結果

問題 No.3243 Multiplication 8 1
ユーザー 👑 potato167
提出日時 2025-08-22 21:21:47
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 78 ms / 2,000 ms
コード長 8,888 bytes
コンパイル時間 3,635 ms
コンパイル使用メモリ 239,448 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-08-22 21:21:51
合計ジャッジ時間 4,222 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 * 1
other AC * 4
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;
//using ll=long long;
//const ll ILL=2167167167167167167;
//const int INF=2100000000;
//#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
//#define all(p) p.begin(),p.end()
//template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
//template<class T> int LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
//template<class T> int UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
//template<class T> bool chmin(T &a,T b){if(b<a){a=b;return 1;}else return 0;}
//template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}
//template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
//template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
//bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}
//template<class T> void vec_out(vector<T> &p,int ty=0){
//    if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
//    else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
//template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
//template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
//template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}
//int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}
//template<class T> T square(T a){return a * a;}
//
//#include "po167_library/fps/FPS_Boston_Mori.hpp"
//using mint = atcoder::modint998244353;
//
//void solve();
//// POP'N ROLL MUSIC / TOMOO
//int main() {
//    ios::sync_with_stdio(false);
//    cin.tie(nullptr);
//
//    int t = 1;
//    cin >> t;
//    rep(i, 0, t) solve();
//}
//
//void solve(){
//    vector<mint> A = {0, 0, 0, 1};
//    vector<mint> B = {1, -3, 3, -1};
//    vector<mint> f = {1, - ((mint::mod() + 1) / 2)};
//    B = atcoder::convolution(B, f);
//    for (auto &x : B) x *= 2;
//    rep(i, 0, 4) B[i] -= A[i];
//    B = atcoder::convolution(B, {1, -1});
//    A = atcoder::convolution(A, f);
//    ll N;
//    cin >> N;
//    mint ans = po167::Boston_Mori(N, A, B).val();
//    ans *= (mint(2)).pow(N);
//    cout << ans.val() << "\n";
//}
//
///*
// * 2 が 3 の倍数個必要
// * 2 の間に -1 が一つでもあればとりあえずはいい
// * そうでない場合、どうする？
// * 最短で打ち切ることにして、(x / (1 - x))^3 * ((1 / 2)/ (1 - x / 2))
// * 残りが 1 + x / (1 - (1 / 2) x)
// * 大変だ
// */#line 1 "d.cpp"
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
const ll ILL=2167167167167167167;
const int INF=2100000000;
#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> int LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> int UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,T b){if(b<a){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}
template<class T> void vec_out(vector<T> &p,int ty=0){
    if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
    else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}
template<class T> T square(T a){return a * a;}

#line 3 "/Users/Shared/po167_library/fps/FPS_Boston_Mori.hpp"
#include <atcoder/convolution>
#line 4 "/Users/Shared/po167_library/fps/FPS_extend.hpp"

namespace po167{
// in  : DFT(v) (len(v) = z)
// out : DFT(v) (len(v) = 2 * z)
template<class T>
void FPS_extend(std::vector<T> &v){
    int z = v.size();
    T e = (T(atcoder::internal::primitive_root_constexpr(T::mod()))).pow(T::mod() / (2 * z));
    auto cp = v;
    atcoder::internal::butterfly_inv(cp);
    T tmp = (T)(1) / (T)(z);
    for (int i = 0; i < z; i++){
        cp[i] *= tmp;
        tmp *= e;
    }
    atcoder::internal::butterfly(cp);
    for (int i = 0; i < z; i++) v.push_back(cp[i]);
};
}
#line 3 "/Users/Shared/po167_library/fps/FPS_pick_even_odd.hpp"

namespace po167{
// s.t |v| = 2 ^ s (no assert)
template<class T>
void FPS_pick_even_odd(std::vector<T> &v, int odd){
    int z = v.size() / 2;
    T half = (T)(1) / (T)(2);
    if (odd == 0){
        for (int i = 0; i < z; i++){
            v[i] = (v[i * 2] + v[i * 2 + 1]) * half;
        }
        v.resize(z);
    } else {
        T e = (T(atcoder::internal::primitive_root_constexpr(T::mod()))).pow(T::mod() / (2 * z));
        T ie = T(1) / e;
        std::vector<T> es = {half};
        while ((int)es.size() != z){
            std::vector<T> n_es((int)es.size() * 2);
            for (int i = 0; i < (int)es.size(); i++){
                n_es[i * 2] = (es[i]);
                n_es[i * 2 + 1] = (es[i] * ie);
            }
            ie *= ie;
            std::swap(n_es, es);
        }
        for (int i = 0; i < z; i ++){
            v[i] = (v[i * 2] - v[i * 2 + 1]) * es[i];
        }
        v.resize(z);
    }
}
}
#line 7 "/Users/Shared/po167_library/fps/FPS_Boston_Mori.hpp"

namespace po167{
// return [x^k] P(x) / Q(x)
template<class T>
T Boston_Mori(long long k, std::vector<T> P, std::vector<T> Q){
    assert(!Q.empty() && Q[0] != 0);
    int z = 1;
    while (z < (int)std::max(P.size(), Q.size())) z *= 2;
    P.resize(z * 2, 0);
    Q.resize(z * 2, 0);
    atcoder::internal::butterfly(P);
    atcoder::internal::butterfly(Q);

    // fast
    while (k){
        // Q(-x)
        std::vector<T> Q_n(z * 2);
        for (int i = 0; i < z; i++){
            Q_n[i * 2] = Q[i * 2 + 1];
            Q_n[i * 2 + 1] = Q[i * 2];
        }
        for (int i = 0; i < z * 2; i++){
            P[i] *= Q_n[i];
            Q[i] *= Q_n[i];
        }
        FPS_pick_even_odd(P, k & 1);
        FPS_pick_even_odd(Q, 0);
        k /= 2;
        if (k == 0) break;
        FPS_extend(P);
        FPS_extend(Q);
    }
    T SP = 0, SQ = 0;
    for (int i = 0; i < z; i++) SP += P[i], SQ += Q[i];
    return SP / SQ;

    // simple
    /*
    while (k){
        auto n_Q = Q;
        for (int i = 0; i < int(Q.size()); i++){
            if (i & 1) n_Q[i] *= -1;
        }
        auto n_P = atcoder::convolution(P, n_Q);
        n_Q = atcoder::convolution(Q, n_Q);
        for (int i = 0; i < int(Q.size()); i++){
            Q[i] = n_Q[i * 2];
        }
        P.clear();
        for (int i = (k & 1); i < int(n_P.size()); i += 2){
            P.push_back(n_P[i]);
        }
        k >>= 1;
    }
    return P[0] / Q[0];
    */
}

template<class T>
// 0 = a[i] * c[0] + a[i - 1] * c[1] + a[i - 2] * c[2] + ... + a[i - d] * c[d]
// a.size() + 1 == c.size()
// c[0] = - 1 ?
// return a[k]
T Kth_Linear(long long k, std::vector<T> a, std::vector<T> c){
    int d = a.size();
    assert(d + 1 == int(c.size()));
    std::vector<T> P = atcoder::convolution(a, c);
    P.resize(d);
    return Boston_Mori(k, P, c);
}
};
#line 26 "d.cpp"
using mint = atcoder::modint998244353;

void solve();
// POP'N ROLL MUSIC / TOMOO
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int t = 1;
    cin >> t;
    rep(i, 0, t) solve();
}

void solve(){
    vector<mint> A = {0, 0, 0, 1};
    vector<mint> B = {1, -3, 3, -1};
    vector<mint> f = {1, - ((mint::mod() + 1) / 2)};
    B = atcoder::convolution(B, f);
    for (auto &x : B) x *= 2;
    rep(i, 0, 4) B[i] -= A[i];
    B = atcoder::convolution(B, {1, -1});
    A = atcoder::convolution(A, f);
    ll N;
    cin >> N;
    mint ans = po167::Boston_Mori(N, A, B).val();
    ans *= (mint(2)).pow(N);
    cout << ans.val() << "\n";
}

/*
 * 2 が 3 の倍数個必要
 * 2 の間に -1 が一つでもあればとりあえずはいい
 * そうでない場合、どうする？
 * 最短で打ち切ることにして、(x / (1 - x))^3 * ((1 / 2)/ (1 - x / 2))
 * 残りが 1 + x / (1 - (1 / 2) x)
 * 大変だ
 */
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