over the elements of a `BinaryHeap`.
    ///
    /// This `struct` is created by the [`into_iter`] method on [`BinaryHeap`][`BinaryHeap`]
    /// (provided by the `IntoIterator` trait). See its documentation for more.
    ///
    /// [`into_iter`]: struct.BinaryHeap.html#method.into_iter
    /// [`BinaryHeap`]: struct.BinaryHeap.html
    #[stable(feature = "rust1", since = "1.0.0")]
    #[derive(Clone)]
    pub struct IntoIter<T> {
        iter: vec::IntoIter<T>,
    }

    #[stable(feature = "collection_debug", since = "1.17.0")]
    impl<T: fmt::Debug> fmt::Debug for IntoIter<T> {
        fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
            f.debug_tuple("IntoIter")
             .field(&self.iter.as_slice())
             .finish()
        }
    }

    #[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> {
        fn is_empty(&self) -> bool {
            self.iter.is_empty()
        }
    }

    #[stable(feature = "fused", since = "1.26.0")]
    impl<T> FusedIterator for IntoIter<T> {}

    /// A draining iterator over the elements of a `BinaryHeap`.
    ///
    /// This `struct` is created by the [`drain`] method on [`BinaryHeap`]. See its
    /// documentation for more.
    ///
    /// [`drain`]: struct.BinaryHeap.html#method.drain
    /// [`BinaryHeap`]: struct.BinaryHeap.html
    #[stable(feature = "drain", since = "1.6.0")]
    #[derive(Debug)]
    pub struct Drain<'a, T: 'a> {
        iter: vec::Drain<'a, T>,
    }

    #[stable(feature = "drain", since = "1.6.0")]
    impl<T> Iterator for Drain<'_, 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 = "drain", since = "1.6.0")]
    impl<T> DoubleEndedIterator for Drain<'_, T> {
        #[inline]
        fn next_back(&mut self) -> Option<T> {
            self.iter.next_back()
        }
    }

    #[stable(feature = "drain", since = "1.6.0")]
    impl<T> ExactSizeIterator for Drain<'_, T> {
        fn is_empty(&self) -> bool {
            self.iter.is_empty()
        }
    }

    #[stable(feature = "fused", since = "1.26.0")]
    impl<T> FusedIterator for Drain<'_, T> {}

    #[stable(feature = "binary_heap_extras_15", since = "1.5.0")]
    impl<T: Ord> From<Vec<T>> for BinaryHeap<T> {
        /// Converts a `Vec<T>` into a `BinaryHeap<T>`.
        ///
        /// This conversion happens in-place, and has `O(n)` time complexity.
        fn from(vec: Vec<T>) -> BinaryHeap<T> {
            let mut heap = BinaryHeap { data: vec };
            heap.rebuild();
            heap
        }
    }

    #[stable(feature = "binary_heap_extras_15", since = "1.5.0")]
    impl<T> From<BinaryHeap<T>> for Vec<T> {
        fn from(heap: BinaryHeap<T>) -> Vec<T> {
            heap.data
        }
    }

    #[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(iter.into_iter().collect::<Vec<_>>())
        }
    }

    #[stable(feature = "rust1", since = "1.0.0")]
    impl<T> 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
        ///
        /// Basic usage:
        ///
        /// ```
        /// use std::collections::BinaryHeap;
        /// let heap = BinaryHeap::from(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> {
        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> {
        #[inline]
        fn extend<I: IntoIterator<Item = T>>(&mut self, iter: I) {
            <Self as SpecExtend<I>>::spec_extend(self, iter);
        }
    }

    impl<T: Ord, I: IntoIterator<Item = T>> SpecExtend<I> for BinaryHeap<T> {
        default fn spec_extend(&mut self, iter: I) {
            self.extend_desugared(iter.into_iter());
        }
    }

    impl<T: Ord> SpecExtend<BinaryHeap<T>> for BinaryHeap<T> {
        fn spec_extend(&mut self, ref mut other: BinaryHeap<T>) {
            self.append(other);
        }
    }

    impl<T: Ord> BinaryHeap<T> {
        fn extend_desugared<I: IntoIterator<Item = T>>(&mut self, iter: I) {
            let iterator = iter.into_iter();
            let (lower, _) = iterator.size_hint();

            self.reserve(lower);

            iterator.for_each(move |elem| self.push(elem));
        }
    }

    #[stable(feature = "extend_ref", since = "1.2.0")]
    impl<'a, T: 'a + Ord + Copy> Extend<&'a T> for BinaryHeap<T> {
        fn extend<I: IntoIterator<Item = &'a T>>(&mut self, iter: I) {
            self.extend(iter.into_iter().cloned());
        }
    }

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