Generate Parentheses Python Solution

Tested Python solution for LeetCode 22 with 11 pytest cases. Generate a practice environment with lcpy.

LeetCode 22, Medium. Topics: String, Dynamic Programming, Backtracking. View on LeetCode.

Generate this problem as a practice environment: tested reference solution, 11 parametrized pytest cases, and a playground notebook:

lcpy gen -n 22   # by problem number
lcpy gen -s generate_parentheses   # by problem name

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Problem

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

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Examples

Input: n = 3
Output: ["((()))","(()())","(())()","()(())","()()()"]

Input: n = 1
Output: ["()"]

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Constraints

• 1 <= n <= 8

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Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(4^n / sqrt(n))
    # Space: O(4^n / sqrt(n))
    def generate_parenthesis(self, n: int) -> list[str]:
        result: list[str] = []

        def backtrack(s: str, open_count: int, close_count: int) -> None:
            if len(s) == 2 * n:
                result.append(s)
                return
            if open_count < n:
                backtrack(s + "(", open_count + 1, close_count)
            if close_count < open_count:
                backtrack(s + ")", open_count, close_count + 1)

        backtrack("", 0, 0)
        return result

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Complexity

Time	Space
O(4^n / sqrt(n))	O(4^n / sqrt(n))

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Tags

Grind, NeetCode 150, NeetCode 250, NeetCode All.