test/verify/yukicoder-502.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: https://yukicoder.me/problems/no/502

Depends on

• Enumeration(組み合わせ) (math/combinatorics/enumeration.hpp)
• Factorial(階乗) (math/combinatorics/factorial.hpp)
• math/combinatorics/montgomery-mod-int.hpp
• Sample Point Shift(標本点シフト) (math/combinatorics/sample-point-shift.hpp)
• Arbitrary Mod Convolution(任意mod畳み込み) (math/fft/arbitrary-mod-convolution.hpp)
• math/fft/fast-fourier-transform.hpp
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/502

#include "../../template/template.hpp"

#include "../../math/combinatorics/montgomery-mod-int.hpp"
#include "../../math/combinatorics/factorial.hpp"

#include "../../math/fft/arbitrary-mod-convolution.hpp"

using mint = modint1000000007;

int main() {
  int N;
  cin >> N;
  ArbitraryModConvolution< mint > fft;
  auto f = [&](vector< mint > &a, vector< mint > &b) { return fft.multiply(a, b); };
  cout << factorial< mint >(N, f) << "\n";
}

#line 1 "test/verify/yukicoder-502.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/502

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yukicoder-502.test.cpp"

#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

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

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

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

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

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

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

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 1 "math/combinatorics/enumeration.hpp"
/**
 * @brief Enumeration(組み合わせ)
 */
template <typename T>
struct Enumeration {
 private:
  static vector<T> _fact, _finv, _inv;

  inline static void expand(size_t sz) {
    if (_fact.size() < sz + 1) {
      int pre_sz = max(1, (int)_fact.size());
      _fact.resize(sz + 1, T(1));
      _finv.resize(sz + 1, T(1));
      _inv.resize(sz + 1, T(1));
      for (int i = pre_sz; i <= (int)sz; i++) {
        _fact[i] = _fact[i - 1] * T(i);
      }
      _finv[sz] = T(1) / _fact[sz];
      for (int i = (int)sz - 1; i >= pre_sz; i--) {
        _finv[i] = _finv[i + 1] * T(i + 1);
      }
      for (int i = pre_sz; i <= (int)sz; i++) {
        _inv[i] = _finv[i] * _fact[i - 1];
      }
    }
  }

 public:
  explicit Enumeration(size_t sz = 0) { expand(sz); }

  static inline T fact(int k) {
    expand(k);
    return _fact[k];
  }

  static inline T finv(int k) {
    expand(k);
    return _finv[k];
  }

  static inline T inv(int k) {
    expand(k);
    return _inv[k];
  }

  static T P(int n, int r) {
    if (r < 0 || n < r) return 0;
    return fact(n) * finv(n - r);
  }

  static T C(int p, int q) {
    if (q < 0 || p < q) return 0;
    return fact(p) * finv(q) * finv(p - q);
  }

  static T H(int n, int r) {
    if (n < 0 || r < 0) return 0;
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

template <typename T>
vector<T> Enumeration<T>::_fact = vector<T>();
template <typename T>
vector<T> Enumeration<T>::_finv = vector<T>();
template <typename T>
vector<T> Enumeration<T>::_inv = vector<T>();
#line 2 "math/combinatorics/sample-point-shift.hpp"

/**
 * @brief Sample Point Shift(標本点シフト)
 */
template <typename Mint, typename F>
vector<Mint> sample_point_shift(const vector<Mint> &ys, const Mint &m,
                                const F &multiply) {
  Enumeration<Mint> comb;
  int d = (int)ys.size() - 1;
  vector<Mint> f(d + 1), g(d * 2 + 1);
  for (int i = 0; i <= d; i++) {
    f[i] = ys[i] * comb.finv(i) * comb.finv(d - i);
    if ((d - i) & 1) f[i] = -f[i];
  }
  for (int i = 0; i <= 2 * d; i++) {
    g[i] = Mint(1) / (m - d + i);
  }
  auto h = multiply(f, g);
  Mint coef = 1;
  for (int i = 0; i <= d; i++) {
    coef *= (m - d + i);
  }
  for (int i = 0; i <= d; i++) {
    h[i + d] *= coef;
    coef *= (m + i + 1) * g[i];
  }
  return vector<Mint>{begin(h) + d, begin(h) + 2 * d + 1};
}
#line 2 "math/combinatorics/factorial.hpp"

/**
 * @brief Factorial(階乗)
 */
template <typename Mint, typename F>
Mint factorial(int64_t n, const F& multiply) {
  if (n <= 1) return 1;
  if (n >= Mint::mod()) return 0;
  int64_t v = 1;
  while (v * v < n) v *= 2;
  Mint iv = Mint(1) / v;
  vector<Mint> G{1, v + 1};
  for (int64_t d = 1; d != v; d <<= 1) {
    vector<Mint> G1 = sample_point_shift(G, Mint(d) * iv, multiply);
    vector<Mint> G2 = sample_point_shift(G, Mint(d * v + v) * iv, multiply);
    vector<Mint> G3 = sample_point_shift(G, Mint(d * v + d + v) * iv, multiply);
    for (int i = 0; i <= d; i++) G[i] *= G1[i], G2[i] *= G3[i];
    copy(begin(G2), end(G2) - 1, back_inserter(G));
  }
  Mint res = 1;
  int64_t i = 0;
  while (i + v <= n) res *= G[i / v], i += v;
  while (i < n) res *= ++i;
  return res;
}
#line 7 "test/verify/yukicoder-502.test.cpp"

#line 1 "math/fft/fast-fourier-transform.hpp"
namespace FastFourierTransform {
using real = double;

struct C {
  real x, y;

  C() : x(0), y(0) {}

  C(real x, real y) : x(x), y(y) {}

  inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

  inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

  inline C operator*(const C &c) const {
    return C(x * c.x - y * c.y, x * c.y + y * c.x);
  }

  inline C conj() const { return C(x, -y); }
};

const real PI = acosl(-1);
int base = 1;
vector<C> rts = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};

void ensure_base(int nbase) {
  if (nbase <= base) return;
  rev.resize(1 << nbase);
  rts.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); i++) {
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
  }
  while (base < nbase) {
    real angle = PI * 2.0 / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      rts[i << 1] = rts[i];
      real angle_i = angle * (2 * i + 1 - (1 << base));
      rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
    }
    ++base;
  }
}

void fft(vector<C> &a, int n) {
  assert((n & (n - 1)) == 0);
  int zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; i++) {
    if (i < (rev[i] >> shift)) {
      swap(a[i], a[rev[i] >> shift]);
    }
  }
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        C z = a[i + j + k] * rts[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}

vector<int64_t> multiply(const vector<int> &a, const vector<int> &b) {
  int need = (int)a.size() + (int)b.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  vector<C> fa(sz);
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = C(x, y);
  }
  fft(fa, sz);
  C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
    fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
    fa[i] = z;
  }
  for (int i = 0; i < (sz >> 1); i++) {
    C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
    C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
    fa[i] = A0 + A1 * s;
  }
  fft(fa, sz >> 1);
  vector<int64_t> ret(need);
  for (int i = 0; i < need; i++) {
    ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
  }
  return ret;
}
};  // namespace FastFourierTransform
#line 2 "math/fft/arbitrary-mod-convolution.hpp"

/*
 * @brief Arbitrary Mod Convolution(任意mod畳み込み)
 */
template <typename T>
struct ArbitraryModConvolution {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;

  ArbitraryModConvolution() = default;

  static vector<T> multiply(const vector<T> &a, const vector<T> &b,
                            int need = -1) {
    if (need == -1) need = a.size() + b.size() - 1;
    int nbase = 0;
    while ((1 << nbase) < need) nbase++;
    FastFourierTransform::ensure_base(nbase);
    int sz = 1 << nbase;
    vector<C> fa(sz);
    for (int i = 0; i < a.size(); i++) {
      fa[i] = C(a[i].val() & ((1 << 15) - 1), a[i].val() >> 15);
    }
    fft(fa, sz);
    vector<C> fb(sz);
    if (a == b) {
      fb = fa;
    } else {
      for (int i = 0; i < b.size(); i++) {
        fb[i] = C(b[i].val() & ((1 << 15) - 1), b[i].val() >> 15);
      }
      fft(fb, sz);
    }
    real ratio = 0.25 / sz;
    C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for (int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C a1 = (fa[i] + fa[j].conj());
      C a2 = (fa[i] - fa[j].conj()) * r2;
      C b1 = (fb[i] + fb[j].conj()) * r3;
      C b2 = (fb[i] - fb[j].conj()) * r4;
      if (i != j) {
        C c1 = (fa[j] + fa[i].conj());
        C c2 = (fa[j] - fa[i].conj()) * r2;
        C d1 = (fb[j] + fb[i].conj()) * r3;
        C d2 = (fb[j] - fb[i].conj()) * r4;
        fa[i] = c1 * d1 + c2 * d2 * r5;
        fb[i] = c1 * d2 + c2 * d1;
      }
      fa[j] = a1 * b1 + a2 * b2 * r5;
      fb[j] = a1 * b2 + a2 * b1;
    }
    fft(fa, sz);
    fft(fb, sz);
    vector<T> ret(need);
    for (int i = 0; i < need; i++) {
      int64_t aa = llround(fa[i].x);
      int64_t bb = llround(fb[i].x);
      int64_t cc = llround(fa[i].y);
      aa = T(aa).val(), bb = T(bb).val(), cc = T(cc).val();
      ret[i] = aa + (bb << 15) + (cc << 30);
    }
    return ret;
  }
};
#line 9 "test/verify/yukicoder-502.test.cpp"

using mint = modint1000000007;

int main() {
  int N;
  cin >> N;
  ArbitraryModConvolution< mint > fft;
  auto f = [&](vector< mint > &a, vector< mint > &b) { return fft.multiply(a, b); };
  cout << factorial< mint >(N, f) << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_n0.txt	AC	6 ms	4 MB
g++	00_n1.txt	AC	6 ms	4 MB
g++	00_n10.txt	AC	6 ms	4 MB
g++	00_n100.txt	AC	6 ms	4 MB
g++	00_n11.txt	AC	6 ms	4 MB
g++	00_n12.txt	AC	6 ms	4 MB
g++	00_n13.txt	AC	6 ms	4 MB
g++	00_n14.txt	AC	6 ms	4 MB
g++	00_n15.txt	AC	6 ms	4 MB
g++	00_n16.txt	AC	6 ms	4 MB
g++	00_n17.txt	AC	6 ms	4 MB
g++	00_n18.txt	AC	6 ms	4 MB
g++	00_n19.txt	AC	6 ms	4 MB
g++	00_n2.txt	AC	6 ms	4 MB
g++	00_n20.txt	AC	6 ms	4 MB
g++	00_n3.txt	AC	6 ms	4 MB
g++	00_n4.txt	AC	6 ms	4 MB
g++	00_n5.txt	AC	6 ms	4 MB
g++	00_n6.txt	AC	6 ms	4 MB
g++	00_n7.txt	AC	6 ms	4 MB
g++	00_n8.txt	AC	6 ms	4 MB
g++	00_n9.txt	AC	6 ms	4 MB
g++	20_small1.txt	AC	8 ms	4 MB
g++	20_small10.txt	AC	8 ms	4 MB
g++	20_small2.txt	AC	7 ms	4 MB
g++	20_small3.txt	AC	8 ms	4 MB
g++	20_small4.txt	AC	7 ms	4 MB
g++	20_small5.txt	AC	7 ms	4 MB
g++	20_small6.txt	AC	7 ms	4 MB
g++	20_small7.txt	AC	7 ms	4 MB
g++	20_small8.txt	AC	7 ms	4 MB
g++	20_small9.txt	AC	7 ms	4 MB
g++	30_medium1.txt	AC	72 ms	8 MB
g++	30_medium10.txt	AC	73 ms	8 MB
g++	30_medium2.txt	AC	72 ms	8 MB
g++	30_medium3.txt	AC	72 ms	8 MB
g++	30_medium4.txt	AC	38 ms	6 MB
g++	30_medium5.txt	AC	73 ms	8 MB
g++	30_medium6.txt	AC	72 ms	8 MB
g++	30_medium7.txt	AC	72 ms	8 MB
g++	30_medium8.txt	AC	72 ms	8 MB
g++	30_medium9.txt	AC	38 ms	6 MB
g++	40_large1.txt	AC	6 ms	4 MB
g++	40_large10.txt	AC	6 ms	4 MB
g++	40_large2.txt	AC	6 ms	4 MB
g++	40_large3.txt	AC	6 ms	4 MB
g++	40_large4.txt	AC	6 ms	4 MB
g++	40_large5.txt	AC	6 ms	4 MB
g++	40_large6.txt	AC	6 ms	4 MB
g++	40_large7.txt	AC	6 ms	4 MB
g++	40_large8.txt	AC	6 ms	4 MB
g++	40_large9.txt	AC	6 ms	4 MB
clang++	00_n0.txt	AC	6 ms	4 MB
clang++	00_n1.txt	AC	6 ms	4 MB
clang++	00_n10.txt	AC	6 ms	4 MB
clang++	00_n100.txt	AC	6 ms	4 MB
clang++	00_n11.txt	AC	6 ms	4 MB
clang++	00_n12.txt	AC	6 ms	4 MB
clang++	00_n13.txt	AC	6 ms	4 MB
clang++	00_n14.txt	AC	6 ms	4 MB
clang++	00_n15.txt	AC	6 ms	4 MB
clang++	00_n16.txt	AC	6 ms	4 MB
clang++	00_n17.txt	AC	6 ms	4 MB
clang++	00_n18.txt	AC	6 ms	4 MB
clang++	00_n19.txt	AC	6 ms	4 MB
clang++	00_n2.txt	AC	6 ms	4 MB
clang++	00_n20.txt	AC	6 ms	4 MB
clang++	00_n3.txt	AC	6 ms	4 MB
clang++	00_n4.txt	AC	6 ms	4 MB
clang++	00_n5.txt	AC	6 ms	4 MB
clang++	00_n6.txt	AC	6 ms	4 MB
clang++	00_n7.txt	AC	6 ms	4 MB
clang++	00_n8.txt	AC	6 ms	4 MB
clang++	00_n9.txt	AC	6 ms	4 MB
clang++	20_small1.txt	AC	8 ms	4 MB
clang++	20_small10.txt	AC	8 ms	4 MB
clang++	20_small2.txt	AC	7 ms	4 MB
clang++	20_small3.txt	AC	8 ms	4 MB
clang++	20_small4.txt	AC	7 ms	4 MB
clang++	20_small5.txt	AC	8 ms	4 MB
clang++	20_small6.txt	AC	7 ms	4 MB
clang++	20_small7.txt	AC	8 ms	4 MB
clang++	20_small8.txt	AC	7 ms	4 MB
clang++	20_small9.txt	AC	8 ms	4 MB
clang++	30_medium1.txt	AC	74 ms	8 MB
clang++	30_medium10.txt	AC	74 ms	8 MB
clang++	30_medium2.txt	AC	74 ms	8 MB
clang++	30_medium3.txt	AC	74 ms	8 MB
clang++	30_medium4.txt	AC	39 ms	6 MB
clang++	30_medium5.txt	AC	74 ms	8 MB
clang++	30_medium6.txt	AC	74 ms	8 MB
clang++	30_medium7.txt	AC	75 ms	8 MB
clang++	30_medium8.txt	AC	74 ms	8 MB
clang++	30_medium9.txt	AC	39 ms	6 MB
clang++	40_large1.txt	AC	6 ms	4 MB
clang++	40_large10.txt	AC	6 ms	4 MB
clang++	40_large2.txt	AC	6 ms	4 MB
clang++	40_large3.txt	AC	6 ms	4 MB
clang++	40_large4.txt	AC	6 ms	4 MB
clang++	40_large5.txt	AC	6 ms	4 MB
clang++	40_large6.txt	AC	6 ms	4 MB
clang++	40_large7.txt	AC	6 ms	4 MB
clang++	40_large8.txt	AC	6 ms	4 MB
clang++	40_large9.txt	AC	6 ms	4 MB

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