Sets in

About Sets

A Set is a collection of items with the following properties:

• Unordered.
• Entries are unique, so attempts to add duplicates are silently ignored.
• Supports many of the operations common with mathematical sets.

Create them with the Set() constructor, using any iterator as the parameter.

julia> s1 = Set(1:4)
Set{Int64} with 4 elements:
  4
  2
  3
  1

Add new elements with push!() (the same as with arrays), and remove them with delete!().

julia> push!(s1, 5)
Set{Int64} with 5 elements:
  5
  4
  2
  3
  1

# Duplicates are ignored
julia> push!(s1, 3)
Set{Int64} with 5 elements:
  5
  4
  2
  3
  1

julia> delete!(s1, 5)
Set{Int64} with 4 elements:
  4
  2
  3
  1

julia> length(s1)  # length counts entries, despite the non-sequential type
4

Set operations

As with several other collection types, check membership with the in or ∈ operator (use \in then tab for the symbol).

julia> 3 ∈ s1
true

The following operations on pairs of Sets are supported (shortcuts to the operator symbol are shown in parentheses).

• union(A, B) or A ∪ B (\cup): all entries in A or B or both.
• intersect(A, B) or A ∩ B (\cap): all entries common to both A and B.
• setdiff(A, B) (no symbol): entries in A but not in B.
• symdiff(A, B) (no symbol): entries in either A or B but not both.
• issubset(A, B) or A ⊆ B (\subseteq) or B ⊇ A (\supseteq): true if all entries in A are also in B.
• issetequal(A, B) (no symbol): true if A and B contain exactly the same entries.
• isdisjoint(A, B) (no symbol): true if A and B contain no entries in common (so intersect is empty).

s1 = Set(1:4)
s2 = Set(3:6)

julia> s1 ∪ s2  # union
Set{Int64} with 6 elements:
  5
  4
  6
  2
  3
  1

julia> s1 ∩ s2  # intersect
Set{Int64} with 2 elements:
  4
  3
  
julia> setdiff(s1, s2)
Set{Int64} with 2 elements:
  2
  1

julia> symdiff(s1, s2)
Set{Int64} with 4 elements:
  5
  6
  2
  1
  
julia> s1 ⊇ s2  # issubset
false

There are also mutating versions of many of these, with ! added to the function name. See the manual for a full list of functions.