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# Generate parentheses challenge

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Problem statement
Given $n$ pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

For example, given $n = 3$, a solution set is:

```[
"((()))",
"(()())",
"(())()",
"()(())",
"()()()"
]
```

Solution

```class Solution(object):
def generate(self, n, open_count, closed_count, s, result, visited):

if open_count == n and closed_count == n:
result.append(s)

for i in range(0, 2*n-len(s)):
if open_count < n and not s+'(' in visited:
self.generate(n,open_count+1, closed_count, s+'(', result, visited)
if closed_count < open_count and not s+')' in visited:
self.generate(n,open_count, closed_count+1, s+')', result, visited)

def generateParenthesis(self, n):
"""
:type n: int
:rtype: List[str]
"""
ans = []
self.generate(n, 0, 0, '', ans, set())
return ans

def main():
solution = Solution()
print(solution.generateParenthesis(10))

if __name__ == "__main__": main()
```