#646864 (C++17) No.1510 Simple Integral

提出ソース
結果

問題	No.1510 Simple Integral
コンテスト
ユーザー	oliverx3
提出日時	2021-04-10 15:40:32
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	48 ms / 2,000 ms
コード長	13,805 bytes
コンパイル時間	4,756 ms
コンパイル使用メモリ	270,884 KB
最終ジャッジ日時	2025-01-20 15:43:04
ジャッジサーバーID （参考情報）	judge3 / 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 * 3
other	AC * 43
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ソースコード

raw source code
#include<bits/stdc++.h>
// using namespace std;
#if __has_include(<atcoder/all>)
#include<atcoder/all>
// using namespace atcoder;
#endif
#define int long long

#pragma region header

#pragma region alias

using lint = long long;
using ll = long long;
using P = std::pair<int,int>;
template<class T> using prique = std::priority_queue<T,std::vector<T>,std::greater<T>>;

#pragma endregion

#pragma region macros

#define rep(i, n) for(int i = 0;i<(int)(n);i++)
#define REP(i, m, n) for(int i = (m);i<(int)(n);i++)
#define drep(i, n) for(int i = (n)-1;i>=0;i--)
#define DREP(i, m, n) for(int i = (m)-1;i>=(int)(n);i--)
#define all(v) (v).begin(),(v).end()
#define reall(v) (v).rbegin(),(v).rend()

template<class T, class U>
bool chmax(T& a,const U b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T, class U>
bool chmin(T& a,const U b) {
    if(a>b) {
        a = b;
        return true;
    }
    return false;
}

std::map<int,int> prime_div(int n) {
    std::map<int,int> mp;
    if(~n&1) while(~n&1) n>>=1,mp[2]++;
    for(int i = 3;i<=std::sqrt(n);i+=2) {
        if(n%i==0) {
            while(n%i==0) {
                n/=i;
                mp[i]++;
            }
        }
    }
    if(n!=1) mp[n]++;
    return mp;
}

bool is_flag(const int &bit, const int &k) { return (bit >> k)&1; }

#pragma endregion

#pragma region constant

constexpr long long inf = 1LL << 61;
constexpr int dx[9] = {1, 0, -1, 0, 1, 1, -1, -1, 0};
constexpr int dy[9] = {0, 1, 0, -1, 1, -1, 1, -1, 0};
constexpr long long mod = 1e9+7;
constexpr long long MOD = 998244353;

#pragma endregion

#pragma region inout

template<class T>
std::ostream& operator<<(std::ostream& stream, const std::vector<T>& v) {
    for(int i = 0; i < (int)(v.size()); i++) {
        stream << v[i];
        if(i != (int)(v.size()) - 1) stream << ' ';
    }
    return stream;
}

template<typename Itr>
inline void print(const Itr& begin, const Itr& end, bool endline = true, const char* BEGIN = "{", const char* mid = ", ", const char* END = "}") {
    if(begin == end) return;
    std::cout << BEGIN << *begin;
    for(Itr itr = begin+1; itr < end; itr++) std::cout << mid << *itr;
    std::cout << END;
    if(endline) std::endl(std::cout);
    return;
}

template<class T>
std::istream& operator>>(std::istream& stream, std::vector<T>& v) {
    for(T& p:v) stream >> p;
    return stream;
}

template<typename Itr>
inline void input(Itr begin, Itr end) {
    for(Itr& itr = begin; itr < end; itr++) std::cin >> *itr;
    return;
}

template<class T, class U>
std::ostream& operator<<(std::ostream& stream, const std::pair<T,U>& pair) {
    return stream << pair.first << ' ' << pair.second;
}

template<class T, class U>
inline void print(const std::pair<T,U>& pair,const bool endline = true, const char* begin = "(", const char* mid = ", ", const char* end = ")") {
    std::cout << begin << pair.first << mid << pair.second << end;
    if(endline) std::endl(std::cout);
    else std::cout << ' ';
    return;
}

template<class T, class U>
std::istream& operator>>(std::istream& stream, std::pair<T,U>& pair) {
    return stream >> pair.first >> pair.second;
}

template<class T, class U>
inline void input(std::pair<T,U>& pair, const bool first = true, const bool second = true) {
    if(first) std::cin >> pair.first;
    if(second) std::cin >> pair.second;
}

#pragma endregion

#pragma region DEBUG

#ifdef _DEBUG
template<class T>
inline void _debug_view(const T& x) noexcept {
    std::cout << x;
    return;
}

template<class T, class U>
inline void _debug_view(const std::pair<T,U>& p) noexcept {
    std::cout << "(";
    _debug_view(p.first);
    std::cout << ", ";
    _debug_view(p.second);
    std::cout << ")";
    return;
}

template<class T>
inline void _debug_view(const std::vector<T>& v) noexcept {
    std::cout << "{";
    for(int i = 0;i<v.size();i++) {
        _debug_view(v[i]);
        std::cout << (i+1 == v.size() ? "" : ", ");
    }
    std::cout << "}";
    return;
}

template<class T, class U>
inline void _debug_view(const std::map<T,U>& mp) noexcept {
    std::cout << "{";
    for(auto itr = mp.begin(); itr != mp.end(); itr++) {
        _debug_view(*itr);
        if(std::next(itr) != mp.end()) std::cout << ", ";
    }
    std::cout << "}";
    return;
}

template<class T> 
inline void _debug_view(const std::set<T>& st) noexcept {
    std::cout << "{";
    for(auto itr = st.begin(); itr != st.end(); itr++) {
        _debug_view(*itr);
        if(std::next(itr) != st.end()) std::cout << ", ";
    }
    std::cout << "}";
    return;
}

#define overload5(_1,_2,_3,_4,_5,name,...) name

#define _debug1(a) {\
    do {\
        std::cout << #a << ": ";\
        _debug_view(a);\
        std::endl(std::cout);\
    }while(0);\
}

#define _debug2(a,b) {\
    do {\
        std::cout << #a << ": ";\
        _debug_view(a);\
        std::cout << ", " << #b << ": ";\
        _debug_view(b);\
        std::endl(std::cout);\
    }while(0);\
}

#define _debug3(a,b,c) {\
    do {\
        std::cout << #a << ": ";\
        _debug_view(a);\
        std::cout << ", " << #b << ": ";\
        _debug_view(b);\
        std::cout << ", " << #c << ": ";\
        _debug_view(c);\
        std::endl(std::cout);\
    }while(0);\
}

#define _debug4(a,b,c,d) {\
    do {\
        std::cout << #a << ": ";\
        _debug_view(a);\
        std::cout << ", " << #b << ": ";\
        _debug_view(b);\
        std::cout << ", " << #c << ": ";\
        _debug_view(c);\
        std::cout << ", " << #d << ": ";\
        _debug_view(d);\
        std::endl(std::cout);\
    }while(0);\
}

#define _debug5(a,b,c,d,e) {\
    do {\
        std::cout << #a << ": ";\
        _debug_view(a);\
        std::cout << ", " << #b << ": ";\
        _debug_view(b);\
        std::cout << ", " << #c << ": ";\
        _debug_view(c);\
        std::cout << ", " << #d << ": ";\
        _debug_view(d);\
        std::cout << ", " << #e << ": ";\
        _debug_view(e);\
        std::endl(std::cout);\
    }while(0);\
}

#define debug(...) overload5(__VA_ARGS__,_debug5,_debug4,_debug3,_debug2,_debug1,)(__VA_ARGS__)

#else
#define debug(...)
#endif

#pragma endregion

#pragma endregion

template<class T>
struct FormalPowerSeries : std::vector<T> {
    
    using std::vector<T>::vector;
    using std::vector<T>::operator=;
    using F = FormalPowerSeries;

    F operator-() const {
        F res(*this);
        for (auto &e : res) e = -e;
        return res;
    }
    F &operator*=(const T &g) {
        for (auto &e : *this) e *= g;
        return *this;
    }
    F &operator/=(const T &g) {
        assert(g != T(0));
        *this *= g.inv();
        return *this;
    }
    F &operator+=(const F &g) {
        int n = (*this).size(), m = g.size();
        rep(i, std::min(n, m)) (*this)[i] += g[i];
        return *this;
    }
    F &operator-=(const F &g) {
        int n = (*this).size(), m = g.size();
        rep(i, std::min(n, m)) (*this)[i] -= g[i];
        return *this;
    }
    F &operator<<=(const int d) {
        int n = (*this).size();
        (*this).insert((*this).begin(), d, 0);
        (*this).resize(n);
        return *this;
    }
    F &operator>>=(const int d) {
        int n = (*this).size();
        (*this).erase((*this).begin(), (*this).begin() + std::min(n, d));
        (*this).resize(n);
        return *this;
    }
    F inv(int d = -1) const {
        int n = (*this).size();
        assert(n != 0 && (*this)[0] != 0);
        if (d == -1) d = n;
        assert(d > 0);
        F res{(*this)[0].inv()};
        while (res.size() < d) {
        int m = size(res);
        F f(begin(*this), begin(*this) + std::min(n, 2*m));
        F r(res);
        f.resize(2*m), atcoder::internal::butterfly(f);
        r.resize(2*m), atcoder::internal::butterfly(r);
        rep(i, 2*m) f[i] *= r[i];
        atcoder::internal::butterfly_inv(f);
        f.erase(f.begin(), f.begin() + m);
        f.resize(2*m), atcoder::internal::butterfly(f);
        rep(i, 2*m) f[i] *= r[i];
        atcoder::internal::butterfly_inv(f);
        T iz = T(2*m).inv(); iz *= -iz;
        rep(i, m) f[i] *= iz;
        res.insert(res.end(), f.begin(), f.begin() + m);
        }
        return {res.begin(), res.begin() + d};
    }

    // fast: FMT-friendly modulus only
    F &operator*=(const F &g) {
      int n = (*this).size();
      *this = convolution(*this, g);
      (*this).resize(n);
      return *this;
    }
    F &operator/=(const F &g) {
      int n = (*this).size();
      *this = convolution(*this, g.inv(n));
      (*this).resize(n);
      return *this;
    }

    // // naive
    // F &operator*=(const F &g) {
    //   int n = (*this).size(), m = g.size();
    //   drep(i, n) {
    //     (*this)[i] *= g[0];
    //     REP(j, 1, std::min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j];
    //   }
    //   return *this;
    // }
    // F &operator/=(const F &g) {
    //   assert(g[0] != T(0));
    //   T ig0 = g[0].inv();
    //   int n = (*this).size(), m = g.size();
    //   rep(i, n) {
    //     REP(j, 1, std::min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j];
    //     (*this)[i] *= ig0;
    //   }
    //   return *this;
    // }

    // sparse
    F &operator*=(std::vector<std::pair<int, T>> g) {
        int n = (*this).size();
        auto [d, c] = g.front();
        if (d == 0) g.erase(g.begin());
        else c = 0;
        drep(i, n) {
        (*this)[i] *= c;
        for (auto &[j, b] : g) {
            if (j > i) break;
            (*this)[i] += (*this)[i-j] * b;
        }
        }
        return *this;
    }
    F &operator/=(std::vector<std::pair<int, T>> g) {
        int n = (*this).size();
        auto [d, c] = g.front();
        assert(d == 0 && c != T(0));
        T ic = c.inv();
        g.erase(g.begin());
        rep(i, n) {
        for (auto &[j, b] : g) {
            if (j > i) break;
            (*this)[i] -= (*this)[i-j] * b;
        }
        (*this)[i] *= ic;
        }
        return *this;
    }

    // multiply and divide (1 + cz^d)
    void multiply(const int d, const T c) { 
        int n = (*this).size();
        if (c == T(1)) drep(i, n-d) (*this)[i+d] += (*this)[i];
        else if (c == T(-1)) drep(i, n-d) (*this)[i+d] -= (*this)[i];
        else drep(i, n-d) (*this)[i+d] += (*this)[i] * c;
    }
    void divide(const int d, const T c) {
        int n = (*this).size();
        if (c == T(1)) rep(i, n-d) (*this)[i+d] -= (*this)[i];
        else if (c == T(-1)) rep(i, n-d) (*this)[i+d] += (*this)[i];
        else rep(i, n-d) (*this)[i+d] -= (*this)[i] * c;
    }

    T eval(const T &a) const {
        T x(1), res(0);
        for (auto e : *this) res += e * x, x *= a;
        return res;
    }

    F operator*(const T &g) const { return F(*this) *= g; }
    F operator/(const T &g) const { return F(*this) /= g; }
    F operator+(const F &g) const { return F(*this) += g; }
    F operator-(const F &g) const { return F(*this) -= g; }
    F operator<<(const int d) const { return F(*this) <<= d; }
    F operator>>(const int d) const { return F(*this) >>= d; }
    F operator*(const F &g) const { return F(*this) *= g; }
    F operator/(const F &g) const { return F(*this) /= g; }
    F operator*(std::vector<std::pair<int, T>> g) const { return F(*this) *= g; }
    F operator/(std::vector<std::pair<int, T>> g) const { return F(*this) /= g; }
};

using mint = atcoder::modint998244353;
using fps = FormalPowerSeries<mint>;
using sfps = std::vector<std::pair<int,mint>>;

const int MAX = 210;

long long fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}

// 二項係数計算
long long COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}


signed main() {
    COMinit();
    int n;
    std::cin >> n;
    std::vector<int> v(n);
    std::cin >> v;
    std::vector<int> a,c;
    std::map<int,int> mp;
    for(const auto &p:v) mp[p]++;
    for(const auto &p:mp) a.push_back(p.first),c.push_back(p.second);
    n = a.size();
    // debug(a,c);
    mint final_ans = 0;
    rep(i, n) {
        fps f;
        f.resize(c[i]);
        f[0] = 1;
        {//最初の式
            fps Y;
            Y.resize(c[i]);
            Y[1] = 1;
            fps sub_f;
            sub_f.resize(c[i]);
            sub_f[0] = 1;
            rep(k, n) {
                if(i==k) continue;
                rep(_j, c[k]) {
                    Y[0] = a[k]*a[k]-a[i]*a[i];
                    sub_f *= Y;
                }
            }
            f*=sub_f;
            // rep(i, 2) std::cout << f[i].val() << " \n"[i==1];
        }

        mint A = f[0];
        
        fps g = f;
        g[0] = 0;
        
        rep(j, c[i]) f[j] = 0;

        rep(k, c[i]) {//2番目の式
            fps sub_f;
            sub_f.resize(c[i]);
            sub_f[0] = 1;
            rep(_j, k) {
                sub_f*=g;
                sub_f/=A;
                sub_f*=-1;
            }
            f+=sub_f;
        }

        std::vector<mint> p(c[i]);
        rep(j, c[i]) p[j] = f[j];

        // rep(i, 3) std::cout << p[i].val() << " \n"[i==2];

        mint ans = 0;
        rep(j, c[i]) {
            mint x;
            x = COM(2*c[i]-2*j,c[i]-j)*(c[i]-j)*p[j];
            mint a_i = a[i];
            x /= (2*a_i).pow(2*c[i]-2*j) * (2*c[i]-2*j-1);
            ans+=x;
        }
        ans*=2*a[i];
        // debug(A.val());
        ans/=A;
        
        final_ans+=ans;
    }
    std::cout << final_ans.val() << std::endl;
    return 0;
}
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結果

ソースコード
