Collections and Data Structures

Iteration

Sequential iteration is implemented by the iterate function. The general for loop:

for i in iter   # or  "for i = iter"
    # body
end

is translated into:

next = iterate(iter)
while next !== nothing
    (i, state) = next
    # body
    next = iterate(iter, state)
end

The state object may be anything, and should be chosen appropriately for each iterable type. See the manual section on the iteration interface for more details about defining a custom iterable type.

# Base.iterate — Function

iterate(iter [, state]) -> Union{Nothing, Tuple{Any, Any}}

Advance the iterator to obtain the next element. If no elements remain, nothing should be returned. Otherwise, a 2-tuple of the next element and the new iteration state should be returned.

# Base.IteratorSize — Type

IteratorSize(itertype::Type) -> IteratorSize

Given the type of an iterator, return one of the following values:

SizeUnknown() if the length (number of elements) cannot be determined in advance.
HasLength() if there is a fixed, finite length.
HasShape{N}() if there is a known length plus a notion of multidimensional shape (as for an array). In this case N should give the number of dimensions, and the axes function is valid for the iterator.
IsInfinite() if the iterator yields values forever.

The default value (for iterators that do not define this function) is HasLength(). This means that most iterators are assumed to implement length.

This trait is generally used to select between algorithms that pre-allocate space for their result, and algorithms that resize their result incrementally.

julia> Base.IteratorSize(1:5)
Base.HasShape{1}()

julia> Base.IteratorSize((2,3))
Base.HasLength()

# Base.IteratorEltype — Type

IteratorEltype(itertype::Type) -> IteratorEltype

Given the type of an iterator, return one of the following values:

EltypeUnknown() if the type of elements yielded by the iterator is not known in advance.
HasEltype() if the element type is known, and eltype would return a meaningful value.

HasEltype() is the default, since iterators are assumed to implement eltype.

This trait is generally used to select between algorithms that pre-allocate a specific type of result, and algorithms that pick a result type based on the types of yielded values.

julia> Base.IteratorEltype(1:5)
Base.HasEltype()

Fully implemented by:

AbstractRange
UnitRange
Tuple
Number
AbstractArray
BitSet
IdDict
Dict
WeakKeyDict
EachLine
AbstractString
Set
Pair
NamedTuple

Constructors and Types

# Base.AbstractRange — Type

AbstractRange{T}

Supertype for ranges with elements of type T. UnitRange and other types are subtypes of this.

# Base.OrdinalRange — Type

OrdinalRange{T, S} <: AbstractRange{T}

Supertype for ordinal ranges with elements of type T with spacing(s) of type S. The steps should be always-exact multiples of oneunit, and T should be a "discrete" type, which cannot have values smaller than oneunit. For example, Integer or Date types would qualify, whereas Float64 would not (since this type can represent values smaller than oneunit(Float64). UnitRange, StepRange, and other types are subtypes of this.

# Base.AbstractUnitRange — Type

AbstractUnitRange{T} <: OrdinalRange{T, T}

Supertype for ranges with a step size of oneunit(T) with elements of type T. UnitRange and other types are subtypes of this.

# Base.StepRange — Type

StepRange{T, S} <: OrdinalRange{T, S}

Ranges with elements of type T with spacing of type S. The step between each element is constant, and the range is defined in terms of a start and stop of type T and a step of type S. Neither T nor S should be floating point types. The syntax a:b:c with b != 0 and a, b, and c all integers creates a StepRange.

Examples

julia> collect(StepRange(1, Int8(2), 10))
5-element Vector{Int64}:
 1
 3
 5
 7
 9

julia> typeof(StepRange(1, Int8(2), 10))
StepRange{Int64, Int8}

julia> typeof(1:3:6)
StepRange{Int64, Int64}

# Base.UnitRange — Type

UnitRange{T<:Real}

A range parameterized by a start and stop of type T, filled with elements spaced by 1 from start until stop is exceeded. The syntax a:b with a and b both Integers creates a UnitRange.

Examples

julia> collect(UnitRange(2.3, 5.2))
3-element Vector{Float64}:
 2.3
 3.3
 4.3

julia> typeof(1:10)
UnitRange{Int64}

# Base.LinRange — Type

LinRange{T,L}

A range with len linearly spaced elements between its start and stop. The size of the spacing is controlled by len, which must be an Integer.

Examples

julia> LinRange(1.5, 5.5, 9)
9-element LinRange{Float64, Int64}:
 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5

Compared to using range, directly constructing a LinRange should have less overhead but won’t try to correct for floating point errors:

julia> collect(range(-0.1, 0.3, length=5))
5-element Vector{Float64}:
 -0.1
  0.0
  0.1
  0.2
  0.3

julia> collect(LinRange(-0.1, 0.3, 5))
5-element Vector{Float64}:
 -0.1
 -1.3877787807814457e-17
  0.09999999999999999
  0.19999999999999998
  0.3

General Collections

# Base.isempty — Function

isempty(collection) -> Bool

Determine whether a collection is empty (has no elements).

isempty(itr) may consume the next element of a stateful iterator itr unless an appropriate Base.isdone(itr) or isempty method is defined. Use of isempty should therefore be avoided when writing generic code which should support any iterator type.

Examples

julia> isempty([])
true

julia> isempty([1 2 3])
false

isempty(condition)

Return true if no tasks are waiting on the condition, false otherwise.

# Base.empty! — Function

empty!(collection) -> collection

Remove all elements from a collection.

Examples

julia> A = Dict("a" => 1, "b" => 2)
Dict{String, Int64} with 2 entries:
  "b" => 2
  "a" => 1

julia> empty!(A);

julia> A
Dict{String, Int64}()

# Base.length — Function

length(collection) -> Integer

Return the number of elements in the collection.

Use lastindex to get the last valid index of an indexable collection.

Iterable Collections

# Base.in — Function

in(item, collection) -> Bool
∈(item, collection) -> Bool

Determine whether an item is in the given collection, in the sense that it is == to one of the values generated by iterating over the collection. Returns a Bool value, except if item is missing or collection contains missing but not item, in which case missing is returned (three-valued logic, matching the behavior of any and ==).

Some collections follow a slightly different definition. For example, Sets check whether the item isequal to one of the elements; Dicts look for key=>value pairs, and the key is compared using isequal.

To test for the presence of a key in a dictionary, use haskey or k in keys(dict). For the collections mentioned above, the result is always a Bool.

When broadcasting with in.(items, collection) or items .∈ collection, both item and collection are broadcasted over, which is often not what is intended. For example, if both arguments are vectors (and the dimensions match), the result is a vector indicating whether each value in collection items is in the value at the corresponding position in collection. To get a vector indicating whether each value in items is in collection, wrap collection in a tuple or a Ref like this: in.(items, Ref(collection)) or items .∈ Ref(collection).

Indexable Collections

# Base.getindex — Function

getindex(collection, key...)

Retrieve the value(s) stored at the given key or index within a collection. The syntax a[i,j,...] is converted by the compiler to getindex(a, i, j, ...).

Dictionaries

Dict is the standard dictionary. Its implementation uses hash as the hashing function for the key, and isequal to determine equality. Define these two functions for custom types to override how they are stored in a hash table.

IdDict is a special hash table where the keys are always object identities.

WeakKeyDict is a hash table implementation where the keys are weak references to objects, and thus may be garbage collected even when referenced in a hash table. Like Dict it uses hash for hashing and isequal for equality, unlike Dict it does not convert keys on insertion.

Dicts can be created by passing pair objects constructed with => to a Dict constructor: Dict("A"=>1, "B"=>2). This call will attempt to infer type information from the keys and values (i.e. this example creates a Dict{String, Int64}). To explicitly specify types use the syntax Dict{KeyType,ValueType}(...). For example, Dict{String,Int32}("A"=>1, "B"=>2).

Dictionaries may also be created with generators. For example, Dict(i => f(i) for i = 1:10).

Given a dictionary D, the syntax D[x] returns the value of key x (if it exists) or throws an error, and D[x] = y stores the key-value pair x => y in D (replacing any existing value for the key x). Multiple arguments to D[...] are converted to tuples; for example, the syntax D[x,y] is equivalent to D[(x,y)], i.e. it refers to the value keyed by the tuple (x,y).

# Base.AbstractDict — Type

AbstractDict{K, V}

Supertype for dictionary-like types with keys of type K and values of type V. Dict, IdDict and other types are subtypes of this. An AbstractDict{K, V} should be an iterator of Pair{K, V}.

# Base.Dict — Type

Dict([itr])

Dict{K,V}() constructs a hash table with keys of type K and values of type V. Keys are compared with isequal and hashed with hash.

Given a single iterable argument, constructs a Dict whose key-value pairs are taken from 2-tuples (key,value) generated by the argument.

Examples

julia> Dict([("A", 1), ("B", 2)])
Dict{String, Int64} with 2 entries:
  "B" => 2
  "A" => 1

Alternatively, a sequence of pair arguments may be passed.

julia> Dict("A"=>1, "B"=>2)
Dict{String, Int64} with 2 entries:
  "B" => 2
  "A" => 1

# Base.IdDict — Type

IdDict([itr])

IdDict{K,V}() constructs a hash table using objectid as hash and === as equality with keys of type K and values of type V.

See Dict for further help. In the example below, The Dict keys are all isequal and therefore get hashed the same, so they get overwritten. The IdDict hashes by object-id, and thus preserves the 3 different keys.

Examples

julia> Dict(true => "yes", 1 => "no", 1.0 => "maybe")
Dict{Real, String} with 1 entry:
  1.0 => "maybe"

julia> IdDict(true => "yes", 1 => "no", 1.0 => "maybe")
IdDict{Any, String} with 3 entries:
  true => "yes"
  1.0  => "maybe"
  1    => "no"

# Base.WeakKeyDict — Type

WeakKeyDict([itr])

WeakKeyDict() constructs a hash table where the keys are weak references to objects which may be garbage collected even when referenced in a hash table.

See Dict for further help. Note, unlike Dict, WeakKeyDict does not convert keys on insertion, as this would imply the key object was unreferenced anywhere before insertion.

# Base.ImmutableDict — Type

ImmutableDict

ImmutableDict is a dictionary implemented as an immutable linked list, which is optimal for small dictionaries that are constructed over many individual insertions. Note that it is not possible to remove a value, although it can be partially overridden and hidden by inserting a new value with the same key.

ImmutableDict(KV::Pair)

Create a new entry in the ImmutableDict for a key => value pair

use (key => value) in dict to see if this particular combination is in the properties set
use get(dict, key, default) to retrieve the most recent value for a particular key

# Base.haskey — Function

haskey(collection, key) -> Bool

Determine whether a collection has a mapping for a given key.

Examples

julia> D = Dict('a'=>2, 'b'=>3)
Dict{Char, Int64} with 2 entries:
  'a' => 2
  'b' => 3

julia> haskey(D, 'a')
true

julia> haskey(D, 'c')
false

# Base.get — Function

get(collection, key, default)

Return the value stored for the given key, or the given default value if no mapping for the key is present.

Compatibility: Julia 1.7

For tuples and numbers, this function requires at least Julia 1.7.

Examples

julia> d = Dict("a"=>1, "b"=>2);

julia> get(d, "a", 3)
1

julia> get(d, "c", 3)
3

get(f::Function, collection, key)

Return the value stored for the given key, or if no mapping for the key is present, return f(). Use get! to also store the default value in the dictionary.

This is intended to be called using do block syntax

get(dict, key) do
    # default value calculated here
    time()
end

# Base.get! — Function

get!(collection, key, default)

Return the value stored for the given key, or if no mapping for the key is present, store key => default, and return default.

Examples

julia> d = Dict("a"=>1, "b"=>2, "c"=>3);

julia> get!(d, "a", 5)
1

julia> get!(d, "d", 4)
4

julia> d
Dict{String, Int64} with 4 entries:
  "c" => 3
  "b" => 2
  "a" => 1
  "d" => 4

get!(f::Function, collection, key)

Return the value stored for the given key, or if no mapping for the key is present, store key => f(), and return f().

This is intended to be called using do block syntax.

Examples

julia> squares = Dict{Int, Int}();

julia> function get_square!(d, i)
           get!(d, i) do
               i^2
           end
       end
get_square! (generic function with 1 method)

julia> get_square!(squares, 2)
4

julia> squares
Dict{Int64, Int64} with 1 entry:
  2 => 4

# Base.getkey — Function

getkey(collection, key, default)

Return the key matching argument key if one exists in collection, otherwise return default.

Examples

julia> D = Dict('a'=>2, 'b'=>3)
Dict{Char, Int64} with 2 entries:
  'a' => 2
  'b' => 3

julia> getkey(D, 'a', 1)
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

julia> getkey(D, 'd', 'a')
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

# Base.delete! — Function

delete!(collection, key)

Delete the mapping for the given key in a collection, if any, and return the collection.

Examples

julia> d = Dict("a"=>1, "b"=>2)
Dict{String, Int64} with 2 entries:
  "b" => 2
  "a" => 1

julia> delete!(d, "b")
Dict{String, Int64} with 1 entry:
  "a" => 1

julia> delete!(d, "b") # d is left unchanged
Dict{String, Int64} with 1 entry:
  "a" => 1

# Base.pop! — Method

pop!(collection, key[, default])

Delete and return the mapping for key if it exists in collection, otherwise return default, or throw an error if default is not specified.

Examples

julia> d = Dict("a"=>1, "b"=>2, "c"=>3);

julia> pop!(d, "a")
1

julia> pop!(d, "d")
ERROR: KeyError: key "d" not found
Stacktrace:
[...]

julia> pop!(d, "e", 4)
4

# Base.keys — Function

keys(iterator)

For an iterator or collection that has keys and values (e.g. arrays and dictionaries), return an iterator over the keys.

# Base.values — Function

values(iterator)

For an iterator or collection that has keys and values, return an iterator over the values. This function simply returns its argument by default, since the elements of a general iterator are normally considered its "values".

Examples

julia> d = Dict("a"=>1, "b"=>2);

julia> values(d)
ValueIterator for a Dict{String, Int64} with 2 entries. Values:
  2
  1

julia> values([2])
1-element Vector{Int64}:
 2

values(a::AbstractDict)

Return an iterator over all values in a collection. collect(values(a)) returns an array of values. When the values are stored internally in a hash table, as is the case for Dict, the order in which they are returned may vary. But keys(a) and values(a) both iterate a and return the elements in the same order.

Examples

julia> D = Dict('a'=>2, 'b'=>3)
Dict{Char, Int64} with 2 entries:
  'a' => 2
  'b' => 3

julia> collect(values(D))
2-element Vector{Int64}:
 2
 3

# Base.pairs — Function

pairs(IndexLinear(), A)
pairs(IndexCartesian(), A)
pairs(IndexStyle(A), A)

An iterator that accesses each element of the array A, returning i => x, where i is the index for the element and x = A[i]. Identical to pairs(A), except that the style of index can be selected. Also similar to enumerate(A), except i will be a valid index for A, while enumerate always counts from 1 regardless of the indices of A.

Specifying IndexLinear() ensures that i will be an integer; specifying IndexCartesian() ensures that i will be a Base.CartesianIndex; specifying IndexStyle(A) chooses whichever has been defined as the native indexing style for array A.

Mutation of the bounds of the underlying array will invalidate this iterator.

Examples

julia> A = ["a" "d"; "b" "e"; "c" "f"];

julia> for (index, value) in pairs(IndexStyle(A), A)
           println("$index $value")
       end
1 a
2 b
3 c
4 d
5 e
6 f

julia> S = view(A, 1:2, :);

julia> for (index, value) in pairs(IndexStyle(S), S)
           println("$index $value")
       end
CartesianIndex(1, 1) a
CartesianIndex(2, 1) b
CartesianIndex(1, 2) d
CartesianIndex(2, 2) e

Set-Like Collections

# Base.AbstractSet — Type

AbstractSet{T}

Supertype for set-like types whose elements are of type T. Set, BitSet and other types are subtypes of this.

# Base.Set — Type

Set{T} <: AbstractSet{T}

Sets are mutable containers that provide fast membership testing.

Sets have efficient implementations of set operations such as in, union and intersect. Elements in a Set are unique, as determined by the elements' definition of isequal. The order of elements in a Set is an implementation detail and cannot be relied on.

Examples

julia> s = Set("aaBca")
Set{Char} with 3 elements:
  'a'
  'c'
  'B'

julia> push!(s, 'b')
Set{Char} with 4 elements:
  'a'
  'c'
  'b'
  'B'

julia> s = Set([NaN, 0.0, 1.0, 2.0]);

julia> -0.0 in s # isequal(0.0, -0.0) is false
false

julia> NaN in s # isequal(NaN, NaN) is true
true

# Base.BitSet — Type

BitSet([itr])

Construct a sorted set of Ints generated by the given iterable object, or an empty set. Implemented as a bit string, and therefore designed for dense integer sets. If the set will be sparse (for example, holding a few very large integers), use Set instead.

# Base.union — Function

union(s, itrs...)
∪(s, itrs...)

Construct an object containing all distinct elements from all of the arguments.

The first argument controls what kind of container is returned. If this is an array, it maintains the order in which elements first appear.

Unicode ∪ can be typed by writing \cup then pressing tab in the Julia REPL, and in many editors. This is an infix operator, allowing s ∪ itr.

Examples

julia> union([1, 2], [3])
3-element Vector{Int64}:
 1
 2
 3

julia> union([4 2 3 4 4], 1:3, 3.0)
4-element Vector{Float64}:
 4.0
 2.0
 3.0
 1.0

julia> (0, 0.0) ∪ (-0.0, NaN)
3-element Vector{Real}:
   0
  -0.0
 NaN

julia> union(Set([1, 2]), 2:3)
Set{Int64} with 3 elements:
  2
  3
  1

# Base.union! — Function

union!(s::Union{AbstractSet,AbstractVector}, itrs...)

Construct the union of passed in sets and overwrite s with the result. Maintain order with arrays.

Examples

julia> a = Set([3, 4, 5]);

julia> union!(a, 1:2:7);

julia> a
Set{Int64} with 5 elements:
  5
  4
  7
  3
  1

# Base.intersect — Function

intersect(s, itrs...)
∩(s, itrs...)

Construct the set containing those elements which appear in all of the arguments.

The first argument controls what kind of container is returned. If this is an array, it maintains the order in which elements first appear.

Unicode ∩ can be typed by writing \cap then pressing tab in the Julia REPL, and in many editors. This is an infix operator, allowing s ∩ itr.

Compatibility: Julia 1.8

As of Julia 1.8 intersect returns a result with the eltype of the type-promoted eltypes of the two inputs

Examples

julia> intersect([1, 2, 3], [3, 4, 5])
1-element Vector{Int64}:
 3

julia> intersect([1, 4, 4, 5, 6], [6, 4, 6, 7, 8])
2-element Vector{Int64}:
 4
 6

julia> intersect(1:16, 7:99)
7:16

julia> (0, 0.0) ∩ (-0.0, 0)
1-element Vector{Real}:
 0

julia> intersect(Set([1, 2]), BitSet([2, 3]), 1.0:10.0)
Set{Float64} with 1 element:
  2.0

# Base.setdiff — Function

setdiff(s, itrs...)

Construct the set of elements in s but not in any of the iterables in itrs. Maintain order with arrays.

See also setdiff!, union and intersect.

Examples

julia> setdiff([1,2,3], [3,4,5])
2-element Vector{Int64}:
 1
 2

# Base.setdiff! — Function

setdiff!(s, itrs...)

Remove from set s (in-place) each element of each iterable from itrs. Maintain order with arrays.

Examples

julia> a = Set([1, 3, 4, 5]);

julia> setdiff!(a, 1:2:6);

julia> a
Set{Int64} with 1 element:
  4

# Base.symdiff — Function

symdiff(s, itrs...)

Construct the symmetric difference of elements in the passed in sets. When s is not an AbstractSet, the order is maintained.

See also symdiff!, setdiff, union and intersect.

Examples

julia> symdiff([1,2,3], [3,4,5], [4,5,6])
3-element Vector{Int64}:
 1
 2
 6

julia> symdiff([1,2,1], [2, 1, 2])
Int64[]

# Base.symdiff! — Function

symdiff!(s::Union{AbstractSet,AbstractVector}, itrs...)

Construct the symmetric difference of the passed in sets, and overwrite s with the result. When s is an array, the order is maintained. Note that in this case the multiplicity of elements matters.

# Base.intersect! — Function

intersect!(s::Union{AbstractSet,AbstractVector}, itrs...)

Intersect all passed in sets and overwrite s with the result. Maintain order with arrays.

# Base.issubset — Function

issubset(a, b) -> Bool
⊆(a, b) -> Bool
⊇(b, a) -> Bool

Determine whether every element of a is also in b, using in.

See also ⊊, ⊈, ∩, ∪, contains.

Examples

julia> issubset([1, 2], [1, 2, 3])
true

julia> [1, 2, 3] ⊆ [1, 2]
false

julia> [1, 2, 3] ⊇ [1, 2]
true

# Base.:⊈ — Function

⊈(a, b) -> Bool
⊉(b, a) -> Bool

Negation of ⊆ and ⊇, i.e. checks that a is not a subset of b.

Dequeues

# Base.push! — Function

push!(collection, items...) -> collection

Insert one or more items in collection. If collection is an ordered container, the items are inserted at the end (in the given order).

Examples

julia> push!([1, 2, 3], 4, 5, 6)
6-element Vector{Int64}:
 1
 2
 3
 4
 5
 6

If collection is ordered, use append! to add all the elements of another collection to it. The result of the preceding example is equivalent to append!([1, 2, 3], [4, 5, 6]). For AbstractSet objects, union! can be used instead.

See sizehint! for notes about the performance model.

Utility Collections

# Core.Pair — Type

Pair(x, y)
x => y

Construct a Pair object with type Pair{typeof(x), typeof(y)}. The elements are stored in the fields first and second. They can also be accessed via iteration (but a Pair is treated as a single "scalar" for broadcasting operations).