Formatting code

Author: inkydragon

src/combinations.jl

@@ -1,31 +1,28 @@
 export combinations,
-       CoolLexCombinations,
-       multiset_combinations,
-       with_replacement_combinations,
-       powerset
+    CoolLexCombinations, multiset_combinations, with_replacement_combinations, powerset
 
 #The Combinations iterator
 struct Combinations
     n::Int
     t::Int
 end
 
-@inline function Base.iterate(c::Combinations, s = [min(c.t - 1, i) for i in 1:c.t])
+@inline function Base.iterate(c::Combinations, s=[min(c.t - 1, i) for i in 1:c.t])
     if c.t == 0 # special case to generate 1 result for t==0
         isempty(s) && return (s, [1])
-        return
+        return nothing
     end
     for i in c.t:-1:1
         s[i] += 1
         if s[i] > (c.n - (c.t - i))
             continue
         end
-        for j in i+1:c.t
+        for j in (i+1):c.t
             s[j] = s[j-1] + 1
         end
         break
     end
-    s[1] > c.n - c.t + 1 && return
+    s[1] > c.n - c.t + 1 && return nothing
     (s, s)
 end
 
@@ -49,14 +46,13 @@ function combinations(a, t::Integer)
     (reorder(c) for c in Combinations(length(a), t))
 end
 
-
 """
     combinations(a)
 
 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) = Iterators.flatten([combinations(a, k) for k = 0:length(a)])
+combinations(a) = Iterators.flatten([combinations(a, k) for k in 0:length(a)])
 
 # cool-lex combinations iterator
 
@@ -102,7 +98,7 @@ function Base.iterate(C::CoolLexCombinations)
 end
 
 function Base.iterate(C::CoolLexCombinations, S::CoolLexIterState)
-    (S.R3 & S.R2 != 0) && return
+    (S.R3 & S.R2 != 0) && return nothing
 
     R0 = S.R0
     R1 = S.R1
@@ -134,7 +130,6 @@ end
 
 Base.length(C::CoolLexCombinations) = max(0, binomial(C.n, C.t))
 
-
 struct MultiSetCombinations{T}
     m::T
     f::Vector{Int}
@@ -158,7 +153,7 @@ function Base.length(c::MultiSetCombinations)
             end
         else
             for j in t:-1:1
-                p[j+1] = sum(p[max(1,j+1-f):(j+1)])
+                p[j+1] = sum(p[max(1, j+1-f):(j+1)])
             end
         end
     end
@@ -167,7 +162,7 @@ end
 
 function multiset_combinations(m, f::Vector{<:Integer}, t::Integer)
     length(m) == length(f) || error("Lengths of m and f are not the same.")
-    ref = length(f) > 0 ? vcat([[i for j in 1:f[i] ] for i in 1:length(f)]...) : Int[]
+    ref = length(f) > 0 ? vcat([[i for j in 1:f[i]] for i in 1:length(f)]...) : Int[]
     if t < 0
         t = length(ref) + 1
     end
@@ -185,8 +180,9 @@ function multiset_combinations(a, t::Integer)
     multiset_combinations(m, f, t)
 end
 
-function Base.iterate(c::MultiSetCombinations, s = c.ref)
-    ((!isempty(s) && max(s[1], c.t) > length(c.ref)) || (isempty(s) && c.t > 0)) && return
+function Base.iterate(c::MultiSetCombinations, s=c.ref)
+    ((!isempty(s) && max(s[1], c.t) > length(c.ref)) || (isempty(s) && c.t > 0)) &&
+        return nothing
 
     ref = c.ref
     n = length(ref)
@@ -196,7 +192,7 @@ function Base.iterate(c::MultiSetCombinations, s = c.ref)
     if t > 0
         s = copy(s)
         for i in t:-1:1
-            if s[i] < ref[i + (n - t)]
+            if s[i] < ref[i+(n-t)]
                 j = 1
                 while ref[j] <= s[i]
                     j += 1
@@ -232,8 +228,8 @@ Generate all combinations with replacement of size `t` from an array `a`.
 """
 with_replacement_combinations(a, t::Integer) = WithReplacementCombinations(a, t)
 
-function Base.iterate(c::WithReplacementCombinations, s = [1 for i in 1:c.t])
-    (!isempty(s) && s[1] > length(c.a) || c.t < 0) && return
+function Base.iterate(c::WithReplacementCombinations, s=[1 for i in 1:c.t])
+    (!isempty(s) && s[1] > length(c.a) || c.t < 0) && return nothing
 
     n = length(c.a)
     t = c.t
@@ -269,7 +265,7 @@ returns an iterator object. Use `collect(powerset(a, min, max))` to get an array
 subsets.
 """
 function powerset(a, min::Integer=0, max::Integer=length(a))
-    itrs = [combinations(a, k) for k = min:max]
+    itrs = [combinations(a, k) for k in min:max]
     min < 1 && append!(itrs, eltype(a)[])
     Iterators.flatten(itrs)
 end

src/factorials.jl

@@ -1,7 +1,6 @@
 #Factorials and elementary coefficients
 
-export
-    derangement,
+export derangement,
     partialderangement,
     factorial,
     subfactorial,
@@ -17,7 +16,7 @@ export
 
 Compute ``n!/k!``.
 """
-function Base.factorial(n::T, k::T) where T<:Integer
+function Base.factorial(n::T, k::T) where {T<:Integer}
     if k < 0 || n < 0 || k > n
         throw(DomainError((n, k), "n and k must be nonnegative with k ≤ n"))
     end
@@ -42,7 +41,6 @@ function Base.factorial(n::BigInt, k::BigInt)
 end
 Base.factorial(n::Integer, k::Integer) = factorial(promote(n, k)...)
 
-
 """
     derangement(n)
 
@@ -98,13 +96,14 @@ end
 # Hyperfactorial
 hyperfactorial(n::Integer) = n==0 ? BigInt(1) : prod(i->i^i, BigInt(1):n)
 
-
 function multifactorial(n::Integer, m::Integer)
     if n < 0
         throw(DomainError(n, "n must be nonnegative"))
     end
     z = Ref{BigInt}(0)
-    ccall((:__gmpz_mfac_uiui, :libgmp), Cvoid, (Ref{BigInt}, UInt, UInt), z, UInt(n), UInt(m))
+    ccall(
+        (:__gmpz_mfac_uiui, :libgmp), Cvoid, (Ref{BigInt}, UInt, UInt), z, UInt(n), UInt(m)
+    )
     return z[]
 end
 

src/multinomials.jl

@@ -10,9 +10,9 @@ end
 
 # Standard stars and bars:
 # https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)
-function Base.iterate(m::MultiExponents, s = nothing)
+function Base.iterate(m::MultiExponents, s=nothing)
     next = s === nothing ? iterate(m.c) : iterate(m.c, s)
-    next === nothing && return
+    next === nothing && return nothing
     stars, ss = next
 
     # stars minus their consecutive
@@ -49,7 +49,7 @@ julia> collect(multiexponents(3, 2))
 """
 function multiexponents(m, n)
     # number of stars and bars = m+n-1
-    c = combinations(1:m+n-1, n)
+    c = combinations(1:(m+n-1), n)
 
     MultiExponents(c, m)
 end

src/numbers.jl

@@ -25,16 +25,15 @@ function bellnum(n::Integer)
     end
     list = Vector{BigInt}(undef, n)
     list[1] = 1
-    for i = 2:n
-        for j = 1:i - 2
-            list[i - j - 1] += list[i - j]
+    for i in 2:n
+        for j in 1:(i-2)
+            list[i-j-1] += list[i-j]
         end
-        list[i] = list[1] + list[i - 1]
+        list[i] = list[1] + list[i-1]
     end
     return list[n]
 end
 
-
 """
     catalannum(n)
 
@@ -55,7 +54,7 @@ end
 Compute the Lobb number `L(m,n)`, or the generalised Catalan number given by ``\\frac{2m+1}{m+n+1} \\binom{2n}{m+n}``.
 Wikipedia : https://en.wikipedia.org/wiki/Lobb_number
 """
-function lobbnum(bm::Integer,bn::Integer)
+function lobbnum(bm::Integer, bn::Integer)
     if !(0 <= bm <= bn)
         throw(DomainError("m and n must be non-negative"))
     else
@@ -71,14 +70,14 @@ end
 Compute the Narayana number `N(n,k)` given by ``\\frac{1}{n}\\binom{n}{k}\\binom{n}{k-1}``
 Wikipedia : https://en.wikipedia.org/wiki/Narayana_number
 """
-function narayana(bn::Integer,bk::Integer)
+function narayana(bn::Integer, bk::Integer)
     if !(1 <= bk <= bn)
         throw(DomainError("Domain is 1 <= k <= n"))
     else
         n = BigInt(bn)
         k = BigInt(bk)
     end
-    div(binomial(n, k)*binomial(n, k - 1) , n)
+    div(binomial(n, k)*binomial(n, k - 1), n)
 end
 
 function fibonaccinum(n::Integer)
@@ -90,7 +89,6 @@ function fibonaccinum(n::Integer)
     return z[]
 end
 
-
 function jacobisymbol(a::Integer, b::Integer)
     ba = Ref{BigInt}(a)
     bb = Ref{BigInt}(b)
@@ -104,8 +102,12 @@ Compute the ``n``th entry in Lassalle's sequence, OEIS entry A180874.
 """
 function lassallenum(m::Integer)
     A = ones(BigInt, m)
-    for n = 2:m
-        A[n] = (-1)^(n-1) * (catalannum(n) + sum(j->(-1)^j*binomial(2n-1, 2j-1)*A[j]*catalannum(n-j), 1:n-1))
+    for n in 2:m
+        A[n] =
+            (-1)^(n-1) * (
+                catalannum(n) +
+                sum(j->(-1)^j*binomial(2n-1, 2j-1)*A[j]*catalannum(n-j), 1:(n-1))
+            )
     end
     A[m]
 end