add few missing methods for set-like operations

NEWS.md

@@ -469,6 +469,20 @@ Library improvements
       linear-to-cartesian conversion ([#24715])
     - It has a new constructor taking an array
 
+  * several missing set-like operations have been added ([#23528]):
+    `union`, `intersect`, `symdiff`, `setdiff` are now implemented for
+    all collections with arbitrary many arguments, as well as the
+    mutating counterparts (`union!` etc.). The performance is also
+    much better in many cases. Note that this change is slightly
+    breaking: all the non-mutating functions always return a new
+    object even if only one argument is passed. Moreover the semantics
+    of `intersect` and `symdiff` is changed for vectors:
+    + `intersect` doesn't preserve the multiplicity anymore (use `filter` for
+      the old behavior)
+    + `symdiff` has been made consistent with the corresponding methods for
+      other containers, by taking the multiplicity of the arguments into account.
+      Use `unique` to get the old behavior.
+
   * The type `LinearIndices` has been added, providing conversion from
     cartesian incices to linear indices using the normal indexing operation. ([#24715])
 

base/abstractarray.jl

@@ -580,8 +580,10 @@ julia> empty([1.0, 2.0, 3.0], String)
 0-element Array{String,1}
 ```
 """
-empty(a::AbstractVector) = empty(a, eltype(a))
-empty(a::AbstractVector, ::Type{T}) where {T} = Vector{T}()
+empty(a::AbstractVector{T}, ::Type{U}=T) where {T,U} = Vector{U}()
+
+# like empty, but should return a mutable collection, a Vector by default
+emptymutable(a::AbstractVector{T}, ::Type{U}=T) where {T,U} = Vector{U}()
 
 ## from general iterable to any array
 

base/array.jl

@@ -2209,99 +2209,53 @@ function filter!(f, a::AbstractVector)
     return a
 end
 
-function filter(f, a::Vector)
-    r = Vector{eltype(a)}()
-    for ai in a
-        if f(ai)
-            push!(r, ai)
-        end
-    end
-    return r
-end
+filter(f, a::Vector) = mapfilter(f, push!, a, similar(a, 0))
 
 # set-like operators for vectors
 # These are moderately efficient, preserve order, and remove dupes.
 
-function intersect(v1, vs...)
-    ret = Vector{promote_eltype(v1, vs...)}()
-    for v_elem in v1
-        inall = true
-        for vsi in vs
-            if !in(v_elem, vsi)
-                inall=false; break
-            end
-        end
-        if inall
-            push!(ret, v_elem)
-        end
+_unique_filter!(pred, update!, state) = function (x)
+    if pred(x, state)
+        update!(state, x)
+        true
+    else
+        false
     end
-    ret
 end
 
-function union(vs...)
-    ret = Vector{promote_eltype(vs...)}()
-    seen = Set()
-    for v in vs
-        for v_elem in v
-            if !in(v_elem, seen)
-                push!(ret, v_elem)
-                push!(seen, v_elem)
-            end
-        end
+_grow_filter!(seen) = _unique_filter!(∉, push!, seen)
+_shrink_filter!(keep) = _unique_filter!(∈, pop!, keep)
+
+function _grow!(pred!, v::AbstractVector, itrs)
+    filter!(pred!, v) # uniquify v
+    foldl(v, itrs) do v, itr
+        mapfilter(pred!, push!, itr, v)
     end
-    ret
 end
-# setdiff only accepts two args
 
-"""
-    setdiff(a, b)
+union!(v::AbstractVector{T}, itrs...) where {T} =
+    _grow!(_grow_filter!(sizehint!(Set{T}(), length(v))), v, itrs)
 
-Construct the set of elements in `a` but not `b`. Maintains order with arrays. Note that
-both arguments must be collections, and both will be iterated over. In particular,
-`setdiff(set,element)` where `element` is a potential member of `set`, will not work in
-general.
+symdiff!(v::AbstractVector{T}, itrs...) where {T} =
+    _grow!(_shrink_filter!(symdiff!(Set{T}(), v, itrs...)), v, itrs)
 
-# Examples
-```jldoctest
-julia> setdiff([1,2,3],[3,4,5])
-2-element Array{Int64,1}:
- 1
- 2
-```
-"""
-function setdiff(a, b)
-    args_type = promote_type(eltype(a), eltype(b))
-    bset = Set(b)
-    ret = Vector{args_type}()
-    seen = Set{eltype(a)}()
-    for a_elem in a
-        if !in(a_elem, seen) && !in(a_elem, bset)
-            push!(ret, a_elem)
-            push!(seen, a_elem)
-        end
-    end
-    ret
+function _shrink!(shrinker!, v::AbstractVector, itrs)
+    seen = Set{eltype(v)}()
+    filter!(_grow_filter!(seen), v)
+    shrinker!(seen, itrs...)
+    filter!(_in(seen), v)
 end
-# symdiff is associative, so a relatively clean
-# way to implement this is by using setdiff and union, and
-# recursing. Has the advantage of keeping order, too, but
-# not as fast as other methods that make a single pass and
-# store counts with a Dict.
-symdiff(a) = a
-symdiff(a, b) = union(setdiff(a,b), setdiff(b,a))
-"""
-    symdiff(a, b, rest...)
 
-Construct the symmetric difference of elements in the passed in sets or arrays.
-Maintains order with arrays.
+intersect!(v::AbstractVector, itrs...) = _shrink!(intersect!, v, itrs)
+setdiff!(  v::AbstractVector, itrs...) = _shrink!(setdiff!, v, itrs)
 
-# Examples
-```jldoctest
-julia> symdiff([1,2,3],[3,4,5],[4,5,6])
-3-element Array{Int64,1}:
- 1
- 2
- 6
-```
-"""
-symdiff(a, b, rest...) = symdiff(a, symdiff(b, rest...))
+vectorfilter(f, v::AbstractVector) = filter(f, v) # TODO: do we want this special case?
+vectorfilter(f, v) = [x for x in v if f(x)]
+
+function _shrink(shrinker!, itr, itrs)
+    keep = shrinker!(Set(itr), itrs...)
+    vectorfilter(_shrink_filter!(keep), itr)
+end
+
+intersect(itr, itrs...) = _shrink(intersect!, itr, itrs)
+setdiff(  itr, itrs...) = _shrink(setdiff!, itr, itrs)

base/bitset.jl

@@ -32,7 +32,12 @@ BitSet(itr) = union!(BitSet(), itr)
 
 eltype(::Type{BitSet}) = Int
 similar(s::BitSet) = BitSet()
+
+empty(s::BitSet, ::Type{Int}=Int) = BitSet()
+emptymutable(s::BitSet, ::Type{Int}=Int) = BitSet()
+
 copy(s1::BitSet) = copy!(BitSet(), s1)
+copymutable(s::BitSet) = copy(s)
 
 """
     copy!(dst, src)
@@ -253,49 +258,17 @@ isempty(s::BitSet) = _check0(s.bits, 1, length(s.bits))
 
 # Mathematical set functions: union!, intersect!, setdiff!, symdiff!
 
-union(s::BitSet) = copy(s)
-union(s1::BitSet, s2::BitSet) = union!(copy(s1), s2)
-union(s1::BitSet, ss::BitSet...) = union(s1, union(ss...))
-union(s::BitSet, ns) = union!(copy(s), ns)
-union!(s::BitSet, ns) = (for n in ns; push!(s, n); end; s)
+union(s::BitSet, sets...) = union!(copy(s), sets...)
 union!(s1::BitSet, s2::BitSet) = _matched_map!(|, s1, s2)
 
-intersect(s1::BitSet) = copy(s1)
-intersect(s1::BitSet, ss::BitSet...) = intersect(s1, intersect(ss...))
-function intersect(s1::BitSet, ns)
-    s = BitSet()
-    for n in ns
-        n in s1 && push!(s, n)
-    end
-    s
-end
 intersect(s1::BitSet, s2::BitSet) =
     length(s1.bits) < length(s2.bits) ? intersect!(copy(s1), s2) : intersect!(copy(s2), s1)
-"""
-    intersect!(s1::BitSet, s2::BitSet)
 
-Intersects sets `s1` and `s2` and overwrites the set `s1` with the result. If needed, `s1`
-will be expanded to the size of `s2`.
-"""
 intersect!(s1::BitSet, s2::BitSet) = _matched_map!(&, s1, s2)
 
-setdiff(s::BitSet, ns) = setdiff!(copy(s), ns)
-setdiff!(s::BitSet, ns) = (for n in ns; delete!(s, n); end; s)
 setdiff!(s1::BitSet, s2::BitSet) = _matched_map!((p, q) -> p & ~q, s1, s2)
 
-symdiff(s::BitSet, ns) = symdiff!(copy(s), ns)
-"""
-    symdiff!(s, itr)
-
-For each element in `itr`, destructively toggle its inclusion in set `s`.
-"""
-symdiff!(s::BitSet, ns) = (for n in ns; int_symdiff!(s, n); end; s)
-"""
-    symdiff!(s, n)
-
-The set `s` is destructively modified to toggle the inclusion of integer `n`.
-"""
-symdiff!(s::BitSet, n::Integer) = int_symdiff!(s, n)
+symdiff!(s::BitSet, ns) = foldl(int_symdiff!, s, ns)
 
 function int_symdiff!(s::BitSet, n::Integer)
     n0 = _check_bitset_bounds(n)
@@ -306,6 +279,8 @@ end
 
 symdiff!(s1::BitSet, s2::BitSet) = _matched_map!(xor, s1, s2)
 
+filter!(f, s::BitSet) = unsafe_filter!(f, s)
+
 @inline in(n::Int, s::BitSet) = _bits_getindex(s.bits, n, s.offset)
 @inline in(n::Integer, s::BitSet) = _is_convertible_Int(n) ? in(Int(n), s) : false