Data commit

Task/Evaluate-binomial-coefficients/Python/evaluate-binomial-coefficients-1.py

@@ -0,0 +1,8 @@
+def binomialCoeff(n, k):
+    result = 1
+    for i in range(1, k+1):
+        result = result * (n-i+1) / i
+    return result
+
+if __name__ == "__main__":
+    print(binomialCoeff(5, 3))

Task/Evaluate-binomial-coefficients/Python/evaluate-binomial-coefficients-2.py

@@ -0,0 +1,23 @@
+from operator import mul
+from functools import reduce
+
+
+def comb(n,r):
+    ''' calculate nCr - the binomial coefficient
+    >>> comb(3,2)
+    3
+    >>> comb(9,4)
+    126
+    >>> comb(9,6)
+    84
+    >>> comb(20,14)
+    38760
+    '''
+
+    if r > n-r:
+        # r = n-r   for smaller intermediate values during computation
+        return ( reduce( mul, range((n - (n-r) + 1), n + 1), 1)
+                 // reduce( mul, range(1, (n-r) + 1), 1) )
+    else:
+        return ( reduce( mul, range((n - r + 1), n + 1), 1)
+                 // reduce( mul, range(1, r + 1), 1) )

Task/Evaluate-binomial-coefficients/Python/evaluate-binomial-coefficients-3.py

@@ -0,0 +1,60 @@
+'''Evaluation of binomial coefficients'''
+
+from functools import reduce
+
+
+# binomialCoefficient :: Int -> Int -> Int
+def binomialCoefficient(n):
+    '''n choose k, expressed in terms of
+       product and factorial functions.
+    '''
+    return lambda k: product(
+        enumFromTo(1 + k)(n)
+    ) // factorial(n - k)
+
+
+# TEST ----------------------------------------------------
+# main :: IO()
+def main():
+    '''Tests'''
+
+    print(
+        binomialCoefficient(5)(3)
+    )
+
+    # k=0 to k=5, where n=5
+    print(
+        list(map(
+            binomialCoefficient(5),
+            enumFromTo(0)(5)
+        ))
+    )
+
+
+# GENERIC -------------------------------------------------
+
+# enumFromTo :: (Int, Int) -> [Int]
+def enumFromTo(m):
+    '''Integer enumeration from m to n.'''
+    return lambda n: list(range(m, 1 + n))
+
+
+# factorial :: Int -> Int
+def factorial(x):
+    '''The factorial of x, where
+       x is a positive integer.
+    '''
+    return product(enumFromTo(1)(x))
+
+
+# product :: [Num] -> Num
+def product(xs):
+    '''The product of a list of
+       numeric values.
+    '''
+    return reduce(lambda a, b: a * b, xs, 1)
+
+
+# TESTS ---------------------------------------------------
+if __name__ == '__main__':
+    main()

Task/Evaluate-binomial-coefficients/Python/evaluate-binomial-coefficients-4.py

@@ -0,0 +1,25 @@
+from typing import (Callable, List, Any)
+from functools import reduce
+from operator import mul
+
+
+def binomialCoefficient(n: int) -> Callable[[int], int]:
+    return lambda k: product(enumFromTo(1 + k)(n)) // factorial(n - k)
+
+
+def enumFromTo(m: int) -> Callable[[int], List[Any]]:
+    return lambda n: list(range(m, 1 + n))
+
+
+def factorial(x: int) -> int:
+    return product(enumFromTo(1)(x))
+
+
+def product(xs: List[Any]) -> int:
+    return reduce(mul, xs, 1)
+
+
+if __name__ == '__main__':
+    print(binomialCoefficient(5)(3))
+    # k=0 to k=5, where n=5
+    print(list(map(binomialCoefficient(5), enumFromTo(0)(5))))