Generate Parentheses

Problem

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

Examples

The brute-force approach

Generate all 2^(2n) strings of "(" and ")". Filter to keep only valid ones (balanced).

for each string s of length 2n with "(" and ")":
    if is_valid(s):
        result.append(s)

O(2^(2n) × n) — exponential with a validity check per string.

Spotting the pattern

This is a Backtracking problem. The key question to ask yourself:

Why does the constraint "add ) only when close < open" guarantee that every complete string is valid? What would go wrong without it?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.