parens.py

from typing import Iterable, List


def generate_split(places: int, max: int) -> Iterable[List[int]]:
    if places == 0:
        yield []
    elif places == 1:
        yield [max]
    else:
        for i in range(0, max + 1):
            for j in generate_split(places - 1, max - i):
                yield [i] + j

def head_to_parens(head: int) -> Iterable[str]:
    for i in range(head):
        for a in generate_split(i + 1, head - i - 1):
            for s in to_parens(a[0], a[1:]):
                yield "(" + s + ")"

def tail_to_parens(splits: List[int]) -> Iterable[str]:
    if len(splits) > 0:
        for parens in to_parens(splits[0], splits[1:]):
            yield parens
    else:
        yield ""
        
def to_parens(head: int, tail_splits: List[int]) -> Iterable[str]:
    for i in ["()"] if head == 0 else head_to_parens(head):
        for j in tail_to_parens(tail_splits):
            yield i + j
    

for r in to_parens(6, []):
    pass
    print(r[1:-1])