22.括号生成

22.括号生成

比较容易想到暴力解法，生成所有的括号然后检验是否有效。

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;
    }

回溯法--只生成有效的括号，

public List<String> generateParenthesis(int n) {
        List<String> ans = new ArrayList<>();
        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)
        }