22. Bracket generation (java implementation) --LeetCode

topic:

The number n represents the logarithm of generating parentheses. Please design a function that can generate all possible and valid parentheses combinations.

Example 1:

输入：n = 3
输出：["((()))","(()())","(())()","()(())","()()()"]

Example 2:

输入：n = 1
输出：["()"]

prompt:

• 1 <= n <= 8

Solution 1: Recursion

/**
 * 思路
 * 重复性，如何用左右括号
 * 括号合法条件：
 * 左括号随时可加，只要不超标
 * 右括号前面必须有左括号，左括号数>右括号
 * 递归的进行
 */
    public List<String> generateParenthesis(int n) {
    
    
        ArrayList<String> res = new ArrayList<>();
        recursive(n,0,0,"",res);
        return res;
    }

    private void recursive(int n, int l, int r, String s, ArrayList<String> res) {
    
    
        if (s.length()==2*n){
    
    
            res.add(s);
            return;
        }
        if (l<n)recursive(n,l+1,r,s+"(",res);
        if (l>r)recursive(n,l,r+1,s+")",res);
    }

Time complexity: On

Space complexity: On