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22.generate-parentheses.py
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22.generate-parentheses.py
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# Tag: String, Dynamic Programming, Backtracking
# Time: O(2^N)
# Space: O(N)
# Ref: -
# Note: Catalan Number
# Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.
#
# Example 1:
# Input: n = 3
# Output: ["((()))","(()())","(())()","()(())","()()()"]
# Example 2:
# Input: n = 1
# Output: ["()"]
#
#
# Constraints:
#
# 1 <= n <= 8
#
#
class Solution:
def generateParenthesis(self, n: int) -> List[str]:
res = []
self.helper(0, 0, n, "", res)
return res
def helper(self, left:int, right: int, n:int, ans: str, res:list):
if left + right == n * 2:
res.append(ans)
return
if left < n:
self.helper(left + 1, right, n, ans + '(', res)
if right < left:
self.helper(left, right + 1, n, ans + ')', res)
class Solution:
def generateParenthesis(self, n: int) -> List[str]:
dp = [[] for i in range(n + 1)]
dp[0] = [""]
for i in range(1, n + 1):
for j in range(i):
left = dp[j]
right = dp[i - j - 1]
for l in left:
for r in right:
dp[i].append("(" + l + ")" + r)
return dp[n]