I found I need to loop through a list to create a brute force algorithm. Therefore, I decided to make a library, but to generalize the result by using a generator. There are three cases which is every single element, every pair of elements, and every triple of elements. The cases store a variable which contains the generator function. Currently, the generator is required to be nested with no parameters inside a function which takes the data structure as a parameter. Therefore, the average space complexity is O(1) in the three cases. The code is below.
def test_generator():
yield "a"
yield "b"
def singles(generator):
"""
average time: O(n) where n is the number of yields from generator
average space: O(1)
"""
for at in generator():
yield at
def test_singles():
assert list(singles(test_generator)) == ["a", "b"]
def pairs(generator):
"""
average time: O(n * n) where n is the number of yields from generator
average space: O(1)
"""
first_generator = generator
second_generator = generator
for first in first_generator():
second_generator = generator
for second in second_generator():
yield first, second
def test_pairs():
assert list(pairs(test_generator)) == [("a", "a"), ("a", "b"), ("b", "a"), ("b", "b")]
def triples(generator):
"""
average time: O(n * n * n) where n is the number of yields
average sapce: O(1)
"""
first_generator = generator
second_generator = generator
third_generator = generator
for first in first_generator():
second_generator = generator
for second in second_generator():
third = third_generator
for third in third_generator():
yield first, second, third
def test_triples():
assert list(triples(test_generator)) == [("a", "a", "a"), ("a", "a", "b"), ("a", "b", "a"),
("a", "b", "b"), ("b", "a", "a"), ("b", "a", "b"), ("b", "b", "a"), ("b", "b", "b")]
def tests():
test_singles()
test_pairs()
test_triples()
if __name__ == "__main__":
tests()
