結果

問題 No.2580 Hyperinflation
ユーザー Kude
提出日時 2023-12-08 18:23:09
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2,901 ms / 4,000 ms
コード長 5,295 bytes
コンパイル時間 3,897 ms
コンパイル使用メモリ 297,148 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-27 02:55:26
合計ジャッジ時間 37,037 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 31
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>

namespace {
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic warning "-Wunused-function"
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using mint = modint998244353;

constexpr int FACT_SIZE = 3000;
mint Fact[FACT_SIZE + 1];
mint iFact[FACT_SIZE + 1];
mint inv[FACT_SIZE + 1];
const auto fact_init = [] {
    Fact[0] = mint::raw(1);
    for(int i = 1; i <= FACT_SIZE; ++i) {
        Fact[i] = Fact[i-1] * i;
    }
    iFact[FACT_SIZE] = Fact[FACT_SIZE].inv();
    for(int i = FACT_SIZE; i; --i) {
        iFact[i-1] = iFact[i] * i;
    }
    for (int i = 1; i <= FACT_SIZE; i++) {
      inv[i] = iFact[i] * Fact[i-1];
    }
    return false;
}();

vector<mint> prod[4096];
void set_prod(int i) {
  assert(0 <= i && i < 2048);
  const mint im = i;
  int p = 2048 + i;
  while (p > 0) {
    auto& f = prod[p];
    f.emplace_back(0);
    rrep(j, ssize(f) - 1) f[j+1] -= im * f[j];
    p >>= 1;
  }
}

vector<mint> get_prod(int l, int r) {
  int len = bit_ceil(1U * (r - l));
  r = l + len;
  assert(((len - 1) & l) == 0);
  int p = (2048 + l) / len;
  assert(p > 0);
  return prod[p];
}

vector<mint> fps_inverse(vector<mint> f, int precision) {
  int n = f.size();
  assert(n >= 1 && f[0] != 0);
  int len = 1;
  const int z = bit_ceil(1U * precision);
  vector<mint> g{f[0].inv()};
  const mint inv4 = mint(4).inv();
  mint inv4k = 1;
  while (len < z) {
    int nlen = 2 * len;
    vector<mint> ft(f.begin(), f.begin() + min(n, nlen));
    ft.resize(nlen);
    butterfly(ft);
    vector<mint> gt = g;
    gt.resize(nlen);
    internal::butterfly(gt);
    for (int i = 0; i < nlen; i++) ft[i] *= gt[i];
    internal::butterfly_inv(ft);
    for (int i = 0; i < len; i++) ft[i] = mint();
    internal::butterfly(ft);
    for (int i = 0; i < nlen; i++) ft[i] *= gt[i];
    internal::butterfly_inv(ft);
    inv4k *= inv4;
    mint c = -inv4k;
    for (int i = len; i < nlen; i++) g.emplace_back(c * ft[i]);
    len = nlen;
  }
  g.resize(precision);
  return g;
}

vector<mint> monomial2factorial(vector<mint> f) {
  // a x = a P^-1 P x = a' P x
  // a' = a P^-1
  int n = f.size();
  if (n == 0) return f;
  ranges::reverse(f);
  f = convolution(f, fps_inverse(prod[1], n));
  f.resize(n);
  auto dfs2 = [&](auto&& self, int l, int r) {
    if (r - l == 1) return;
    int c = l + bit_ceil(1U * (r - l)) / 2;
    auto g = convolution(vector<mint>(f.begin() + n - r, f.begin() + n - l), get_prod(c, r));
    copy(g.begin() + r - c, g.begin() + r - l, f.begin() + n - c);
    self(self, l, c);
    self(self, c, r);
  };
  dfs2(dfs2, 0, n);
  ranges::reverse(f);
  return f;
}

vector<mint> factorial2monomial(vector<mint> f) {
  // a x = a P^-1 P x = a' P x
  // a = a' P
  int n = f.size();
  auto dfs = [&](auto&& self, int l, int r) {
    if (r - l == 1) return;
    int c = l + bit_ceil(1U * (r - l)) / 2;
    self(self, l, c);
    self(self, c, r);

    int p = [&](int l, int r) {
      int len = bit_ceil(1U * (r - l));
      r = l + len;
      assert(((len - 1) & l) == 0);
      return (2048 + l) / len;
    }(l, c);
    assert(p > 0);
    ranges::reverse(prod[p]);
    auto g = convolution(vector<mint>(f.begin() + c, f.begin() + r), prod[p]);
    ranges::reverse(prod[p]);
    for (int i = l; i < c; i++) f[i] += g[i - l];
    for (int i = c; i < r; i++) f[i] = g[i - l];
    return;
  };
  dfs(dfs, 0, n);
  return f;
}

vector<mint> Taylor_shift(vector<mint> f, mint c) {
  int n = f.size();
  for (int i = 0; i < n; i++) {
    f[i] *= Fact[i];
  }
  vector<mint> g(n);
  mint pow_c = 1;
  for (int i = 0; i < n; i++) {
    g[n - 1 - i] = pow_c * iFact[i];
    pow_c *= c;
  }
  vector<mint> h = convolution(f, g);
  h.erase(h.begin(), h.end() - n);
  for (int i = 0; i < n; i++) {
    h[i] *= iFact[i];
  }
  return h;
}

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  VI a(n);
  rep(i, n - 1) cin >> a[i];
  string m;
  cin >> m;
  for (char& c : m) c -= '0';
  vector<mint> c(n);
  rep(i, n - 1) {
    unsigned int now = 0;
    rep(j, ssize(m)) {
      now = 10 * now + m[j];
      m[j] = now / a[i];
      now %= a[i];
    }
    c[i] = now;
  }
  {
    mint now;
    for (char c : m) now = 10 * now + c;
    c[n - 1] = now;
  }
  rep(k, 12) for (int i = 1 << k; i < 1 << (k + 1); i++) prod[i].reserve((1 << (11 - k)) + 1);
  rep(i, 4096) prod[i] = {1};
  vector<mint> f{1};
  set_prod(0);
  for (int i = 1; i < n; i++) {
    f = monomial2factorial(move(f));
    f.insert(f.begin(), mint());
    for (int j = 1; j <= i; j++) f[j] *= inv[j];
    set_prod(i);
    f = factorial2monomial(move(f));
    f = Taylor_shift(move(f), 1 + c[i]);
    mint aj = 1;
    rep(j, i + 1) {
      f[j] *= aj;
      aj *= a[i];
    }
  }
  cout << f[0].val() << '\n';
}
0