Rewrite cool_lex using iterator protocol

Author: jiahao

src/combinations.jl

@@ -1,4 +1,4 @@
-export combinations
+export combinations, CoolLexCombinations
 
 #The Combinations iterator
 
@@ -50,3 +50,85 @@ but sequence at each order is lazy
 """
 combinations(a) = chain([combinations(a,k) for k=1:length(a)]...)
 
+
+
+# cool-lex combinations iterator
+
+"""
+Produces (n,k)-combinations in cool-lex order
+
+Implements the cool-lex algorithm to generate (n,k)-combinations
+@article{Ruskey:2009fk,
+	Author = {Frank Ruskey and Aaron Williams},
+	Doi = {10.1016/j.disc.2007.11.048},
+	Journal = {Discrete Mathematics},
+	Month = {September},
+	Number = {17},
+	Pages = {5305-5320},
+	Title = {The coolest way to generate combinations},
+	Url = {http://www.sciencedirect.com/science/article/pii/S0012365X07009570},
+	Volume = {309},
+	Year = {2009}}
+"""
+immutable CoolLexCombinations
+    n :: Int
+    t :: Int
+end
+
+immutable CoolLexIterState{T<:Integer}
+    R0:: T
+    R1:: T
+    R2:: T
+    R3:: T
+end
+
+function start(C::CoolLexCombinations)
+    if C.n < 0
+        throw(DomainError())
+    end
+    if C.t ≤ 0
+        throw(DomainError())
+    end
+
+    #What integer size should I use?
+    if C.n < 8sizeof(Int)
+        T = Int
+    else
+        T = BigInt
+    end
+
+    CoolLexIterState{T}(0, 0, T(1) << C.n, (T(1) << C.t) - 1)
+end
+
+function next(C::CoolLexCombinations, S::CoolLexIterState)
+    R0 = S.R0
+    R1 = S.R1
+    R2 = S.R2
+    R3 = S.R3
+
+    R0 = R3 & (R3 + 1)
+    R1 = R0 $ (R0 - 1)
+    R0 = R1 + 1
+    R1 &= R3
+    R0 = max((R0 & R3) - 1, 0)
+    R3 += R1 - R0
+
+    _cool_lex_visit(S.R3), CoolLexIterState(R0, R1, R2, R3)
+end
+
+#Converts an integer bit pattern X into a subset
+#If X & 2^k == 1, then k is in the subset
+function _cool_lex_visit(X::Int)
+  subset = Int[]
+  n=1
+  while X != 0
+    if X & 1 == 1 push!(subset, n) end
+    X >>= 1
+    n += 1
+  end
+  subset
+end
+
+done(C::CoolLexCombinations, S::CoolLexIterState) = (S.R3 & S.R2 != 0)
+
+length(C::CoolLexCombinations) = max(0, binomial(C.n, C.t))

src/partitions.jl

@@ -1,7 +1,6 @@
 #Partitions
 
 export
-    cool_lex,
     integer_partitions,
     ncpartitions,
     partitions,
@@ -412,52 +411,9 @@ function integer_partitions(n::Integer)
     list
 end
 
-"""
-Produces (n,k)-combinations in cool-lex order
-
-Implements the cool-lex algorithm to generate (n,k)-combinations
-@article{Ruskey:2009fk,
-	Author = {Frank Ruskey and Aaron Williams},
-	Doi = {10.1016/j.disc.2007.11.048},
-	Journal = {Discrete Mathematics},
-	Month = {September},
-	Number = {17},
-	Pages = {5305-5320},
-	Title = {The coolest way to generate combinations},
-	Url = {http://www.sciencedirect.com/science/article/pii/S0012365X07009570},
-	Volume = {309},
-	Year = {2009}}
-"""
-function cool_lex(n::Integer, t::Integer)
-  s = n-t
-  if n > 64 error("Not implemented for n > 64") end
-  if t < 1 error("Need t>1") end
-  R0::Int64=R1::Int64=0
-  R2::Int64 = 1 << (s+t)
-  R3::Int64 = (1 << t) - 1
-  while R3 & R2 == 0
-    produce(visit(R3))
-    R0 = R3 & (R3 + 1)
-    R1 = R0 $ (R0 - 1)
-    R0 = R1 + 1
-    R1 &= R3
-    R0 = max((R0 & R3) - 1, 0)
-    R3 += R1 - R0
-  end
-end
 
-#Converts an integer word X into a subset
-#If X & 2^k == 1, then k is in the subset
-function visit(X::Integer)
-  subset = Int[]
-  n::Int=1
-  while X != 0
-    if X & 1 == 1 push!(subset, n) end
-    X >>= 1
-    n += 1
-  end
-  subset
-end
+
+#Noncrossing partitions
 
 #Produces noncrossing partitions of length n
 ncpartitions(n::Integer)=ncpart(1,n,n,Any[])

test/combinations.jl

@@ -10,8 +10,13 @@ import Combinatorics: combinations
 @test collect(combinations("abc",3)) == Any[['a','b','c']]
 @test collect(combinations("abc",2)) == Any[['a','b'],['a','c'],['b','c']]
 @test collect(combinations("abc",1)) == Any[['a'],['b'],['c']]
-@test collect(combinations("abc",0)) == Any[Char[]]
-@test collect(combinations("abc",-1)) == Any[]
+@test collect(combinations("abc",0)) == Any[[]]
+@test collect(combinations("abc",-1)) == []
 
 @test collect(filter(x->(iseven(x[1])),combinations([1,2,3],2))) == Any[[2,3]]
 
+#cool-lex iterator
+@test_throws DomainError collect(CoolLexCombinations(-1, 1))
+@test_throws DomainError collect(CoolLexCombinations(5, 0))
+@test collect(CoolLexCombinations(4,2)) == Vector[[1,2], [2,3], [1,3], [2,4], [3,4], [1,4]]
+