Is Generate Parentheses easy or hard?

Generate Parentheses is typically classified as a medium difficulty problem. The challenge comes from recognizing that you should prune invalid states during generation rather than checking validity afterward. Once the backtracking constraint is clear, the implementation becomes straightforward.

How to solve Generate Parentheses in O(n)?

Generating all valid parentheses combinations cannot be done in O(n) time because the output size itself grows exponentially. The optimal approach generates exactly the valid sequences using backtracking with pruning, which runs in O(Cn) time where Cn is the Catalan number.

What is the best approach for Generate Parentheses?

Backtracking with pruning is the standard solution. Build the string step by step while tracking how many opening and closing parentheses have been used. Only add a closing parenthesis when it does not exceed the number of openings. This avoids generating invalid sequences and produces exactly the Catalan number of valid results.

Is Generate Parentheses asked at Google/Amazon/Meta?

Generate Parentheses is a common interview problem at major tech companies including Google, Amazon, Meta, and Microsoft. It tests recursion, backtracking, and understanding of constrained combinatorial generation, which frequently appears in coding interviews.

What data structure is used in Generate Parentheses?

Most implementations use recursion with a mutable string builder or array to construct the sequence. Conceptually it relies on backtracking and the call stack rather than a complex data structure. Some validation approaches also use a stack to check correctness of parentheses.

What is the time complexity of Generate Parentheses?

The optimal backtracking solution runs in O(Cn) time, where Cn is the nth Catalan number. This is approximately O(4^n / √n). Each valid combination of length 2n must be generated once, and recursion depth requires O(n) auxiliary space.

Generate Parentheses Python or Java solution approach

In both Python and Java, the common approach uses recursive backtracking. Track the count of opening and closing parentheses and append characters while maintaining validity rules. The recursion stops when the string length reaches 2n and the combination is added to the result list.

Description Solution Video 13:37

22. Generate Parentheses

Medium79.6% acceptance40 companies

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

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22. Generate Parentheses

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