22.generate-parentheses

Statement

• Difficulty: Medium
• Tag: `字符串` `动态规划` `回溯`

``````输入：n = 3

``````

``````输入：n = 1

``````

• `1 <= n <= 8`

• Difficulty: Medium
• Tag: `String` `Dynamic Programming` `Backtracking`

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`

Solution

``````#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <string>
#include <vector>

#define endl "\n"
#define fi first
#define se second
#define all(x) begin(x), end(x)
#define rall rbegin(a), rend(a)
#define bitcnt(x) (__builtin_popcountll(x))
#define complete_unique(a) a.erase(unique(begin(a), end(a)), end(a))
#define mst(x, a) memset(x, a, sizeof(x))
#define MP make_pair

using ll = long long;
using ull = unsigned long long;
using db = double;
using ld = long double;
using VLL = std::vector<ll>;
using VI = std::vector<int>;
using PII = std::pair<int, int>;
using PLL = std::pair<ll, ll>;

using namespace __gnu_pbds;
using namespace std;
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

template <typename T, typename S>
inline bool chmax(T &a, const S &b) {
return a < b ? a = b, 1 : 0;
}

template <typename T, typename S>
inline bool chmin(T &a, const S &b) {
return a > b ? a = b, 1 : 0;
}

#ifdef LOCAL
#include <debug.hpp>
#else
#define dbg(...)
#endif

class Solution {
public:
vector<string> generateParenthesis(int n) {
const auto ok = [](const string &s) {
int l = 0;

for (const char &c : s) {
if (c == '(') {
++l;
} else {
if (!l) {
return false;
}
--l;
}
}

return !l;
};

auto res = vector<string>();
n <<= 1;

for (int S = 0; S < 1 << n; S++) {
auto s = string();

for (int i = 0; i < n; i++) {
s += string(1, (S >> i & 1) ? '(' : ')');
}

if (ok(s)) {
res.push_back(s);
}
}

return res;
}
};

#ifdef LOCAL

int main() {
return 0;
}

#endif
``````