Cartesian product of two or more lists: Difference between revisions

and we could define our own '''cartesianProduct''', in terms of a general applicative function:

<lang python>from functools import (reduce)

# cartesianProduct :: [a] -> [b] -> [(a, b)]

def cartesianProduct(xs):

return lambda ys: ap(

map(lambda x: lambda y: (x, y), xs)

)(ys)

# GENERIC FUNCTIONS --------------------------------

# apList (<*>) :: [(a -> b)] -> [a] -> [b]

def ap(fs):

return lambda xs: reduce(

lambda a, f: a + reduce(

lambda a, x: a + [f(x)], xs, []

), fs, []

)

# uncurry :: (a -> b -> c) -> ((a, b) -> c)

def uncurry(f):

def g(x, y):

return f(x)(y)

return g

# TEST ------------------------------------------------

for product in map(lambda x: uncurry(cartesianProduct)(*x), ([

([1, 2], [3, 4]),

([3, 4], [1, 2]),

([1, 2], []),

([], [1, 2])

])):

print (product)</lang>

{{Out}}

<pre>[(1, 3), (1, 4), (2, 3), (2, 4)]

[(3, 1), (3, 2), (4, 1), (4, 2)]

[]

[]</pre>