Merge pull request #4025 from JuliaLang/kms/combinatorics

Combinatorics updates

base/array.jl

@@ -1161,10 +1161,10 @@ rotr90(A::AbstractMatrix, k::Integer) = rotl90(A,-k)
 rot180(A::AbstractMatrix, k::Integer) = mod(k, 2) == 1 ? rot180(A) : copy(A)
 
 reverse(v::StridedVector) = (n=length(v); [ v[n-i+1] for i=1:n ])
-function reverse!(v::AbstractVector)
-    n = length(v)
+reverse(v::StridedVector, s=1, n=length(v)) = [[v[i] for i=1:s-1], [v[n-i] for i = 0:n-s], [v[i] for i = n+1:endof(v)]]
+function reverse!(v::AbstractVector, s=1, n=length(v))
     r = n
-    for i=1:div(n,2)
+    for i=s:div(s+n-1,2)
         v[i], v[r] = v[r], v[i]
         r -= 1
     end

base/combinatorics.jl

@@ -186,6 +186,8 @@ immutable Combinations{T}
 end
 
 eltype(c::Combinations) = typeof(c.a)
+eltype{T}(c::Combinations{Range1{T}}) = Array{T,1}
+eltype{T}(c::Combinations{Range{T}}) = Array{T,1}
 
 function combinations(a, t::Integer)
     if t < 0
@@ -197,25 +199,57 @@ end
 
 start(c::Combinations) = [1:c.t]
 function next(c::Combinations, s)
+    comb = c.a[s]
     if c.t == 0
         # special case to generate 1 result for t==0
-        return (c.a[s],[length(c.a)+2])
+        return (comb,[length(c.a)+2])
     end
-    sn = copy(s)
-    for i = length(sn):-1:1
-        sn[i] += 1
-        if sn[i] > (length(c.a) - (length(sn)-i))
+    for i = length(s):-1:1
+        s[i] += 1
+        if s[i] > (length(c.a) - (length(s)-i))
             continue
         end
-        for j = i+1:endof(sn)
-            sn[j] = sn[j-1]+1
+        for j = i+1:endof(s)
+            s[j] = s[j-1]+1
         end
         break
     end
-    (c.a[s],sn)
+    (comb,s)
 end
 done(c::Combinations, s) = !isempty(s) && s[1] > length(c.a)-c.t+1
 
+immutable Permutations{T}
+    a::T
+end
+
+eltype(c::Permutations) = typeof(c.a)
+eltype{T}(c::Permutations{Range1{T}}) = Array{T,1}
+eltype{T}(c::Permutations{Range{T}}) = Array{T,1}
+
+permutations(a) = Permutations(a)
+
+start(p::Permutations) = [1:length(p.a)]
+function next(p::Permutations, s)
+    if length(p.a) == 0
+        # special case to generate 1 result for len==0
+        return (p.a,[1])
+    end
+    perm = p.a[s]
+    k = length(s)-1
+    while k > 0 && s[k] > s[k+1];  k -= 1;  end
+    if k == 0
+        s[1] = length(s)+1   # done
+    else
+        l = length(s)
+        while s[k] >= s[l];  l -= 1;  end
+        s[k],s[l] = s[l],s[k]
+        reverse!(s,k+1)
+    end
+    (perm,s)
+end
+done(p::Permutations, s) = !isempty(s) && s[1] > length(p.a)
+
+
 # Algorithm H from TAoCP 7.2.1.4
 # Partition n into m parts
 function integer_partitions{T<:Integer}(n::T, m::T)

base/exports.jl

@@ -524,6 +524,7 @@ export
     parentindexes,
     partitions,
     pascal,
+    permutations,
     permute!,
     permutedims,
     prod,

doc/helpdb.jl

@@ -4569,24 +4569,33 @@ popdisplay(d::Display)
 
 "),
 
-("Combinatorics","Base","reverse","reverse(v)
+("Combinatorics","Base","reverse","reverse(v[, start=1[, stop=length(v)]])
 
-   Reverse vector \"v\".
+   Reverse vector \"v\", optionally from start to stop.
 
 "),
 
-("Combinatorics","Base","reverse!","reverse!(v) -> v
+("Combinatorics","Base","reverse!","reverse!(v[, start=1[, stop=length(v)]]) -> v
 
    In-place version of \"reverse()\".
 
 "),
 
-("Combinatorics","Base","combinations","combinations(array, n)
+("Combinatorics","Base","combinations","combinations(itr, n)
 
-   Generate all combinations of \"n\" elements from a given array.
-   Because the number of combinations can be very large, this function
-   returns an iterator object. Use \"collect(combinations(a,n))\" to
-   get an array of all combinations.
+   Generate all combinations of \"n\" elements from a given iterable
+   object.  Because the number of combinations can be very large, this
+   function returns an iterator object. Use
+   \"collect(combinations(a,n))\" to get an array of all combinations.
+
+"),
+
+("Combinatorics","Base","permutations","permutations(itr)
+
+   Generate all permutations of a given iterable object.  Because the
+   number of permutations can be very large, this function returns an
+   iterator object. Use \"collect(permutations(a,n))\" to get an array
+   of all permutations.
 
 "),
 

doc/stdlib/base.rst

@@ -3108,20 +3108,27 @@ Combinatorics
 
    In-place version of :func:`shuffle`.
 
-.. function:: reverse(v)
+.. function:: reverse(v [, start=1 [, stop=length(v) ]] )
 
-   Reverse vector ``v``.
+   Reverse vector ``v``, optionally from start to stop.
 
-.. function:: reverse!(v) -> v
+.. function:: reverse!(v [, start=1 [, stop=length(v) ]]) -> v
 
    In-place version of :func:`reverse`.
 
-.. function:: combinations(array, n)
+.. function:: combinations(itr, n)
 
-   Generate all combinations of ``n`` elements from a given array. Because
-   the number of combinations can be very large, this function returns an
-   iterator object. Use ``collect(combinations(a,n))`` to get an array of all
-   combinations.
+   Generate all combinations of ``n`` elements from a given iterable
+   object.  Because the number of combinations can be very large, this
+   function returns an iterator object. Use
+   ``collect(combinations(a,n))`` to get an array of all combinations.
+
+.. function:: permutations(itr)
+
+   Generate all permutations of a given iterable object.  Because the
+   number of permutations can be very large, this function returns an
+   iterator object. Use ``collect(permutations(a,n))`` to get an array
+   of all permutations.
 
 .. function:: integer_partitions(n, m)
 

test/Makefile

@@ -5,7 +5,8 @@ TESTS = all core keywordargs numbers strings unicode collections hashing	\
 	remote iostring arrayops linalg blas fft dsp sparse bitarray random	\
 	math functional bigint sorting statistics spawn parallel arpack file	\
 	git pkg pkg2 resolve resolve2 suitesparse complex version pollfd mpfr	\
-	broadcast socket floatapprox priorityqueue readdlm regex float16
+	broadcast socket floatapprox priorityqueue readdlm regex float16        \
+	combinations
 
 $(TESTS) ::
 	@$(PRINT_JULIA) $(call spawn,$(JULIA_EXECUTABLE)) ./runtests.jl $@

test/arrayops.jl

@@ -662,3 +662,14 @@ end
 
 @test_throws (10.^[-1])[1] == 0.1
 @test (10.^[-1.])[1] == 0.1
+
+# reverse
+@test reverse([2,3,1]) == [1,3,2]
+@test reverse([1:10],1,4) == [4,3,2,1,5,6,7,8,9,10]
+@test reverse([1:10],3,6) == [1,2,6,5,4,3,7,8,9,10]
+@test reverse([1:10],6,10) == [1,2,3,4,5,10,9,8,7,6]
+@test reverse!([1:10],1,4) == [4,3,2,1,5,6,7,8,9,10]
+@test reverse!([1:10],3,6) == [1,2,6,5,4,3,7,8,9,10]
+@test reverse!([1:10],6,10) == [1,2,3,4,5,10,9,8,7,6]
+
+

test/combinatorics.jl

@@ -0,0 +1,9 @@
+
+@test factorial(7) = 5040
+@test factorial(7,3) == 7*6*5*4
+@test binomial(5,3) == 10
+@test isperm(shuffle([1:1000]))
+a = randcycle(10)
+@test ipermute!(permute!([1:10], a),a) == [1:10]
+@test collect(combinations("abc",2)) == ["ab","ac","bc"]
+@test collect(collect(permutations("abc"))) == ["abc","acb","bac","bca","cab","cba"]