生成括号对数
给出 n 代表生成括号的对数，请你写出一个函数，使其能够生成所有可能的并且有效的括号组合。
例如，给出 n =3，生成结果为：
[
"((()))",
"(()())",
"(())()",
"()(())",
"()()()"
]
class Solution {
public List<String> generateParenthesis(int n) {
List<String> combinations = new ArrayList();
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);
}
}
class Solution {
public List<String> generateParenthesis(int n) {
List<String> ans = new ArrayList();
backtrack(ans, "", 0, 0, n);
return ans;
}
public void backtrack(List<String> ans, String cur, int open, int close, int max){
if (cur.length() == max * 2) {
ans.add(cur);
return;
}
if (open < max)
backtrack(ans, cur+"(", open+1, close, max);
if (close < open)
backtrack(ans, cur+")", open, close+1, max);
}
}
