#1007976 (C++17) No.2877 Gunegune Hyperion

提出ソース

結果

問題	No.2877 Gunegune Hyperion
ユーザー	👑 potato167
提出日時	2024-09-06 23:27:49
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	317 ms / 6,000 ms
コード長	9,475 bytes
コンパイル時間	4,282 ms
コンパイル使用メモリ	256,512 KB
実行使用メモリ	17,100 KB
最終ジャッジ日時	2024-09-06 23:28:35
合計ジャッジ時間	8,608 ms
ジャッジサーバーID （参考情報）	judge1 / judge5

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 6,812 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	43 ms 6,944 KB
testcase_04	AC	74 ms 6,940 KB
testcase_05	AC	63 ms 8,444 KB
testcase_06	AC	61 ms 10,688 KB
testcase_07	AC	157 ms 11,476 KB
testcase_08	AC	155 ms 11,152 KB
testcase_09	AC	95 ms 9,140 KB
testcase_10	AC	179 ms 14,632 KB
testcase_11	AC	151 ms 9,552 KB
testcase_12	AC	14 ms 6,940 KB
testcase_13	AC	30 ms 6,940 KB
testcase_14	AC	24 ms 6,940 KB
testcase_15	AC	151 ms 9,316 KB
testcase_16	AC	317 ms 17,100 KB
testcase_17	AC	77 ms 14,852 KB
testcase_18	AC	46 ms 6,948 KB
testcase_19	AC	49 ms 7,256 KB
testcase_20	AC	3 ms 6,940 KB
testcase_21	AC	179 ms 14,712 KB
testcase_22	AC	63 ms 8,716 KB
testcase_23	AC	126 ms 15,552 KB
testcase_24	AC	179 ms 13,412 KB
testcase_25	AC	201 ms 17,020 KB
testcase_26	AC	48 ms 6,940 KB
testcase_27	AC	73 ms 10,304 KB
testcase_28	AC	130 ms 14,336 KB
testcase_29	AC	200 ms 17,024 KB
testcase_30	AC	128 ms 14,456 KB
testcase_31	AC	200 ms 17,020 KB
testcase_32	AC	62 ms 12,852 KB

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ソースコード

raw source code

/*
 * [x ^ {a - 1}]f(x) := 最初に真横になるのが a 日目である確率
 * [x ^ {a}]g(x) := 真横になった日から次に真横になるまで a 日間かかる確率
 * 以上の二つがもとまっているとき、
 * 「fg^{N - H} の (N - 1) 次までの係数の和」
 * は
 * 「高さが H 未満になる確率」
 * と同じになるので、1 からそれを引くと答えが求まる。
 * K = 3 として、
 * f, g (mod x ^{N}) は O(NK^2)
 * fg^{N - H} (mod x^{N}) は log-exp を用いて O(N log(N)) で求まる
 */

#line 1 "a.cpp"
#include <bits/stdc++.h>
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
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> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll 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(a>b){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=0){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> bool inside(T l,T x,T r){return l<=x&&x<r;}

#include <atcoder/modint>
using mint = atcoder::modint998244353;
#line 2 "/Users/Shared/po167_library/fps/FPS_pow.hpp"

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

#line 4 "/Users/Shared/po167_library/fps/FPS_cyclic_convolution.hpp"

namespace po167{
// |f| = |g| = 2 ^ n
    template<class T>
    std::vector<T> FPS_cyclic_convolution(std::vector<T> f, std::vector<T> g){
        atcoder::internal::butterfly(f);
        atcoder::internal::butterfly(g);
        for (int i = 0; i < (int)f.size(); i++) f[i] *= g[i];
        atcoder::internal::butterfly_inv(f);
        T iz = (T)(1) / (T)(f.size());
        for (int i = 0; i < (int)f.size(); i++) f[i] *= iz;
        return f;
    }
}
#line 3 "/Users/Shared/po167_library/fps/FPS_differetial.hpp"

namespace po167{
// return f'
    template <class T>
    std::vector<T> FPS_differential(std::vector<T> f){
        if (f.empty()) return f;
        for (int i = 0; i < (int)f.size() - 1; i++){
            f[i] = f[i + 1] * (T)(i + 1);
        }
        f.pop_back();
        return f;
    }
}
#line 3 "/Users/Shared/po167_library/fps/FPS_integral.hpp"

namespace po167{
    template <class T>
    std::vector<T> FPS_integral(std::vector<T> f){
        if (f.empty()) return f;
        std::vector<T> num_inv((int)f.size() + 1);
        num_inv[0] = 1;
        num_inv[1] = 1;
        auto m = T::mod();
        for (int i = 2; i <= (int)f.size(); i++){
            num_inv[i] = (0 - num_inv[m % i]) * (T)(m / i);
        }
        f.reserve((int)f.size() + 1);
        f.push_back(0);
        for (int i = (int)f.size() - 1; i > 0; i--){
            f[i] = f[i - 1] * num_inv[i];
        }
        f[0] = 0;
        return f;
    }
}
#line 4 "/Users/Shared/po167_library/fps/FPS_inv.hpp"

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 8 "/Users/Shared/po167_library/fps/FPS_exp.hpp"

namespace po167{
    template<class T>
    std::vector<T> FPS_exp(std::vector<T> f, int len = -1){
        if (len == -1) len = f.size();
        if (len == 0) return {};
        if (len == 1) return {T(1)};
        assert(!f.empty() && f[0] == 0);
        int s = 1;
        // simple
        std::vector<T> g = {T(1)};
        while (s < len){
            // g' / g
            // A * B
            std::vector<T> A = g, B = g;
            A = FPS_differential(A);
            B = FPS_inv(B, 2 * s);
            A.resize(2 * s);
            A = FPS_cyclic_convolution(A, B);
            A.pop_back();
            A = FPS_integral(A);
            for (int i = 0; i < s; i++) A[i] = 0;
            for (int i = s; i < s * 2; i++) A[i] = (i < (int)f.size() ? f[i] : 0) - A[i];
            // g_hat = g (1 - g + f)
            // g += B = g * A
            g.resize(2 * s);
            B = FPS_cyclic_convolution(A, g);
            for (int i = s; i < s * 2; i++) g[i] = B[i];
            s *= 2;
        }
        g.resize(len);
        return g;
    }
}
#line 5 "/Users/Shared/po167_library/fps/FPS_log.hpp"

namespace po167{
    template<class T>
    std::vector<T> FPS_log(std::vector<T> f, int len = -1){
        if (len == -1) len = f.size();
        if (len == 0) return {};
        if (len == 1) return {T(0)};
        assert(!f.empty() && f[0] == 1);
        std::vector<T> res = atcoder::convolution(FPS_differential(f), FPS_inv(f, len));
        res.resize(len - 1);
        return FPS_integral(res);
    }
}
#line 8 "/Users/Shared/po167_library/fps/FPS_pow.hpp"

namespace po167{
    template<class T>
    std::vector<T> FPS_pow(std::vector<T> f,long long M, int len = -1){
        if (len == -1) len = f.size();
        std::vector<T> res(len, 0);
        if (M == 0){
            res[0] = 1;
            return res;
        }
        for (int i = 0; i < (int)f.size(); i++){
            if (f[i] == 0) continue;
            if (i > (len - 1) / M) break;
            std::vector<T> g((int)f.size() - i);
            T v = (T)(1) / (T)(f[i]);
            for (int j = i; j < (int)f.size(); j++){
                g[j - i] = f[j] * v;
            }
            long long zero = i * M;
            if (i) len -= i * M;
            g = FPS_log(g, len);
            for (T &x : g) x *= M;
            g = FPS_exp(g, len);
            v = (T)(1) / v;
            T c = 1;
            while (M){
                if (M & 1) c = c * v;
                v = v * v;
                M >>= 1;
            }
            for (int i = 0; i < len; i++) res[i + zero] = g[i] * c;
            return res;
        }
        return res;
    }
}
#line 32 "a.cpp"

void solve();
// CYAN / FREDERIC
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

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

void solve(){
    ll N, H;
    cin >> N >> H;
    vector base(2, vector<mint>(N));
    vector<mint> inv(6);
    rep(i, 1, 6) inv[i] = (mint)(1) / (mint)(i);
    vector to(3, vector<mint>(3));
    to[0][0] = inv[2];
    to[0][1] = inv[2];
    to[1][0] = inv[3];
    to[1][1] = inv[3];
    to[1][2] = inv[3];
    to[2][1] = inv[3] * 2;
    to[2][2] = inv[3];
    rep(i, 0, 2){
        vector<mint> dp(3);
        if (i == 0) dp[0] = 1;
        else dp[1] = 2, dp[2] = 1;
        rep(j, 0, N - 1){
            vector<mint> n_dp(3);
            rep(n, 0, 3) rep(m, 0, 3) n_dp[m] += dp[n] * to[n][m];
            swap(n_dp, dp);
            for (int k = 0; k < 3; k += 3){
                base[i][j + 1] += dp[k];
                dp[k] = 0;
            }
        }
    }
    vector<mint> f(N), g = base[0];
    rep(i, 0, 2){
        if (i == 0) f[0] += inv[5] * 2;
        else rep(j, 0, N) f[j] += base[i][j] * inv[5];
    }
    auto gp = po167::FPS_pow(g, N - H);
    f = atcoder::convolution(f, gp);
    f.resize(N);
    cout << (1 - vec_sum(f)).val() << "\n";
}

yukicoder

結果

テストケース

ソースコード