結果

問題 No.1289 RNG and OR
ユーザー minatominato
提出日時 2021-01-04 09:47:29
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 130 ms / 2,000 ms
コード長 8,512 bytes
コンパイル時間 2,309 ms
コンパイル使用メモリ 211,760 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-10-14 10:31:11
合計ジャッジ時間 3,757 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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
6,816 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 2 ms
6,820 KB
testcase_03 AC 3 ms
6,816 KB
testcase_04 AC 2 ms
6,820 KB
testcase_05 AC 2 ms
6,816 KB
testcase_06 AC 2 ms
6,820 KB
testcase_07 AC 2 ms
6,816 KB
testcase_08 AC 2 ms
6,816 KB
testcase_09 AC 2 ms
6,816 KB
testcase_10 AC 2 ms
6,816 KB
testcase_11 AC 2 ms
6,820 KB
testcase_12 AC 2 ms
6,820 KB
testcase_13 AC 3 ms
6,816 KB
testcase_14 AC 3 ms
6,816 KB
testcase_15 AC 5 ms
6,820 KB
testcase_16 AC 10 ms
6,820 KB
testcase_17 AC 17 ms
6,816 KB
testcase_18 AC 29 ms
6,816 KB
testcase_19 AC 62 ms
6,820 KB
testcase_20 AC 130 ms
6,816 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;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template<class T> using vec = vector<T>;
template<class T> using vvec = vector<vector<T>>;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--)
#define all(x) (x).begin(), (x).end()
constexpr char ln = '\n';
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
    return os << "(" << p.first << ", " << p.second << ")";
}
template<class T> 
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    for (int i = 0; i < int(v.size()); i++) {
        if (i) os << ", ";
        os << v[i];
    }
    return os << "}";
}
template<class Container> inline int SZ(Container& v) { return int(v.size()); }
template<class T> inline void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template<class T1, class T2> inline bool chmax(T1& a, T2 b) { if (a < b) {a = b; return true ;} return false ;}
template<class T1, class T2> inline bool chmin(T1& a, T2 b) { if (a > b) {a = b; return true ;} return false ;}
inline int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
inline int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
inline int popcount(ull x) { return __builtin_popcountll(x); }
inline int kthbit(ull x, int k) { return (x>>k) & 1; }
inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x-1) * 10; }
inline void print() { cout << "\n"; }
template<class T>
inline void print(const vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        if (i) cout << " ";
        cout << v[i];
    }
    print();
}
template<class T, class... Args>
inline void print(const T& x, const Args& ... args) {
    cout << x << " ";
    print(args...);
}
#ifdef MINATO_LOCAL
inline void debug_out() { cerr << endl; }
template <class T, class... Args>
inline void debug_out(const T& x, const Args& ... args) {
    cerr << " " << x;
    debug_out(args...);
}
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

template<int m> 
struct ModInt {
  public:
    static constexpr int mod() { return m; }
    static ModInt raw(int v) {
        ModInt x;
        x._v = v;
        return x;
    }

    ModInt() : _v(0) {}
    ModInt(long long v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }

    unsigned int val() const { return _v; }

    ModInt& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    ModInt& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    ModInt operator++(int) {
        ModInt result = *this;
        ++*this;
        return result;
    }
    ModInt operator--(int) {
        ModInt result = *this;
        --*this;
        return result;
    }

    ModInt& operator+=(const ModInt& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    ModInt& operator*=(const ModInt& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    ModInt& operator^=(long long n) {
        ModInt x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) { return *this = *this * rhs.inv(); }

    ModInt operator+() const { return *this; }
    ModInt operator-() const { return ModInt() - *this; }

    ModInt pow(long long n) const {
        ModInt r = *this;
        r ^= n;
        return r;
    }
    ModInt inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (; ; ) {
            t = a / b; a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return ModInt(b * z);
            }
            y -= t * z;
            t = b / a; b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return ModInt(a * y);
            }
            z -= t * y;
        }
    }

    friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; }
    friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; }
    friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; }
    friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; }
    friend ModInt operator^(const ModInt& lhs, long long rhs) { return ModInt(lhs) ^= rhs; }
    friend bool operator==(const ModInt& lhs, const ModInt& rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) { return lhs._v != rhs._v; }
    friend ModInt operator+(long long lhs, const ModInt& rhs) { return (ModInt(lhs) += rhs); }
    friend ModInt operator-(long long lhs, const ModInt& rhs) { return (ModInt(lhs) -= rhs); }
    friend ModInt operator*(long long lhs, const ModInt& rhs) { return (ModInt(lhs) *= rhs); }
    friend ostream& operator<<(ostream& os, const ModInt& M) { return os << M._v; }
    friend istream& operator>>(istream& is, ModInt& M) {
        long long x; is >> x;
        M = ModInt(x);
        return is;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
};

//constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;

using mint = ModInt<MOD>;

struct ModCombination {
  private:
    int max_n;
    vector<mint> fac_,facinv_;

  public:
    ModCombination() {}
    ModCombination(int n) : max_n(n), fac_(n+1), facinv_(n+1) {
        assert(1 <= n);
        fac_[0] = 1;
        for (int i = 1; i <= n; i++) fac_[i] = fac_[i-1]*i;
        facinv_[n] = fac_[n].inv();
        for (int i = n; i >= 1; i--) facinv_[i-1] = facinv_[i]*i;
    }

    mint fac(int k) const { 
        assert(0 <= k and k <= max_n);
        return fac_[k]; 
    }
    mint facinv(int k) const {
        assert(0 <= k and k <= max_n); 
        return facinv_[k]; 
    }
    mint invs(int k) const { 
        assert(1 <= k and k <= max_n);
        return facinv_[k]*fac_[k-1]; 
    }

    mint P(int n, int k) const {
        if (k < 0 or k > n) return mint(0);
        assert(n <= max_n);
        return fac_[n]*facinv_[n-k];
    }
    mint C(int n, int k) const {
        if (k < 0 or k > n) return mint(0);
        assert(n <= max_n);
        return fac_[n]*facinv_[n-k]*facinv_[k];
    }
    mint H(int n, int k) const {
        if (n == 0 and k == 0) return mint(1);
        return C(n+k-1,n);
    }
    mint catalan(int n) const {
        if (n == 0) return mint(1);
        return C(n*2,n) - C(n*2,n-1);
    }
};

int main() {
    int N; cin >> N;
    int M = 1<<N;
    vector<mint> A(M);
    rep(i,M) cin >> A[i];

    mint S = accumulate(all(A),mint(0));
    vector<mint> p(M);
    rep(i,M) p[i] = A[i]/S;

    rep(i,N) {
        rep(mask,M) {
            if (kthbit(mask,i)) {
                p[mask] += p[mask^(1<<i)];
            }
        }
    }
    mint ans = 0;
    rep(i,M-1) {
        if (popcount(i)&1) ans += p[i]/(mint(1)-p[i]);
        else ans -= p[i]/(mint(1)-p[i]);
    }
    if (N&1) ans = -ans;
    ans++;

    cout << ans << ln;
}
0