結果

問題 No.1302 Random Tree Score
ユーザー eSeF
提出日時 2020-12-16 00:09:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 193 ms / 3,000 ms
コード長 20,097 bytes
コンパイル時間 3,610 ms
コンパイル使用メモリ 231,076 KB
最終ジャッジ日時 2025-01-17 01:15:56
ジャッジサーバーID
(参考情報)
judge4 / judge3
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 * 14
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ソースコード

diff #
プレゼンテーションモードにする

//FPS (ei1333)
#include <bits/stdc++.h>
using namespace std;
using int64 = long long;
//const int mod = 1e9 + 7;
const int mod = 998244353;
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 {
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)};
}
static constexpr uint32_t mul_inv(uint32_t n, int e = 5, uint32_t x = 1) {
return e == 0 ? x : mul_inv(n, e - 1, x * (2 - x * n));
}
template< uint32_t mod, bool fast = false >
struct ModInt2 {
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 inv = mul_inv(mod);
static constexpr u32 r2 = -uint64_t(mod) % mod;
uint32_t x;
ModInt2() : x(0) {}
ModInt2(const int64_t &y)
: x(reduce(u64(fast ? y : (y >= 0 ? y % mod : (mod - (-y) % mod) % mod)) * r2)) {}
u32 reduce(const u64 &w) const {
return u32(w >> 32) + mod - u32((u64(u32(w) * inv) * mod) >> 32);
}
ModInt2 &operator+=(const ModInt2 &p) {
if(int(x += p.x - 2 * mod) < 0) x += 2 * mod;
return *this;
}
ModInt2 &operator-=(const ModInt2 &p) {
if(int(x -= p.x) < 0) x += 2 * mod;
return *this;
}
ModInt2 &operator*=(const ModInt2 &p) {
x = reduce(uint64_t(x) * p.x);
return *this;
}
ModInt2 &operator/=(const ModInt2 &p) {
*this *= p.inverse();
return *this;
}
ModInt2 operator-() const { return ModInt2() - *this; }
ModInt2 operator+(const ModInt2 &p) const { return ModInt2(*this) += p; }
ModInt2 operator-(const ModInt2 &p) const { return ModInt2(*this) -= p; }
ModInt2 operator*(const ModInt2 &p) const { return ModInt2(*this) *= p; }
ModInt2 operator/(const ModInt2 &p) const { return ModInt2(*this) /= p; }
bool operator==(const ModInt2 &p) const { return get() == p.get(); }
bool operator!=(const ModInt2 &p) const { return get() != p.get(); }
int get() const { return reduce(x) % mod; }
ModInt2 pow(int64_t n) const {
ModInt2 ret(1), mul(*this);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
ModInt2 inverse() const {
return pow(mod - 2);
}
friend ostream &operator<<(ostream &os, const ModInt2 &p) {
return os << p.get();
}
friend istream &operator>>(istream &is, ModInt2 &a) {
int64_t t;
is >> t;
a = ModInt2< mod, fast >(t);
return (is);
}
static int get_mod() { return mod; }
};
using modint = ModInt2< mod >;
template< typename Mint >
struct NumberTheoreticTransformFriendlyModInt {
vector< Mint > dw, idw;
int max_base;
Mint root;
NumberTheoreticTransformFriendlyModInt() {
const unsigned mod = Mint::get_mod();
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while(tmp % 2 == 0) tmp >>= 1, max_base++;
root = 2;
while(root.pow((mod - 1) >> 1) == 1) root += 1;
assert(root.pow(mod - 1) == 1);
dw.resize(max_base);
idw.resize(max_base);
for(int i = 0; i < max_base; i++) {
dw[i] = -root.pow((mod - 1) >> (i + 2));
idw[i] = Mint(1) / dw[i];
}
}
void ntt(vector< Mint > &a) {
const int n = (int) a.size();
assert((n & (n - 1)) == 0);
assert(__builtin_ctz(n) <= max_base);
for(int m = n; m >>= 1;) {
Mint w = 1;
for(int s = 0, k = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; ++i, ++j) {
auto x = a[i], y = a[j] * w;
a[i] = x + y, a[j] = x - y;
}
w *= dw[__builtin_ctz(++k)];
}
}
}
void intt(vector< Mint > &a, bool f = true) {
const int n = (int) a.size();
assert((n & (n - 1)) == 0);
assert(__builtin_ctz(n) <= max_base);
for(int m = 1; m < n; m *= 2) {
Mint w = 1;
for(int s = 0, k = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; ++i, ++j) {
auto x = a[i], y = a[j];
a[i] = x + y, a[j] = (x - y) * w;
}
w *= idw[__builtin_ctz(++k)];
}
}
if(f) {
Mint inv_sz = Mint(1) / n;
for(int i = 0; i < n; i++) a[i] *= inv_sz;
}
}
vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
Mint inv_sz = Mint(1) / sz;
for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
intt(a, false);
a.resize(need);
return a;
}
};
/**
* @brief Formal-Power-Series()
*/
template< typename T >
struct FormalPowerSeries : vector< T > {
using vector< T >::vector;
using P = FormalPowerSeries;
using MULT = function< vector< T >(P, P) >;
using FFT = function< void(P &) >;
using SQRT = function< T(T) >;
static MULT &get_mult() {
static MULT mult = nullptr;
return mult;
}
static void set_mult(MULT f) {
get_mult() = f;
}
static FFT &get_fft() {
static FFT fft = nullptr;
return fft;
}
static FFT &get_ifft() {
static FFT ifft = nullptr;
return ifft;
}
static void set_fft(FFT f, FFT g) {
get_fft() = f;
get_ifft() = g;
if(get_mult() == nullptr) {
auto mult = [&](P a, P b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
int sz = 1 << nbase;
a.resize(sz, T(0));
b.resize(sz, T(0));
get_fft()(a);
get_fft()(b);
for(int i = 0; i < sz; i++) a[i] *= b[i];
get_ifft()(a);
a.resize(need);
return a;
};
set_mult(mult);
}
}
static SQRT &get_sqrt() {
static SQRT sqr = nullptr;
return sqr;
}
static void set_sqrt(SQRT sqr) {
get_sqrt() = sqr;
}
void shrink() {
while(this->size() && this->back() == T(0)) this->pop_back();
}
P operator+(const P &r) const { return P(*this) += r; }
P operator+(const T &v) const { return P(*this) += v; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator-(const T &v) const { return P(*this) -= v; }
P operator*(const P &r) const { return P(*this) *= r; }
P operator*(const T &v) const { return P(*this) *= v; }
P operator/(const P &r) const { return P(*this) /= r; }
P operator%(const P &r) const { return P(*this) %= r; }
P &operator+=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] += r[i];
return *this;
}
P &operator+=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
P &operator-=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i];
shrink();
return *this;
}
P &operator-=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] -= r;
shrink();
return *this;
}
P &operator*=(const T &v) {
const int n = (int) this->size();
for(int k = 0; k < n; k++) (*this)[k] *= v;
return *this;
}
P &operator*=(const P &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
assert(get_mult() != nullptr);
auto ret = get_mult()(*this, r);
return *this = P(begin(ret), end(ret));
}
P &operator%=(const P &r) {
return *this -= *this / r * r;
}
P operator-() const {
P ret(this->size());
for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
P &operator/=(const P &r) {
if(this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
}
P dot(P r) const {
P ret(min(this->size(), r.size()));
for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
P pre(int sz) const {
return P(begin(*this), begin(*this) + min((int) this->size(), sz));
}
P operator>>(int sz) const {
if(this->size() <= sz) return {};
P ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
P operator<<(int sz) const {
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
P rev(int deg = -1) const {
P ret(*this);
if(deg != -1) ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
T operator()(T x) const {
T r = 0, w = 1;
for(auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
P diff() const;
P integral() const;
// F(0) must not be 0
P inv_fast() const;
P inv(int deg = -1) const;
// F(0) must be 1
P log(int deg = -1) const;
P sqrt(int deg = -1) const;
// F(0) must be 0
P exp_fast(int deg = -1) const;
P exp(int deg = -1) const;
P pow(int64_t k, int deg = -1) const;
P mod_pow(int64_t k, P g) const;
};
/**
* @brief Integral ($\int f(x) dx$)
* @docs docs/integral.md
*/
template< typename T >
typename FormalPowerSeries< T >::P FormalPowerSeries< T >::integral() const {
const int n = (int) this->size();
P ret(n + 1);
ret[0] = T(0);
vector< T > invs(n + 1);
invs[1] = 1;
for(int i = 2; i <= n; i++) invs[i] = invs[T::get_mod() % i] * (T::get_mod() - T::get_mod() / i);
for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] * invs[i + 1];
return ret;
}
/**
* @brief Diff ($f'(x)$)
* @docs docs/diff.md
*/
template< typename T >
typename FormalPowerSeries< T >::P FormalPowerSeries< T >::diff() const {
const int n = (int) this->size();
P ret(max(0, n - 1));
for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
/**
* @brief Inv ($\frac {1} {f(x)}$)
*/
template< typename T >
typename FormalPowerSeries< T >::P FormalPowerSeries< T >::inv_fast() const {
assert(((*this)[0]) != T(0));
const int n = (int) this->size();
P res{T(1) / (*this)[0]};
for(int d = 1; d < n; d <<= 1) {
P f(2 * d), g(2 * d);
for(int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j];
for(int j = 0; j < d; j++) g[j] = res[j];
get_fft()(f);
get_fft()(g);
for(int j = 0; j < 2 * d; j++) f[j] *= g[j];
get_ifft()(f);
for(int j = 0; j < d; j++) {
f[j] = 0;
f[j + d] = -f[j + d];
}
get_fft()(f);
for(int j = 0; j < 2 * d; j++) f[j] *= g[j];
get_ifft()(f);
for(int j = 0; j < d; j++) f[j] = res[j];
res = f;
}
return res.pre(n);
}
template< typename T >
typename FormalPowerSeries< T >::P FormalPowerSeries< T >::inv(int deg) const {
assert(((*this)[0]) != T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
if(get_fft() != nullptr) {
P ret(*this);
ret.resize(deg, T(0));
return ret.inv_fast();
}
P ret({T(1) / (*this)[0]});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
}
return ret.pre(deg);
}
/**
* @brief Log ($\log {f(x)}$)
* @docs docs/log.md
*/
template< typename T >
typename FormalPowerSeries< T >::P FormalPowerSeries< T >::log(int deg) const {
assert((*this)[0] == 1);
const int n = (int) this->size();
if(deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
/**
* @brief Exp ($e^{f(x)}$)
* @docs docs/exp.md
*/
template< typename T >
typename FormalPowerSeries< T >::P FormalPowerSeries< T >::exp_fast(int deg) const {
if(deg == -1) deg = this->size();
assert((*this)[0] == T(0));
P inv;
inv.reserve(deg + 1);
inv.push_back(T(0));
inv.push_back(T(1));
auto inplace_integral = [&](P &F) -> void {
const int n = (int) F.size();
auto mod = T::get_mod();
while((int) inv.size() <= n) {
int i = inv.size();
inv.push_back((-inv[mod % i]) * (mod / i));
}
F.insert(begin(F), T(0));
for(int i = 1; i <= n; i++) F[i] *= inv[i];
};
auto inplace_diff = [](P &F) -> void {
if(F.empty()) return;
F.erase(begin(F));
T coeff = 1, one = 1;
for(int i = 0; i < (int) F.size(); i++) {
F[i] *= coeff;
coeff += one;
}
};
P b{1, 1 < (int) this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
for(int m = 2; m < deg; m *= 2) {
auto y = b;
y.resize(2 * m);
get_fft()(y);
z1 = z2;
P z(m);
for(int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
get_ifft()(z);
fill(begin(z), begin(z) + m / 2, T(0));
get_fft()(z);
for(int i = 0; i < m; ++i) z[i] *= -z1[i];
get_ifft()(z);
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c;
z2.resize(2 * m);
get_fft()(z2);
P x(begin(*this), begin(*this) + min< int >(this->size(), m));
inplace_diff(x);
x.push_back(T(0));
get_fft()(x);
for(int i = 0; i < m; ++i) x[i] *= y[i];
get_ifft()(x);
x -= b.diff();
x.resize(2 * m);
for(int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = T(0);
get_fft()(x);
for(int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
get_ifft()(x);
x.pop_back();
inplace_integral(x);
for(int i = m; i < min< int >(this->size(), 2 * m); ++i) x[i] += (*this)[i];
fill(begin(x), begin(x) + m, T(0));
get_fft()(x);
for(int i = 0; i < 2 * m; ++i) x[i] *= y[i];
get_ifft()(x);
b.insert(end(b), begin(x) + m, end(x));
}
return P{begin(b), begin(b) + deg};
}
template< typename T >
typename FormalPowerSeries< T >::P FormalPowerSeries< T >::exp(int deg) const {
assert((*this)[0] == T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
if(get_fft() != nullptr) {
P ret(*this);
ret.resize(deg, T(0));
return ret.exp_fast(deg);
}
P ret({T(1)});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
/**
* @brief Pow ($f(x)^k$)
*/
template< typename T >
typename FormalPowerSeries< T >::P FormalPowerSeries< T >::pow(int64_t k, int deg) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
for(int i = 0; i < n; i++) {
if((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
if(i * k > deg) return P(deg, T(0));
ret = (ret << (i * k)).pre(deg);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return *this;
}
const int MOD = 998244353;
using mint = ModInt2< MOD, true >;
/**
* @brief Scanner()
*/
struct Scanner {
public:
explicit Scanner(FILE *fp) : fp(fp) {}
template< typename T, typename... E >
void read(T &t, E &... e) {
read_single(t);
read(e...);
}
private:
static constexpr size_t line_size = 1 << 16;
static constexpr size_t int_digits = 20;
char line[line_size + 1] = {};
FILE *fp = nullptr;
char *st = line;
char *ed = line;
void read() {}
static inline bool is_space(char c) {
return c <= ' ';
}
void reread() {
ptrdiff_t len = ed - st;
memmove(line, st, len);
char *tmp = line + len;
ed = tmp + fread(tmp, 1, line_size - len, fp);
*ed = 0;
st = line;
}
void skip_space() {
while(true) {
if(st == ed) reread();
while(*st && is_space(*st)) ++st;
if(st != ed) return;
}
}
template< typename T, enable_if_t< is_integral< T >::value, int > = 0 >
void read_single(T &s) {
skip_space();
if(st + int_digits >= ed) reread();
bool neg = false;
if(is_signed< T >::value && *st == '-') {
neg = true;
++st;
}
typename make_unsigned< T >::type y = *st++ - '0';
while(*st >= '0') {
y = 10 * y + *st++ - '0';
}
s = (neg ? -y : y);
}
template< typename T, enable_if_t< is_same< T, string >::value, int > = 0 >
void read_single(T &s) {
s = "";
skip_space();
while(true) {
char *base = st;
while(*st && !is_space(*st)) ++st;
s += string(base, st);
if(st != ed) return;
reread();
}
}
template< typename T >
void read_single(vector< T > &s) {
for(auto &d : s) read(d);
}
};
/**
* @brief Printer()
*/
struct Printer {
public:
explicit Printer(FILE *fp) : fp(fp) {}
~Printer() { flush(); }
template< bool f = false, typename T, typename... E >
void write(const T &t, const E &... e) {
if(f) write_single(' ');
write_single(t);
write< true >(e...);
}
template< typename... T >
void writeln(const T &...t) {
write(t...);
write_single('\n');
}
void flush() {
fwrite(line, 1, st - line, fp);
st = line;
}
private:
FILE *fp = nullptr;
static constexpr size_t line_size = 1 << 16;
static constexpr size_t int_digits = 20;
char line[line_size + 1] = {};
char small[32] = {};
char *st = line;
template< bool f = false >
void write() {}
void write_single(const char &t) {
if(st + 1 >= line + line_size) flush();
*st++ = t;
}
template< typename T, enable_if_t< is_integral< T >::value, int > = 0 >
void write_single(T s) {
if(st + int_digits >= line + line_size) flush();
if(s == 0) {
write_single('0');
return;
}
if(s < 0) {
write_single('-');
s = -s;
}
char *mp = small + sizeof(small);
typename make_unsigned< T >::type y = s;
size_t len = 0;
while(y > 0) {
*--mp = y % 10 + '0';
y /= 10;
++len;
}
memmove(st, mp, len);
st += len;
}
void write_single(const string &s) {
for(auto &c : s) write_single(c);
}
void write_single(const char *s) {
while(*s != 0) write_single(*s++);
}
template< typename T >
void write_single(const vector< T > &s) {
for(size_t i = 0; i < s.size(); i++) {
if(i) write_single(' ');
write_single(s[i]);
}
}
};
int main() {
NumberTheoreticTransformFriendlyModInt< mint > ntt;
using FPS = FormalPowerSeries< mint >;
FPS::set_fft([&](FPS &a) { ntt.ntt(a); }, [&](FPS &a) { ntt.intt(a); });
Scanner input(stdin);
Printer output(stdout);
int N;
cin >> N;
FPS F(N);
modint fac[N];
fac[0]=1;
for(int i=1;i<N;i++)fac[i]=(fac[i-1]*i);
for(int i=0;i<=N-2;i++){
modint m = i+1;
m/=fac[i];
F[i] = m.get();
}
//for(int i=0;i<=N-2;i++)cout << F[i].get() << endl;
F = F.pow(N);
//for(int i=0;i<=N-2;i++)cout << F[i].get() << endl;
modint ans = F[N-2].get();
//cout << ans << endl;
for(int i=0;i<N-2;i++)ans/=N;
ans*=fac[N-2];
cout << ans << endl;
}
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