結果

問題 No.1289 RNG and OR
ユーザー tokusakuraitokusakurai
提出日時 2020-11-14 16:27:16
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 109 ms / 2,000 ms
コード長 7,655 bytes
コンパイル時間 2,667 ms
コンパイル使用メモリ 207,284 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-22 23:09:01
合計ジャッジ時間 2,902 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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 2 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 1 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 3 ms
5,376 KB
testcase_14 AC 4 ms
5,376 KB
testcase_15 AC 5 ms
5,376 KB
testcase_16 AC 8 ms
5,376 KB
testcase_17 AC 14 ms
5,376 KB
testcase_18 AC 28 ms
5,376 KB
testcase_19 AC 55 ms
5,376 KB
testcase_20 AC 109 ms
5,376 KB
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 rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define each(e, v) for(auto &e: v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
#define pq(type, name) priority_queue<type> name
#define iq(type, name) priority_queue<type, vector<type>, greater<type>> name
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
const double pi = acos(-1.0);
const double EPS = 1e-10;
template<typename T> bool chmax(T &x, const T &y){
    if(x < y) {x = y; return true;}
    return false;
}
template<typename T> bool chmin(T &x, const T &y){
    if(x > y) {x = y; return true;}
    return false;
}
void in() {}
template<typename Head, typename ...Tail> void in(Head &&head, Tail &&...tail){
    cin >> head;
    in(forward<Tail>(tail)...);
}
void out() {cout << '\n';}
template<typename Head, typename ...Tail> void out(Head &&head, Tail &&...tail){
    cout << head << ' ';
    out(forward<Tail>(tail)...);
}
void outn() {}
template<typename Head, typename ...Tail> void outn(Head &&head, Tail &&...tail){
    cout << head << '\n';
    outn(forward<Tail>(tail)...);
}
template<typename T, typename U> void in(pair<T, U> &p){
    cin >> p.first >> p.second;
}
template<typename T, typename U> void out(pair<T, U> p){
    cout << p.first << ' ' << p.second << '\n';
}
using vi = vector<int>;
using vll = vector<ll>;
#define vec1(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC1(type, ...) vector<type>(__VA_ARGS__)
#define vec2(type, name, a, ...) vector<vector<type>> name(a, VEC1(type, __VA_ARGS__))
#define VEC2(type, a, ...) vector<vector<type>>(a, VEC1(type, __VA_ARGS__))
#define vec3(type, name, a, b, ...) vector<vector<vector<type>>> name(a, VEC2(type, b, __VA_ARGS__))
#define VEC3(type, a, b, ...) vector<vector<vector<type>>>(a, VEC2(type, b, __VA_ARGS__))
#define vec4(type, name, a, b, c, ...) vector<vector<vector<vector<type>>>> name(a, VEC3(type, b, c, __VA_ARGS__))
#define VEC4(type, a, b, c, ...) vector<vector<vector<vector<type>>>>(a, VEC3(type, b, c, __VA_ARGS__))
#define vec5(type, name, a, b, c, d, ...) vector<vector<vector<vector<vector<type>>>>> name(a, VEC4(type, b, c, d, __VA_ARGS__))
#define VEC5(type, a, b, c, d, ...) vector<vector<vector<vector<vector<type>>>>>(a, VEC4(type, b, c, d, __VA_ARGS__))
template<typename T> void vin(vector<T> &a){
    rep(i, sz(a)) cin >> a[i];
}
template<typename T> void vout(const vector<T> &a){
    for(auto &e: a) cout << e << ' ';
    cout << '\n';
}
template<typename T> void voutn(const vector<T> &a){
    for(auto &e: a) cout << e << '\n';
}
template<typename T> void unique(vector<T> &a){
    sort(all(a)), a.erase(unique(all(a)), a.end());
}
vector<int> iota(int n){
    vector<int> ret(n);
    iota(all(ret), 0);
    return ret;
}
template<typename T> vector<int> iota(const vector<T> &a, bool greater = false){
    vector<int> ret = iota(sz(a));
    sort(all(ret), [&](int i, int j){
        return (a[i] < a[j])^greater;
    });
    return ret;
}
struct io_setup{
    io_setup(){
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;
#define VEC(type, name, n) vector<type> name(n); vin(name)
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define CHAR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
//const int MOD = 1000000007;
const int MOD = 998244353;

template<int mod>
struct Mod_Int{
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(ll y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    Mod_Int &operator += (const Mod_Int &p){
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator -= (const Mod_Int &p){
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator *= (const Mod_Int &p){
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator /= (const Mod_Int &p){
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator ++ () {return *this += Mod_Int(1);}

    Mod_Int operator ++ (int){
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator -- () {return *this -= Mod_Int(1);}

    Mod_Int operator -- (int){
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator - () const {return Mod_Int(-x);}

    Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;}

    Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;}

    Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;}

    Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;}

    bool operator == (const Mod_Int &p) const {return x == p.x;}

    bool operator != (const Mod_Int &p) const {return x != p.x;}

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod-2);
    }

    Mod_Int pow(ll k) const{
        Mod_Int now = *this, ret = 1;
        for(; k; k >>= 1, now *= now){
            if(k&1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator << (ostream &os, const Mod_Int &p){
        return os << p.x;
    }

    friend istream &operator >> (istream &is, Mod_Int &p){
        ll a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

template<int mod>
struct Combination{
    using Mint = Mod_Int<mod>;
    vector<Mint> _fac, _ifac;

    Combination(int n){
        _fac.resize(n+1), _ifac.resize(n+1);
        _fac[0] = 1;
        rep2(i, 1, n) _fac[i] = _fac[i-1]*i;
        _ifac[n] = _fac[n].inverse();
        rep3(i, n, 1) _ifac[i-1] = _ifac[i]*i;
    }

    Mint fac(int k) const {return _fac[k];}

    Mint ifac(int k) const {return _ifac[k];}

    Mint comb(int n, int k) const{
        if(k < 0 || n < k) return 0;
        return fac(n) * ifac(n-k) * ifac(k);
    }

    Mint perm(int n, int k) const{
        if(k < 0 || n < k) return 0;
        return fac(n) * ifac(n-k);
    }

    Mint second_stirling_number(ll n, int k){ //n個の区別できるボールをk個の区別できない箱に分割
        Mint ret = 0;
        rep(i, k+1){
            Mint tmp = comb(k, i)*Mint(k-i).pow(n);
            ret += ((i&1)? -tmp : tmp);
        }
        return ret*ifac(k);
    }
};

using mint = Mod_Int<MOD>;
using comb = Combination<MOD>;

template<typename T>
void Fast_Zeta_Transform(vector<T> &f, int n, bool upper){
    rep(j, n){
        rep(i, 1<<n){
            if(upper && !(i&(1<<j))) f[i] += f[i|(1<<j)];
            if(!upper && (i&(1<<j))) f[i] += f[i&~(1<<j)];
        }
    }
}

template<typename T>
void Fast_Mobius_Transform(vector<T> &g, int n, bool upper){
    rep(j, n){
        rep(i, 1<<n){
            if(upper && !(i&(1<<j))) g[i] -= g[i|(1<<j)];
            if(!upper && (i&(1<<j))) g[i] -= g[i&~(1<<j)];
        }
    }
}

int main(){
    INT(N);
    VEC(mint, A, (1<<N));
    mint S = 0;
    each(e, A) S += e;
    Fast_Zeta_Transform(A, N, false);
    mint ans = 0;
    rep(i, 1<<N){
        int k = N-__builtin_popcount(i);
        if(k == 0) continue;
        mint P = A[i]/S;
        if(k&1) ans += (-P+1).inverse();
        else ans -= (-P+1).inverse();
    }
    out(ans);
}
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