Generate Parentheses

Problem Statement

Given a set of balanced parentheses, generate all possible combinations of well-formed parentheses that can be obtained by inserting additional pairs of parentheses around existing ones.

Rules and Constraints

• The generated combinations should only contain valid parentheses (
  '('
  and
  ')'
  ).
• The resulting strings must have the same number of open and close parentheses.
• No generated string should have any unmatched open or close parentheses.
• The order of the parentheses does not matter.

Output Requirements

The solution should return a list of all valid combinations of well-formed parentheses that meet the above constraints.

Notes

• The input may be an empty string or a string containing balanced parentheses.
• The time complexity of the solution should be optimized to handle large inputs efficiently.

By following these requirements, you can generate all possible combinations of well-formed parentheses from the input set.

Example

Input: {"n":3} Output: ["((()))","(()())","(())()","()(())","()()()"]