Parentheses Pairs

2021-09-13.py

question = """
Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

Example:

$ formParens(1)
$ ["()"]

$ formParens(3)
$ ["((()))","(()())","(())()","()(())","()()()"]

"""

def formParens(n):
    paren_array_keys = {}
    paren_array = []
    if n == 1:
        return [ "()" ]
    if n > 1:
        lower_set = formParens(n - 1)
        for set in lower_set:
            prepend_set = '()' + set
            append_set = set + '()'
            encase_set = '(' + set + ')'

            paren_array_keys[prepend_set] = 1
            paren_array_keys[append_set] = 1
            paren_array_keys[encase_set] = 1
    for key in paren_array_keys.keys():
        paren_array.append(key)
    return paren_array

print(formParens(1))

print(formParens(3))

Hi!

Just leaving a comment in case it's useful for you 🙌

I tried a similar approach, however I discarded because I missed some options.

I think it works for 1, 2 and 3 pairs. However, formParens(4) doesn't show:

(())(())

formParens(5) doesn't show:

((())(()))
((()))(())
(()())(())
(())((()))
(())(()())
(())(())()
(())()(())
()(())(())

formParens(6) doesn't show:

(((())(())))
(((()))(()))
(((())))(())
((()())(()))
((()()))(())
((())((())))
((())(()()))
((())(())())
((())(()))()
((())()(()))
((())())(())
((()))((()))
((()))(()())
((()))(())()
((()))()(())
(()(())(()))
(()(()))(())
(()()())(())
(()())((()))
(()())(()())
(()())(())()
(()())()(())
(())(((())))
(())((()()))
(())((())())
(())((()))()
(())(()(()))
(())(()()())
(())(()())()
(())(())(())
(())(())()()
(())()((()))
(())()(()())
(())()(())()
(())()()(())
()((())(()))
()((()))(())
()(()())(())
()(())((()))
()(())(()())
()(())(())()
()(())()(())
()()(())(())

Kind regards!

Rachel: Thank you very much ; I had only focused on the requested results and did not see if it would work beyond that. Here is a change that seems to help: for char in range(0, len(set)): new_parens = '(' + set[:char] + ')' + set[char:] paren_array_keys[new_parens] = 1 # prepend_set = '()' + set # append_set = set + '()' # encase_set = '(' + set + ')' # paren_array_keys[prepend_set] = 1 # paren_array_keys[append_set] = 1 # paren_array_keys[encase_set] = 1 Les

…

On Mon, Sep 20, 2021 at 8:19 AM Rachel M. Carmena ***@***.***> wrote: ***@***.**** commented on this gist. ------------------------------ Hi! Just leaving a comment in case it's useful for you 🙌 I tried a similar approach, however I discarded because I missed some options. I think it works for 1, 2 and 3 pairs. However, formParens(4) doesn't show: (())(()) formParens(5) doesn't show: ((())(())) ((()))(()) (()())(()) (())((())) (())(()()) (())(())() (())()(()) ()(())(()) formParens(6) doesn't show: (((())(()))) (((()))(())) (((())))(()) ((()())(())) ((()()))(()) ((())((()))) ((())(()())) ((())(())()) ((())(()))() ((())()(())) ((())())(()) ((()))((())) ((()))(()()) ((()))(())() ((()))()(()) (()(())(())) (()(()))(()) (()()())(()) (()())((())) (()())(()()) (()())(())() (()())()(()) (())(((()))) (())((()())) (())((())()) (())((()))() (())(()(())) (())(()()()) (())(()())() (())(())(()) (())(())()() (())()((())) (())()(()()) (())()(())() (())()()(()) ()((())(())) ()((()))(()) ()(()())(()) ()(())((())) ()(())(()()) ()(())(())() ()(())()(()) ()()(())(()) Kind regards! — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <https://gist.github.com/e1f6dbfd70628b37f65c9197ba2fb818#gistcomment-3898891>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACJV2UYVZH2T3VLMPRBWUULUC4RFXANCNFSM5EL2OTFQ> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>.

Thank you very much

Thanks to you!

Here is a change that seems to help:

Yes, you got it! 👏 Congrats!