#1100185 (C++17) No.3190 Scoring

提出ソース
結果

問題	No.3190 Scoring
ユーザー	👑 potato167
提出日時	2025-06-20 22:26:29
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	1,579 ms / 10,000 ms
コード長	12,811 bytes
コンパイル時間	3,725 ms
コンパイル使用メモリ	251,192 KB
実行使用メモリ	73,268 KB
最終ジャッジ日時	2025-06-20 22:27:07
合計ジャッジ時間	32,712 ms
ジャッジサーバーID （参考情報）	judge4 / judge3
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 * 32
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ソースコード

raw source code
//#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/Multipoint_Evaluation.hpp"
//#include "po167_library/math/Binomial.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(){
//    int N, S, M;
//    cin >> N >> S >> M;
//    if (N == 1){
//        cout << S << "\n";
//        return;
//    }
//    mint ans = 0;
//    po167::Binomial<mint> table;
//    mint pro_sum = table.ruiseki(S, N);
//    vector<mint> f(M + 1);
//    rep(i, 0, (M + 2) / 2){
//        f[i] = table.C(M, i);
//        f[i] *= table.fact(i);
//    }
//    reverse(all(f));
//    vector<mint> g(M + 1);
//    rep(i, 0, M + 1){
//        g[i] = table.invfact(i) * (i & 1 ? -1 : 1);
//    }
//    f = atcoder::convolution(f, g);
//    f.resize(M + 1);
//    rep(i, 0, M + 1) f[i] *= table.invfact(M - i);
//    mint inv = pro_sum.inv();
//    mint tmp = 1;
//    vector<mint> X(S);
//    rep(i, 0, S){
//        tmp -= table.ruiseki(S - i, N - 1) * inv;
//        X[i] = tmp;
//    }
//    auto Y = po167::Multipoint_Evaluation(f, X);
//    for (auto x : Y) ans += x;
//    ans *= N;
//    cout << ans.val() << "\n";
//}
//
#line 1 "g.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 2 "/Users/Shared/po167_library/fps/Multipoint_Evaluation.hpp"
#include <atcoder/convolution>
#line 4 "/Users/Shared/po167_library/fps/FPS_division.hpp"

#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 6 "/Users/Shared/po167_library/fps/FPS_division.hpp"
namespace po167{
template<class T>
// f = g * res.first + res.second
// |res.first| <= |f| - |g| + 1
// |res.second| <= |g| - 1
std::pair<std::vector<T>, std::vector<T>>
FPS_division(std::vector<T> f, std::vector<T> g){
    while (!f.empty() && f.back() == 0) f.pop_back();
    assert(!g.empty() && g.back() != 0);
    if (f.size() < g.size()){
        return {{}, f};
    }
    // rev(f) / rev(g) = rev(q) (mod x ^ {|f| - |g| + 1})
    std::vector<T> r = f;
    std::reverse(f.begin(), f.end());
    std::reverse(g.begin(), g.end());
    int z = (int)f.size() - (int)g.size() + 1;
    f.resize(z);
    std::vector<T> q = atcoder::convolution(f, FPS_inv(g, z));
    q.resize(z);
    std::reverse(g.begin(), g.end());
    std::reverse(q.begin(), q.end());
    f = atcoder::convolution(q, g);
    for (int i = 0; i < (int)f.size(); i++) r[i] -= f[i];
    while (!q.empty() && q.back() == 0) q.pop_back();
    while (!r.empty() && r.back() == 0) r.pop_back();
    return {q, r};
}
}
#line 4 "/Users/Shared/po167_library/fps/Multipoint_Evaluation.hpp"

namespace po167{
// return {f(p[0]), f(p[1]), f(p[2]), ... }
template <class T>
std::vector<T> Multipoint_Evaluation(
    std::vector<T> f,
    std::vector<T> p
){
    int m = p.size();
    if (m == 0) return {};
    if (m == 1){
        T res = 0;
        T tmp = 1;
        for (auto x : f) res += tmp * x, tmp *= p[0];
        return {res};
    }
    int size = 1;
    while (size < m) size *= 2;
    std::vector<std::vector<T>> prod(size * 2);
    for (int i = 0; i < size; i++){
        if (i < m) prod[i + size] = {(T)(-1) * p[i], 1};
        else prod[i + size] = {1};
    }
    for (int i = size - 1; i > 0; i--){
        prod[i] = atcoder::convolution(prod[i * 2], prod[i * 2 + 1]);
    }
    std::vector<T> res(m);
    auto calc = [&](auto self, int l, int r, int ind, std::vector<T> tmp) -> void {
        if (m <= l) return;
        if (l + 1 == r){
            res[l] = (tmp.empty() ? T(0) : tmp[0]);
            return;
        }
        int mid = (l + r) / 2;
        self(self, l, mid, ind * 2, po167::FPS_division(tmp, prod[ind * 2]).second);
        self(self, mid, r, ind * 2 + 1, po167::FPS_division(tmp, prod[ind * 2 + 1]).second);
    };calc(calc, 0, size, 1, f);
    return res;
}
}
#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 27 "g.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(){
    int N, S, M;
    cin >> N >> S >> M;
    if (N == 1){
        cout << S << "\n";
        return;
    }
    mint ans = 0;
    po167::Binomial<mint> table;
    mint pro_sum = table.ruiseki(S, N);
    vector<mint> f(M + 1);
    rep(i, 0, (M + 2) / 2){
        f[i] = table.C(M, i);
        f[i] *= table.fact(i);
    }
    reverse(all(f));
    vector<mint> g(M + 1);
    rep(i, 0, M + 1){
        g[i] = table.invfact(i) * (i & 1 ? -1 : 1);
    }
    f = atcoder::convolution(f, g);
    f.resize(M + 1);
    rep(i, 0, M + 1) f[i] *= table.invfact(M - i);
    mint inv = pro_sum.inv();
    mint tmp = 1;
    vector<mint> X(S);
    rep(i, 0, S){
        tmp -= table.ruiseki(S - i, N - 1) * inv;
        X[i] = tmp;
    }
    auto Y = po167::Multipoint_Evaluation(f, X);
    for (auto x : Y) ans += x;
    ans *= N;
    cout << ans.val() << "\n";
}
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結果

ソースコード
