map.rs

use core::borrow::Borrow;
use core::cmp::Ordering;
use core::fmt::{self, Debug};
use core::hash::{Hash, Hasher};
use core::iter::{FromIterator, FusedIterator, Peekable};
use core::marker::PhantomData;
use core::mem::{self, ManuallyDrop};
use core::ops::Bound::{Excluded, Included, Unbounded};
use core::ops::{Index, RangeBounds};
use core::ptr;

use super::node::{self, marker, ForceResult::*, Handle, InsertResult::*, NodeRef};
use super::search::{self, SearchResult::*};
use super::unwrap_unchecked;

use Entry::*;
use UnderflowResult::*;

/// A map based on a B-Tree.
///
/// B-Trees represent a fundamental compromise between cache-efficiency and actually minimizing
/// the amount of work performed in a search. In theory, a binary search tree (BST) is the optimal
/// choice for a sorted map, as a perfectly balanced BST performs the theoretical minimum amount of
/// comparisons necessary to find an element (log<sub>2</sub>n). However, in practice the way this
/// is done is *very* inefficient for modern computer architectures. In particular, every element
/// is stored in its own individually heap-allocated node. This means that every single insertion
/// triggers a heap-allocation, and every single comparison should be a cache-miss. Since these
/// are both notably expensive things to do in practice, we are forced to at very least reconsider
/// the BST strategy.
///
/// A B-Tree instead makes each node contain B-1 to 2B-1 elements in a contiguous array. By doing
/// this, we reduce the number of allocations by a factor of B, and improve cache efficiency in
/// searches. However, this does mean that searches will have to do *more* comparisons on average.
/// The precise number of comparisons depends on the node search strategy used. For optimal cache
/// efficiency, one could search the nodes linearly. For optimal comparisons, one could search
/// the node using binary search. As a compromise, one could also perform a linear search
/// that initially only checks every i<sup>th</sup> element for some choice of i.
///
/// Currently, our implementation simply performs naive linear search. This provides excellent
/// performance on *small* nodes of elements which are cheap to compare. However in the future we
/// would like to further explore choosing the optimal search strategy based on the choice of B,
/// and possibly other factors. Using linear search, searching for a random element is expected
/// to take O(B * log(n)) comparisons, which is generally worse than a BST. In practice,
/// however, performance is excellent.
///
/// It is a logic error for a key to be modified in such a way that the key's ordering relative to
/// any other key, as determined by the [`Ord`] trait, changes while it is in the map. This is
/// normally only possible through [`Cell`], [`RefCell`], global state, I/O, or unsafe code.
///
/// [`Ord`]: core::cmp::Ord
/// [`Cell`]: core::cell::Cell
/// [`RefCell`]: core::cell::RefCell
///
/// # Examples
///
/// ```
/// use std::collections::BTreeMap;
///
/// // type inference lets us omit an explicit type signature (which
/// // would be `BTreeMap<&str, &str>` in this example).
/// let mut movie_reviews = BTreeMap::new();
///
/// // review some movies.
/// movie_reviews.insert("Office Space",       "Deals with real issues in the workplace.");
/// movie_reviews.insert("Pulp Fiction",       "Masterpiece.");
/// movie_reviews.insert("The Godfather",      "Very enjoyable.");
/// movie_reviews.insert("The Blues Brothers", "Eye lyked it a lot.");
///
/// // check for a specific one.
/// if !movie_reviews.contains_key("Les Misérables") {
///     println!("We've got {} reviews, but Les Misérables ain't one.",
///              movie_reviews.len());
/// }
///
/// // oops, this review has a lot of spelling mistakes, let's delete it.
/// movie_reviews.remove("The Blues Brothers");
///
/// // look up the values associated with some keys.
/// let to_find = ["Up!", "Office Space"];
/// for movie in &to_find {
///     match movie_reviews.get(movie) {
///        Some(review) => println!("{}: {}", movie, review),
///        None => println!("{} is unreviewed.", movie)
///     }
/// }
///
/// // Look up the value for a key (will panic if the key is not found).
/// println!("Movie review: {}", movie_reviews["Office Space"]);
///
/// // iterate over everything.
/// for (movie, review) in &movie_reviews {
///     println!("{}: \"{}\"", movie, review);
/// }
/// ```
///
/// `BTreeMap` also implements an [`Entry API`](#method.entry), which allows
/// for more complex methods of getting, setting, updating and removing keys and
/// their values:
///
/// ```
/// use std::collections::BTreeMap;
///
/// // type inference lets us omit an explicit type signature (which
/// // would be `BTreeMap<&str, u8>` in this example).
/// let mut player_stats = BTreeMap::new();
///
/// fn random_stat_buff() -> u8 {
///     // could actually return some random value here - let's just return
///     // some fixed value for now
///     42
/// }
///
/// // insert a key only if it doesn't already exist
/// player_stats.entry("health").or_insert(100);
///
/// // insert a key using a function that provides a new value only if it
/// // doesn't already exist
/// player_stats.entry("defence").or_insert_with(random_stat_buff);
///
/// // update a key, guarding against the key possibly not being set
/// let stat = player_stats.entry("attack").or_insert(100);
/// *stat += random_stat_buff();
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
pub struct BTreeMap<K, V> {
    root: Option<node::Root<K, V>>,
    length: usize,
}

#[stable(feature = "btree_drop", since = "1.7.0")]
unsafe impl<#[may_dangle] K, #[may_dangle] V> Drop for BTreeMap<K, V> {
    fn drop(&mut self) {
        unsafe {
            drop(ptr::read(self).into_iter());
        }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: Clone, V: Clone> Clone for BTreeMap<K, V> {
    fn clone(&self) -> BTreeMap<K, V> {
        fn clone_subtree<'a, K: Clone, V: Clone>(
            node: node::NodeRef<marker::Immut<'a>, K, V, marker::LeafOrInternal>,
        ) -> BTreeMap<K, V>
        where
            K: 'a,
            V: 'a,
        {
            match node.force() {
                Leaf(leaf) => {
                    let mut out_tree = BTreeMap { root: Some(node::Root::new_leaf()), length: 0 };

                    {
                        let root = out_tree.root.as_mut().unwrap(); // unwrap succeeds because we just wrapped
                        let mut out_node = match root.node_as_mut().force() {
                            Leaf(leaf) => leaf,
                            Internal(_) => unreachable!(),
                        };

                        let mut in_edge = leaf.first_edge();
                        while let Ok(kv) = in_edge.right_kv() {
                            let (k, v) = kv.into_kv();
                            in_edge = kv.right_edge();

                            out_node.push(k.clone(), v.clone());
                            out_tree.length += 1;
                        }
                    }

                    out_tree
                }
                Internal(internal) => {
                    let mut out_tree = clone_subtree(internal.first_edge().descend());

                    {
                        let out_root = BTreeMap::ensure_is_owned(&mut out_tree.root);
                        let mut out_node = out_root.push_internal_level();
                        let mut in_edge = internal.first_edge();
                        while let Ok(kv) = in_edge.right_kv() {
                            let (k, v) = kv.into_kv();
                            in_edge = kv.right_edge();

                            let k = (*k).clone();
                            let v = (*v).clone();
                            let subtree = clone_subtree(in_edge.descend());

                            // We can't destructure subtree directly
                            // because BTreeMap implements Drop
                            let (subroot, sublength) = unsafe {
                                let subtree = ManuallyDrop::new(subtree);
                                let root = ptr::read(&subtree.root);
                                let length = subtree.length;
                                (root, length)
                            };

                            out_node.push(k, v, subroot.unwrap_or_else(node::Root::new_leaf));
                            out_tree.length += 1 + sublength;
                        }
                    }

                    out_tree
                }
            }
        }

        if self.is_empty() {
            // Ideally we'd call `BTreeMap::new` here, but that has the `K:
            // Ord` constraint, which this method lacks.
            BTreeMap { root: None, length: 0 }
        } else {
            clone_subtree(self.root.as_ref().unwrap().node_as_ref()) // unwrap succeeds because not empty
        }
    }
}

impl<K, Q: ?Sized> super::Recover<Q> for BTreeMap<K, ()>
where
    K: Borrow<Q> + Ord,
    Q: Ord,
{
    type Key = K;

    fn get(&self, key: &Q) -> Option<&K> {
        let root_node = self.root.as_ref()?.node_as_ref();
        match search::search_tree(root_node, key) {
            Found(handle) => Some(handle.into_kv().0),
            GoDown(_) => None,
        }
    }

    fn take(&mut self, key: &Q) -> Option<K> {
        let root_node = self.root.as_mut()?.node_as_mut();
        match search::search_tree(root_node, key) {
            Found(handle) => Some(
                OccupiedEntry { handle, length: &mut self.length, _marker: PhantomData }
                    .remove_kv()
                    .0,
            ),
            GoDown(_) => None,
        }
    }

    fn replace(&mut self, key: K) -> Option<K> {
        let root = Self::ensure_is_owned(&mut self.root);
        match search::search_tree::<marker::Mut<'_>, K, (), K>(root.node_as_mut(), &key) {
            Found(handle) => Some(mem::replace(handle.into_key_mut(), key)),
            GoDown(handle) => {
                VacantEntry { key, handle, length: &mut self.length, _marker: PhantomData }
                    .insert(());
                None
            }
        }
    }
}

/// An iterator over the entries of a `BTreeMap`.
///
/// This `struct` is created by the [`iter`] method on [`BTreeMap`]. See its
/// documentation for more.
///
/// [`iter`]: BTreeMap::iter
#[stable(feature = "rust1", since = "1.0.0")]
pub struct Iter<'a, K: 'a, V: 'a> {
    range: Range<'a, K, V>,
    length: usize,
}

#[stable(feature = "collection_debug", since = "1.17.0")]
impl<K: fmt::Debug, V: fmt::Debug> fmt::Debug for Iter<'_, K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_list().entries(self.clone()).finish()
    }
}

/// A mutable iterator over the entries of a `BTreeMap`.
///
/// This `struct` is created by the [`iter_mut`] method on [`BTreeMap`]. See its
/// documentation for more.
///
/// [`iter_mut`]: BTreeMap::iter_mut
#[stable(feature = "rust1", since = "1.0.0")]
#[derive(Debug)]
pub struct IterMut<'a, K: 'a, V: 'a> {
    range: RangeMut<'a, K, V>,
    length: usize,
}

/// An owning iterator over the entries of a `BTreeMap`.
///
/// This `struct` is created by the [`into_iter`] method on [`BTreeMap`]
/// (provided by the `IntoIterator` trait). See its documentation for more.
///
/// [`into_iter`]: IntoIterator::into_iter
#[stable(feature = "rust1", since = "1.0.0")]
pub struct IntoIter<K, V> {
    front: Option<Handle<NodeRef<marker::Owned, K, V, marker::Leaf>, marker::Edge>>,
    back: Option<Handle<NodeRef<marker::Owned, K, V, marker::Leaf>, marker::Edge>>,
    length: usize,
}

#[stable(feature = "collection_debug", since = "1.17.0")]
impl<K: fmt::Debug, V: fmt::Debug> fmt::Debug for IntoIter<K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        let range = Range {
            front: self.front.as_ref().map(|f| f.reborrow()),
            back: self.back.as_ref().map(|b| b.reborrow()),
        };
        f.debug_list().entries(range).finish()
    }
}

/// An iterator over the keys of a `BTreeMap`.
///
/// This `struct` is created by the [`keys`] method on [`BTreeMap`]. See its
/// documentation for more.
///
/// [`keys`]: BTreeMap::keys
#[stable(feature = "rust1", since = "1.0.0")]
pub struct Keys<'a, K: 'a, V: 'a> {
    inner: Iter<'a, K, V>,
}

#[stable(feature = "collection_debug", since = "1.17.0")]
impl<K: fmt::Debug, V> fmt::Debug for Keys<'_, K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_list().entries(self.clone()).finish()
    }
}

/// An iterator over the values of a `BTreeMap`.
///
/// This `struct` is created by the [`values`] method on [`BTreeMap`]. See its
/// documentation for more.
///
/// [`values`]: BTreeMap::values
#[stable(feature = "rust1", since = "1.0.0")]
pub struct Values<'a, K: 'a, V: 'a> {
    inner: Iter<'a, K, V>,
}

#[stable(feature = "collection_debug", since = "1.17.0")]
impl<K, V: fmt::Debug> fmt::Debug for Values<'_, K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_list().entries(self.clone()).finish()
    }
}

/// A mutable iterator over the values of a `BTreeMap`.
///
/// This `struct` is created by the [`values_mut`] method on [`BTreeMap`]. See its
/// documentation for more.
///
/// [`values_mut`]: BTreeMap::values_mut
#[stable(feature = "map_values_mut", since = "1.10.0")]
#[derive(Debug)]
pub struct ValuesMut<'a, K: 'a, V: 'a> {
    inner: IterMut<'a, K, V>,
}

/// An owning iterator over the keys of a `BTreeMap`.
///
/// This `struct` is created by the [`into_keys`] method on [`BTreeMap`].
/// See its documentation for more.
///
/// [`into_keys`]: BTreeMap::into_keys
#[unstable(feature = "map_into_keys_values", issue = "75294")]
#[derive(Debug)]
pub struct IntoKeys<K, V> {
    inner: IntoIter<K, V>,
}

/// An owning iterator over the values of a `BTreeMap`.
///
/// This `struct` is created by the [`into_values`] method on [`BTreeMap`].
/// See its documentation for more.
///
/// [`into_values`]: BTreeMap::into_values
#[unstable(feature = "map_into_keys_values", issue = "75294")]
#[derive(Debug)]
pub struct IntoValues<K, V> {
    inner: IntoIter<K, V>,
}

/// An iterator over a sub-range of entries in a `BTreeMap`.
///
/// This `struct` is created by the [`range`] method on [`BTreeMap`]. See its
/// documentation for more.
///
/// [`range`]: BTreeMap::range
#[stable(feature = "btree_range", since = "1.17.0")]
pub struct Range<'a, K: 'a, V: 'a> {
    front: Option<Handle<NodeRef<marker::Immut<'a>, K, V, marker::Leaf>, marker::Edge>>,
    back: Option<Handle<NodeRef<marker::Immut<'a>, K, V, marker::Leaf>, marker::Edge>>,
}

#[stable(feature = "collection_debug", since = "1.17.0")]
impl<K: fmt::Debug, V: fmt::Debug> fmt::Debug for Range<'_, K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_list().entries(self.clone()).finish()
    }
}

/// A mutable iterator over a sub-range of entries in a `BTreeMap`.
///
/// This `struct` is created by the [`range_mut`] method on [`BTreeMap`]. See its
/// documentation for more.
///
/// [`range_mut`]: BTreeMap::range_mut
#[stable(feature = "btree_range", since = "1.17.0")]
pub struct RangeMut<'a, K: 'a, V: 'a> {
    front: Option<Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>>,
    back: Option<Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>>,

    // Be invariant in `K` and `V`
    _marker: PhantomData<&'a mut (K, V)>,
}

#[stable(feature = "collection_debug", since = "1.17.0")]
impl<K: fmt::Debug, V: fmt::Debug> fmt::Debug for RangeMut<'_, K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        let range = Range {
            front: self.front.as_ref().map(|f| f.reborrow()),
            back: self.back.as_ref().map(|b| b.reborrow()),
        };
        f.debug_list().entries(range).finish()
    }
}

/// A view into a single entry in a map, which may either be vacant or occupied.
///
/// This `enum` is constructed from the [`entry`] method on [`BTreeMap`].
///
/// [`entry`]: BTreeMap::entry
#[stable(feature = "rust1", since = "1.0.0")]
pub enum Entry<'a, K: 'a, V: 'a> {
    /// A vacant entry.
    #[stable(feature = "rust1", since = "1.0.0")]
    Vacant(#[stable(feature = "rust1", since = "1.0.0")] VacantEntry<'a, K, V>),

    /// An occupied entry.
    #[stable(feature = "rust1", since = "1.0.0")]
    Occupied(#[stable(feature = "rust1", since = "1.0.0")] OccupiedEntry<'a, K, V>),
}

#[stable(feature = "debug_btree_map", since = "1.12.0")]
impl<K: Debug + Ord, V: Debug> Debug for Entry<'_, K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        match *self {
            Vacant(ref v) => f.debug_tuple("Entry").field(v).finish(),
            Occupied(ref o) => f.debug_tuple("Entry").field(o).finish(),
        }
    }
}

/// A view into a vacant entry in a `BTreeMap`.
/// It is part of the [`Entry`] enum.
///
/// [`Entry`]: enum.Entry.html
#[stable(feature = "rust1", since = "1.0.0")]
pub struct VacantEntry<'a, K: 'a, V: 'a> {
    key: K,
    handle: Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>,
    length: &'a mut usize,

    // Be invariant in `K` and `V`
    _marker: PhantomData<&'a mut (K, V)>,
}

#[stable(feature = "debug_btree_map", since = "1.12.0")]
impl<K: Debug + Ord, V> Debug for VacantEntry<'_, K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_tuple("VacantEntry").field(self.key()).finish()
    }
}

/// A view into an occupied entry in a `BTreeMap`.
/// It is part of the [`Entry`] enum.
///
/// [`Entry`]: enum.Entry.html
#[stable(feature = "rust1", since = "1.0.0")]
pub struct OccupiedEntry<'a, K: 'a, V: 'a> {
    handle: Handle<NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, marker::KV>,

    length: &'a mut usize,

    // Be invariant in `K` and `V`
    _marker: PhantomData<&'a mut (K, V)>,
}

#[stable(feature = "debug_btree_map", since = "1.12.0")]
impl<K: Debug + Ord, V: Debug> Debug for OccupiedEntry<'_, K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_struct("OccupiedEntry").field("key", self.key()).field("value", self.get()).finish()
    }
}

// An iterator for merging two sorted sequences into one
struct MergeIter<K, V, I: Iterator<Item = (K, V)>> {
    left: Peekable<I>,
    right: Peekable<I>,
}

impl<K: Ord, V> BTreeMap<K, V> {
    /// Makes a new empty BTreeMap.
    ///
    /// Does not allocate anything on its own.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    ///
    /// // entries can now be inserted into the empty map
    /// map.insert(1, "a");
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_btree_new", issue = "71835")]
    pub const fn new() -> BTreeMap<K, V> {
        BTreeMap { root: None, length: 0 }
    }

    /// Clears the map, removing all elements.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// a.insert(1, "a");
    /// a.clear();
    /// assert!(a.is_empty());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn clear(&mut self) {
        *self = BTreeMap::new();
    }

    /// Returns a reference to the value corresponding to the key.
    ///
    /// The key may be any borrowed form of the map's key type, but the ordering
    /// on the borrowed form *must* match the ordering on the key type.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// assert_eq!(map.get(&1), Some(&"a"));
    /// assert_eq!(map.get(&2), None);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn get<Q: ?Sized>(&self, key: &Q) -> Option<&V>
    where
        K: Borrow<Q>,
        Q: Ord,
    {
        let root_node = self.root.as_ref()?.node_as_ref();
        match search::search_tree(root_node, key) {
            Found(handle) => Some(handle.into_kv().1),
            GoDown(_) => None,
        }
    }

    /// Returns the key-value pair corresponding to the supplied key.
    ///
    /// The supplied key may be any borrowed form of the map's key type, but the ordering
    /// on the borrowed form *must* match the ordering on the key type.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// assert_eq!(map.get_key_value(&1), Some((&1, &"a")));
    /// assert_eq!(map.get_key_value(&2), None);
    /// ```
    #[stable(feature = "map_get_key_value", since = "1.40.0")]
    pub fn get_key_value<Q: ?Sized>(&self, k: &Q) -> Option<(&K, &V)>
    where
        K: Borrow<Q>,
        Q: Ord,
    {
        let root_node = self.root.as_ref()?.node_as_ref();
        match search::search_tree(root_node, k) {
            Found(handle) => Some(handle.into_kv()),
            GoDown(_) => None,
        }
    }

    /// Returns the first key-value pair in the map.
    /// The key in this pair is the minimum key in the map.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// #![feature(map_first_last)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// assert_eq!(map.first_key_value(), None);
    /// map.insert(1, "b");
    /// map.insert(2, "a");
    /// assert_eq!(map.first_key_value(), Some((&1, &"b")));
    /// ```
    #[unstable(feature = "map_first_last", issue = "62924")]
    pub fn first_key_value(&self) -> Option<(&K, &V)> {
        let root_node = self.root.as_ref()?.node_as_ref();
        root_node.first_leaf_edge().right_kv().ok().map(Handle::into_kv)
    }

    /// Returns the first entry in the map for in-place manipulation.
    /// The key of this entry is the minimum key in the map.
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(map_first_last)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// map.insert(2, "b");
    /// if let Some(mut entry) = map.first_entry() {
    ///     if *entry.key() > 0 {
    ///         entry.insert("first");
    ///     }
    /// }
    /// assert_eq!(*map.get(&1).unwrap(), "first");
    /// assert_eq!(*map.get(&2).unwrap(), "b");
    /// ```
    #[unstable(feature = "map_first_last", issue = "62924")]
    pub fn first_entry(&mut self) -> Option<OccupiedEntry<'_, K, V>> {
        let root_node = self.root.as_mut()?.node_as_mut();
        let kv = root_node.first_leaf_edge().right_kv().ok()?;
        Some(OccupiedEntry {
            handle: kv.forget_node_type(),
            length: &mut self.length,
            _marker: PhantomData,
        })
    }

    /// Removes and returns the first element in the map.
    /// The key of this element is the minimum key that was in the map.
    ///
    /// # Examples
    ///
    /// Draining elements in ascending order, while keeping a usable map each iteration.
    ///
    /// ```
    /// #![feature(map_first_last)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// map.insert(2, "b");
    /// while let Some((key, _val)) = map.pop_first() {
    ///     assert!(map.iter().all(|(k, _v)| *k > key));
    /// }
    /// assert!(map.is_empty());
    /// ```
    #[unstable(feature = "map_first_last", issue = "62924")]
    pub fn pop_first(&mut self) -> Option<(K, V)> {
        self.first_entry().map(|entry| entry.remove_entry())
    }

    /// Returns the last key-value pair in the map.
    /// The key in this pair is the maximum key in the map.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// #![feature(map_first_last)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "b");
    /// map.insert(2, "a");
    /// assert_eq!(map.last_key_value(), Some((&2, &"a")));
    /// ```
    #[unstable(feature = "map_first_last", issue = "62924")]
    pub fn last_key_value(&self) -> Option<(&K, &V)> {
        let root_node = self.root.as_ref()?.node_as_ref();
        root_node.last_leaf_edge().left_kv().ok().map(Handle::into_kv)
    }

    /// Returns the last entry in the map for in-place manipulation.
    /// The key of this entry is the maximum key in the map.
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(map_first_last)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// map.insert(2, "b");
    /// if let Some(mut entry) = map.last_entry() {
    ///     if *entry.key() > 0 {
    ///         entry.insert("last");
    ///     }
    /// }
    /// assert_eq!(*map.get(&1).unwrap(), "a");
    /// assert_eq!(*map.get(&2).unwrap(), "last");
    /// ```
    #[unstable(feature = "map_first_last", issue = "62924")]
    pub fn last_entry(&mut self) -> Option<OccupiedEntry<'_, K, V>> {
        let root_node = self.root.as_mut()?.node_as_mut();
        let kv = root_node.last_leaf_edge().left_kv().ok()?;
        Some(OccupiedEntry {
            handle: kv.forget_node_type(),
            length: &mut self.length,
            _marker: PhantomData,
        })
    }

    /// Removes and returns the last element in the map.
    /// The key of this element is the maximum key that was in the map.
    ///
    /// # Examples
    ///
    /// Draining elements in descending order, while keeping a usable map each iteration.
    ///
    /// ```
    /// #![feature(map_first_last)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// map.insert(2, "b");
    /// while let Some((key, _val)) = map.pop_last() {
    ///     assert!(map.iter().all(|(k, _v)| *k < key));
    /// }
    /// assert!(map.is_empty());
    /// ```
    #[unstable(feature = "map_first_last", issue = "62924")]
    pub fn pop_last(&mut self) -> Option<(K, V)> {
        self.last_entry().map(|entry| entry.remove_entry())
    }

    /// Returns `true` if the map contains a value for the specified key.
    ///
    /// The key may be any borrowed form of the map's key type, but the ordering
    /// on the borrowed form *must* match the ordering on the key type.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// assert_eq!(map.contains_key(&1), true);
    /// assert_eq!(map.contains_key(&2), false);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn contains_key<Q: ?Sized>(&self, key: &Q) -> bool
    where
        K: Borrow<Q>,
        Q: Ord,
    {
        self.get(key).is_some()
    }

    /// Returns a mutable reference to the value corresponding to the key.
    ///
    /// The key may be any borrowed form of the map's key type, but the ordering
    /// on the borrowed form *must* match the ordering on the key type.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// if let Some(x) = map.get_mut(&1) {
    ///     *x = "b";
    /// }
    /// assert_eq!(map[&1], "b");
    /// ```
    // See `get` for implementation notes, this is basically a copy-paste with mut's added
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn get_mut<Q: ?Sized>(&mut self, key: &Q) -> Option<&mut V>
    where
        K: Borrow<Q>,
        Q: Ord,
    {
        let root_node = self.root.as_mut()?.node_as_mut();
        match search::search_tree(root_node, key) {
            Found(handle) => Some(handle.into_val_mut()),
            GoDown(_) => None,
        }
    }

    /// Inserts a key-value pair into the map.
    ///
    /// If the map did not have this key present, `None` is returned.
    ///
    /// If the map did have this key present, the value is updated, and the old
    /// value is returned. The key is not updated, though; this matters for
    /// types that can be `==` without being identical. See the [module-level
    /// documentation] for more.
    ///
    /// [module-level documentation]: index.html#insert-and-complex-keys
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// assert_eq!(map.insert(37, "a"), None);
    /// assert_eq!(map.is_empty(), false);
    ///
    /// map.insert(37, "b");
    /// assert_eq!(map.insert(37, "c"), Some("b"));
    /// assert_eq!(map[&37], "c");
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn insert(&mut self, key: K, value: V) -> Option<V> {
        match self.entry(key) {
            Occupied(mut entry) => Some(entry.insert(value)),
            Vacant(entry) => {
                entry.insert(value);
                None
            }
        }
    }

    /// Removes a key from the map, returning the value at the key if the key
    /// was previously in the map.
    ///
    /// The key may be any borrowed form of the map's key type, but the ordering
    /// on the borrowed form *must* match the ordering on the key type.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// assert_eq!(map.remove(&1), Some("a"));
    /// assert_eq!(map.remove(&1), None);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn remove<Q: ?Sized>(&mut self, key: &Q) -> Option<V>
    where
        K: Borrow<Q>,
        Q: Ord,
    {
        self.remove_entry(key).map(|(_, v)| v)
    }

    /// Removes a key from the map, returning the stored key and value if the key
    /// was previously in the map.
    ///
    /// The key may be any borrowed form of the map's key type, but the ordering
    /// on the borrowed form *must* match the ordering on the key type.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(1, "a");
    /// assert_eq!(map.remove_entry(&1), Some((1, "a")));
    /// assert_eq!(map.remove_entry(&1), None);
    /// ```
    #[stable(feature = "btreemap_remove_entry", since = "1.45.0")]
    pub fn remove_entry<Q: ?Sized>(&mut self, key: &Q) -> Option<(K, V)>
    where
        K: Borrow<Q>,
        Q: Ord,
    {
        let root_node = self.root.as_mut()?.node_as_mut();
        match search::search_tree(root_node, key) {
            Found(handle) => Some(
                OccupiedEntry { handle, length: &mut self.length, _marker: PhantomData }
                    .remove_entry(),
            ),
            GoDown(_) => None,
        }
    }

    /// Moves all elements from `other` into `Self`, leaving `other` empty.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// a.insert(1, "a");
    /// a.insert(2, "b");
    /// a.insert(3, "c");
    ///
    /// let mut b = BTreeMap::new();
    /// b.insert(3, "d");
    /// b.insert(4, "e");
    /// b.insert(5, "f");
    ///
    /// a.append(&mut b);
    ///
    /// assert_eq!(a.len(), 5);
    /// assert_eq!(b.len(), 0);
    ///
    /// assert_eq!(a[&1], "a");
    /// assert_eq!(a[&2], "b");
    /// assert_eq!(a[&3], "d");
    /// assert_eq!(a[&4], "e");
    /// assert_eq!(a[&5], "f");
    /// ```
    #[stable(feature = "btree_append", since = "1.11.0")]
    pub fn append(&mut self, other: &mut Self) {
        // Do we have to append anything at all?
        if other.is_empty() {
            return;
        }

        // We can just swap `self` and `other` if `self` is empty.
        if self.is_empty() {
            mem::swap(self, other);
            return;
        }

        // First, we merge `self` and `other` into a sorted sequence in linear time.
        let self_iter = mem::take(self).into_iter();
        let other_iter = mem::take(other).into_iter();
        let iter = MergeIter { left: self_iter.peekable(), right: other_iter.peekable() };

        // Second, we build a tree from the sorted sequence in linear time.
        self.from_sorted_iter(iter);
    }

    /// Constructs a double-ended iterator over a sub-range of elements in the map.
    /// The simplest way is to use the range syntax `min..max`, thus `range(min..max)` will
    /// yield elements from min (inclusive) to max (exclusive).
    /// The range may also be entered as `(Bound<T>, Bound<T>)`, so for example
    /// `range((Excluded(4), Included(10)))` will yield a left-exclusive, right-inclusive
    /// range from 4 to 10.
    ///
    /// # Panics
    ///
    /// Panics if range `start > end`.
    /// Panics if range `start == end` and both bounds are `Excluded`.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::ops::Bound::Included;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(3, "a");
    /// map.insert(5, "b");
    /// map.insert(8, "c");
    /// for (&key, &value) in map.range((Included(&4), Included(&8))) {
    ///     println!("{}: {}", key, value);
    /// }
    /// assert_eq!(Some((&5, &"b")), map.range(4..).next());
    /// ```
    #[stable(feature = "btree_range", since = "1.17.0")]
    pub fn range<T: ?Sized, R>(&self, range: R) -> Range<'_, K, V>
    where
        T: Ord,
        K: Borrow<T>,
        R: RangeBounds<T>,
    {
        if let Some(root) = &self.root {
            let (f, b) = range_search(root.node_as_ref(), range);

            Range { front: Some(f), back: Some(b) }
        } else {
            Range { front: None, back: None }
        }
    }

    /// Constructs a mutable double-ended iterator over a sub-range of elements in the map.
    /// The simplest way is to use the range syntax `min..max`, thus `range(min..max)` will
    /// yield elements from min (inclusive) to max (exclusive).
    /// The range may also be entered as `(Bound<T>, Bound<T>)`, so for example
    /// `range((Excluded(4), Included(10)))` will yield a left-exclusive, right-inclusive
    /// range from 4 to 10.
    ///
    /// # Panics
    ///
    /// Panics if range `start > end`.
    /// Panics if range `start == end` and both bounds are `Excluded`.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, i32> = ["Alice", "Bob", "Carol", "Cheryl"]
    ///     .iter()
    ///     .map(|&s| (s, 0))
    ///     .collect();
    /// for (_, balance) in map.range_mut("B".."Cheryl") {
    ///     *balance += 100;
    /// }
    /// for (name, balance) in &map {
    ///     println!("{} => {}", name, balance);
    /// }
    /// ```
    #[stable(feature = "btree_range", since = "1.17.0")]
    pub fn range_mut<T: ?Sized, R>(&mut self, range: R) -> RangeMut<'_, K, V>
    where
        T: Ord,
        K: Borrow<T>,
        R: RangeBounds<T>,
    {
        if let Some(root) = &mut self.root {
            let (f, b) = range_search(root.node_as_mut(), range);

            RangeMut { front: Some(f), back: Some(b), _marker: PhantomData }
        } else {
            RangeMut { front: None, back: None, _marker: PhantomData }
        }
    }

    /// Gets the given key's corresponding entry in the map for in-place manipulation.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut count: BTreeMap<&str, usize> = BTreeMap::new();
    ///
    /// // count the number of occurrences of letters in the vec
    /// for x in vec!["a","b","a","c","a","b"] {
    ///     *count.entry(x).or_insert(0) += 1;
    /// }
    ///
    /// assert_eq!(count["a"], 3);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn entry(&mut self, key: K) -> Entry<'_, K, V> {
        // FIXME(@porglezomp) Avoid allocating if we don't insert
        let root = Self::ensure_is_owned(&mut self.root);
        match search::search_tree(root.node_as_mut(), &key) {
            Found(handle) => {
                Occupied(OccupiedEntry { handle, length: &mut self.length, _marker: PhantomData })
            }
            GoDown(handle) => {
                Vacant(VacantEntry { key, handle, length: &mut self.length, _marker: PhantomData })
            }
        }
    }

    fn from_sorted_iter<I: Iterator<Item = (K, V)>>(&mut self, iter: I) {
        let root = Self::ensure_is_owned(&mut self.root);
        let mut cur_node = root.node_as_mut().last_leaf_edge().into_node();
        // Iterate through all key-value pairs, pushing them into nodes at the right level.
        for (key, value) in iter {
            // Try to push key-value pair into the current leaf node.
            if cur_node.len() < node::CAPACITY {
                cur_node.push(key, value);
            } else {
                // No space left, go up and push there.
                let mut open_node;
                let mut test_node = cur_node.forget_type();
                loop {
                    match test_node.ascend() {
                        Ok(parent) => {
                            let parent = parent.into_node();
                            if parent.len() < node::CAPACITY {
                                // Found a node with space left, push here.
                                open_node = parent;
                                break;
                            } else {
                                // Go up again.
                                test_node = parent.forget_type();
                            }
                        }
                        Err(_) => {
                            // We are at the top, create a new root node and push there.
                            open_node = root.push_internal_level();
                            break;
                        }
                    }
                }

                // Push key-value pair and new right subtree.
                let tree_height = open_node.height() - 1;
                let mut right_tree = node::Root::new_leaf();
                for _ in 0..tree_height {
                    right_tree.push_internal_level();
                }
                open_node.push(key, value, right_tree);

                // Go down to the right-most leaf again.
                cur_node = open_node.forget_type().last_leaf_edge().into_node();
            }

            self.length += 1;
        }
        Self::fix_right_edge(root)
    }

    fn fix_right_edge(root: &mut node::Root<K, V>) {
        // Handle underfull nodes, start from the top.
        let mut cur_node = root.node_as_mut();
        while let Internal(internal) = cur_node.force() {
            // Check if right-most child is underfull.
            let mut last_edge = internal.last_edge();
            let right_child_len = last_edge.reborrow().descend().len();
            if right_child_len < node::MIN_LEN {
                // We need to steal.
                let mut last_kv = match last_edge.left_kv() {
                    Ok(left) => left,
                    Err(_) => unreachable!(),
                };
                last_kv.bulk_steal_left(node::MIN_LEN - right_child_len);
                last_edge = last_kv.right_edge();
            }

            // Go further down.
            cur_node = last_edge.descend();
        }
    }

    /// Splits the collection into two at the given key. Returns everything after the given key,
    /// including the key.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// a.insert(1, "a");
    /// a.insert(2, "b");
    /// a.insert(3, "c");
    /// a.insert(17, "d");
    /// a.insert(41, "e");
    ///
    /// let b = a.split_off(&3);
    ///
    /// assert_eq!(a.len(), 2);
    /// assert_eq!(b.len(), 3);
    ///
    /// assert_eq!(a[&1], "a");
    /// assert_eq!(a[&2], "b");
    ///
    /// assert_eq!(b[&3], "c");
    /// assert_eq!(b[&17], "d");
    /// assert_eq!(b[&41], "e");
    /// ```
    #[stable(feature = "btree_split_off", since = "1.11.0")]
    pub fn split_off<Q: ?Sized + Ord>(&mut self, key: &Q) -> Self
    where
        K: Borrow<Q>,
    {
        if self.is_empty() {
            return Self::new();
        }

        let total_num = self.len();
        let left_root = self.root.as_mut().unwrap(); // unwrap succeeds because not empty

        let mut right = Self::new();
        let right_root = Self::ensure_is_owned(&mut right.root);
        for _ in 0..left_root.height() {
            right_root.push_internal_level();
        }

        {
            let mut left_node = left_root.node_as_mut();
            let mut right_node = right_root.node_as_mut();

            loop {
                let mut split_edge = match search::search_node(left_node, key) {
                    // key is going to the right tree
                    Found(handle) => handle.left_edge(),
                    GoDown(handle) => handle,
                };

                split_edge.move_suffix(&mut right_node);

                match (split_edge.force(), right_node.force()) {
                    (Internal(edge), Internal(node)) => {
                        left_node = edge.descend();
                        right_node = node.first_edge().descend();
                    }
                    (Leaf(_), Leaf(_)) => {
                        break;
                    }
                    _ => {
                        unreachable!();
                    }
                }
            }
        }

        left_root.fix_right_border();
        right_root.fix_left_border();

        if left_root.height() < right_root.height() {
            self.recalc_length();
            right.length = total_num - self.len();
        } else {
            right.recalc_length();
            self.length = total_num - right.len();
        }

        right
    }

    /// Creates an iterator which uses a closure to determine if an element should be removed.
    ///
    /// If the closure returns true, the element is removed from the map and yielded.
    /// If the closure returns false, or panics, the element remains in the map and will not be
    /// yielded.
    ///
    /// Note that `drain_filter` lets you mutate every value in the filter closure, regardless of
    /// whether you choose to keep or remove it.
    ///
    /// If the iterator is only partially consumed or not consumed at all, each of the remaining
    /// elements will still be subjected to the closure and removed and dropped if it returns true.
    ///
    /// It is unspecified how many more elements will be subjected to the closure
    /// if a panic occurs in the closure, or a panic occurs while dropping an element,
    /// or if the `DrainFilter` value is leaked.
    ///
    /// # Examples
    ///
    /// Splitting a map into even and odd keys, reusing the original map:
    ///
    /// ```
    /// #![feature(btree_drain_filter)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<i32, i32> = (0..8).map(|x| (x, x)).collect();
    /// let evens: BTreeMap<_, _> = map.drain_filter(|k, _v| k % 2 == 0).collect();
    /// let odds = map;
    /// assert_eq!(evens.keys().copied().collect::<Vec<_>>(), vec![0, 2, 4, 6]);
    /// assert_eq!(odds.keys().copied().collect::<Vec<_>>(), vec![1, 3, 5, 7]);
    /// ```
    #[unstable(feature = "btree_drain_filter", issue = "70530")]
    pub fn drain_filter<F>(&mut self, pred: F) -> DrainFilter<'_, K, V, F>
    where
        F: FnMut(&K, &mut V) -> bool,
    {
        DrainFilter { pred, inner: self.drain_filter_inner() }
    }
    pub(super) fn drain_filter_inner(&mut self) -> DrainFilterInner<'_, K, V> {
        let root_node = self.root.as_mut().map(|r| r.node_as_mut());
        let front = root_node.map(|rn| rn.first_leaf_edge());
        DrainFilterInner { length: &mut self.length, cur_leaf_edge: front }
    }

    /// Calculates the number of elements if it is incorrect.
    fn recalc_length(&mut self) {
        fn dfs<'a, K, V>(node: NodeRef<marker::Immut<'a>, K, V, marker::LeafOrInternal>) -> usize
        where
            K: 'a,
            V: 'a,
        {
            let mut res = node.len();

            if let Internal(node) = node.force() {
                let mut edge = node.first_edge();
                loop {
                    res += dfs(edge.reborrow().descend());
                    match edge.right_kv() {
                        Ok(right_kv) => {
                            edge = right_kv.right_edge();
                        }
                        Err(_) => {
                            break;
                        }
                    }
                }
            }

            res
        }

        self.length = dfs(self.root.as_ref().unwrap().node_as_ref());
    }

    /// Creates a consuming iterator visiting all the keys, in sorted order.
    /// The map cannot be used after calling this.
    /// The iterator element type is `K`.
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(map_into_keys_values)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// a.insert(2, "b");
    /// a.insert(1, "a");
    ///
    /// let keys: Vec<i32> = a.into_keys().collect();
    /// assert_eq!(keys, [1, 2]);
    /// ```
    #[inline]
    #[unstable(feature = "map_into_keys_values", issue = "75294")]
    pub fn into_keys(self) -> IntoKeys<K, V> {
        IntoKeys { inner: self.into_iter() }
    }

    /// Creates a consuming iterator visiting all the values, in order by key.
    /// The map cannot be used after calling this.
    /// The iterator element type is `V`.
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(map_into_keys_values)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// a.insert(1, "hello");
    /// a.insert(2, "goodbye");
    ///
    /// let values: Vec<&str> = a.into_values().collect();
    /// assert_eq!(values, ["hello", "goodbye"]);
    /// ```
    #[inline]
    #[unstable(feature = "map_into_keys_values", issue = "75294")]
    pub fn into_values(self) -> IntoValues<K, V> {
        IntoValues { inner: self.into_iter() }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K, V> IntoIterator for &'a BTreeMap<K, V> {
    type Item = (&'a K, &'a V);
    type IntoIter = Iter<'a, K, V>;

    fn into_iter(self) -> Iter<'a, K, V> {
        self.iter()
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K: 'a, V: 'a> Iterator for Iter<'a, K, V> {
    type Item = (&'a K, &'a V);

    fn next(&mut self) -> Option<(&'a K, &'a V)> {
        if self.length == 0 {
            None
        } else {
            self.length -= 1;
            unsafe { Some(self.range.next_unchecked()) }
        }
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        (self.length, Some(self.length))
    }

    fn last(mut self) -> Option<(&'a K, &'a V)> {
        self.next_back()
    }

    fn min(mut self) -> Option<(&'a K, &'a V)> {
        self.next()
    }

    fn max(mut self) -> Option<(&'a K, &'a V)> {
        self.next_back()
    }
}

#[stable(feature = "fused", since = "1.26.0")]
impl<K, V> FusedIterator for Iter<'_, K, V> {}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K: 'a, V: 'a> DoubleEndedIterator for Iter<'a, K, V> {
    fn next_back(&mut self) -> Option<(&'a K, &'a V)> {
        if self.length == 0 {
            None
        } else {
            self.length -= 1;
            unsafe { Some(self.range.next_back_unchecked()) }
        }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> ExactSizeIterator for Iter<'_, K, V> {
    fn len(&self) -> usize {
        self.length
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> Clone for Iter<'_, K, V> {
    fn clone(&self) -> Self {
        Iter { range: self.range.clone(), length: self.length }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K, V> IntoIterator for &'a mut BTreeMap<K, V> {
    type Item = (&'a K, &'a mut V);
    type IntoIter = IterMut<'a, K, V>;

    fn into_iter(self) -> IterMut<'a, K, V> {
        self.iter_mut()
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K: 'a, V: 'a> Iterator for IterMut<'a, K, V> {
    type Item = (&'a K, &'a mut V);

    fn next(&mut self) -> Option<(&'a K, &'a mut V)> {
        if self.length == 0 {
            None
        } else {
            self.length -= 1;
            let (k, v) = unsafe { self.range.next_unchecked() };
            Some((k, v)) // coerce k from `&mut K` to `&K`
        }
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        (self.length, Some(self.length))
    }

    fn last(mut self) -> Option<(&'a K, &'a mut V)> {
        self.next_back()
    }

    fn min(mut self) -> Option<(&'a K, &'a mut V)> {
        self.next()
    }

    fn max(mut self) -> Option<(&'a K, &'a mut V)> {
        self.next_back()
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K: 'a, V: 'a> DoubleEndedIterator for IterMut<'a, K, V> {
    fn next_back(&mut self) -> Option<(&'a K, &'a mut V)> {
        if self.length == 0 {
            None
        } else {
            self.length -= 1;
            let (k, v) = unsafe { self.range.next_back_unchecked() };
            Some((k, v)) // coerce k from `&mut K` to `&K`
        }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> ExactSizeIterator for IterMut<'_, K, V> {
    fn len(&self) -> usize {
        self.length
    }
}

#[stable(feature = "fused", since = "1.26.0")]
impl<K, V> FusedIterator for IterMut<'_, K, V> {}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> IntoIterator for BTreeMap<K, V> {
    type Item = (K, V);
    type IntoIter = IntoIter<K, V>;

    fn into_iter(self) -> IntoIter<K, V> {
        let mut me = ManuallyDrop::new(self);
        if let Some(root) = me.root.take() {
            let (f, b) = full_range_search(root.into_ref());

            IntoIter { front: Some(f), back: Some(b), length: me.length }
        } else {
            IntoIter { front: None, back: None, length: 0 }
        }
    }
}

#[stable(feature = "btree_drop", since = "1.7.0")]
impl<K, V> Drop for IntoIter<K, V> {
    fn drop(&mut self) {
        struct DropGuard<'a, K, V>(&'a mut IntoIter<K, V>);

        impl<'a, K, V> Drop for DropGuard<'a, K, V> {
            fn drop(&mut self) {
                // Continue the same loop we perform below. This only runs when unwinding, so we
                // don't have to care about panics this time (they'll abort).
                while let Some(_) = self.0.next() {}

                unsafe {
                    let mut node =
                        unwrap_unchecked(ptr::read(&self.0.front)).into_node().forget_type();
                    while let Some(parent) = node.deallocate_and_ascend() {
                        node = parent.into_node().forget_type();
                    }
                }
            }
        }

        while let Some(pair) = self.next() {
            let guard = DropGuard(self);
            drop(pair);
            mem::forget(guard);
        }

        unsafe {
            if let Some(front) = ptr::read(&self.front) {
                let mut node = front.into_node().forget_type();
                // Most of the nodes have been deallocated while traversing
                // but one pile from a leaf up to the root is left standing.
                while let Some(parent) = node.deallocate_and_ascend() {
                    node = parent.into_node().forget_type();
                }
            }
        }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> Iterator for IntoIter<K, V> {
    type Item = (K, V);

    fn next(&mut self) -> Option<(K, V)> {
        if self.length == 0 {
            None
        } else {
            self.length -= 1;
            Some(unsafe { self.front.as_mut().unwrap().next_unchecked() })
        }
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        (self.length, Some(self.length))
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> DoubleEndedIterator for IntoIter<K, V> {
    fn next_back(&mut self) -> Option<(K, V)> {
        if self.length == 0 {
            None
        } else {
            self.length -= 1;
            Some(unsafe { self.back.as_mut().unwrap().next_back_unchecked() })
        }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> ExactSizeIterator for IntoIter<K, V> {
    fn len(&self) -> usize {
        self.length
    }
}

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

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K, V> Iterator for Keys<'a, K, V> {
    type Item = &'a K;

    fn next(&mut self) -> Option<&'a K> {
        self.inner.next().map(|(k, _)| k)
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        self.inner.size_hint()
    }

    fn last(mut self) -> Option<&'a K> {
        self.next_back()
    }

    fn min(mut self) -> Option<&'a K> {
        self.next()
    }

    fn max(mut self) -> Option<&'a K> {
        self.next_back()
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K, V> DoubleEndedIterator for Keys<'a, K, V> {
    fn next_back(&mut self) -> Option<&'a K> {
        self.inner.next_back().map(|(k, _)| k)
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> ExactSizeIterator for Keys<'_, K, V> {
    fn len(&self) -> usize {
        self.inner.len()
    }
}

#[stable(feature = "fused", since = "1.26.0")]
impl<K, V> FusedIterator for Keys<'_, K, V> {}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> Clone for Keys<'_, K, V> {
    fn clone(&self) -> Self {
        Keys { inner: self.inner.clone() }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K, V> Iterator for Values<'a, K, V> {
    type Item = &'a V;

    fn next(&mut self) -> Option<&'a V> {
        self.inner.next().map(|(_, v)| v)
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        self.inner.size_hint()
    }

    fn last(mut self) -> Option<&'a V> {
        self.next_back()
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<'a, K, V> DoubleEndedIterator for Values<'a, K, V> {
    fn next_back(&mut self) -> Option<&'a V> {
        self.inner.next_back().map(|(_, v)| v)
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> ExactSizeIterator for Values<'_, K, V> {
    fn len(&self) -> usize {
        self.inner.len()
    }
}

#[stable(feature = "fused", since = "1.26.0")]
impl<K, V> FusedIterator for Values<'_, K, V> {}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K, V> Clone for Values<'_, K, V> {
    fn clone(&self) -> Self {
        Values { inner: self.inner.clone() }
    }
}

/// An iterator produced by calling `drain_filter` on BTreeMap.
#[unstable(feature = "btree_drain_filter", issue = "70530")]
pub struct DrainFilter<'a, K, V, F>
where
    K: 'a,
    V: 'a,
    F: 'a + FnMut(&K, &mut V) -> bool,
{
    pred: F,
    inner: DrainFilterInner<'a, K, V>,
}
/// Most of the implementation of DrainFilter, independent of the type
/// of the predicate, thus also serving for BTreeSet::DrainFilter.
pub(super) struct DrainFilterInner<'a, K: 'a, V: 'a> {
    length: &'a mut usize,
    cur_leaf_edge: Option<Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>>,
}

#[unstable(feature = "btree_drain_filter", issue = "70530")]
impl<K, V, F> Drop for DrainFilter<'_, K, V, F>
where
    F: FnMut(&K, &mut V) -> bool,
{
    fn drop(&mut self) {
        self.for_each(drop);
    }
}

#[unstable(feature = "btree_drain_filter", issue = "70530")]
impl<K, V, F> fmt::Debug for DrainFilter<'_, K, V, F>
where
    K: fmt::Debug,
    V: fmt::Debug,
    F: FnMut(&K, &mut V) -> bool,
{
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_tuple("DrainFilter").field(&self.inner.peek()).finish()
    }
}

#[unstable(feature = "btree_drain_filter", issue = "70530")]
impl<K, V, F> Iterator for DrainFilter<'_, K, V, F>
where
    F: FnMut(&K, &mut V) -> bool,
{
    type Item = (K, V);

    fn next(&mut self) -> Option<(K, V)> {
        self.inner.next(&mut self.pred)
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        self.inner.size_hint()
    }
}

impl<'a, K: 'a, V: 'a> DrainFilterInner<'a, K, V> {
    /// Allow Debug implementations to predict the next element.
    pub(super) fn peek(&self) -> Option<(&K, &V)> {
        let edge = self.cur_leaf_edge.as_ref()?;
        edge.reborrow().next_kv().ok().map(|kv| kv.into_kv())
    }

    /// Implementation of a typical `DrainFilter::next` method, given the predicate.
    pub(super) fn next<F>(&mut self, pred: &mut F) -> Option<(K, V)>
    where
        F: FnMut(&K, &mut V) -> bool,
    {
        while let Ok(mut kv) = self.cur_leaf_edge.take()?.next_kv() {
            let (k, v) = kv.kv_mut();
            if pred(k, v) {
                *self.length -= 1;
                let (kv, pos) = kv.remove_kv_tracking();
                self.cur_leaf_edge = Some(pos);
                return Some(kv);
            }
            self.cur_leaf_edge = Some(kv.next_leaf_edge());
        }
        None
    }

    /// Implementation of a typical `DrainFilter::size_hint` method.
    pub(super) fn size_hint(&self) -> (usize, Option<usize>) {
        (0, Some(*self.length))
    }
}

#[unstable(feature = "btree_drain_filter", issue = "70530")]
impl<K, V, F> FusedIterator for DrainFilter<'_, K, V, F> where F: FnMut(&K, &mut V) -> bool {}

#[stable(feature = "btree_range", since = "1.17.0")]
impl<'a, K, V> Iterator for Range<'a, K, V> {
    type Item = (&'a K, &'a V);

    fn next(&mut self) -> Option<(&'a K, &'a V)> {
        if self.is_empty() { None } else { unsafe { Some(self.next_unchecked()) } }
    }

    fn last(mut self) -> Option<(&'a K, &'a V)> {
        self.next_back()
    }

    fn min(mut self) -> Option<(&'a K, &'a V)> {
        self.next()
    }

    fn max(mut self) -> Option<(&'a K, &'a V)> {
        self.next_back()
    }
}

#[stable(feature = "map_values_mut", since = "1.10.0")]
impl<'a, K, V> Iterator for ValuesMut<'a, K, V> {
    type Item = &'a mut V;

    fn next(&mut self) -> Option<&'a mut V> {
        self.inner.next().map(|(_, v)| v)
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        self.inner.size_hint()
    }

    fn last(mut self) -> Option<&'a mut V> {
        self.next_back()
    }
}

#[stable(feature = "map_values_mut", since = "1.10.0")]
impl<'a, K, V> DoubleEndedIterator for ValuesMut<'a, K, V> {
    fn next_back(&mut self) -> Option<&'a mut V> {
        self.inner.next_back().map(|(_, v)| v)
    }
}

#[stable(feature = "map_values_mut", since = "1.10.0")]
impl<K, V> ExactSizeIterator for ValuesMut<'_, K, V> {
    fn len(&self) -> usize {
        self.inner.len()
    }
}

#[stable(feature = "fused", since = "1.26.0")]
impl<K, V> FusedIterator for ValuesMut<'_, K, V> {}

impl<'a, K, V> Range<'a, K, V> {
    fn is_empty(&self) -> bool {
        self.front == self.back
    }

    unsafe fn next_unchecked(&mut self) -> (&'a K, &'a V) {
        unsafe { unwrap_unchecked(self.front.as_mut()).next_unchecked() }
    }
}

#[unstable(feature = "map_into_keys_values", issue = "75294")]
impl<K, V> Iterator for IntoKeys<K, V> {
    type Item = K;

    fn next(&mut self) -> Option<K> {
        self.inner.next().map(|(k, _)| k)
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        self.inner.size_hint()
    }

    fn last(mut self) -> Option<K> {
        self.next_back()
    }

    fn min(mut self) -> Option<K> {
        self.next()
    }

    fn max(mut self) -> Option<K> {
        self.next_back()
    }
}

#[unstable(feature = "map_into_keys_values", issue = "75294")]
impl<K, V> DoubleEndedIterator for IntoKeys<K, V> {
    fn next_back(&mut self) -> Option<K> {
        self.inner.next_back().map(|(k, _)| k)
    }
}

#[unstable(feature = "map_into_keys_values", issue = "75294")]
impl<K, V> ExactSizeIterator for IntoKeys<K, V> {
    fn len(&self) -> usize {
        self.inner.len()
    }
}

#[unstable(feature = "map_into_keys_values", issue = "75294")]
impl<K, V> FusedIterator for IntoKeys<K, V> {}

#[unstable(feature = "map_into_keys_values", issue = "75294")]
impl<K, V> Iterator for IntoValues<K, V> {
    type Item = V;

    fn next(&mut self) -> Option<V> {
        self.inner.next().map(|(_, v)| v)
    }

    fn size_hint(&self) -> (usize, Option<usize>) {
        self.inner.size_hint()
    }

    fn last(mut self) -> Option<V> {
        self.next_back()
    }
}

#[unstable(feature = "map_into_keys_values", issue = "75294")]
impl<K, V> DoubleEndedIterator for IntoValues<K, V> {
    fn next_back(&mut self) -> Option<V> {
        self.inner.next_back().map(|(_, v)| v)
    }
}

#[unstable(feature = "map_into_keys_values", issue = "75294")]
impl<K, V> ExactSizeIterator for IntoValues<K, V> {
    fn len(&self) -> usize {
        self.inner.len()
    }
}

#[unstable(feature = "map_into_keys_values", issue = "75294")]
impl<K, V> FusedIterator for IntoValues<K, V> {}

#[stable(feature = "btree_range", since = "1.17.0")]
impl<'a, K, V> DoubleEndedIterator for Range<'a, K, V> {
    fn next_back(&mut self) -> Option<(&'a K, &'a V)> {
        if self.is_empty() { None } else { Some(unsafe { self.next_back_unchecked() }) }
    }
}

impl<'a, K, V> Range<'a, K, V> {
    unsafe fn next_back_unchecked(&mut self) -> (&'a K, &'a V) {
        unsafe { unwrap_unchecked(self.back.as_mut()).next_back_unchecked() }
    }
}

#[stable(feature = "fused", since = "1.26.0")]
impl<K, V> FusedIterator for Range<'_, K, V> {}

#[stable(feature = "btree_range", since = "1.17.0")]
impl<K, V> Clone for Range<'_, K, V> {
    fn clone(&self) -> Self {
        Range { front: self.front, back: self.back }
    }
}

#[stable(feature = "btree_range", since = "1.17.0")]
impl<'a, K, V> Iterator for RangeMut<'a, K, V> {
    type Item = (&'a K, &'a mut V);

    fn next(&mut self) -> Option<(&'a K, &'a mut V)> {
        if self.is_empty() {
            None
        } else {
            let (k, v) = unsafe { self.next_unchecked() };
            Some((k, v)) // coerce k from `&mut K` to `&K`
        }
    }

    fn last(mut self) -> Option<(&'a K, &'a mut V)> {
        self.next_back()
    }

    fn min(mut self) -> Option<(&'a K, &'a mut V)> {
        self.next()
    }

    fn max(mut self) -> Option<(&'a K, &'a mut V)> {
        self.next_back()
    }
}

impl<'a, K, V> RangeMut<'a, K, V> {
    fn is_empty(&self) -> bool {
        self.front == self.back
    }

    unsafe fn next_unchecked(&mut self) -> (&'a mut K, &'a mut V) {
        unsafe { unwrap_unchecked(self.front.as_mut()).next_unchecked() }
    }
}

#[stable(feature = "btree_range", since = "1.17.0")]
impl<'a, K, V> DoubleEndedIterator for RangeMut<'a, K, V> {
    fn next_back(&mut self) -> Option<(&'a K, &'a mut V)> {
        if self.is_empty() {
            None
        } else {
            let (k, v) = unsafe { self.next_back_unchecked() };
            Some((k, v)) // coerce k from `&mut K` to `&K`
        }
    }
}

#[stable(feature = "fused", since = "1.26.0")]
impl<K, V> FusedIterator for RangeMut<'_, K, V> {}

impl<'a, K, V> RangeMut<'a, K, V> {
    unsafe fn next_back_unchecked(&mut self) -> (&'a mut K, &'a mut V) {
        unsafe { unwrap_unchecked(self.back.as_mut()).next_back_unchecked() }
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: Ord, V> FromIterator<(K, V)> for BTreeMap<K, V> {
    fn from_iter<T: IntoIterator<Item = (K, V)>>(iter: T) -> BTreeMap<K, V> {
        let mut map = BTreeMap::new();
        map.extend(iter);
        map
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: Ord, V> Extend<(K, V)> for BTreeMap<K, V> {
    #[inline]
    fn extend<T: IntoIterator<Item = (K, V)>>(&mut self, iter: T) {
        iter.into_iter().for_each(move |(k, v)| {
            self.insert(k, v);
        });
    }

    #[inline]
    fn extend_one(&mut self, (k, v): (K, V)) {
        self.insert(k, v);
    }
}

#[stable(feature = "extend_ref", since = "1.2.0")]
impl<'a, K: Ord + Copy, V: Copy> Extend<(&'a K, &'a V)> for BTreeMap<K, V> {
    fn extend<I: IntoIterator<Item = (&'a K, &'a V)>>(&mut self, iter: I) {
        self.extend(iter.into_iter().map(|(&key, &value)| (key, value)));
    }

    #[inline]
    fn extend_one(&mut self, (&k, &v): (&'a K, &'a V)) {
        self.insert(k, v);
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: Hash, V: Hash> Hash for BTreeMap<K, V> {
    fn hash<H: Hasher>(&self, state: &mut H) {
        for elt in self {
            elt.hash(state);
        }
    }
}

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

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: PartialEq, V: PartialEq> PartialEq for BTreeMap<K, V> {
    fn eq(&self, other: &BTreeMap<K, V>) -> bool {
        self.len() == other.len() && self.iter().zip(other).all(|(a, b)| a == b)
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: Eq, V: Eq> Eq for BTreeMap<K, V> {}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: PartialOrd, V: PartialOrd> PartialOrd for BTreeMap<K, V> {
    #[inline]
    fn partial_cmp(&self, other: &BTreeMap<K, V>) -> Option<Ordering> {
        self.iter().partial_cmp(other.iter())
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: Ord, V: Ord> Ord for BTreeMap<K, V> {
    #[inline]
    fn cmp(&self, other: &BTreeMap<K, V>) -> Ordering {
        self.iter().cmp(other.iter())
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: Debug, V: Debug> Debug for BTreeMap<K, V> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.debug_map().entries(self.iter()).finish()
    }
}

#[stable(feature = "rust1", since = "1.0.0")]
impl<K: Ord, Q: ?Sized, V> Index<&Q> for BTreeMap<K, V>
where
    K: Borrow<Q>,
    Q: Ord,
{
    type Output = V;

    /// Returns a reference to the value corresponding to the supplied key.
    ///
    /// # Panics
    ///
    /// Panics if the key is not present in the `BTreeMap`.
    #[inline]
    fn index(&self, key: &Q) -> &V {
        self.get(key).expect("no entry found for key")
    }
}

/// Finds the leaf edges delimiting a specified range in or underneath a node.
fn range_search<BorrowType, K, V, Q: ?Sized, R: RangeBounds<Q>>(
    root: NodeRef<BorrowType, K, V, marker::LeafOrInternal>,
    range: R,
) -> (
    Handle<NodeRef<BorrowType, K, V, marker::Leaf>, marker::Edge>,
    Handle<NodeRef<BorrowType, K, V, marker::Leaf>, marker::Edge>,
)
where
    Q: Ord,
    K: Borrow<Q>,
{
    match (range.start_bound(), range.end_bound()) {
        (Excluded(s), Excluded(e)) if s == e => {
            panic!("range start and end are equal and excluded in BTreeMap")
        }
        (Included(s) | Excluded(s), Included(e) | Excluded(e)) if s > e => {
            panic!("range start is greater than range end in BTreeMap")
        }
        _ => {}
    };

    // We duplicate the root NodeRef here -- we will never access it in a way
    // that overlaps references obtained from the root.
    let mut min_node = unsafe { ptr::read(&root) };
    let mut max_node = root;
    let mut min_found = false;
    let mut max_found = false;

    loop {
        let front = match (min_found, range.start_bound()) {
            (false, Included(key)) => match search::search_node(min_node, key) {
                Found(kv) => {
                    min_found = true;
                    kv.left_edge()
                }
                GoDown(edge) => edge,
            },
            (false, Excluded(key)) => match search::search_node(min_node, key) {
                Found(kv) => {
                    min_found = true;
                    kv.right_edge()
                }
                GoDown(edge) => edge,
            },
            (true, Included(_)) => min_node.last_edge(),
            (true, Excluded(_)) => min_node.first_edge(),
            (_, Unbounded) => min_node.first_edge(),
        };

        let back = match (max_found, range.end_bound()) {
            (false, Included(key)) => match search::search_node(max_node, key) {
                Found(kv) => {
                    max_found = true;
                    kv.right_edge()
                }
                GoDown(edge) => edge,
            },
            (false, Excluded(key)) => match search::search_node(max_node, key) {
                Found(kv) => {
                    max_found = true;
                    kv.left_edge()
                }
                GoDown(edge) => edge,
            },
            (true, Included(_)) => max_node.first_edge(),
            (true, Excluded(_)) => max_node.last_edge(),
            (_, Unbounded) => max_node.last_edge(),
        };

        if front.partial_cmp(&back) == Some(Ordering::Greater) {
            panic!("Ord is ill-defined in BTreeMap range");
        }
        match (front.force(), back.force()) {
            (Leaf(f), Leaf(b)) => {
                return (f, b);
            }
            (Internal(min_int), Internal(max_int)) => {
                min_node = min_int.descend();
                max_node = max_int.descend();
            }
            _ => unreachable!("BTreeMap has different depths"),
        };
    }
}

/// Equivalent to `range_search(k, v, ..)` without the `Ord` bound.
fn full_range_search<BorrowType, K, V>(
    root: NodeRef<BorrowType, K, V, marker::LeafOrInternal>,
) -> (
    Handle<NodeRef<BorrowType, K, V, marker::Leaf>, marker::Edge>,
    Handle<NodeRef<BorrowType, K, V, marker::Leaf>, marker::Edge>,
) {
    // We duplicate the root NodeRef here -- we will never access it in a way
    // that overlaps references obtained from the root.
    let mut min_node = unsafe { ptr::read(&root) };
    let mut max_node = root;
    loop {
        let front = min_node.first_edge();
        let back = max_node.last_edge();
        match (front.force(), back.force()) {
            (Leaf(f), Leaf(b)) => {
                return (f, b);
            }
            (Internal(min_int), Internal(max_int)) => {
                min_node = min_int.descend();
                max_node = max_int.descend();
            }
            _ => unreachable!("BTreeMap has different depths"),
        };
    }
}

impl<K, V> BTreeMap<K, V> {
    /// Gets an iterator over the entries of the map, sorted by key.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert(3, "c");
    /// map.insert(2, "b");
    /// map.insert(1, "a");
    ///
    /// for (key, value) in map.iter() {
    ///     println!("{}: {}", key, value);
    /// }
    ///
    /// let (first_key, first_value) = map.iter().next().unwrap();
    /// assert_eq!((*first_key, *first_value), (1, "a"));
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn iter(&self) -> Iter<'_, K, V> {
        if let Some(root) = &self.root {
            let (f, b) = full_range_search(root.node_as_ref());

            Iter { range: Range { front: Some(f), back: Some(b) }, length: self.length }
        } else {
            Iter { range: Range { front: None, back: None }, length: 0 }
        }
    }

    /// Gets a mutable iterator over the entries of the map, sorted by key.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map = BTreeMap::new();
    /// map.insert("a", 1);
    /// map.insert("b", 2);
    /// map.insert("c", 3);
    ///
    /// // add 10 to the value if the key isn't "a"
    /// for (key, value) in map.iter_mut() {
    ///     if key != &"a" {
    ///         *value += 10;
    ///     }
    /// }
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn iter_mut(&mut self) -> IterMut<'_, K, V> {
        if let Some(root) = &mut self.root {
            let (f, b) = full_range_search(root.node_as_mut());

            IterMut {
                range: RangeMut { front: Some(f), back: Some(b), _marker: PhantomData },
                length: self.length,
            }
        } else {
            IterMut { range: RangeMut { front: None, back: None, _marker: PhantomData }, length: 0 }
        }
    }

    /// Gets an iterator over the keys of the map, in sorted order.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// a.insert(2, "b");
    /// a.insert(1, "a");
    ///
    /// let keys: Vec<_> = a.keys().cloned().collect();
    /// assert_eq!(keys, [1, 2]);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn keys(&self) -> Keys<'_, K, V> {
        Keys { inner: self.iter() }
    }

    /// Gets an iterator over the values of the map, in order by key.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// a.insert(1, "hello");
    /// a.insert(2, "goodbye");
    ///
    /// let values: Vec<&str> = a.values().cloned().collect();
    /// assert_eq!(values, ["hello", "goodbye"]);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn values(&self) -> Values<'_, K, V> {
        Values { inner: self.iter() }
    }

    /// Gets a mutable iterator over the values of the map, in order by key.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// a.insert(1, String::from("hello"));
    /// a.insert(2, String::from("goodbye"));
    ///
    /// for value in a.values_mut() {
    ///     value.push_str("!");
    /// }
    ///
    /// let values: Vec<String> = a.values().cloned().collect();
    /// assert_eq!(values, [String::from("hello!"),
    ///                     String::from("goodbye!")]);
    /// ```
    #[stable(feature = "map_values_mut", since = "1.10.0")]
    pub fn values_mut(&mut self) -> ValuesMut<'_, K, V> {
        ValuesMut { inner: self.iter_mut() }
    }

    /// Returns the number of elements in the map.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// assert_eq!(a.len(), 0);
    /// a.insert(1, "a");
    /// assert_eq!(a.len(), 1);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn len(&self) -> usize {
        self.length
    }

    /// Returns `true` if the map contains no elements.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut a = BTreeMap::new();
    /// assert!(a.is_empty());
    /// a.insert(1, "a");
    /// assert!(!a.is_empty());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn is_empty(&self) -> bool {
        self.len() == 0
    }

    /// If the root node is the empty (non-allocated) root node, allocate our
    /// own node. Is an associated function to avoid borrowing the entire BTreeMap.
    fn ensure_is_owned(root: &mut Option<node::Root<K, V>>) -> &mut node::Root<K, V> {
        root.get_or_insert_with(node::Root::new_leaf)
    }
}

impl<'a, K: Ord, V> Entry<'a, K, V> {
    /// Ensures a value is in the entry by inserting the default if empty, and returns
    /// a mutable reference to the value in the entry.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// map.entry("poneyland").or_insert(12);
    ///
    /// assert_eq!(map["poneyland"], 12);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn or_insert(self, default: V) -> &'a mut V {
        match self {
            Occupied(entry) => entry.into_mut(),
            Vacant(entry) => entry.insert(default),
        }
    }

    /// Ensures a value is in the entry by inserting the result of the default function if empty,
    /// and returns a mutable reference to the value in the entry.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, String> = BTreeMap::new();
    /// let s = "hoho".to_string();
    ///
    /// map.entry("poneyland").or_insert_with(|| s);
    ///
    /// assert_eq!(map["poneyland"], "hoho".to_string());
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn or_insert_with<F: FnOnce() -> V>(self, default: F) -> &'a mut V {
        match self {
            Occupied(entry) => entry.into_mut(),
            Vacant(entry) => entry.insert(default()),
        }
    }

    #[unstable(feature = "or_insert_with_key", issue = "71024")]
    /// Ensures a value is in the entry by inserting, if empty, the result of the default function,
    /// which takes the key as its argument, and returns a mutable reference to the value in the
    /// entry.
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(or_insert_with_key)]
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    ///
    /// map.entry("poneyland").or_insert_with_key(|key| key.chars().count());
    ///
    /// assert_eq!(map["poneyland"], 9);
    /// ```
    #[inline]
    pub fn or_insert_with_key<F: FnOnce(&K) -> V>(self, default: F) -> &'a mut V {
        match self {
            Occupied(entry) => entry.into_mut(),
            Vacant(entry) => {
                let value = default(entry.key());
                entry.insert(value)
            }
        }
    }

    /// Returns a reference to this entry's key.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// assert_eq!(map.entry("poneyland").key(), &"poneyland");
    /// ```
    #[stable(feature = "map_entry_keys", since = "1.10.0")]
    pub fn key(&self) -> &K {
        match *self {
            Occupied(ref entry) => entry.key(),
            Vacant(ref entry) => entry.key(),
        }
    }

    /// Provides in-place mutable access to an occupied entry before any
    /// potential inserts into the map.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    ///
    /// map.entry("poneyland")
    ///    .and_modify(|e| { *e += 1 })
    ///    .or_insert(42);
    /// assert_eq!(map["poneyland"], 42);
    ///
    /// map.entry("poneyland")
    ///    .and_modify(|e| { *e += 1 })
    ///    .or_insert(42);
    /// assert_eq!(map["poneyland"], 43);
    /// ```
    #[stable(feature = "entry_and_modify", since = "1.26.0")]
    pub fn and_modify<F>(self, f: F) -> Self
    where
        F: FnOnce(&mut V),
    {
        match self {
            Occupied(mut entry) => {
                f(entry.get_mut());
                Occupied(entry)
            }
            Vacant(entry) => Vacant(entry),
        }
    }
}

impl<'a, K: Ord, V: Default> Entry<'a, K, V> {
    #[stable(feature = "entry_or_default", since = "1.28.0")]
    /// Ensures a value is in the entry by inserting the default value if empty,
    /// and returns a mutable reference to the value in the entry.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, Option<usize>> = BTreeMap::new();
    /// map.entry("poneyland").or_default();
    ///
    /// assert_eq!(map["poneyland"], None);
    /// ```
    pub fn or_default(self) -> &'a mut V {
        match self {
            Occupied(entry) => entry.into_mut(),
            Vacant(entry) => entry.insert(Default::default()),
        }
    }
}

impl<'a, K: Ord, V> VacantEntry<'a, K, V> {
    /// Gets a reference to the key that would be used when inserting a value
    /// through the VacantEntry.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// assert_eq!(map.entry("poneyland").key(), &"poneyland");
    /// ```
    #[stable(feature = "map_entry_keys", since = "1.10.0")]
    pub fn key(&self) -> &K {
        &self.key
    }

    /// Take ownership of the key.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::collections::btree_map::Entry;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    ///
    /// if let Entry::Vacant(v) = map.entry("poneyland") {
    ///     v.into_key();
    /// }
    /// ```
    #[stable(feature = "map_entry_recover_keys2", since = "1.12.0")]
    pub fn into_key(self) -> K {
        self.key
    }

    /// Sets the value of the entry with the `VacantEntry`'s key,
    /// and returns a mutable reference to it.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::collections::btree_map::Entry;
    ///
    /// let mut map: BTreeMap<&str, u32> = BTreeMap::new();
    ///
    /// if let Entry::Vacant(o) = map.entry("poneyland") {
    ///     o.insert(37);
    /// }
    /// assert_eq!(map["poneyland"], 37);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn insert(self, value: V) -> &'a mut V {
        *self.length += 1;

        let out_ptr = match self.handle.insert_recursing(self.key, value) {
            (Fit(_), val_ptr) => val_ptr,
            (Split(ins), val_ptr) => {
                let root = ins.left.into_root_mut();
                root.push_internal_level().push(ins.k, ins.v, ins.right);
                val_ptr
            }
        };
        // Now that we have finished growing the tree using borrowed references,
        // dereference the pointer to a part of it, that we picked up along the way.
        unsafe { &mut *out_ptr }
    }
}

impl<'a, K: Ord, V> OccupiedEntry<'a, K, V> {
    /// Gets a reference to the key in the entry.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// map.entry("poneyland").or_insert(12);
    /// assert_eq!(map.entry("poneyland").key(), &"poneyland");
    /// ```
    #[stable(feature = "map_entry_keys", since = "1.10.0")]
    pub fn key(&self) -> &K {
        self.handle.reborrow().into_kv().0
    }

    /// Take ownership of the key and value from the map.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::collections::btree_map::Entry;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// map.entry("poneyland").or_insert(12);
    ///
    /// if let Entry::Occupied(o) = map.entry("poneyland") {
    ///     // We delete the entry from the map.
    ///     o.remove_entry();
    /// }
    ///
    /// // If now try to get the value, it will panic:
    /// // println!("{}", map["poneyland"]);
    /// ```
    #[stable(feature = "map_entry_recover_keys2", since = "1.12.0")]
    pub fn remove_entry(self) -> (K, V) {
        self.remove_kv()
    }

    /// Gets a reference to the value in the entry.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::collections::btree_map::Entry;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// map.entry("poneyland").or_insert(12);
    ///
    /// if let Entry::Occupied(o) = map.entry("poneyland") {
    ///     assert_eq!(o.get(), &12);
    /// }
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn get(&self) -> &V {
        self.handle.reborrow().into_kv().1
    }

    /// Gets a mutable reference to the value in the entry.
    ///
    /// If you need a reference to the `OccupiedEntry` that may outlive the
    /// destruction of the `Entry` value, see [`into_mut`].
    ///
    /// [`into_mut`]: #method.into_mut
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::collections::btree_map::Entry;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// map.entry("poneyland").or_insert(12);
    ///
    /// assert_eq!(map["poneyland"], 12);
    /// if let Entry::Occupied(mut o) = map.entry("poneyland") {
    ///     *o.get_mut() += 10;
    ///     assert_eq!(*o.get(), 22);
    ///
    ///     // We can use the same Entry multiple times.
    ///     *o.get_mut() += 2;
    /// }
    /// assert_eq!(map["poneyland"], 24);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn get_mut(&mut self) -> &mut V {
        self.handle.kv_mut().1
    }

    /// Converts the entry into a mutable reference to its value.
    ///
    /// If you need multiple references to the `OccupiedEntry`, see [`get_mut`].
    ///
    /// [`get_mut`]: #method.get_mut
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::collections::btree_map::Entry;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// map.entry("poneyland").or_insert(12);
    ///
    /// assert_eq!(map["poneyland"], 12);
    /// if let Entry::Occupied(o) = map.entry("poneyland") {
    ///     *o.into_mut() += 10;
    /// }
    /// assert_eq!(map["poneyland"], 22);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn into_mut(self) -> &'a mut V {
        self.handle.into_val_mut()
    }

    /// Sets the value of the entry with the `OccupiedEntry`'s key,
    /// and returns the entry's old value.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::collections::btree_map::Entry;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// map.entry("poneyland").or_insert(12);
    ///
    /// if let Entry::Occupied(mut o) = map.entry("poneyland") {
    ///     assert_eq!(o.insert(15), 12);
    /// }
    /// assert_eq!(map["poneyland"], 15);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn insert(&mut self, value: V) -> V {
        mem::replace(self.get_mut(), value)
    }

    /// Takes the value of the entry out of the map, and returns it.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::collections::BTreeMap;
    /// use std::collections::btree_map::Entry;
    ///
    /// let mut map: BTreeMap<&str, usize> = BTreeMap::new();
    /// map.entry("poneyland").or_insert(12);
    ///
    /// if let Entry::Occupied(o) = map.entry("poneyland") {
    ///     assert_eq!(o.remove(), 12);
    /// }
    /// // If we try to get "poneyland"'s value, it'll panic:
    /// // println!("{}", map["poneyland"]);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    pub fn remove(self) -> V {
        self.remove_kv().1
    }

    // Body of `remove_entry`, separate to keep the above implementations short.
    fn remove_kv(self) -> (K, V) {
        *self.length -= 1;

        let (old_kv, _) = self.handle.remove_kv_tracking();
        old_kv
    }
}

impl<'a, K: 'a, V: 'a> Handle<NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, marker::KV> {
    /// Removes a key/value-pair from the map, and returns that pair, as well as
    /// the leaf edge corresponding to that former pair.
    fn remove_kv_tracking(
        self,
    ) -> ((K, V), Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>) {
        let (old_kv, mut pos, was_internal) = match self.force() {
            Leaf(leaf) => {
                let (old_kv, pos) = leaf.remove();
                (old_kv, pos, false)
            }
            Internal(mut internal) => {
                // Replace the location freed in the internal node with an
                // adjacent KV, and remove that adjacent KV from its leaf.
                // Always choose the adjacent KV on the left side because
                // it is typically faster to pop an element from the end
                // of the KV arrays without needing to shift other elements.

                let key_loc = internal.kv_mut().0 as *mut K;
                let val_loc = internal.kv_mut().1 as *mut V;

                let to_remove = internal.left_edge().descend().last_leaf_edge().left_kv().ok();
                let to_remove = unsafe { unwrap_unchecked(to_remove) };

                let (kv, pos) = to_remove.remove();

                let old_key = unsafe { mem::replace(&mut *key_loc, kv.0) };
                let old_val = unsafe { mem::replace(&mut *val_loc, kv.1) };

                ((old_key, old_val), pos, true)
            }
        };

        // Handle underflow
        let mut cur_node = unsafe { ptr::read(&pos).into_node().forget_type() };
        let mut at_leaf = true;
        while cur_node.len() < node::MIN_LEN {
            match handle_underfull_node(cur_node) {
                AtRoot => break,
                Merged(edge, merged_with_left, offset) => {
                    // If we merged with our right sibling then our tracked
                    // position has not changed. However if we merged with our
                    // left sibling then our tracked position is now dangling.
                    if at_leaf && merged_with_left {
                        let idx = pos.idx() + offset;
                        let node = match unsafe { ptr::read(&edge).descend().force() } {
                            Leaf(leaf) => leaf,
                            Internal(_) => unreachable!(),
                        };
                        pos = unsafe { Handle::new_edge(node, idx) };
                    }

                    let parent = edge.into_node();
                    if parent.len() == 0 {
                        // The parent that was just emptied must be the root,
                        // because nodes on a lower level would not have been
                        // left with a single child.
                        parent.into_root_mut().pop_internal_level();
                        break;
                    } else {
                        cur_node = parent.forget_type();
                        at_leaf = false;
                    }
                }
                Stole(stole_from_left) => {
                    // Adjust the tracked position if we stole from a left sibling
                    if stole_from_left && at_leaf {
                        // SAFETY: This is safe since we just added an element to our node.
                        unsafe {
                            pos.next_unchecked();
                        }
                    }
                    break;
                }
            }
        }

        // If we deleted from an internal node then we need to compensate for
        // the earlier swap and adjust the tracked position to point to the
        // next element.
        if was_internal {
            pos = unsafe { unwrap_unchecked(pos.next_kv().ok()).next_leaf_edge() };
        }

        (old_kv, pos)
    }
}

impl<K, V> node::Root<K, V> {
    /// Removes empty levels on the top, but keep an empty leaf if the entire tree is empty.
    fn fix_top(&mut self) {
        while self.height() > 0 && self.node_as_ref().len() == 0 {
            self.pop_internal_level();
        }
    }

    fn fix_right_border(&mut self) {
        self.fix_top();

        {
            let mut cur_node = self.node_as_mut();

            while let Internal(node) = cur_node.force() {
                let mut last_kv = node.last_kv();

                if last_kv.can_merge() {
                    cur_node = last_kv.merge().descend();
                } else {
                    let right_len = last_kv.reborrow().right_edge().descend().len();
                    // `MINLEN + 1` to avoid readjust if merge happens on the next level.
                    if right_len < node::MIN_LEN + 1 {
                        last_kv.bulk_steal_left(node::MIN_LEN + 1 - right_len);
                    }
                    cur_node = last_kv.right_edge().descend();
                }
            }
        }

        self.fix_top();
    }

    /// The symmetric clone of `fix_right_border`.
    fn fix_left_border(&mut self) {
        self.fix_top();

        {
            let mut cur_node = self.node_as_mut();

            while let Internal(node) = cur_node.force() {
                let mut first_kv = node.first_kv();

                if first_kv.can_merge() {
                    cur_node = first_kv.merge().descend();
                } else {
                    let left_len = first_kv.reborrow().left_edge().descend().len();
                    if left_len < node::MIN_LEN + 1 {
                        first_kv.bulk_steal_right(node::MIN_LEN + 1 - left_len);
                    }
                    cur_node = first_kv.left_edge().descend();
                }
            }
        }

        self.fix_top();
    }
}

enum UnderflowResult<'a, K, V> {
    AtRoot,
    Merged(Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::Edge>, bool, usize),
    Stole(bool),
}

fn handle_underfull_node<K, V>(
    node: NodeRef<marker::Mut<'_>, K, V, marker::LeafOrInternal>,
) -> UnderflowResult<'_, K, V> {
    let parent = match node.ascend() {
        Ok(parent) => parent,
        Err(_) => return AtRoot,
    };

    // Prefer the left KV if it exists. Merging with the left side is faster,
    // since merging happens towards the left and `node` has fewer elements.
    // Stealing from the left side is faster, since we can pop from the end of
    // the KV arrays.
    let (is_left, mut handle) = match parent.left_kv() {
        Ok(left) => (true, left),
        Err(parent) => {
            let right = unsafe { unwrap_unchecked(parent.right_kv().ok()) };
            (false, right)
        }
    };

    if handle.can_merge() {
        let offset = if is_left { handle.reborrow().left_edge().descend().len() + 1 } else { 0 };
        Merged(handle.merge(), is_left, offset)
    } else {
        if is_left {
            handle.steal_left();
        } else {
            handle.steal_right();
        }
        Stole(is_left)
    }
}

impl<K: Ord, V, I: Iterator<Item = (K, V)>> Iterator for MergeIter<K, V, I> {
    type Item = (K, V);

    fn next(&mut self) -> Option<(K, V)> {
        let res = match (self.left.peek(), self.right.peek()) {
            (Some(&(ref left_key, _)), Some(&(ref right_key, _))) => left_key.cmp(right_key),
            (Some(_), None) => Ordering::Less,
            (None, Some(_)) => Ordering::Greater,
            (None, None) => return None,
        };

        // Check which elements comes first and only advance the corresponding iterator.
        // If two keys are equal, take the value from `right`.
        match res {
            Ordering::Less => self.left.next(),
            Ordering::Greater => self.right.next(),
            Ordering::Equal => {
                self.left.next();
                self.right.next()
            }
        }
    }
}

#[cfg(test)]
mod tests;