261. Valid Parentheses IV - Generate Valid Parentheses

You're building a code generator that needs to generate all valid combinations of parentheses. This is useful for generating test cases, creating balanced expressions, or building parser test data.

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

Requirements

1. Basic Functionality

• Generate all valid parentheses combinations
• Each combination must have n pairs
• Parentheses must be well-formed (balanced)
• Return array of all valid strings

Example Usage

generateParenthesis(3);
// ["((()))","(()())","(())()","()(())","()()()"]

generateParenthesis(1);
// ["()"]

Real-World Context

This problem models real code generation scenarios:

• Code generation: Generate valid code structures
• Parser testing: Create test cases for parsers
• Expression generation: Generate balanced expressions
• Combinatorics: Generate all valid combinations