22. 括号生成

class Solution {
    /**
     * 回溯法生成括号
     * 时间复杂度: O(4^n / sqrt(n))
     * 空间复杂度: O(4^n / sqrt(n))
     */
    public List<String> generateParenthesis(int n) {
        List<String> ans = new ArrayList<String>();
        backtrack(ans, new StringBuilder(), 0, 0, n);
        return ans;
    }

    public void backtrack(List<String> ans, StringBuilder cur, int open, int close, int max) {
        if (cur.length() == max * 2) {
            ans.add(cur.toString());
            return;
        }
        if (open < max) {
            cur.append('(');
            backtrack(ans, cur, open + 1, close, max);
            cur.deleteCharAt(cur.length() - 1);
        }
        if (close < open) {
            cur.append(')');
            backtrack(ans, cur, open, close + 1, max);
            cur.deleteCharAt(cur.length() - 1);
        }
    }
}

class Solution {
    /**
     * 暴力法生成括号
     * 时间复杂度: O(2^(2n) * n)
     * 空间复杂度: O(2^(2n) * n)
     */
    public List<String> generateParenthesis(int n) {
        List<String> combinations = new ArrayList<String>();
        generateAll(new char[2 * n], 0, combinations);
        return combinations;
    }

    public void generateAll(char[] current, int pos, List<String> result) {
        if (pos == current.length) {
            if (valid(current)) {
                result.add(new String(current));
            }
        } else {
            current[pos] = '(';
            generateAll(current, pos + 1, result);
            current[pos] = ')';
            generateAll(current, pos + 1, result);
        }
    }

    public boolean valid(char[] current) {
        int balance = 0;
        for (char c: current) {
            if (c == '(') {
                ++balance;
            } else {
                --balance;
            }
            if (balance < 0) {
                return false;
            }
        }
        return balance == 0;
    }
}