結果

問題 No.3099 Parentheses Decomposition
ユーザー rogi52
提出日時 2025-04-11 22:01:17
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 18 ms / 2,000 ms
コード長 10,533 bytes
コンパイル時間 3,815 ms
コンパイル使用メモリ 297,912 KB
実行使用メモリ 7,848 KB
最終ジャッジ日時 2025-04-11 22:01:22
合計ジャッジ時間 4,616 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 20
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 2 "/Users/korogi/Desktop/cp-cpp/template.hpp"
#include <bits/stdc++.h>
using namespace std;

using i32 = int;
using i64 = long long;
using i128 = __int128;
using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = unsigned __int128;
using f32 = double;
using f64 = long double;
using f128 = __float128;

#define DMP(x) cout << "[" << __LINE__ << "]" << " " << #x << ":" << " " << x << endl;

#define FOR1(n)          for(int _ =  0 , n_ = (n); _ < n_; _++)
#define FOR2(i, n)       for(int i =  0 , n_ = (n); i < n_; i++)
#define FOR3(i, s, t)    for(int i = (s), t_ = (t); i < t_; i++)
#define FOR4(i, s, t, d) for(int i = (s), t_ = (t), d_ = (d); i < t_; i += d_)
#define OVERLOAD4(a, b, c, d, e, ...) e
#define FOR(...) OVERLOAD4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)

#define REV1(n)          for(int _ = (n) - 1; _ >=  0 ; _--)
#define REV2(i, n)       for(int i = (n) - 1; i >=  0 ; i--)
#define REV3(i, s, t)    for(int i = (t) - 1, s_ = (s); i >= s_; i--)
#define REV4(i, s, t, d) for(int i = (t) - 1, s_ = (s), d_ = (d); i >= s_; i -= d_)
#define OVERLOAD3(a, b, c, d, ...) d
#define REV(...) OVERLOAD4(__VA_ARGS__, REV4, REV3, REV2, REV1)(__VA_ARGS__)

#define FOR_SUBSET(T, S) for(int S_ = (S), T = S_; T >= 0; T = (T == 0 ? -1 : (T - 1) & S_))

#define MULTI for(int testcase_ = in(), testcase = 0; testcase < testcase_; testcase++) [&]

template < class T > using heap_max = priority_queue< T, vector< T >, less< T > >;
template < class T > using heap_min = priority_queue< T, vector< T >, greater< T >>;

template < class T, class U > bool chmin(T& a, const U& b) { return a > b ? a = b, 1 : 0; }
template < class T, class U > bool chmax(T& a, const U& b) { return a < b ? a = b, 1 : 0; }

i64 floor_div(const i64 n, const i64 d) { assert(d != 0); return n / d - ((n ^ d) <  0 && n % d != 0); }
i64  ceil_div(const i64 n, const i64 d) { assert(d != 0); return n / d + ((n ^ d) >= 0 && n % d != 0); }

template < class T, class F > T bin_search(T ok, T ng, F check) { while(abs(ok - ng) > 1) { T mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return ok; }
template < class T, class F > T bin_search_real(T ok, T ng, F check, int step = 100) { FOR(step) { T mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return ok; }

template < class T, class U > T accum(const vector< U >& a) { return accumulate(a.begin(), a.end(), T(0)); }
template < class T > pair< T, int > min(const vector< T >& a) { auto itr = min_element(a.begin(), a.end()); return {*itr, itr - a.begin()}; }
template < class T > pair< T, int > max(const vector< T >& a) { auto itr = max_element(a.begin(), a.end()); return {*itr, itr - a.begin()}; }
template < class T > void sort(vector< T >& a) { sort(a.begin(), a.end()); }
template < class T > void rsort(vector< T >& a) { sort(a.rbegin(), a.rend()); }
template < class T > void reverse(vector< T >& a) { reverse(a.begin(), a.end()); }
void sort(string& s) { sort(s.begin(), s.end()); }
void rsort(string& s) { sort(s.rbegin(), s.rend()); }
void reverse(string& s) { reverse(s.begin(), s.end()); }
template < class T, class Cmp > void sort(vector< T >& a, Cmp cmp) { sort(a.begin(), a.end(), cmp); }
template < class T > int LB(vector< T >& a, T x) { return distance(a.begin(), lower_bound(a.begin(), a.end(), x)); }
template < class T > int UB(vector< T >& a, T x) { return distance(a.begin(), upper_bound(a.begin(), a.end(), x)); }
template < class T > void unique(vector< T >& a) { sort(a.begin(), a.end()); a.erase(unique(a.begin(), a.end()), a.end()); }
vector<int> iota(int n) { vector<int> a(n); iota(a.begin(), a.end(), 0); return a; }

istream& operator >> (istream& is, i128& x) {
    string s; is >> s;
    int m = (s[0] == '-');
    x = 0;
    FOR(i, m, ssize(s)) x = x * 10 + (s[i] - '0');
    if(m) x *= -1;
    return is;
}
ostream& operator << (ostream& os, const i128& x) {
    if(x == 0) return os << '0';
    i128 y = x; if(y < 0) { os << '-'; y *= -1; }
    vector<int> ny;
    while(y) ny.push_back(y % 10), y /= 10;
    REV(i, ssize(ny)) os << ny[i];
    return os;
}
namespace scan {
struct x0 { template < class T > operator T() { T x; cin >> x; return x; } };
struct x1 { int n; x1(int n) : n(n) {} template < class T > operator vector< T >() { vector< T > a(n); for(T& x : a) cin >> x; return a; } };
struct x2 { int h, w; x2(int h, int w) : h(h), w(w) {} template < class T > operator vector< vector< T > >() { vector m(h, vector< T >(w)); for(vector< T >& a : m) for(T& x : a) cin >> x; return m; } };
struct cppio { cppio() { cin.tie(0); ios::sync_with_stdio(0); } } cppio_instance;
}
scan::x0 in() { return scan::x0(); }
scan::x1 in(int n) { return scan::x1(n); }
scan::x2 in(int h, int w) { return scan::x2(h, w); }

template < class T > ostream& operator << (ostream& os, const vector< T > a) {
    const int n = a.size();
    FOR(i, n) { os << a[i]; if(i + 1 != n) os << ' '; }
    return os;
}
template < class T > int print_n(const vector< T > a) { for(T x : a) cout << x << '\n'; return 0; }
int print() { cout << '\n'; return 0; }
template < class Head, class... Tail > int print(Head&& h, Tail&&... t) { cout << h; if(sizeof...(Tail)) cout << ' '; return print(forward<Tail>(t)...); }
namespace printer {
    void prec(int n) { cout << fixed << setprecision(n); }
    void flush() { cout.flush(); }
}

constexpr pair<int, int> dir4[] = {{-1, 0}, {0, -1}, {+1, 0}, {0, +1}};

vector<int>& operator ++ (vector<int>& a) { for(auto& e : a) e++; return a; }
vector<int>& operator -- (vector<int>& a) { for(auto& e : a) e--; return a; }
vector<int>  operator ++ (vector<int>& a, int) { vector<int> b = a; ++a; return b; }
vector<int>  operator -- (vector<int>& a, int) { vector<int> b = a; --a; return b; }

template < class T > vector<pair< T, int>> RLE(const vector< T >& a) { vector<pair< T, int>> v; for(const T& x : a) { if(not v.empty() and v.back().first == x) v.back().second++; else v.emplace_back(x, 1); } return v; }
vector<pair<char, int>> RLE(const string& s) { vector<pair<char, int>> v; for(const char& c : s) { if(not v.empty() and v.back().first == c) v.back().second++; else v.emplace_back(c, 1); } return v; }
template < class String, class Same > vector<String> RLE(const String& a, const Same same) { vector<String> v; for(const auto& x : a) { if(not v.empty() and same(v.back().back(), x)) v.back().push_back(x); else v.push_back({x}); } return v; }

int YESNO(bool yes) { return print(yes ? "YES" : "NO"); }
int YesNo(bool yes) { return print(yes ? "Yes" : "No"); }

constexpr i32 INF32 = 1e9;
constexpr i64 INF64 = 1e18;
#line 3 "/Users/korogi/Desktop/cp-cpp/mod/modint.hpp"

template < u32 mod_, u32 prime_, u32 root_ > struct static_modint {
    static constexpr u32 const & mod = mod_;
    static constexpr u32 const & prime = prime_;
    static constexpr u32 const & root = root_;
    u32 v;
    using mint = static_modint;
    constexpr mint& s(u32 v) { this->v = v < mod ? v : v - mod; return *this; }
    constexpr static_modint(i64 v = 0) { s(v % mod + mod); }
    mint operator - () const { return mint() - *this; }
    mint operator + () const { return *this; }
    mint& operator += (const mint& r) { return s(v + r.v); }
    mint& operator -= (const mint& r) { return s(v + mod - r.v); }
    mint& operator *= (const mint& r) { v = u64(v) * r.v % mod; return *this; }
    mint& operator /= (const mint& r) { return *this *= inv(r); }
    mint operator + (const mint& r) const { return mint(*this) += r; }
    mint operator - (const mint& r) const { return mint(*this) -= r; }
    mint operator * (const mint& r) const { return mint(*this) *= r; }
    mint operator / (const mint& r) const { return mint(*this) /= r; }
    bool operator == (const mint& r) const { return v == r.v; }
    bool operator != (const mint& r) const { return v != r.v; }
};
// x^n
template < u32 mod, u32 prime, u32 root > static_modint<mod, prime, root> pow(static_modint<mod, prime, root> x, u64 n) {
    static_modint<mod, prime, root> p(1);
    for(; n; n >>= 1) { if(n & 1) p *= x; x *= x; }
    return p;
}
// x^{-1}
template < u32 mod, u32 prime, u32 root > static_modint<mod, prime, root> inv(static_modint<mod, prime, root> x) {
    int a = x.v, b = mod, u = 1, v = 0;
    while(b) { int t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); }
    return static_modint<mod, prime, root>(u);
}
template < u32 mod, u32 prime, u32 root > istream& operator >> (istream& is, static_modint<mod, prime, root>& x) { i64 v; is >> v; x = static_modint<mod, prime, root>(v); return is; }
template < u32 mod, u32 prime, u32 root > ostream& operator << (ostream& os, const static_modint<mod, prime, root>& x) { return os << x.v; }

using modint998 = static_modint<  998'244'353, 1, 3>;
using modint107 = static_modint<1'000'000'007, 1, 5>;
#line 3 "a.cpp"
using mint = modint998;
#line 2 "/Users/korogi/Desktop/cp-cpp/mod/binom.hpp"

template < class mint > mint fact(int n) {
    static const u32 mod = mint::mod;
    assert(0 <= n); assert(n < mod); assert(mint::prime);
    static vector<mint> data = {1, 1};
    while(ssize(data) <= n) { const int i = ssize(data); data.push_back(data.back() * i); }
    return data[n];
}
template < class mint > mint inv(int n) {
    static const u32 mod = mint::mod;
    assert(0 <= n); assert(n < mod); assert(mint::prime);
    static vector<mint> data = {1, 1};
    while(ssize(data) <= n) { const int i = ssize(data); data.push_back(-data[mod % i] * (mod / i)); }
    return data[n];
}
template < class mint > mint fact_inv(int n) {
    static const u32 mod = mint::mod;
    assert(0 <= n); assert(n < mod); assert(mint::prime);
    static vector<mint> data = {1, 1};
    while(ssize(data) <= n) { const int i = ssize(data); data.push_back(data.back() * inv<mint>(i)); }
    return data[n];
}
template < class mint > mint comb(int n, int k) {
    return 0 <= k and k <= n ? fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k) : 0;
}

template < class T > struct powers {
    T a; vector< T > data;
    powers(const T a) : a(a), data({1}) {}
    // a^n
    T get(int n) {
        assert(0 <= n);
        while(ssize(data) <= n) data.push_back(data.back() * a);
        return data[n];
    }
};
#line 5 "a.cpp"

int main() {
    int N = in();
    string S = in();

    bool typeA = [&] {
        FOR(i, N / 2) if(S[i] == ')') return false;
        return true;
    }();

    if(typeA) {
        mint ans = 0;
        for(int k = 0; k <= N / 2; k++) ans += comb<mint>(N / 2, k) * comb<mint>(N / 2, k);
        print(ans);
    } else {
        print(pow(mint(2), N / 2));
    }
}
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