結果

問題 No.125 悪の花弁
ユーザー rsk0315
提出日時 2019-08-16 23:32:51
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 60 ms / 5,000 ms
コード長 3,373 bytes
コンパイル時間 1,090 ms
コンパイル使用メモリ 62,424 KB
最終ジャッジ日時 2025-01-07 13:00:30
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
other AC * 6
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:126:8: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  126 |   scanf("%zu", &K);
      |   ~~~~~^~~~~~~~~~~
main.cpp:129:26: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  129 |   for (auto& ci: C) scanf("%jd", &ci);
      |                     ~~~~~^~~~~~~~~~~~

ソースコード

diff #
プレゼンテーションモードにする

#include <cstdio>
#include <cstdint>
#include <vector>
#include <algorithm>
#include <numeric>
#include <utility>
intmax_t gcd(intmax_t m, intmax_t n) {
  while (n) std::swap(m %= n, n);
  return m;
}
std::vector<intmax_t> divisor(intmax_t n) {
  std::vector<intmax_t> res;
  for (intmax_t i = 1; i*i <= n; ++i) {
    if (n % i == 0) {
      res.push_back(i);
      if (i != n/i) res.push_back(n/i);
    }
  }
  std::sort(res.begin(), res.end());
  return res;
}
constexpr intmax_t  operator ""_jd(unsigned long long n) { return n; }
constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; }
constexpr size_t    operator ""_zu(unsigned long long n) { return n; }
// constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; }
template <typename Tp>
Tp gcd(Tp a, Tp b, Tp& x, Tp& y) {
  x = Tp(0);
  y = Tp(1);
  for (Tp u = y, v = x; a;) {
    Tp q = b/a;
    std::swap(x -= q*u, u);
    std::swap(y -= q*v, v);
    std::swap(b -= q*a, a);
  }
  return b;
}
template <typename Tp>
Tp modinv(Tp a, Tp mod) {
  Tp x, y;
  gcd(a, mod, x, y);
  x %= mod;
  if (x < 0) x += mod;
  return x;
}
template <typename Tp>
Tp modadd(Tp a, Tp b, Tp mod) {
  a += b % mod;
  if (a < 0) a += mod;
  if (a >= mod) a -= mod;
  return a;
}
template <typename Tp>
Tp modadd(std::initializer_list<Tp> const& adds, Tp mod) {
  Tp res = 0;
  for (auto const& add: adds) {
    res += add % mod;
    if (res < 0) res += mod;
    if (res >= mod) res -= mod;
  }
  return res;
}
template <typename Tp>
Tp modsub(Tp a, Tp b, Tp mod) {
  a -= b % mod;
  if (a < 0) a += mod;
  if (a >= mod) a -= mod;
  return a;
}
template <typename Tp>
Tp modmul(std::initializer_list<Tp> const& muls, Tp mod) {
  Tp res = 1;
  for (auto const& mul: muls) (res *= mul) %= mod;
  return res;
}
template <typename Tp>
Tp modpow(Tp base, intmax_t iexp, Tp mod) {
  Tp res = 1;
  for (Tp dbl = base; iexp; iexp >>= 1) {
    if (iexp & 1) res = res * dbl % mod;
    dbl = dbl * dbl % mod;
  }
  return res;
}
class modfactorial {
  std::vector<intmax_t> fact, fact_inv;
  intmax_t mod;
public:
  modfactorial(intmax_t N, intmax_t mod): mod(mod) {
    fact.resize(N+1);
    fact_inv.resize(N+1);
    fact[0] = 1;
    for (intmax_t i = 1; i <= N; ++i)
      fact[i] = fact[i-1] * i % mod;
    fact_inv[N] = modinv(fact[N], mod);
    for (intmax_t i = N; i--;)
      fact_inv[i] = fact_inv[i+1] * (i+1) % mod;
  }
  intmax_t operator ()(intmax_t k) const {
    return fact[k];
  }
  intmax_t inverse(intmax_t k) const {
    return fact_inv[k];
  }
};
constexpr intmax_t mod = 1e9+7;
int main() {
  size_t K;
  scanf("%zu", &K);
  std::vector<intmax_t> C(K);
  for (auto& ci: C) scanf("%jd", &ci);
  intmax_t cs = std::accumulate(C.begin(), C.end(), 0_jd);
  intmax_t cg = std::accumulate(C.begin(), C.end(), 0_jd, [](auto x, auto y) { return gcd(x, y); });
  modfactorial mf(cs, mod);
  auto ds = divisor(cg);
  std::vector<intmax_t> f(ds.size());
  for (size_t i = 0; i < ds.size(); ++i) {
    intmax_t d = ds[i];
    f[i] = mf(cs/d);
    for (size_t j = 0; j < K; ++j)
      (f[i] *= mf.inverse(C[j] / d)) %= mod;
  }
  intmax_t res = 0;
  for (size_t i = ds.size(); i--;) {
    for (size_t j = i+1; j < ds.size(); ++j) {
      if (ds[j] % ds[i] == 0)
        f[i] = (f[i]+mod-f[j]) % mod;
    }
    (res += f[i] * modinv(cs/ds[i], mod)) %= mod;
  }
  printf("%jd\n", res);
}
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