結果

問題 No.3099 Parentheses Decomposition
ユーザー Astral__
提出日時 2025-04-11 21:26:18
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 25 ms / 2,000 ms
コード長 7,969 bytes
コンパイル時間 5,837 ms
コンパイル使用メモリ 334,004 KB
実行使用メモリ 10,164 KB
最終ジャッジ日時 2025-04-11 21:26:27
合計ジャッジ時間 6,754 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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 # 

#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
std::istream &operator>>(std::istream &is, atcoder::modint &v) {
    long long value;
    is >> value;
    v = value;
    return is;
}
std::ostream &operator<<(std::ostream &os, const atcoder::modint &v) {
    os << v.val();
    return os;
}
std::ostream &operator<<(std::ostream &os, const atcoder::modint998244353 &v) {
    os << v.val();
    return os;
}
std::istream &operator>>(std::istream &is, atcoder::modint998244353 &v) {
    long long x;
    is >> x;
    v = x;
    return is;
}
std::ostream &operator<<(std::ostream &os, const atcoder::modint1000000007 &v) {
    os << v.val();
    return os;
}
std::istream &operator>>(std::istream &is, atcoder::modint1000000007 &v) {
    long long x;
    is >> x;
    v = x;
    return is;
}
#endif

using namespace std;
using ll = long long;
using lint = __int128_t;
using pll = pair<ll, ll>;
#define newl '\n';
#define rep(i, s, t) for (ll i = s; i < (ll)(t); i++)
#define rrep(i, s, t) for (ll i = (ll)(t) - 1; i >= (ll)(s); i--)
#define all(x) begin(x), end(x)
#define SZ(x) ll(x.size())
#define eb emplace_back
#define pb push_back
#define TT template <typename T>
TT using vec = vector<T>;
TT using vvec = vec<vec<T>>;
TT using vvvec = vec<vvec<T>>;
TT using minheap = priority_queue<T, vector<T>, greater<T>>;
TT using maxheap = priority_queue<T>;
TT bool chmin(T &x, T y) {
    return x > y ? (x = y, true) : false;
}
TT bool chmax(T &x, T y) {
    return x < y ? (x = y, true) : false;
}
TT T smod(T x, T mod) {
    x %= mod;
    if (x < 0)
        x += mod;
    return x;
}
TT bool rng(T l, T x, T r) {
    return l <= x && x < r;
}
TT T flr(T a, T b) {
    if (b < 0)
        a = -a, b = -b;
    return a >= 0 ? a / b : (a + 1) / b - 1;
}

TT T cil(T a, T b) {
    if (b < 0)
        a = -a, b = -b;
    return a > 0 ? (a - 1) / b + 1 : a / b;
}
TT T sqr(T x) {
    return x * x;
}

//{0, 1, ... } -> {p[0], p[1], ...}
template <typename T, typename S>
void rearrange(vector<T> &A, vector<S> const &p) {
    assert(p.size() == A.size());
    vector<T> a = A;
    for (int i = 0; i < ssize(A); ++i) {
        a[i] = A[p[i]];
    }
    swap(a, A);
}
template <typename T, typename S, typename... Ts>
void rearrange(vector<T> &A, vector<S> p, vector<Ts> &...rest) {
    rearrange(A, p);
    (rearrange(rest, p), ...);
}
template <typename T, typename Compare, typename... Ts>
void rearrange(vector<T> &A, Compare cmp, vector<Ts> &...rest) {
    vector<int> p(ssize(A));
    iota(p.begin(), p.end(), 0);
    sort(p.begin(), p.end(), cmp);
    rearrange(A, p);
    (rearrange(rest, p), ...);
}
struct io_setup {
    io_setup() {
        ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        cout << fixed << setprecision(15);
    }
} io_setup;

template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
    os << p.first << " " << p.second;
    return os;
}

TT ostream &operator<<(ostream &os, const vector<T> &v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 != v.size() ? " " : "");
    }
    return os;
}

template <typename T, size_t n>
ostream &operator<<(ostream &os, const array<T, n> &v) {
    for (size_t i = 0; i < n; i++) {
        os << v[i] << (i + 1 != n ? " " : "");
    }
    return os;
}

template <typename T> ostream &operator<<(ostream &os, const vvec<T> &v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 != v.size() ? "\n" : "");
    }
    return os;
}

TT istream &operator>>(istream &is, vector<T> &v) {
    for (size_t i = 0; i < v.size(); i++) {
        is >> v[i];
    }
    return is;
}

#if __has_include(<debug/debug.hpp>)
#include <debug/debug.hpp>
#else
#define dbg(...) true
#define DBG(...) true
#define OUT(...) true
#endif
template <typename T, long long mod> struct combination {
    vector<long long> fac, ifac, inv;
    long long N;
    combination() {
        fac.resize(2, 1);
        ifac.resize(2, 1);
        inv.resize(2, 1);
        N = 1;
    }

    void reserve(long long n) {
        expand(n);
    }

    T operator()(int n, int k) {
        return C(n, k);
    }

    T raw(long long n, long long k) const {
        if (k < 0)
            return 0;
        if (k == 0)
            return 1;
        if (n < k)
            return 0;

        if (n - k < k) {
            k = n - k;
        }
        long long p = 1, q = 1;
        for (long long i = 0; i < k; i++) {
            p *= (n - i) % mod;
            p %= mod;
            q *= (k - i) % mod;
            q %= mod;
        }
        return p * modinv(q) % mod;
    }

    T C(int n, int k) {
        if (k < 0)
            return 0;
        if (k == 0)
            return 1;
        if (n < k)
            return 0;
        if (N < n)
            expand(n);
        return fac[n] * ifac[n - k] % mod * ifac[k] % mod;
    }

    T P(int n, int k) {
        if (k < 0)
            return 0;
        if (k == 0)
            return 1;
        if (n < k)
            return 0;
        if (N < n)
            expand(n);
        return fac[n] * ifac[n - k] % mod;
    }

    T B(int n) {
        if (N < n)
            expand(n);
        return (n < 0 ? 0 : fac[n]);
    }
    T invB(int n) {
        if (N < n)
            expand(n);
        return (n < 0 ? 0 : ifac[n]);
    }

    T H(int n, int k) {
        return C(n + k - 1, k);
    }

    T Cn(int n) {
        return C(2 * n, n) * inv[n + 1] % mod;
    }

  private:
    constexpr static bool is_prime_constexpr(long long x) {
        if (x <= 1)
            return false;
        for (long long i = 2; i * i <= x; i++) {
            if (x % i == 0)
                return false;
        }
        return true;
    }

    static_assert(is_prime_constexpr(mod), "mod must be prime");
    static_assert(__int128_t(mod - 1) * (mod - 1) <= __int128_t(LLONG_MAX),
                  "(mod - 1) * (mod - 1) <= LLONG_MAX must be satisfied");

    long long extgcd(long long a, long long b, long long &x,
                     long long &y) const {
        if (b == 0) {
            x = 1;
            y = 0;
            return a;
        }
        auto d = extgcd(b, a % b, y, x);
        y -= a / b * x;
        return d;
    }

    long long modinv(long long a) const {
        long long x, y;
        extgcd(a, mod, x, y);
        x %= mod;
        if (x < 0)
            x += mod;
        return x;
    }

    void expand(long long new_max_n) {
        if (new_max_n <= N)
            return;
        long long nx = N;

        // 2冪で大きくしていく。
        while (nx < new_max_n)
            nx <<= 1;
        new_max_n = nx;

        long long pre = N;
        N = new_max_n;
        fac.resize(N + 1);
        ifac.resize(N + 1);
        inv.resize(N + 1);
        for (long long i = pre + 1; i <= N; i++) {
            fac[i] = fac[i - 1] * i % mod;
        }
        ifac[N] = modinv(fac[N]);
        inv[N] = ifac[N] * fac[N - 1] % mod;
        for (long long i = N - 1; i >= pre + 1; i--) {
            ifac[i] = ifac[i + 1] * (i + 1) % mod;
            inv[i] = ifac[i] * fac[i - 1] % mod;
        }
        return;
    }
};
/*
@brief combination
@docs doc/cmb.md
*/
using combination998244353 = combination<atcoder::modint998244353, 998244353>;
combination998244353 cmb;
using mint = atcoder::modint998244353;
int main() {
    auto type = [&](string A) {
        ll n = A.size();
        rep(i, 0, n / 2) if (A[i] != '(') return 1;
        return 0;
    };

    ll n;
    cin >> n;
    string S;
    cin >> S;
    if (type(S) == 0) {
        mint ret = 0;
        rep(c, 0, n/2 + 1) {
            ret += cmb(n/2, c) * cmb(n/2, c);
        }
        cout << ret << endl;
    }
    else {
        mint ret = 0;
        rep(c, 0, n/2 + 1) {
            ret += cmb(n/2, c);
        }
        cout << ret << endl;
    }
}

/*
同じ議論を繰り返さない
do smth instead of nothing and stay organized
WRITE STUFF DOWN
DON'T GET STUCK ON ONE APPROACH
*/
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