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# std.container.rbtree

This module implements a red-black tree container.
This module is a submodule of std.container.

Source std/container/rbtree.d

License:
Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at boost.org/LICENSE_1_0.txt).
Authors:
Steven Schveighoffer, Andrei Alexandrescu
Examples:

    import std.algorithm.comparison : equal;
    import std.container.rbtree;

    auto rbt = redBlackTree(3, 1, 4, 2, 5);
    writeln(rbt.front); // 1
    assert(equal(rbt[], [1, 2, 3, 4, 5]));

    rbt.removeKey(1, 4);
    assert(equal(rbt[], [2, 3, 5]));

    rbt.removeFront();
    assert(equal(rbt[], [3, 5]));

    rbt.insert([1, 2, 4]);
    assert(equal(rbt[], [1, 2, 3, 4, 5]));

    // Query bounds in O(log(n))
    assert(rbt.lowerBound(3).equal([1, 2]));
    assert(rbt.equalRange(3).equal([3]));
    assert(rbt.upperBound(3).equal([4, 5]));

    // A Red Black tree with the highest element at front:
    import std.range : iota;
    auto maxTree = redBlackTree!"a > b"(iota(5));
    assert(equal(maxTree[], [4, 3, 2, 1, 0]));

    // adding duplicates will not add them, but return 0
    auto rbt2 = redBlackTree(1, 3);
    writeln(rbt2.insert(1)); // 0
    assert(equal(rbt2[], [1, 3]));
    writeln(rbt2.insert(2)); // 1

    // however you can allow duplicates
    auto ubt = redBlackTree!true([0, 1, 0, 1]);
    assert(equal(ubt[], [0, 0, 1, 1]));

class `RedBlackTree`(T, alias less = "a < b", bool allowDuplicates = false) if (is(typeof(binaryFun!less(T.init, T.init))));
  Implementation of a red-black tree container.
  All inserts, removes, searches, and any function in general has complexity of Ο(lg(n)).
  To use a different comparison than "a < b", pass a different operator string that can be used by std.functional.binaryFun, or pass in a function, delegate, functor, or any type where less(a, b) results in a bool value.
  Note that less should produce a strict ordering. That is, for two unequal elements a and b, less(a, b) == !less(b, a). less(a, a) should always equal false.
  If allowDuplicates is set to true, then inserting the same element more than once continues to add more elements. If it is false, duplicate elements are ignored on insertion. If duplicates are allowed, then new elements are inserted after all existing duplicate elements.
  alias `Elem` = T;
    Element type for the tree
  alias `Range` = RBRange!(RBNode*);
  alias `ConstRange` = RBRange!(const(RBNode)*);
  alias `ImmutableRange` = RBRange!(immutable(RBNode)*);
    The range types for RedBlackTree
  const @property bool `empty`();
    Check if any elements exist in the container. Returns false if at least one element exists.
  const @property size_t `length`();
    Returns the number of elements in the container.

    Complexity Ο(1).

  @property RedBlackTree `dup`();
    Duplicate this container. The resulting container contains a shallow copy of the elements.

    Complexity Ο(n)

  Range `opSlice`();
  const ConstRange `opSlice`();
  immutable ImmutableRange `opSlice`();
    Fetch a range that spans all the elements in the container.

    Complexity Ο(1)

  inout inout(Elem) `front`();
    The front element in the container

    Complexity Ο(1)

  inout inout(Elem) `back`();
    The last element in the container

    Complexity Ο(log(n))

  const bool `opBinaryRight`(string op)(Elem `e`)
  if (op == "in");
    in operator. Check to see if the given element exists in the container.

    Complexity Ο(log(n))

  bool `opEquals`(Object `rhs`);
    Compares two trees for equality.

    Complexity Ο(n)

  nothrow @safe size_t `toHash`();
    Generates a hash for the tree. Note that with a custom comparison function it may not hold that if two rbtrees are equal, the hashes of the trees will be equal.
  void `clear`();
    Removes all elements from the container.

    Complexity Ο(1)

  size_t `stableInsert`(Stuff)(Stuff `stuff`)
  if (isImplicitlyConvertible!(Stuff, Elem));
    Insert a single element in the container. Note that this does not invalidate any ranges currently iterating the container.
    Returns:
    The number of elements inserted.

    Complexity Ο(log(n))

  size_t `stableInsert`(Stuff)(scope Stuff `stuff`)
  if (isInputRange!Stuff && isImplicitlyConvertible!(ElementType!Stuff, Elem));
  alias `insert` = stableInsert;
    Insert a range of elements in the container. Note that this does not invalidate any ranges currently iterating the container.
    Returns:
    The number of elements inserted.

    Complexity Ο(m * log(n))

  Elem `removeAny`();
    Remove an element from the container and return its value.

    Complexity Ο(log(n))

  void `removeFront`();
    Remove the front element from the container.

    Complexity Ο(log(n))

  void `removeBack`();
    Remove the back element from the container.

    Complexity Ο(log(n))

  Range `remove`(Range `r`);
    Removes the given range from the container.
    Returns:
    A range containing all of the elements that were after the given range.

    Complexity Ο(m * log(n)) (where m is the number of elements in the range)

  Range `remove`(Take!Range `r`);
    Removes the given Take!Range from the container
    Returns:
    A range containing all of the elements that were after the given range.

    Complexity Ο(m * log(n)) (where m is the number of elements in the range)

  size_t `removeKey`(U...)(U `elems`)
  if (allSatisfy!(isImplicitlyConvertibleToElem, U));
  size_t `removeKey`(U)(scope U[] `elems`)
  if (isImplicitlyConvertible!(U, Elem));
  size_t `removeKey`(Stuff)(Stuff `stuff`)
  if (isInputRange!Stuff && isImplicitlyConvertible!(ElementType!Stuff, Elem) && !isDynamicArray!Stuff);
    Removes elements from the container that are equal to the given values according to the less comparator. One element is removed for each value given which is in the container. If allowDuplicates is true, duplicates are removed only if duplicate values are given.
    Returns:
    The number of elements removed.

    Complexity Ο(m log(n)) (where m is the number of elements to remove)

    Example

        auto rbt = redBlackTree!true(0, 1, 1, 1, 4, 5, 7);
        rbt.removeKey(1, 4, 7);
        assert(equal(rbt[], [0, 1, 1, 5]));
        rbt.removeKey(1, 1, 0);
        assert(equal(rbt[], [5]));

  Range `upperBound`(Elem `e`);
  const ConstRange `upperBound`(Elem `e`);
  immutable ImmutableRange `upperBound`(Elem `e`);
    Get a range from the container with all elements that are > e according to the less comparator

    Complexity Ο(log(n))

  Range `lowerBound`(Elem `e`);
  const ConstRange `lowerBound`(Elem `e`);
  immutable ImmutableRange `lowerBound`(Elem `e`);
    Get a range from the container with all elements that are < e according to the less comparator

    Complexity Ο(log(n))

  auto `equalRange`(this This)(Elem `e`);
    Get a range from the container with all elements that are == e according to the less comparator

    Complexity Ο(log(n))

  const void `toString`(scope void delegate(const(char)[]) `sink`, ref scope const FormatSpec!char `fmt`);
    Formats the RedBlackTree into a sink function. For more info see std.format.formatValue. Note that this only is available when the element type can be formatted. Otherwise, the default toString from Object is used.
  this(Elem[] `elems`...);
    Constructor. Pass in an array of elements, or individual elements to initialize the tree with.
  this(Stuff)(Stuff `stuff`)
  if (isInputRange!Stuff && isImplicitlyConvertible!(ElementType!Stuff, Elem));
    Constructor. Pass in a range of elements to initialize the tree with.
  this();
auto `redBlackTree`(E)(E[] `elems`...);
auto `redBlackTree`(bool allowDuplicates, E)(E[] `elems`...);
auto `redBlackTree`(alias less, E)(E[] `elems`...)
if (is(typeof(binaryFun!less(E.init, E.init))));
auto `redBlackTree`(alias less, bool allowDuplicates, E)(E[] `elems`...)
if (is(typeof(binaryFun!less(E.init, E.init))));
auto `redBlackTree`(Stuff)(Stuff `range`)
if (isInputRange!Stuff && !isArray!Stuff);
auto `redBlackTree`(bool allowDuplicates, Stuff)(Stuff `range`)
if (isInputRange!Stuff && !isArray!Stuff);
auto `redBlackTree`(alias less, Stuff)(Stuff `range`)
if (is(typeof(binaryFun!less((ElementType!Stuff).init, (ElementType!Stuff).init))) && isInputRange!Stuff && !isArray!Stuff);
auto `redBlackTree`(alias less, bool allowDuplicates, Stuff)(Stuff `range`)
if (is(typeof(binaryFun!less((ElementType!Stuff).init, (ElementType!Stuff).init))) && isInputRange!Stuff && !isArray!Stuff);
  Convenience function for creating a RedBlackTree!E from a list of values.
  Parameters:

  allowDuplicates | Whether duplicates should be allowed (optional, default: false)
  less | predicate to sort by (optional)
  E[] `elems` | elements to insert into the rbtree (variadic arguments)
  Stuff `range` | range elements to insert into the rbtree (alternative to elems)

  Examples:

      import std.range : iota;

      auto rbt1 = redBlackTree(0, 1, 5, 7);
      auto rbt2 = redBlackTree!string("hello", "world");
      auto rbt3 = redBlackTree!true(0, 1, 5, 7, 5);
      auto rbt4 = redBlackTree!"a > b"(0, 1, 5, 7);
      auto rbt5 = redBlackTree!("a > b", true)(0.1, 1.3, 5.9, 7.2, 5.9);

      // also works with ranges
      auto rbt6 = redBlackTree(iota(3));
      auto rbt7 = redBlackTree!true(iota(3));
      auto rbt8 = redBlackTree!"a > b"(iota(3));
      auto rbt9 = redBlackTree!("a > b", true)(iota(3));

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