Generate Parentheses

 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: ["()"]


class Solution {
 public List<String> generateParenthesis(int n) {
        List<String> result = new ArrayList<>();  // Initialize an empty list to store the results
        backtrack(result, "", 0, 0, n);  // Start the backtracking process
        return result;  // Return the list of valid combinations
    }
   
    // Helper function for backtracking
    private void backtrack(List<String> result, String currentString, int openCount, int closeCount, int max) {
        // If the current string length is equal to 2 * n, it means we have used all parentheses
        if (currentString.length() == max * 2) {
            result.add(currentString);  // Add the current valid combination to the result list
            return;
        }
       
        // If we can still add an open parenthesis, add it and recurse
        if (openCount < max) {
            backtrack(result, currentString + "(", openCount + 1, closeCount, max);
        }
       
        // If we can add a close parenthesis without invalidating the sequence, add it and recurse
        if (closeCount < openCount) {
            backtrack(result, currentString + ")", openCount, closeCount + 1, max);
        }
    }
}

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