What is the optimal time complexity of solving Generate Parentheses?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Generate Parentheses?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Generate Parentheses?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Generate Parentheses?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Generate Parentheses

Learn how to solve the 'Generate Parentheses' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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

Write a function generateParenthesis(n: int) -> List[str].

Constraints

•1 <= n <= 8

Examples

Example 1

Input

n = 3

Output

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

Explanation

All 5 valid combinations of 3 pairs of parentheses.

Example 2

Input

n = 1

Output

["()"]

Explanation

Only one valid combination with 1 pair.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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