Update Combinatorics for Julia 1.0 (#69)

* Update Combinatorics for 1.0

* Remove dependence on Compat

.travis.yml

@@ -2,7 +2,8 @@ language: julia
 os:
     - linux
 julia:
-    - 0.6
+    - 0.7
+    - 1.0
     - nightly
 sudo: false
 notifications:

REQUIRE

@@ -1,4 +1,2 @@
-julia 0.6
-Compat 0.59.0
+julia 0.7
 Polynomials
-IterTools

src/Combinatorics.jl

@@ -2,9 +2,7 @@ VERSION < v"0.7.0-beta2.199" && __precompile__()
 
 module Combinatorics
 
-using Compat
 using Polynomials
-using IterTools
 
 include("numbers.jl")
 include("factorials.jl")

src/combinations.jl

@@ -11,8 +11,9 @@ struct Combinations{T}
     t::Int
 end
 
-Base.start(c::Combinations) = collect(1:c.t)
-function Base.next(c::Combinations, s)
+function Base.iterate(c::Combinations, s = collect(1:c.t))
+    (!isempty(s) && s[1] > length(c.a) - c.t + 1) && return
+
     comb = [c.a[si] for si in s]
     if c.t == 0
         # special case to generate 1 result for t==0
@@ -31,7 +32,6 @@ function Base.next(c::Combinations, s)
     end
     (comb, s)
 end
-Base.done(c::Combinations, s) = !isempty(s) && s[1] > length(c.a) - c.t + 1
 
 Base.length(c::Combinations) = binomial(length(c.a), c.t)
 
@@ -59,7 +59,7 @@ end
 Generate combinations of the elements of `a` of all orders. Chaining of order iterators
 is eager, but the sequence at each order is lazy.
 """
-combinations(a) = IterTools.chain([combinations(a, k) for k = 1:length(a)]...)
+combinations(a) = Iterators.flatten([combinations(a, k) for k = 1:length(a)])
 
 
 
@@ -87,7 +87,7 @@ struct CoolLexIterState{T<:Integer}
     R3::T
 end
 
-function Base.start(C::CoolLexCombinations)
+function Base.iterate(C::CoolLexCombinations)
     if C.n < 0
         throw(DomainError(C.n))
     end
@@ -102,10 +102,13 @@ function Base.start(C::CoolLexCombinations)
         T = BigInt
     end
 
-    CoolLexIterState{T}(0, 0, T(1) << C.n, (T(1) << C.t) - 1)
+    state = CoolLexIterState{T}(0, 0, T(1) << C.n, (T(1) << C.t) - 1)
+    iterate(C, state)
 end
 
-function Base.next(C::CoolLexCombinations, S::CoolLexIterState)
+function Base.iterate(C::CoolLexCombinations, S::CoolLexIterState)
+    (S.R3 & S.R2 != 0) && return
+
     R0 = S.R0
     R1 = S.R1
     R2 = S.R2
@@ -134,8 +137,6 @@ function _cool_lex_visit(X::Integer)
     subset
 end
 
-Base.done(C::CoolLexCombinations, S::CoolLexIterState) = (S.R3 & S.R2 != 0)
-
 Base.length(C::CoolLexCombinations) = max(0, binomial(C.n, C.t))
 
 
@@ -189,8 +190,9 @@ function multiset_combinations(a, t::Integer)
     multiset_combinations(m, f, t)
 end
 
-Base.start(c::MultiSetCombinations) = c.ref
-function Base.next(c::MultiSetCombinations, s)
+function Base.iterate(c::MultiSetCombinations, s = c.ref)
+    ((!isempty(s) && max(s[1], c.t) > length(c.ref)) || (isempty(s) && c.t > 0)) && return
+
     ref = c.ref
     n = length(ref)
     t = c.t
@@ -218,8 +220,6 @@ function Base.next(c::MultiSetCombinations, s)
     end
     (comb, s)
 end
-Base.done(c::MultiSetCombinations, s) =
-    (!isempty(s) && max(s[1], c.t) > length(c.ref)) || (isempty(s) && c.t > 0)
 
 struct WithReplacementCombinations{T}
     a::T
@@ -237,8 +237,9 @@ Generate all combinations with replacement of size `t` from an array `a`.
 """
 with_replacement_combinations(a, t::Integer) = WithReplacementCombinations(a, t)
 
-Base.start(c::WithReplacementCombinations) = [1 for i in 1:c.t]
-function Base.next(c::WithReplacementCombinations, s)
+function Base.iterate(c::WithReplacementCombinations, s = [1 for i in 1:c.t])
+    (!isempty(s) && s[1] > length(c.a) || c.t < 0) && return
+
     n = length(c.a)
     t = c.t
     comb = [c.a[si] for si in s]
@@ -261,7 +262,6 @@ function Base.next(c::WithReplacementCombinations, s)
     end
     (comb, s)
 end
-Base.done(c::WithReplacementCombinations, s) = !isempty(s) && s[1] > length(c.a) || c.t < 0
 
 ## Power set
 
@@ -276,5 +276,5 @@ subsets.
 function powerset(a, min::Integer=0, max::Integer=length(a))
     itrs = [combinations(a, k) for k = min:max]
     min < 1 && append!(itrs, eltype(a)[])
-    IterTools.chain(itrs...)
+    Iterators.flatten(itrs)
 end

src/multinomials.jl

@@ -8,12 +8,12 @@ struct MultiExponents{T}
     nterms::Int
 end
 
-Base.start(m::MultiExponents) = start(m.c)
-
 # Standard stars and bars:
 # https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)
-function Base.next(m::MultiExponents, s)
-    stars, ss = next(m.c, s)
+function Base.iterate(m::MultiExponents, s = nothing)
+    next = s === nothing ? iterate(m.c) : iterate(m.c, s)
+    next === nothing && return
+    stars, ss = next
 
     # stars minus their consecutive
     # position becomes their index
@@ -25,8 +25,6 @@ function Base.next(m::MultiExponents, s)
     result, ss
 end
 
-Base.done(m::MultiExponents, s) = done(m.c, s)
-
 Base.length(m::MultiExponents) = length(m.c)
 
 """

src/partitions.jl

@@ -16,9 +16,11 @@ end
 
 Base.length(p::IntegerPartitions) = npartitions(p.n)
 
-Base.start(p::IntegerPartitions) = Int[]
-Base.done(p::IntegerPartitions, xs) = length(xs) == p.n
-Base.next(p::IntegerPartitions, xs) = (xs = nextpartition(p.n,xs); (xs,xs))
+function Base.iterate(p::IntegerPartitions, xs = Int[])
+    length(xs) == p.n && return
+    xs = nextpartition(p.n,xs)
+    (xs, xs)
+end
 
 """
     partitions(n)
@@ -105,13 +107,15 @@ partitions(n::Integer, m::Integer) =
         FixedPartitions(n, m) :
         throw(DomainError((n, m), "n and m must be positive"))
 
-Base.start(f::FixedPartitions) = Int[]
-function Base.done(f::FixedPartitions, s::Vector{Int})
-    f.m <= f.n || return true
-    isempty(s) && return false
-    return f.m == 1 || s[1]-1 <= s[end]
+function Base.iterate(f::FixedPartitions, s::Vector{Int} = Int[])
+    f.m <= f.n || return
+    if !isempty(s)
+        (f.m == 1 || s[1]-1 <= s[end]) && return
+    end
+
+    xs = nextfixedpartition(f.n,f.m,s)
+    (xs, xs)
 end
-Base.next(f::FixedPartitions, s::Vector{Int}) = (xs = nextfixedpartition(f.n,f.m,s); (xs,xs))
 
 function nextfixedpartition(n, m, bs)
     as = copy(bs)
@@ -177,9 +181,14 @@ number of partitions to generate can be efficiently computed using
 """
 partitions(s::AbstractVector) = SetPartitions(s)
 
-Base.start(p::SetPartitions) = (n = length(p.s); (zeros(Int32, n), ones(Int32, n-1), n, 1))
-Base.done(p::SetPartitions, s) = s[1][1] > 0
-Base.next(p::SetPartitions, s) = nextsetpartition(p.s, s...)
+function Base.iterate(p::SetPartitions)
+    n = length(p.s)
+    iterate(p, (zeros(Int32, n), ones(Int32, n-1), n, 1))
+end
+function Base.iterate(p::SetPartitions, s)
+    s[1][1] > 0 && return
+    nextsetpartition(p.s, s...)
+end
 
 function nextsetpartition(s::AbstractVector, a, b, n, m)
     function makeparts(s, a, m)
@@ -255,18 +264,22 @@ partitions(s::AbstractVector, m::Int) =
         FixedSetPartitions(s, m) :
         throw(DomainError((length(s), m), "length(s) and m must be positive"))
 
-function Base.start(p::FixedSetPartitions)
+function Base.iterate(p::FixedSetPartitions)
     n = length(p.s)
     m = p.m
-    m <= n ? (vcat(ones(Int, n-m),1:m), vcat(1,n-m+2:n), n) : (Int[], Int[], n)
+    state = m <= n ? (vcat(ones(Int, n-m),1:m), vcat(1,n-m+2:n), n) : (Int[], Int[], n)
+    # state consists of:
+    # vector a of length n describing to which partition every element of s belongs
+    # vector b of length n describing the first index b[i] that belongs to partition i
+    # integer n
+
+    iterate(p, state)
 end
-# state consists of:
-# vector a of length n describing to which partition every element of s belongs
-# vector b of length n describing the first index b[i] that belongs to partition i
-# integer n
 
-Base.done(p::FixedSetPartitions, s) = isempty(s[1]) || s[1][1] > 1
-Base.next(p::FixedSetPartitions, s) = nextfixedsetpartition(p.s,p.m, s...)
+function Base.iterate(p::FixedSetPartitions, s)
+    (isempty(s[1]) || s[1][1] > 1) && return
+    nextfixedsetpartition(p.s,p.m, s...)
+end
 
 function nextfixedsetpartition(s::AbstractVector, m, a, b, n)
     function makeparts(s, a)
@@ -310,7 +323,7 @@ function nextfixedsetpartition(s::AbstractVector, m, a, b, n)
             end
             b[k] -= 1
             b[k+1:m] = n-m+k+1:n
-            a[1:n] = 1
+            a[1:n] .= 1
             a[b] = 1:m
         end
     end
@@ -496,4 +509,3 @@ function _ncpart!(a::Int, b::Int, nn::Int, x::Vector, partitions::Vector)
         end
     end
 end
-

src/permutations.jl

@@ -39,8 +39,10 @@ function permutations(a, t::Integer)
     Permutations(a, t)
 end
 
-Base.start(p::Permutations) = collect(1:length(p.a))
-Base.next(p::Permutations, s) = nextpermutation(p.a, p.t ,s)
+function Base.iterate(p::Permutations, s = collect(1:length(p.a)))
+    (!isempty(s) && max(s[1], p.t) > length(p.a) || (isempty(s) && p.t > 0)) && return
+    nextpermutation(p.a, p.t ,s)
+end
 
 function nextpermutation(m, t, state)
     perm = [m[state[i]] for i in 1:t]
@@ -73,8 +75,6 @@ function nextpermutation(m, t, state)
     return (perm, s)
 end
 
-Base.done(p::Permutations, s) = !isempty(s) && max(s[1], p.t) > length(p.a) || (isempty(s) && p.t > 0)
-
 struct MultiSetPermutations{T}
     m::T
     f::Vector{Int}
@@ -134,11 +134,10 @@ function multiset_permutations(m, f::Vector{<:Integer}, t::Integer)
     MultiSetPermutations(m, f, t, ref)
 end
 
-Base.start(p::MultiSetPermutations) = p.ref
-Base.next(p::MultiSetPermutations, s) = nextpermutation(p.m, p.t, s)
-Base.done(p::MultiSetPermutations, s) =
-    !isempty(s) && max(s[1], p.t) > length(p.ref) || (isempty(s) && p.t > 0)
-
+function Base.iterate(p::MultiSetPermutations, s = p.ref)
+    (!isempty(s) && max(s[1], p.t) > length(p.ref) || (isempty(s) && p.t > 0)) && return
+    nextpermutation(p.m, p.t, s)
+end
 
 
 """
@@ -195,9 +194,9 @@ end
 
 # Parity of permutations
 
-const levicivita_lut = cat(3, [0 0  0;  0 0 1; 0 -1 0],
-                              [0 0 -1;  0 0 0; 1  0 0],
-                              [0 1  0; -1 0 0; 0  0 0])
+const levicivita_lut = cat([0 0  0;  0 0 1; 0 -1 0],
+                           [0 0 -1;  0 0 0; 1  0 0],
+                           [0 1  0; -1 0 0; 0  0 0]; dims=3)
 
 """
     levicivita(p)

src/youngdiagrams.jl

@@ -52,10 +52,10 @@ function isrimhook(ξ::SkewDiagram)
     l = maximum(λ.x)
     youngdiagram = zeros(Int, m, l)
     for i = 1:n
-        youngdiagram[i, μ[i]+1:λ[i]] = 1
+        youngdiagram[i, μ[i]+1:λ[i]] .= 1
     end
     for i = n+1:m
-        youngdiagram[i, 1:λ[i]] = 1
+        youngdiagram[i, 1:λ[i]] .= 1
     end
     #Condition 1. Must be edgewise connected
     youngdiagramList = Any[]
@@ -114,10 +114,10 @@ function leglength(ξ::SkewDiagram)
     l = maximum(λ.x)
     youngdiagram = zeros(Int, m, l)
     for i = 1:n
-        youngdiagram[i, μ[i]+1:λ[i]] = 1
+        youngdiagram[i, μ[i]+1:λ[i]] .= 1
     end
     for i = n+1:m
-        youngdiagram[i, 1:λ[i]] = 1
+        youngdiagram[i, 1:λ[i]] .= 1
     end
     for i = m:-1:1
         any(==(1), youngdiagram[i,:]) && return i-1

test/combinations.jl

@@ -1,7 +1,3 @@
-using Combinatorics
-using Compat
-using Compat.Test
-
 @test [combinations([])...] == []
 @test [combinations(['a', 'b', 'c'])...] == Any[['a'],['b'],['c'],['a','b'],['a','c'],['b','c'],['a','b','c']]
 
@@ -38,7 +34,7 @@ using Compat.Test
 @test_throws DomainError [CoolLexCombinations(-1, 1)...]
 @test_throws DomainError [CoolLexCombinations(5, 0)...]
 @test [CoolLexCombinations(4,2)...] == Vector[[1,2], [2,3], [1,3], [2,4], [3,4], [1,4]]
-@test isa(start(CoolLexCombinations(1000, 20)), Combinatorics.CoolLexIterState{BigInt})
+@test isa(iterate(CoolLexCombinations(1000, 20))[2], Combinatorics.CoolLexIterState{BigInt})
 
 # Power set
 @test collect(powerset([])) == Any[[]]

test/factorials.jl

@@ -1,7 +1,3 @@
-using Combinatorics
-using Compat
-using Compat.Test
-
 @test factorial(7,3) == 7*6*5*4
 @test_throws DomainError factorial(3,7)
 @test_throws DomainError factorial(-3,-7)

test/multinomials.jl

@@ -1,7 +1,4 @@
-using Combinatorics
-using Compat
-using Compat.Test
-using Compat.LinearAlgebra
+using LinearAlgebra
 
 # degenerate cases (x₁ + x₂ + ⋯ + xₘ)¹
 @test [multiexponents(1,1)...] == [[1]]

test/numbers.jl

@@ -1,7 +1,3 @@
-using Combinatorics
-using Compat
-using Compat.Test
-
 # catalan
 @test catalannum(5) == 42
 @test catalannum(30) == parse(BigInt,"3814986502092304")

test/partitions.jl

@@ -1,7 +1,3 @@
-using Combinatorics
-using Compat
-using Compat.Test
-
 @test collect(partitions(4)) ==  Any[[4], [3,1], [2,2], [2,1,1], [1,1,1,1]]
 @test collect(partitions(8,3)) == Any[[6,1,1], [5,2,1], [4,3,1], [4,2,2], [3,3,2]]
 @test collect(partitions(8, 1)) == Any[[8]]