#705883 (C++17) No.1706 Many Bus Stops (hard)

提出ソース

結果

問題	No.1706 Many Bus Stops (hard)
ユーザー	stoq
提出日時	2021-10-08 22:44:51
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	18 ms / 2,000 ms
コード長	11,657 bytes
コンパイル時間	6,070 ms
コンパイル使用メモリ	286,140 KB
実行使用メモリ	9,216 KB
最終ジャッジ日時	2024-07-23 05:50:22
合計ジャッジ時間	7,376 ms
ジャッジサーバーID （参考情報）	judge2 / judge1

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	17 ms 9,216 KB
testcase_01	AC	17 ms 9,216 KB
testcase_02	AC	17 ms 9,088 KB
testcase_03	AC	17 ms 9,088 KB
testcase_04	AC	17 ms 9,088 KB
testcase_05	AC	17 ms 9,088 KB
testcase_06	AC	18 ms 9,216 KB
testcase_07	AC	17 ms 9,088 KB
testcase_08	AC	17 ms 9,088 KB
testcase_09	AC	17 ms 9,088 KB
testcase_10	AC	16 ms 9,088 KB
testcase_11	AC	17 ms 9,088 KB
testcase_12	AC	17 ms 9,088 KB
testcase_13	AC	17 ms 9,088 KB
testcase_14	AC	17 ms 9,216 KB
testcase_15	AC	18 ms 9,216 KB
testcase_16	AC	17 ms 9,216 KB
testcase_17	AC	17 ms 9,088 KB
testcase_18	AC	18 ms 9,088 KB
testcase_19	AC	17 ms 9,088 KB
testcase_20	AC	18 ms 9,216 KB
testcase_21	AC	18 ms 9,088 KB
testcase_22	AC	17 ms 9,216 KB
testcase_23	AC	17 ms 9,088 KB
testcase_24	AC	18 ms 9,088 KB
testcase_25	AC	18 ms 9,088 KB
testcase_26	AC	18 ms 9,216 KB
testcase_27	AC	17 ms 9,088 KB
testcase_28	AC	17 ms 9,216 KB
testcase_29	AC	17 ms 9,088 KB
testcase_30	AC	17 ms 9,216 KB
testcase_31	AC	17 ms 9,088 KB
testcase_32	AC	17 ms 9,088 KB
testcase_33	AC	17 ms 9,088 KB
testcase_34	AC	17 ms 9,216 KB
testcase_35	AC	18 ms 9,216 KB
testcase_36	AC	17 ms 9,216 KB
testcase_37	AC	18 ms 9,088 KB
testcase_38	AC	17 ms 9,088 KB
testcase_39	AC	18 ms 9,088 KB
testcase_40	AC	18 ms 9,216 KB
testcase_41	AC	17 ms 9,216 KB
testcase_42	AC	17 ms 9,088 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

#define MOD_TYPE 1

#pragma region Macros

#include <bits/stdc++.h>
using namespace std;

#include <atcoder/all>

using namespace atcoder;

#if 0
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
using Int = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
#endif

#if 1
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif

using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;

#if MOD_TYPE == 1
constexpr ll MOD = ll(1e9 + 7);
#else
#if MOD_TYPE == 2
constexpr ll MOD = 998244353;
#else
constexpr ll MOD = 1000003;
#endif
#endif

using mint = static_modint<MOD>;
constexpr int INF = (int)1e9 + 10;
constexpr ll LINF = (ll)4e18;
constexpr double PI = acos(-1.0);
constexpr double EPS = 1e-11;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};

#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define possible(n) cout << ((n) ? "possible" : "impossible") << "\n"
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n"
#define Yay(n) cout << ((n) ? "Yay!" : ":(") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";
#define UNIQUE(v) v.erase(unique(all(v)), v.end())

struct io_init {
  io_init() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(30) << setiosflags(ios::fixed);
  };
} io_init;
template <typename T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; }
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val) {
  fill((T *)array, (T *)(array + N), val);
}
template <typename T>
vector<T> compress(vector<T> &v) {
  vector<T> val = v;
  sort(all(val)), val.erase(unique(all(val)), val.end());
  for (auto &&vi : v) vi = lower_bound(all(val), vi) - val.begin();
  return val;
}
template <typename T, typename U>
constexpr istream &operator>>(istream &is, pair<T, U> &p) noexcept {
  is >> p.first >> p.second;
  return is;
}
template <typename T, typename U>
constexpr ostream &operator<<(ostream &os, pair<T, U> p) noexcept {
  os << p.first << " " << p.second;
  return os;
}
ostream &operator<<(ostream &os, mint m) {
  os << m.val();
  return os;
}

random_device seed_gen;
mt19937_64 engine(seed_gen());

struct BiCoef {
  vector<mint> fact_, inv_, finv_;
  BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
    fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
    for (int i = 2; i < n; i++) {
      fact_[i] = fact_[i - 1] * i;
      inv_[i] = -inv_[MOD % i] * (MOD / i);
      finv_[i] = finv_[i - 1] * inv_[i];
    }
  }
  mint C(ll n, ll k) const noexcept {
    if (n < k || n < 0 || k < 0) return 0;
    return fact_[n] * finv_[k] * finv_[n - k];
  }
  mint P(ll n, ll k) const noexcept { return C(n, k) * fact_[k]; }
  mint H(ll n, ll k) const noexcept { return C(n + k - 1, k); }
  mint Ch1(ll n, ll k) const noexcept {
    if (n < 0 || k < 0) return 0;
    mint res = 0;
    for (int i = 0; i < n; i++)
      res += C(n, i) * mint(n - i).pow(k) * (i & 1 ? -1 : 1);
    return res;
  }
  mint fact(ll n) const noexcept {
    if (n < 0) return 0;
    return fact_[n];
  }
  mint inv(ll n) const noexcept {
    if (n < 0) return 0;
    return inv_[n];
  }
  mint finv(ll n) const noexcept {
    if (n < 0) return 0;
    return finv_[n];
  }
};

BiCoef bc(500010);

#pragma endregion

#pragma region FPS

// 引用：
// https://opt-cp.com/fps-implementation/

#define fastprod 0

#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)

template <class T>
struct FormalPowerSeries : vector<T> {
  using vector<T>::vector;
  using 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();
    repi(i, min(n, m))(*this)[i] += g[i];
    return *this;
  }
  F &operator-=(const F &g) {
    int n = (*this).size(), m = g.size();
    repi(i, 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() + 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) + min(n, 2 * m));
      F r(res);
      f.resize(2 * m), internal::butterfly(f);
      r.resize(2 * m), internal::butterfly(r);
      repi(i, 2 * m) f[i] *= r[i];
      internal::butterfly_inv(f);
      f.erase(f.begin(), f.begin() + m);
      f.resize(2 * m), internal::butterfly(f);
      repi(i, 2 * m) f[i] *= r[i];
      internal::butterfly_inv(f);
      T iz = T(2 * m).inv();
      iz *= -iz;
      repi(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
#if fastprod
  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;
  }

#else
  F &operator*=(const F &g) {
    int n = (*this).size(), m = g.size();
    drep(i, n) {
      (*this)[i] *= g[0];
      REPI(j, 1, 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();
    repi(i, n) {
      REPI(j, 1, min(i + 1, m))(*this)[i] -= (*this)[i - j] * g[j];
      (*this)[i] *= ig0;
    }
    return *this;
  }

#endif

  // sparse
  F &operator*=(vector<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/=(vector<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());
    repi(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))
      repi(i, n - d)(*this)[i + d] -= (*this)[i];
    else if (c == T(-1))
      repi(i, n - d)(*this)[i + d] += (*this)[i];
    else
      repi(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;
  }

  void differentiate() {
    int n = (*this).size();
    (*this) >>= 1;
    REPI(i, 1, n - 1)(*this)[i] *= (i + 1);
  }

  void integrate(bool ext = true) {
    if (ext) (*this).push_back(0);
    int n = (*this).size();
    (*this) <<= 1;
    REPI(i, 1, n)(*this)[i] *= bc.inv(i);
  }

  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*(vector<pair<int, T>> g) const { return F(*this) *= g; }
  F operator/(vector<pair<int, T>> g) const { return F(*this) /= g; }
};

using fps = FormalPowerSeries<mint>;
using sfps = vector<pair<int, mint>>;

void add_ext(fps &f, fps &g) {
  f.resize(max(f.size(), g.size()));
  f += g;
}

void prod_ext(fps &f, fps &g) {
  f.resize(f.size() + g.size() - 1, 0);
  f *= g;
}

void prod_ext(fps &f, sfps &g) {
  int m = 0;
  for (auto [d, c] : g) {
    if (m < d) m = d;
  }
  f.resize(f.size() + m);
  f *= g;
}

#pragma endregion

fps Berlekamp_Massey(const fps &a) {
  int n = a.size();
  fps c{-1}, c2{0};
  mint r2 = 1;
  int i2 = -1;
  for (int i = 0; i < n; i++) {
    mint r = 0;
    int d = c.size();
    for (int j = 0; j < d; j++) r += c[j] * a[i - j];
    if (r == 0) continue;
    mint coef = -r / r2;
    int d2 = c2.size();
    if (d - i >= d2 - i2) {
      for (int j = 0; j < d2; j++) c[j + i - i2] += c2[j] * coef;
    } else {
      fps tmp(c);
      c.resize(d2 + i - i2);
      for (int j = 0; j < d2; j++) c[j + i - i2] += c2[j] * coef;
      c2 = std::move(tmp);
      i2 = i, r2 = r;
    }
  }
  return {c.begin() + 1, c.end()};
}

// return generating function of a, s.t. F(x) = P(x) / Q(x)
std::pair<fps, fps> find_generating_function(fps a) {
  auto q = Berlekamp_Massey(a);
  int d = q.size();
  a.resize(d);
  q.insert(q.begin(), 1);
  for (int i = 1; i < (int)q.size(); i++) q[i] *= -1;
  a *= q;
  return {a, q};
}

// return [x^k] p(x) / q(x)
mint compute_Kthterm(fps p, fps q, ll k) {
  int d = q.size();
  assert(q[0] == 1 and p.size() + 1 <= d);
  while (k) {
    auto q_minus = q;
    for (int i = 1; i < d; i += 2) q_minus[i] *= -1;
    p.resize(2 * d);
    q.resize(2 * d);
    p *= q_minus;
    q *= q_minus;
    for (int i = 0; i < d - 1; i++) p[i] = p[(i << 1) | (k & 1)];
    for (int i = 0; i < d; i++) q[i] = q[i << 1];
    p.resize(d - 1);
    q.resize(d);
    k >>= 1;
  }
  return p[0];
}

mint compute_Kthterm(std::pair<fps, fps> f, ll k) {
  return compute_Kthterm(f.first, f.second, k);
}

void solve() {
  ll c, n, m;
  cin >> c >> n >> m;
  const int d = 10;
  fps a(d, 0), b(d, 0);
  a[0] = 1, b[0] = 0;
  REP(i, 1, d) {
    a[i] += a[i - 1];
    if (i >= 2) a[i] += b[i - 2];
    a[i] *= bc.inv(c);
    if (i >= 2) b[i] += a[i - 2] * (c - 1) + b[i - 2] * (c - 2);
    b[i] += b[i - 1];
    b[i] *= bc.inv(c);
  }
  auto g = find_generating_function(a);

  mint p = 1 - compute_Kthterm(g, n);
  p = p.pow(m);
  cout << 1 - p << "\n";
}

int main() { solve(); }

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結果

テストケース

ソースコード