Merge pull request #6 from gajomi/combinations

method,test,docs,require for combinations

Author: jiahao

README.md

@@ -12,6 +12,7 @@ most of the functions always return `BigInt`, and are marked as such below.
 This library provides the following functions:
  - `bell(n)`: returns the n-th Bell number; always returns a `BigInt`;
  - `catalan(n)`: returns the n-th Catalan number; always returns a `BigInt`;
+  - `combinations(a)`: returns combinations of all order by chaining calls to `Base.combinations(a,n);
  - `derangement(n)`/`subfactorial(n)`: returns the number of permutations of n with no fixed points; always returns a `BigInt`;
  - `doublefactorial(n)`: returns the double factorial n!!; always returns a `BigInt`;
  - `fibonacci(n)`: the n-th Fibonacci number; always returns a `BigInt`;

REQUIRE

@@ -1,3 +1,4 @@
 julia 0.3+
 Compat
 Polynomials
+Iterators

src/Combinatorics.jl

@@ -1,6 +1,8 @@
 module Combinatorics
 
-using Compat, Polynomials
+using Compat, Polynomials, Iterators
+
+import Base:combinations
 
 export  bell,
         derangement,
@@ -49,6 +51,10 @@ function catalan(bn::Integer)
     div(binomial(2*n, n), (n + 1))
 end
 
+#generate combinations of all orders, chaining of order iterators is eager,
+#but sequence at each order is lazy
+combinations(a) = chain([combinations(a,k) for k=1:length(a)]...)
+
 # The number of permutations of n with no fixed points (subfactorial)
 function derangement(sn::Integer)
     n = BigInt(sn)

test/basic.jl

@@ -2,6 +2,10 @@
 @test Combinatorics.catalan(5) == 42
 @test Combinatorics.catalan(30) == parse(BigInt,"3814986502092304")
 
+#combinations
+@test collect(combinations([])) == []
+@test collect(combinations("abc")) == ["a","b","c","ab","ac","bc","abc"]
+
 # derangement
 @test derangement(4) == 9
 @test derangement(24) == parse(BigInt,"228250211305338670494289")