|
return int( reduce( mul, range((n-r+1), n+1), 1) /
reduce( mul, range(1,r+1), 1) )</lang>
Or, updating for Python 3, and abstracting a little more for legibility and ease of reuse, while currying for ease of mapping and general composition:
<lang python>from functools import reduce
# binomialCoefficient :: Int -> Int -> Int
def binomialCoefficient(n):
return lambda k: product(
enumFromTo(1 + k)(n)
) // factorial(n - k)
# GENERIC -------------------------------------------------
# enumFromTo :: Int -> Int -> [Int]
def enumFromTo(m):
return lambda n: range(m, 1 + n)
# factorial :: Int -> Int
def factorial(x):
return product(enumFromTo(1)(x))
# product :: [Num] -> Num
def product(xs):
return reduce(lambda a, b: a * b, xs, 1)
# TESTS ---------------------------------------------------
print(
binomialCoefficient(5)(3)
)
# k=0 to k=5, where n=5
print(
list(map(
binomialCoefficient(5),
enumFromTo(0)(5)
))
)</lang>
{{Out}}
<pre>10
[1, 5, 10, 10, 5, 1]</pre>
=={{header|R}}==
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