src/liballoc/collections/btree/set.rs - third_party/rust - Git at Google

 // This is pretty much entirely stolen from TreeSet, since BTreeMap has an identical interface
 // to TreeMap

 use core::borrow::Borrow;
 use core::cmp::Ordering::{self, Less, Greater, Equal};
 use core::cmp::max;
 use core::fmt::{self, Debug};
 use core::iter::{Peekable, FromIterator, FusedIterator};
 use core::ops::{BitOr, BitAnd, BitXor, Sub, RangeBounds};

 use crate::collections::btree_map::{self, BTreeMap, Keys};
 use super::Recover;

 // FIXME(conventions): implement bounded iterators

 /// A set based on a B-Tree.
 ///
 /// See [`BTreeMap`]'s documentation for a detailed discussion of this collection's performance
 /// benefits and drawbacks.
 ///
 /// It is a logic error for an item to be modified in such a way that the item's ordering relative
 /// to any other item, as determined by the [`Ord`] trait, changes while it is in the set. This is
 /// normally only possible through [`Cell`], [`RefCell`], global state, I/O, or unsafe code.
 ///
 /// [`BTreeMap`]: struct.BTreeMap.html
 /// [`Ord`]: ../../std/cmp/trait.Ord.html
 /// [`Cell`]: ../../std/cell/struct.Cell.html
 /// [`RefCell`]: ../../std/cell/struct.RefCell.html
 ///
 /// # Examples
 ///
 /// ```
 /// use std::collections::BTreeSet;
 ///
 /// // Type inference lets us omit an explicit type signature (which
 /// // would be `BTreeSet<&str>` in this example).
 /// let mut books = BTreeSet::new();
 ///
 /// // Add some books.
 /// books.insert("A Dance With Dragons");
 /// books.insert("To Kill a Mockingbird");
 /// books.insert("The Odyssey");
 /// books.insert("The Great Gatsby");
 ///
 /// // Check for a specific one.
 /// if !books.contains("The Winds of Winter") {
 ///     println!("We have {} books, but The Winds of Winter ain't one.",
 ///              books.len());
 /// }
 ///
 /// // Remove a book.
 /// books.remove("The Odyssey");
 ///
 /// // Iterate over everything.
 /// for book in &books {
 ///     println!("{}", book);
 /// }
 /// ```
 #[derive(Clone, Hash, PartialEq, Eq, Ord, PartialOrd)]
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct BTreeSet<T> {
     map: BTreeMap<T, ()>,
 }

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

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

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

 /// An iterator over a sub-range of items in a `BTreeSet`.
 ///
 /// This `struct` is created by the [`range`] method on [`BTreeSet`].
 /// See its documentation for more.
 ///
 /// [`BTreeSet`]: struct.BTreeSet.html
 /// [`range`]: struct.BTreeSet.html#method.range
 #[derive(Debug)]
 #[stable(feature = "btree_range", since = "1.17.0")]
 pub struct Range<'a, T: 'a> {
     iter: btree_map::Range<'a, T, ()>,
 }

 /// A lazy iterator producing elements in the difference of `BTreeSet`s.
 ///
 /// This `struct` is created by the [`difference`] method on [`BTreeSet`].
 /// See its documentation for more.
 ///
 /// [`BTreeSet`]: struct.BTreeSet.html
 /// [`difference`]: struct.BTreeSet.html#method.difference
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct Difference<'a, T: 'a> {
     inner: DifferenceInner<'a, T>,
 }
 enum DifferenceInner<'a, T: 'a> {
     Stitch {
         self_iter: Iter<'a, T>,
         other_iter: Peekable<Iter<'a, T>>,
     },
     Search {
         self_iter: Iter<'a, T>,
         other_set: &'a BTreeSet<T>,
     },
 }

 #[stable(feature = "collection_debug", since = "1.17.0")]
 impl<T: fmt::Debug> fmt::Debug for Difference<'_, T> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         match &self.inner {
             DifferenceInner::Stitch {
                 self_iter,
                 other_iter,
             } => f
                 .debug_tuple("Difference")
                 .field(&self_iter)
                 .field(&other_iter)
                 .finish(),
             DifferenceInner::Search {
                 self_iter,
                 other_set: _,
             } => f.debug_tuple("Difference").field(&self_iter).finish(),
         }
     }
 }

 /// A lazy iterator producing elements in the symmetric difference of `BTreeSet`s.
 ///
 /// This `struct` is created by the [`symmetric_difference`] method on
 /// [`BTreeSet`]. See its documentation for more.
 ///
 /// [`BTreeSet`]: struct.BTreeSet.html
 /// [`symmetric_difference`]: struct.BTreeSet.html#method.symmetric_difference
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct SymmetricDifference<'a, T: 'a> {
     a: Peekable<Iter<'a, T>>,
     b: Peekable<Iter<'a, T>>,
 }

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

 /// A lazy iterator producing elements in the intersection of `BTreeSet`s.
 ///
 /// This `struct` is created by the [`intersection`] method on [`BTreeSet`].
 /// See its documentation for more.
 ///
 /// [`BTreeSet`]: struct.BTreeSet.html
 /// [`intersection`]: struct.BTreeSet.html#method.intersection
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct Intersection<'a, T: 'a> {
     inner: IntersectionInner<'a, T>,
 }
 enum IntersectionInner<'a, T: 'a> {
     Stitch {
         small_iter: Iter<'a, T>, // for size_hint, should be the smaller of the sets
         other_iter: Iter<'a, T>,
     },
     Search {
         small_iter: Iter<'a, T>,
         large_set: &'a BTreeSet<T>,
     },
 }

 #[stable(feature = "collection_debug", since = "1.17.0")]
 impl<T: fmt::Debug> fmt::Debug for Intersection<'_, T> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         match &self.inner {
             IntersectionInner::Stitch {
                 small_iter,
                 other_iter,
             } => f
                 .debug_tuple("Intersection")
                 .field(&small_iter)
                 .field(&other_iter)
                 .finish(),
             IntersectionInner::Search {
                 small_iter,
                 large_set: _,
             } => f.debug_tuple("Intersection").field(&small_iter).finish(),
         }
     }
 }

 /// A lazy iterator producing elements in the union of `BTreeSet`s.
 ///
 /// This `struct` is created by the [`union`] method on [`BTreeSet`].
 /// See its documentation for more.
 ///
 /// [`BTreeSet`]: struct.BTreeSet.html
 /// [`union`]: struct.BTreeSet.html#method.union
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct Union<'a, T: 'a> {
     a: Peekable<Iter<'a, T>>,
     b: Peekable<Iter<'a, T>>,
 }

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

 // This constant is used by functions that compare two sets.
 // It estimates the relative size at which searching performs better
 // than iterating, based on the benchmarks in
 // https://github.com/ssomers/rust_bench_btreeset_intersection;
 // It's used to divide rather than multiply sizes, to rule out overflow,
 // and it's a power of two to make that division cheap.
 const ITER_PERFORMANCE_TIPPING_SIZE_DIFF: usize = 16;

 impl<T: Ord> BTreeSet<T> {
     /// Makes a new `BTreeSet` with a reasonable choice of B.
     ///
     /// # Examples
     ///
     /// ```
     /// # #![allow(unused_mut)]
     /// use std::collections::BTreeSet;
     ///
     /// let mut set: BTreeSet<i32> = BTreeSet::new();
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn new() -> BTreeSet<T> {
         BTreeSet { map: BTreeMap::new() }
     }

     /// Constructs a double-ended iterator over a sub-range of elements in the set.
     /// 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.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     /// use std::ops::Bound::Included;
     ///
     /// let mut set = BTreeSet::new();
     /// set.insert(3);
     /// set.insert(5);
     /// set.insert(8);
     /// for &elem in set.range((Included(&4), Included(&8))) {
     ///     println!("{}", elem);
     /// }
     /// assert_eq!(Some(&5), set.range(4..).next());
     /// ```
     #[stable(feature = "btree_range", since = "1.17.0")]
     pub fn range<K: ?Sized, R>(&self, range: R) -> Range<'_, T>
         where K: Ord, T: Borrow<K>, R: RangeBounds<K>
     {
         Range { iter: self.map.range(range) }
     }

     /// Visits the values representing the difference,
     /// i.e., the values that are in `self` but not in `other`,
     /// in ascending order.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut a = BTreeSet::new();
     /// a.insert(1);
     /// a.insert(2);
     ///
     /// let mut b = BTreeSet::new();
     /// b.insert(2);
     /// b.insert(3);
     ///
     /// let diff: Vec<_> = a.difference(&b).cloned().collect();
     /// assert_eq!(diff, [1]);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn difference<'a>(&'a self, other: &'a BTreeSet<T>) -> Difference<'a, T> {
         if self.len() > other.len() / ITER_PERFORMANCE_TIPPING_SIZE_DIFF {
             // Self is bigger than or not much smaller than other set.
             // Iterate both sets jointly, spotting matches along the way.
             Difference {
                 inner: DifferenceInner::Stitch {
                     self_iter: self.iter(),
                     other_iter: other.iter().peekable(),
                 },
             }
         } else {
             // Self is much smaller than other set, or both sets are empty.
             // Iterate the small set, searching for matches in the large set.
             Difference {
                 inner: DifferenceInner::Search {
                     self_iter: self.iter(),
                     other_set: other,
                 },
             }
         }
     }

     /// Visits the values representing the symmetric difference,
     /// i.e., the values that are in `self` or in `other` but not in both,
     /// in ascending order.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut a = BTreeSet::new();
     /// a.insert(1);
     /// a.insert(2);
     ///
     /// let mut b = BTreeSet::new();
     /// b.insert(2);
     /// b.insert(3);
     ///
     /// let sym_diff: Vec<_> = a.symmetric_difference(&b).cloned().collect();
     /// assert_eq!(sym_diff, [1, 3]);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn symmetric_difference<'a>(&'a self,
                                     other: &'a BTreeSet<T>)
                                     -> SymmetricDifference<'a, T> {
         SymmetricDifference {
             a: self.iter().peekable(),
             b: other.iter().peekable(),
         }
     }

     /// Visits the values representing the intersection,
     /// i.e., the values that are both in `self` and `other`,
     /// in ascending order.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut a = BTreeSet::new();
     /// a.insert(1);
     /// a.insert(2);
     ///
     /// let mut b = BTreeSet::new();
     /// b.insert(2);
     /// b.insert(3);
     ///
     /// let intersection: Vec<_> = a.intersection(&b).cloned().collect();
     /// assert_eq!(intersection, [2]);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn intersection<'a>(&'a self, other: &'a BTreeSet<T>) -> Intersection<'a, T> {
         let (small, other) = if self.len() <= other.len() {
             (self, other)
         } else {
             (other, self)
         };
         if small.len() > other.len() / ITER_PERFORMANCE_TIPPING_SIZE_DIFF {
             // Small set is not much smaller than other set.
             // Iterate both sets jointly, spotting matches along the way.
             Intersection {
                 inner: IntersectionInner::Stitch {
                     small_iter: small.iter(),
                     other_iter: other.iter(),
                 },
             }
         } else {
             // Big difference in number of elements, or both sets are empty.
             // Iterate the small set, searching for matches in the large set.
             Intersection {
                 inner: IntersectionInner::Search {
                     small_iter: small.iter(),
                     large_set: other,
                 },
             }
         }
     }

     /// Visits the values representing the union,
     /// i.e., all the values in `self` or `other`, without duplicates,
     /// in ascending order.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut a = BTreeSet::new();
     /// a.insert(1);
     ///
     /// let mut b = BTreeSet::new();
     /// b.insert(2);
     ///
     /// let union: Vec<_> = a.union(&b).cloned().collect();
     /// assert_eq!(union, [1, 2]);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn union<'a>(&'a self, other: &'a BTreeSet<T>) -> Union<'a, T> {
         Union {
             a: self.iter().peekable(),
             b: other.iter().peekable(),
         }
     }

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

     /// Returns `true` if the set contains a value.
     ///
     /// The value may be any borrowed form of the set's value type,
     /// but the ordering on the borrowed form *must* match the
     /// ordering on the value type.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let set: BTreeSet<_> = [1, 2, 3].iter().cloned().collect();
     /// assert_eq!(set.contains(&1), true);
     /// assert_eq!(set.contains(&4), false);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn contains<Q: ?Sized>(&self, value: &Q) -> bool
         where T: Borrow<Q>,
               Q: Ord
     {
         self.map.contains_key(value)
     }

     /// Returns a reference to the value in the set, if any, that is equal to the given value.
     ///
     /// The value may be any borrowed form of the set's value type,
     /// but the ordering on the borrowed form *must* match the
     /// ordering on the value type.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let set: BTreeSet<_> = [1, 2, 3].iter().cloned().collect();
     /// assert_eq!(set.get(&2), Some(&2));
     /// assert_eq!(set.get(&4), None);
     /// ```
     #[stable(feature = "set_recovery", since = "1.9.0")]
     pub fn get<Q: ?Sized>(&self, value: &Q) -> Option<&T>
         where T: Borrow<Q>,
               Q: Ord
     {
         Recover::get(&self.map, value)
     }

     /// Returns `true` if `self` has no elements in common with `other`.
     /// This is equivalent to checking for an empty intersection.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let a: BTreeSet<_> = [1, 2, 3].iter().cloned().collect();
     /// let mut b = BTreeSet::new();
     ///
     /// assert_eq!(a.is_disjoint(&b), true);
     /// b.insert(4);
     /// assert_eq!(a.is_disjoint(&b), true);
     /// b.insert(1);
     /// assert_eq!(a.is_disjoint(&b), false);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn is_disjoint(&self, other: &BTreeSet<T>) -> bool {
         self.intersection(other).next().is_none()
     }

     /// Returns `true` if the set is a subset of another,
     /// i.e., `other` contains at least all the values in `self`.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let sup: BTreeSet<_> = [1, 2, 3].iter().cloned().collect();
     /// let mut set = BTreeSet::new();
     ///
     /// assert_eq!(set.is_subset(&sup), true);
     /// set.insert(2);
     /// assert_eq!(set.is_subset(&sup), true);
     /// set.insert(4);
     /// assert_eq!(set.is_subset(&sup), false);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn is_subset(&self, other: &BTreeSet<T>) -> bool {
         // Same result as self.difference(other).next().is_none()
         // but the 3 paths below are faster (in order: hugely, 20%, 5%).
         if self.len() > other.len() {
             false
         } else if self.len() > other.len() / ITER_PERFORMANCE_TIPPING_SIZE_DIFF {
             // Self is not much smaller than other set.
             // Stolen from TreeMap
             let mut x = self.iter();
             let mut y = other.iter();
             let mut a = x.next();
             let mut b = y.next();
             while a.is_some() {
                 if b.is_none() {
                     return false;
                 }

                 let a1 = a.unwrap();
                 let b1 = b.unwrap();

                 match b1.cmp(a1) {
                     Less => (),
                     Greater => return false,
                     Equal => a = x.next(),
                 }

                 b = y.next();
             }
             true
         } else {
             // Big difference in number of elements, or both sets are empty.
             // Iterate the small set, searching for matches in the large set.
             for next in self {
                 if !other.contains(next) {
                     return false;
                 }
             }
             true
         }
     }

     /// Returns `true` if the set is a superset of another,
     /// i.e., `self` contains at least all the values in `other`.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let sub: BTreeSet<_> = [1, 2].iter().cloned().collect();
     /// let mut set = BTreeSet::new();
     ///
     /// assert_eq!(set.is_superset(&sub), false);
     ///
     /// set.insert(0);
     /// set.insert(1);
     /// assert_eq!(set.is_superset(&sub), false);
     ///
     /// set.insert(2);
     /// assert_eq!(set.is_superset(&sub), true);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn is_superset(&self, other: &BTreeSet<T>) -> bool {
         other.is_subset(self)
     }

     /// Adds a value to the set.
     ///
     /// If the set did not have this value present, `true` is returned.
     ///
     /// If the set did have this value present, `false` is returned, and the
     /// entry is not updated. See the [module-level documentation] for more.
     ///
     /// [module-level documentation]: index.html#insert-and-complex-keys
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut set = BTreeSet::new();
     ///
     /// assert_eq!(set.insert(2), true);
     /// assert_eq!(set.insert(2), false);
     /// assert_eq!(set.len(), 1);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn insert(&mut self, value: T) -> bool {
         self.map.insert(value, ()).is_none()
     }

     /// Adds a value to the set, replacing the existing value, if any, that is equal to the given
     /// one. Returns the replaced value.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut set = BTreeSet::new();
     /// set.insert(Vec::<i32>::new());
     ///
     /// assert_eq!(set.get(&[][..]).unwrap().capacity(), 0);
     /// set.replace(Vec::with_capacity(10));
     /// assert_eq!(set.get(&[][..]).unwrap().capacity(), 10);
     /// ```
     #[stable(feature = "set_recovery", since = "1.9.0")]
     pub fn replace(&mut self, value: T) -> Option<T> {
         Recover::replace(&mut self.map, value)
     }

     /// Removes a value from the set. Returns whether the value was
     /// present in the set.
     ///
     /// The value may be any borrowed form of the set's value type,
     /// but the ordering on the borrowed form *must* match the
     /// ordering on the value type.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut set = BTreeSet::new();
     ///
     /// set.insert(2);
     /// assert_eq!(set.remove(&2), true);
     /// assert_eq!(set.remove(&2), false);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn remove<Q: ?Sized>(&mut self, value: &Q) -> bool
         where T: Borrow<Q>,
               Q: Ord
     {
         self.map.remove(value).is_some()
     }

     /// Removes and returns the value in the set, if any, that is equal to the given one.
     ///
     /// The value may be any borrowed form of the set's value type,
     /// but the ordering on the borrowed form *must* match the
     /// ordering on the value type.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut set: BTreeSet<_> = [1, 2, 3].iter().cloned().collect();
     /// assert_eq!(set.take(&2), Some(2));
     /// assert_eq!(set.take(&2), None);
     /// ```
     #[stable(feature = "set_recovery", since = "1.9.0")]
     pub fn take<Q: ?Sized>(&mut self, value: &Q) -> Option<T>
         where T: Borrow<Q>,
               Q: Ord
     {
         Recover::take(&mut self.map, value)
     }

     /// Moves all elements from `other` into `Self`, leaving `other` empty.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let mut a = BTreeSet::new();
     /// a.insert(1);
     /// a.insert(2);
     /// a.insert(3);
     ///
     /// let mut b = BTreeSet::new();
     /// b.insert(3);
     /// b.insert(4);
     /// b.insert(5);
     ///
     /// a.append(&mut b);
     ///
     /// assert_eq!(a.len(), 5);
     /// assert_eq!(b.len(), 0);
     ///
     /// assert!(a.contains(&1));
     /// assert!(a.contains(&2));
     /// assert!(a.contains(&3));
     /// assert!(a.contains(&4));
     /// assert!(a.contains(&5));
     /// ```
     #[stable(feature = "btree_append", since = "1.11.0")]
     pub fn append(&mut self, other: &mut Self) {
         self.map.append(&mut other.map);
     }

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

 impl<T> BTreeSet<T> {
     /// Gets an iterator that visits the values in the `BTreeSet` in ascending order.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let set: BTreeSet<usize> = [1, 2, 3].iter().cloned().collect();
     /// let mut set_iter = set.iter();
     /// assert_eq!(set_iter.next(), Some(&1));
     /// assert_eq!(set_iter.next(), Some(&2));
     /// assert_eq!(set_iter.next(), Some(&3));
     /// assert_eq!(set_iter.next(), None);
     /// ```
     ///
     /// Values returned by the iterator are returned in ascending order:
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let set: BTreeSet<usize> = [3, 1, 2].iter().cloned().collect();
     /// let mut set_iter = set.iter();
     /// assert_eq!(set_iter.next(), Some(&1));
     /// assert_eq!(set_iter.next(), Some(&2));
     /// assert_eq!(set_iter.next(), Some(&3));
     /// assert_eq!(set_iter.next(), None);
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn iter(&self) -> Iter<'_, T> {
         Iter { iter: self.map.keys() }
     }

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

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

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

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

     /// Gets an iterator for moving out the `BTreeSet`'s contents.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let set: BTreeSet<usize> = [1, 2, 3, 4].iter().cloned().collect();
     ///
     /// let v: Vec<_> = set.into_iter().collect();
     /// assert_eq!(v, [1, 2, 3, 4]);
     /// ```
     fn into_iter(self) -> IntoIter<T> {
         IntoIter { iter: self.map.into_iter() }
     }
 }

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<'a, T> IntoIterator for &'a BTreeSet<T> {
     type Item = &'a T;
     type IntoIter = Iter<'a, T>;

     fn into_iter(self) -> Iter<'a, T> {
         self.iter()
     }
 }

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

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

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T: Ord> Default for BTreeSet<T> {
     /// Makes an empty `BTreeSet<T>` with a reasonable choice of B.
     fn default() -> BTreeSet<T> {
         BTreeSet::new()
     }
 }

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T: Ord + Clone> Sub<&BTreeSet<T>> for &BTreeSet<T> {
     type Output = BTreeSet<T>;

     /// Returns the difference of `self` and `rhs` as a new `BTreeSet<T>`.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let a: BTreeSet<_> = vec![1, 2, 3].into_iter().collect();
     /// let b: BTreeSet<_> = vec![3, 4, 5].into_iter().collect();
     ///
     /// let result = &a - &b;
     /// let result_vec: Vec<_> = result.into_iter().collect();
     /// assert_eq!(result_vec, [1, 2]);
     /// ```
     fn sub(self, rhs: &BTreeSet<T>) -> BTreeSet<T> {
         self.difference(rhs).cloned().collect()
     }
 }

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T: Ord + Clone> BitXor<&BTreeSet<T>> for &BTreeSet<T> {
     type Output = BTreeSet<T>;

     /// Returns the symmetric difference of `self` and `rhs` as a new `BTreeSet<T>`.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let a: BTreeSet<_> = vec![1, 2, 3].into_iter().collect();
     /// let b: BTreeSet<_> = vec![2, 3, 4].into_iter().collect();
     ///
     /// let result = &a ^ &b;
     /// let result_vec: Vec<_> = result.into_iter().collect();
     /// assert_eq!(result_vec, [1, 4]);
     /// ```
     fn bitxor(self, rhs: &BTreeSet<T>) -> BTreeSet<T> {
         self.symmetric_difference(rhs).cloned().collect()
     }
 }

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T: Ord + Clone> BitAnd<&BTreeSet<T>> for &BTreeSet<T> {
     type Output = BTreeSet<T>;

     /// Returns the intersection of `self` and `rhs` as a new `BTreeSet<T>`.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let a: BTreeSet<_> = vec![1, 2, 3].into_iter().collect();
     /// let b: BTreeSet<_> = vec![2, 3, 4].into_iter().collect();
     ///
     /// let result = &a & &b;
     /// let result_vec: Vec<_> = result.into_iter().collect();
     /// assert_eq!(result_vec, [2, 3]);
     /// ```
     fn bitand(self, rhs: &BTreeSet<T>) -> BTreeSet<T> {
         self.intersection(rhs).cloned().collect()
     }
 }

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T: Ord + Clone> BitOr<&BTreeSet<T>> for &BTreeSet<T> {
     type Output = BTreeSet<T>;

     /// Returns the union of `self` and `rhs` as a new `BTreeSet<T>`.
     ///
     /// # Examples
     ///
     /// ```
     /// use std::collections::BTreeSet;
     ///
     /// let a: BTreeSet<_> = vec![1, 2, 3].into_iter().collect();
     /// let b: BTreeSet<_> = vec![3, 4, 5].into_iter().collect();
     ///
     /// let result = &a | &b;
     /// let result_vec: Vec<_> = result.into_iter().collect();
     /// assert_eq!(result_vec, [1, 2, 3, 4, 5]);
     /// ```
     fn bitor(self, rhs: &BTreeSet<T>) -> BTreeSet<T> {
         self.union(rhs).cloned().collect()
     }
 }

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T: Debug> Debug for BTreeSet<T> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         f.debug_set().entries(self.iter()).finish()
     }
 }

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T> Clone for Iter<'_, T> {
     fn clone(&self) -> Self {
         Iter { iter: self.iter.clone() }
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<'a, T> Iterator for Iter<'a, T> {
     type Item = &'a T;

     fn next(&mut self) -> Option<&'a T> {
         self.iter.next()
     }
     fn size_hint(&self) -> (usize, Option<usize>) {
         self.iter.size_hint()
     }
     fn last(mut self) -> Option<&'a T> {
         self.next_back()
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<'a, T> DoubleEndedIterator for Iter<'a, T> {
     fn next_back(&mut self) -> Option<&'a T> {
         self.iter.next_back()
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T> ExactSizeIterator for Iter<'_, T> {
     fn len(&self) -> usize { self.iter.len() }
 }

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

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

     fn next(&mut self) -> Option<T> {
         self.iter.next().map(|(k, _)| k)
     }
     fn size_hint(&self) -> (usize, Option<usize>) {
         self.iter.size_hint()
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T> DoubleEndedIterator for IntoIter<T> {
     fn next_back(&mut self) -> Option<T> {
         self.iter.next_back().map(|(k, _)| k)
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T> ExactSizeIterator for IntoIter<T> {
     fn len(&self) -> usize { self.iter.len() }
 }

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

 #[stable(feature = "btree_range", since = "1.17.0")]
 impl<T> Clone for Range<'_, T> {
     fn clone(&self) -> Self {
         Range { iter: self.iter.clone() }
     }
 }

 #[stable(feature = "btree_range", since = "1.17.0")]
 impl<'a, T> Iterator for Range<'a, T> {
     type Item = &'a T;

     fn next(&mut self) -> Option<&'a T> {
         self.iter.next().map(|(k, _)| k)
     }

     fn last(mut self) -> Option<&'a T> {
         self.next_back()
     }
 }

 #[stable(feature = "btree_range", since = "1.17.0")]
 impl<'a, T> DoubleEndedIterator for Range<'a, T> {
     fn next_back(&mut self) -> Option<&'a T> {
         self.iter.next_back().map(|(k, _)| k)
     }
 }

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

 /// Compares `x` and `y`, but return `short` if x is None and `long` if y is None
 fn cmp_opt<T: Ord>(x: Option<&T>, y: Option<&T>, short: Ordering, long: Ordering) -> Ordering {
     match (x, y) {
         (None, _) => short,
         (_, None) => long,
         (Some(x1), Some(y1)) => x1.cmp(y1),
     }
 }

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T> Clone for Difference<'_, T> {
     fn clone(&self) -> Self {
         Difference {
             inner: match &self.inner {
                 DifferenceInner::Stitch {
                     self_iter,
                     other_iter,
                 } => DifferenceInner::Stitch {
                     self_iter: self_iter.clone(),
                     other_iter: other_iter.clone(),
                 },
                 DifferenceInner::Search {
                     self_iter,
                     other_set,
                 } => DifferenceInner::Search {
                     self_iter: self_iter.clone(),
                     other_set,
                 },
             },
         }
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<'a, T: Ord> Iterator for Difference<'a, T> {
     type Item = &'a T;

     fn next(&mut self) -> Option<&'a T> {
         match &mut self.inner {
             DifferenceInner::Stitch {
                 self_iter,
                 other_iter,
             } => {
                 let mut self_next = self_iter.next()?;
                 loop {
                     match other_iter
                         .peek()
                         .map_or(Less, |other_next| Ord::cmp(self_next, other_next))
                     {
                         Less => return Some(self_next),
                         Equal => {
                             self_next = self_iter.next()?;
                             other_iter.next();
                         }
                         Greater => {
                             other_iter.next();
                         }
                     }
                 }
             }
             DifferenceInner::Search {
                 self_iter,
                 other_set,
             } => loop {
                 let self_next = self_iter.next()?;
                 if !other_set.contains(&self_next) {
                     return Some(self_next);
                 }
             },
         }
     }

     fn size_hint(&self) -> (usize, Option<usize>) {
         let (self_len, other_len) = match &self.inner {
             DifferenceInner::Stitch {
                 self_iter,
                 other_iter
             } => (self_iter.len(), other_iter.len()),
             DifferenceInner::Search {
                 self_iter,
                 other_set
             } => (self_iter.len(), other_set.len()),
         };
         (self_len.saturating_sub(other_len), Some(self_len))
     }
 }

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

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T> Clone for SymmetricDifference<'_, T> {
     fn clone(&self) -> Self {
         SymmetricDifference {
             a: self.a.clone(),
             b: self.b.clone(),
         }
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<'a, T: Ord> Iterator for SymmetricDifference<'a, T> {
     type Item = &'a T;

     fn next(&mut self) -> Option<&'a T> {
         loop {
             match cmp_opt(self.a.peek(), self.b.peek(), Greater, Less) {
                 Less => return self.a.next(),
                 Equal => {
                     self.a.next();
                     self.b.next();
                 }
                 Greater => return self.b.next(),
             }
         }
     }

     fn size_hint(&self) -> (usize, Option<usize>) {
         (0, Some(self.a.len() + self.b.len()))
     }
 }

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

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T> Clone for Intersection<'_, T> {
     fn clone(&self) -> Self {
         Intersection {
             inner: match &self.inner {
                 IntersectionInner::Stitch {
                     small_iter,
                     other_iter,
                 } => IntersectionInner::Stitch {
                     small_iter: small_iter.clone(),
                     other_iter: other_iter.clone(),
                 },
                 IntersectionInner::Search {
                     small_iter,
                     large_set,
                 } => IntersectionInner::Search {
                     small_iter: small_iter.clone(),
                     large_set,
                 },
             },
         }
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<'a, T: Ord> Iterator for Intersection<'a, T> {
     type Item = &'a T;

     fn next(&mut self) -> Option<&'a T> {
         match &mut self.inner {
             IntersectionInner::Stitch {
                 small_iter,
                 other_iter,
             } => {
                 let mut small_next = small_iter.next()?;
                 let mut other_next = other_iter.next()?;
                 loop {
                     match Ord::cmp(small_next, other_next) {
                         Less => small_next = small_iter.next()?,
                         Greater => other_next = other_iter.next()?,
                         Equal => return Some(small_next),
                     }
                 }
             }
             IntersectionInner::Search {
                 small_iter,
                 large_set,
             } => loop {
                 let small_next = small_iter.next()?;
                 if large_set.contains(&small_next) {
                     return Some(small_next);
                 }
             },
         }
     }

     fn size_hint(&self) -> (usize, Option<usize>) {
         let min_len = match &self.inner {
             IntersectionInner::Stitch { small_iter, .. } => small_iter.len(),
             IntersectionInner::Search { small_iter, .. } => small_iter.len(),
         };
         (0, Some(min_len))
     }
 }

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

 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T> Clone for Union<'_, T> {
     fn clone(&self) -> Self {
         Union {
             a: self.a.clone(),
             b: self.b.clone(),
         }
     }
 }
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<'a, T: Ord> Iterator for Union<'a, T> {
     type Item = &'a T;

     fn next(&mut self) -> Option<&'a T> {
         match cmp_opt(self.a.peek(), self.b.peek(), Greater, Less) {
             Less => self.a.next(),
             Equal => {
                 self.b.next();
                 self.a.next()
             }
             Greater => self.b.next(),
         }
     }

     fn size_hint(&self) -> (usize, Option<usize>) {
         let a_len = self.a.len();
         let b_len = self.b.len();
         (max(a_len, b_len), Some(a_len + b_len))
     }
 }

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