#1007902 (C++17) No.2876 Infection

提出ソース

結果

問題	No.2876 Infection
ユーザー	Aging1986
提出日時	2024-09-06 23:07:41
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	504 ms / 2,000 ms
コード長	12,375 bytes
コンパイル時間	2,485 ms
コンパイル使用メモリ	215,452 KB
実行使用メモリ	7,936 KB
最終ジャッジ日時	2024-09-06 23:07:51
合計ジャッジ時間	7,366 ms
ジャッジサーバーID （参考情報）	judge4 / judge1

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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 6,820 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,820 KB
testcase_03	AC	1 ms 6,944 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	156 ms 7,936 KB
testcase_06	AC	343 ms 7,680 KB
testcase_07	AC	504 ms 7,552 KB
testcase_08	AC	474 ms 7,808 KB
testcase_09	AC	483 ms 7,808 KB
testcase_10	AC	71 ms 6,940 KB
testcase_11	AC	60 ms 6,944 KB
testcase_12	AC	39 ms 6,944 KB
testcase_13	AC	105 ms 6,940 KB
testcase_14	AC	394 ms 6,948 KB
testcase_15	AC	180 ms 6,940 KB
testcase_16	AC	11 ms 6,940 KB
testcase_17	AC	2 ms 6,944 KB
testcase_18	AC	33 ms 6,940 KB
testcase_19	AC	3 ms 6,940 KB
testcase_20	AC	177 ms 6,944 KB
testcase_21	AC	6 ms 6,940 KB
testcase_22	AC	224 ms 6,940 KB
testcase_23	AC	112 ms 6,940 KB
testcase_24	AC	72 ms 6,944 KB
testcase_25	AC	189 ms 6,944 KB
testcase_26	AC	4 ms 6,940 KB
testcase_27	AC	84 ms 6,944 KB
testcase_28	AC	7 ms 6,940 KB
testcase_29	AC	350 ms 6,940 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

raw source code


#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vll> vvll;
typedef vector<vvll> vvvll;
typedef vector<pii> vpii;
typedef vector<vpii> vvpii;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;
typedef vector<pdd> vpdd;
typedef vector<vd> vvd;
#define yn(ans) printf("%s\n", (ans)?"Yes":"No");
#define YN(ans) printf("%s\n", (ans)?"YES":"NO");
    template<class T> bool chmax(T &a, T b) {
	if (a >= b) return false;
	a = b; return true;
}
template<class T> bool chmin(T &a, T b) {
	if (a <= b) return false;
	a = b; return true;
}
#define FOR(i, s, e, t) for ((i) = (s); (i) < (e); (i) += (t)) 
#define REP(i, e) for (int i = 0; i < (e); ++i) 
#define REP1(i, s, e) for (int i = (s); i < (e); ++i)
#define RREP(i, e) for (int i = (e); i >= 0; --i)
#define RREP1(i, e, s) for (int i = (e); i >= (s); --i)
#define all(v) v.begin(), v.end()
#define pb push_back
#define qb pop_back
#define pf push_front
#define qf pop_front
#define maxe max_element
#define mine min_element
ll inf = 1e18;
#define DEBUG printf("%d\n", __LINE__); fflush(stdout);
template<class T> void print(vector<T> &v, bool withSize = false) {
	if (withSize) cout << v.size() << endl;
	REP(i, v.size()) cout << v[i] << " "; 
	cout << endl;
}
mt19937_64 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());

int __FAST_IO__ = []() {
	std::ios::sync_with_stdio(0);
	std::cin.tie(0);
	std::cout.tie(0);
	return 0;
}();

// Mint & Combinatorics
 
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  return u;
}
 
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
 
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
 
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
 
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }
 
  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) { Modular result(*this); *this += 1; return result; }
  Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
  Modular operator-() const { return Modular(-value); }
 
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
    long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
 
  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
 
  friend const Type& abs(const Modular& x) { return x.value; }
 
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
 
  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
 
  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);
 
 private:
  Type value;
};
 
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
 
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
 
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
 
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
 
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
 
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
 
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
 
template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
 
template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}
 
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
 
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}
 
// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
 
struct MOD {
    static int value;
};
int MOD::value = 998244353;
using Mint = Modular<MOD>;
typedef vector<Mint> vm;
typedef vector<vm> vvm;
typedef vector<vvm> vvvm;

vector<Mint> fac, ifac;
void initFac(int N) {
	fac.resize(N + 1);
	ifac.resize(N + 1);
	fac[0] = ifac[0] = 1;
	REP1(i, 1, N + 1) {
		fac[i] = fac[i - 1] * i;
	}
	ifac[N] = 1 / fac[N];
	RREP1(i, N - 1, 1) {
		ifac[i] = (i + 1) * ifac[i + 1];
	}
}
 
Mint C(int m, int n) {
	if (m < n || n < 0) return 0;
	return fac[m] * ifac[n] * ifac[m - n]; 
}

Mint P(int m, int n) {
	if (m < n || n < 0) return 0;
	return fac[m] * ifac[m - n];
}

template< typename Mint >
struct NumberTheoreticTransformFriendlyModInt {
 
  vector< Mint > dw, idw;
  int max_base;
  Mint root;
 
  NumberTheoreticTransformFriendlyModInt() {
    const unsigned mod = Mint::mod();
    assert(mod >= 3 && mod % 2 == 1);
    auto tmp = mod - 1;
    max_base = 0;
    while(tmp % 2 == 0) tmp >>= 1, max_base++;
    root = 2;
    while(power(root, (mod - 1) >> 1) == 1) root += 1;
    assert(power(root, mod - 1) == 1);
    dw.resize(max_base);
    idw.resize(max_base);
    for(int i = 0; i < max_base; i++) {
      dw[i] = -power(root, (mod - 1) >> (i + 2));
      idw[i] = Mint(1) / dw[i];
    }
  }
  
  void ntt(vector< Mint > &a) {
    const int n = (int) a.size();
    assert((n & (n - 1)) == 0);
    assert(__builtin_ctz(n) <= max_base);
    for(int m = n; m >>= 1;) {
      Mint w = 1;
      for(int s = 0, k = 0; s < n; s += 2 * m) {
        for(int i = s, j = s + m; i < s + m; ++i, ++j) {
          auto x = a[i], y = a[j] * w;
          a[i] = x + y, a[j] = x - y;
        }
        w *= dw[__builtin_ctz(++k)];
      }
    }
  }
 
  void intt(vector< Mint > &a, bool f = true) {
    const int n = (int) a.size();
    assert((n & (n - 1)) == 0);
    assert(__builtin_ctz(n) <= max_base);
    for(int m = 1; m < n; m *= 2) {
      Mint w = 1;
      for(int s = 0, k = 0; s < n; s += 2 * m) {
        for(int i = s, j = s + m; i < s + m; ++i, ++j) {
          auto x = a[i], y = a[j];
          a[i] = x + y, a[j] = (x - y) * w;
        }
        w *= idw[__builtin_ctz(++k)];
      }
    }
    if(f) {
      Mint inv_sz = Mint(1) / n;
      for(int i = 0; i < n; i++) a[i] *= inv_sz;
    }
  }
 
  vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    Mint inv_sz = Mint(1) / sz;
    for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
    intt(a, false);
    a.resize(need);
    return a;
  }
  void sq(vector<Mint> &a, vector<Mint> &b, bool mult) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    int sz = 1 << nbase;
    
    b.resize(sz, 0);
    ntt(b);
    Mint inv_sz = Mint(1) / sz;
    if (mult) {
        a.resize(sz, 0);
        ntt(a);
        for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
        intt(a, false);
        a.resize(need);
    }
    for (int i = 0; i < sz; i++) b[i] *= b[i] * inv_sz;
    intt(b, false);
    b.resize(need);
  }
  
  void pow(vector<Mint> &a, vector<Mint> &b, int p) {
    int len = a.size();
    while (p) {
        sq(a, b, p & 1);
        a.resize(len);
        b.resize(len);
        p >>= 1;
    }
  }
}; 

NumberTheoreticTransformFriendlyModInt<Mint> ntt;

#define TESTS int t; cin >> t; while (t--)
#define TEST 
int main() {
    int N, X;
    cin >> N >> X;
    initFac(N);
    Mint p = Mint(X) / 100;
    
    vm pw(N + 1, 1), qw(N + 1, 1);
    REP(i, N) pw[i + 1] = pw[i] * p, qw[i + 1] = qw[i] * (1 - p);
    
    vvm dp(N + 1, vm(N + 1, 0));
    dp[1][N - 1] = 1;
    
    RREP1(tot, N, 1) {
      //  REP(j, tot + 1) printf("%d %d %d\n", tot - j, j, dp[tot - j][j]);
        vm A(tot + 1, 0), B(tot + 1, 0);
        REP(j, tot + 1) {
            if (j < tot) A[j] = dp[tot - j][j] * fac[j];
            B[tot - j] = pw[j] * ifac[j];
        }
      //  print(A), print(B);
        vm C = ntt.multiply(A, B);
      //  print(C);
        REP1(j, tot, C.size()) {
            int nj = j - tot, ni = tot - 1 - nj;
            if (ni >= 0) dp[ni][nj] = C[j] * qw[nj] * ifac[nj];
        }
    }
    
    Mint ans = 0;
    REP(i, N + 1) {
        ans += dp[0][i] * (N - i);
    }
    printf("%d\n", ans);
    return 0;
}

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結果

テストケース

ソースコード