Generate All Valid Parentheses
Given an integer n, generate all strings with n matching parentheses.
"matching" parentheses mean
- there is equal number of opening and closing parentheses.
- each opening parenthesis has matching closing parentheses.
For example, () is a valid string but )( is not a valid string because ) has no matching parenthesis before it and ( has no matching parenthesis after it.
Input
n: number of matching parentheses
Output
all valid strings with n matching parentheses
Examples
Example 1:
Input:
1n = 2
Output: (()) ()()
Explanation:
There are two ways to create a string with 2 matching parentheses.
Example 2:
Input:
1n = 3
Output: ((())) (()()) (())() ()(()) ()()()
Explanation:
There are 5 ways to create a string with 3 matching parentheses.