# 0022. Generate Parentheses

https://leetcode.com/problems/generate-parentheses

## Description

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:** ["()"]
```

**Constraints:**

* `1 <= n <= 8`

## ac

```java
class Solution {
    public List<String> generateParenthesis(int n) {
        List<String> res = new ArrayList<>();
        process(0, 0, n, new StringBuilder(), res);
        return res;
    }

    private void process(int left, int right, int n, StringBuilder sb, List<String> res) {
        if (left == n && right == n) {
            res.add(sb.toString());
        }

        if (left < n) {
            sb.append("(");
            process(left + 1, right, n, sb, res);
            sb.setLength(sb.length() - 1);
        }

        if (right < n && left > right) {
            sb.append(")");
            process(left, right + 1, n, sb, res);
            sb.setLength(sb.length() - 1);
        }
    }
}
```

```java
class Solution {
    public List<String> generateParenthesis(int n) {
        List<String> list = new ArrayList<String>();
        backtrack(list, "", 0, 0, n);
        return list;
    }

    public void backtrack(List<String> list, String str, int open, int close, int max){

        if(str.length() == max*2){
            list.add(str);
            return;
        }

        if(open < max)
            backtrack(list, str+"(", open+1, close, max);
        if(close < open)
            backtrack(list, str+")", open, close+1, max);
    }
}
```
