結果

問題 No.2580 Hyperinflation
ユーザー KudeKude
提出日時 2023-12-08 13:58:57
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 5,091 bytes
コンパイル時間 4,237 ms
コンパイル使用メモリ 295,672 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-27 02:48:55
合計ジャッジ時間 53,738 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 20 TLE * 11
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:106:14: warning: 'std::vector<{anonymous}::atcoder::static_modint<998244353> > {anonymous}::factorial2monomial(std::vector<atcoder::static_modint<998244353> >)' defined but not used [-Wunused-function]
  106 | vector<mint> factorial2monomial(vector<mint> f) {
      |              ^~~~~~~~~~~~~~~~~~

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> 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;
  vector<vector<mint>> prod(2 * n - 1);
  auto dfs1 = [&](auto&& self, int l, int r, int idx) {
    if (r - l == 1) {
      prod[idx] = {1, -l};
      return;
    }
    int c = (l + r) / 2;
    self(self, l, c, idx + 1);
    self(self, c, r, idx + 2 * (c - l));
    prod[idx] = convolution(prod[idx + 1], prod[idx + 2 * (c - l)]);
  };
  dfs1(dfs1, 0, n, 0);
  ranges::reverse(f);
  f = convolution(f, fps_inverse(prod[0], n));
  f.resize(n);
  auto dfs2 = [&](auto&& self, int l, int r, int idx) {
    if (r - l == 1) return;
    int c = (l + r) / 2;
    auto g = convolution(vector<mint>(f.begin() + n - r, f.begin() + n - l), prod[idx + 2 * (c - l)]);
    copy(g.begin() + r - c, g.begin() + r - l, f.begin() + n - c);
    self(self, l, c, idx + 1);
    self(self, c, r, idx + 2 * (c - l));
  };
  dfs2(dfs2, 0, n, 0);
  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 vector<mint>{-l, 1};
    int c = (l + r) / 2;
    auto pl = self(self, l, c);
    auto pr = self(self, c, r);
    auto g = convolution(vector<mint>(f.begin() + c, f.begin() + r), pl);
    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 l != 0 || r != n ? convolution(pl, pr) : vector<mint>{};
  };
  dfs(dfs, 0, n);
  return f;
}


vector<mint> factorial2monomial_shifted(vector<mint> f, mint shift) {
  // 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 vector<mint>{-l + shift, 1};
    int c = (l + r) / 2;
    auto pl = self(self, l, c);
    auto pr = self(self, c, r);
    auto g = convolution(vector<mint>(f.begin() + c, f.begin() + r), pl);
    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 l != 0 || r != n ? convolution(pl, pr) : vector<mint>{};
  };
  dfs(dfs, 0, n);
  return f;
}

} 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;
  }
  vector<mint> f{1};
  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];
    f = factorial2monomial_shifted(move(f), 1 + c[i]);
    mint aj = 1;
    rep(j, i + 1) {
      f[j] *= aj;
      aj *= a[i];
    }
  }
  cout << f[0].val() << '\n';
}
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