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# std.container.rbtree

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

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));