結果

問題 No.3146 RE: Parentheses Counting
ユーザー 👑 potato167
提出日時 2025-05-16 22:45:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 471 ms / 2,000 ms
コード長 6,344 bytes
コンパイル時間 3,246 ms
コンパイル使用メモリ 240,964 KB
実行使用メモリ 29,860 KB
最終ジャッジ日時 2025-05-16 22:46:25
合計ジャッジ時間 24,206 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 * 1
other AC * 43
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>
//using namespace std;
//#define all(p) p.begin(), p.end()
//#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
//
//#include<atcoder/modint>
//using mint = atcoder::modint998244353;
//
//#include "po167_library/math/Binomial.hpp"
//#include "po167_library/fps/FPS_inv.hpp"
//
//int main(){
//    int T;
//    cin >> T;
//    const int L = 500'500;
//    po167::Binomial<mint> table;
//    vector<mint> f(L);
//    rep(i, 0, L - 1){
//        f[i + 1] -= table.Catalan_pow(i, 2);
//    }
//    f[0] = 1;
//    auto g = po167::FPS_inv(f);
//    f[0] = 0;
//    f = atcoder::convolution(f, g);
//    f.resize(L);
//    f = atcoder::convolution(f, f);
//    auto ans = f;
//    // vector<mint> ans(L);
//    while (T--){
//        int N;
//        cin >> N;
//        if (N & 1) cout << "0\n";
//        else cout << ans[N / 2].val() << "\n";
//    }
//}#line 1 "d.cpp"
#include <bits/stdc++.h>
using namespace std;
#define all(p) p.begin(), p.end()
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)

#include<atcoder/modint>
using mint = atcoder::modint998244353;

#line 2 "/Users/Shared/po167_library/math/Binomial.hpp"

#line 5 "/Users/Shared/po167_library/math/Binomial.hpp"

namespace po167{
template<class T>
struct Binomial{
    std::vector<T> fact_vec, fact_inv_vec;
    void extend(int m = -1){
        int n = fact_vec.size();
        if (m == -1) m = n * 2;
        if (n >= m) return;
        fact_vec.resize(m);
        fact_inv_vec.resize(m);
        for (int i = n; i < m; i++){
            fact_vec[i] = fact_vec[i - 1] * T(i);
        }
        fact_inv_vec[m - 1] = T(1) / fact_vec[m - 1];
        for (int i = m - 1; i > n; i--){
            fact_inv_vec[i - 1] = fact_inv_vec[i] * T(i);
        }
    }
    Binomial(int MAX = 0){
        fact_vec.resize(1, T(1));
        fact_inv_vec.resize(1, T(1));
        extend(MAX + 1);
    }

    T fact(int i){
        if (i < 0) return 0;
        while (int(fact_vec.size()) <= i) extend();
        return fact_vec[i];
    }
    T invfact(int i){
        if (i < 0) return 0;
        while (int(fact_inv_vec.size()) <= i) extend();
        return fact_inv_vec[i];
    }
    T C(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(a) * invfact(b) * invfact(a - b);
    }
    T invC(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(b) * fact(a - b) *invfact(a);
    }
    T P(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(a) * invfact(a - b);
    }
    T inv(int a){
        if (a < 0) return inv(-a) * T(-1);
        if (a == 0) return 1;
        return fact(a - 1) * invfact(a);
    }
    T Catalan(int n){
        if (n < 0) return 0;
        return fact(2 * n) * invfact(n + 1) * invfact(n);
    }
    T narayana(int n, int k){
        if (n <= 0 || n < k || k < 1) return 0;
        return C(n, k) *  C(n, k - 1) * inv(n);
    }
    T Catalan_pow(int n,int d){
        if (n < 0 || d < 0) return 0;
        if (d == 0){
            if (n == 0) return 1;
            return 0;
        }
        return T(d) * inv(d + n) * C(2 * n + d - 1, n);
    }
    // retrun [x^a] 1/(1-x)^b
    T ruiseki(int a,int b){
        if (a < 0 || b < 0) return 0;
        if (a == 0){
            return 1;
        }
        return C(a + b - 1, b - 1);
    }
    // (a, b) -> (c, d)
    // always x + e >= y
    T mirror(int a, int b, int c, int d, int e = 0){
        if (a + e < b || c + e < d) return 0;
        if (a > c || b > d) return 0;
        a += e;
        c += e;
        return C(c + d - a - b, c - a) - C(c + d - a - b, c - b + 1); 
    }
    // return sum_{i = 0, ... , a} sum_{j = 0, ... , b} C(i + j, i)
    // return C(a + b + 2, a + 1) - 1;
    T gird_sum(int a, int b){
        if (a < 0 || b < 0) return 0;
        return C(a + b + 2, a + 1) - 1;
    }
    // return sum_{i = a, ..., b - 1} sum_{j = c, ... , d - 1} C(i + j, i)
    // AGC 018 E
    T gird_sum_2(int a, int b, int c, int d){
        if (a >= b || c >= d) return 0;
        a--, b--, c--, d--;
        return gird_sum(a, c) - gird_sum(a, d) - gird_sum(b, c) + gird_sum(b, d);
    }

    // the number of diagonal dissections of a convex n-gon into k+1 regions.
    // OEIS A033282
    // AGC065D
    T diagonal(int n, int k){
        if (n <= 2 || n - 3 < k || k < 0) return 0;
        return C(n - 3, k) * C(n + k - 1, k) * inv(k + 1);
    }
};
}
#line 3 "/Users/Shared/po167_library/fps/FPS_inv.hpp"
#include <atcoder/convolution>

namespace po167{
// return 1 / f
template <class T>
std::vector<T> FPS_inv(std::vector<T> f, int len = -1){
    if (len == -1) len = f.size();
    assert(f[0] != 0);
    std::vector<T> g = {1 / f[0]};
    int s = 1;
    while(s < len){
        // g = 2g_s - f(g_s)^2 (mod x ^ (2 * s))
        // g = g - (fg - 1)g
        // (fg - 1) = 0 (mod x ^ (s))
        std::vector<T> n_g(s * 2, 0);
        std::vector<T> f_s(s * 2, 0);
        g.resize(s * 2);
        for (int i = 0; i < s * 2; i++){
            if (int(f.size()) > i) f_s[i] = f[i];
            n_g[i] = g[i];
        }
        atcoder::internal::butterfly(g);
        atcoder::internal::butterfly(f_s);
        for (int i = 0; i < s * 2; i++){
            f_s[i] *= g[i];
        }
        atcoder::internal::butterfly_inv(f_s);
        T iz = 1 / (T)(s * 2);
        for (int i = s; i < s * 2; i++){
            f_s[i] *= iz;
        }
        for (int i = 0; i < s; i++){
            f_s[i] = 0;
        }
        atcoder::internal::butterfly(f_s);
        for (int i = 0; i < s * 2; i++){
            f_s[i] *= g[i];
        }
        atcoder::internal::butterfly_inv(f_s);
        for (int i = s; i < s * 2; i++){
            n_g[i] -= f_s[i] * iz;
        }
        std::swap(n_g, g);
        s *= 2;
    }
    g.resize(len);
    return g;
}
}
#line 11 "d.cpp"

int main(){
    int T;
    cin >> T;
    const int L = 500'500;
    po167::Binomial<mint> table;
    vector<mint> f(L);
    rep(i, 0, L - 1){
        f[i + 1] -= table.Catalan_pow(i, 2);
    }
    f[0] = 1;
    auto g = po167::FPS_inv(f);
    f[0] = 0;
    f = atcoder::convolution(f, g);
    f.resize(L);
    f = atcoder::convolution(f, f);
    auto ans = f;
    // vector<mint> ans(L);
    while (T--){
        int N;
        cin >> N;
        if (N & 1) cout << "0\n";
        else cout << ans[N / 2].val() << "\n";
    }
}
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