結果

問題 No.2580 Hyperinflation
ユーザー KudeKude
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 #
プレゼンテーションモードにする

#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';
}
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