結果

問題 No.1302 Random Tree Score
ユーザー ぷら
提出日時 2023-06-04 03:52:42
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,963 ms / 3,000 ms
コード長 4,411 bytes
コンパイル時間 2,752 ms
コンパイル使用メモリ 204,764 KB
最終ジャッジ日時 2025-02-13 22:32:31
ジャッジサーバーID
(参考情報)
judge5 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 14
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>
using namespace std;
constexpr int mod = 998244353;
template< int mod >
struct NumberTheoreticTransform {
vector< int > rev, rts;
int base, max_base, root;
NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while(tmp % 2 == 0) tmp >>= 1, max_base++;
root = 2;
while(mod_pow(root, (mod - 1) >> 1) == 1) ++root;
assert(mod_pow(root, mod - 1) == 1);
root = mod_pow(root, (mod - 1) >> max_base);
}
inline int mod_pow(int x, int n) {
int ret = 1;
while(n > 0) {
if(n & 1) ret = mul(ret, x);
x = mul(x, x);
n >>= 1;
}
return ret;
}
inline int inverse(int x) {
return mod_pow(x, mod - 2);
}
inline unsigned add(unsigned x, unsigned y) {
x += y;
if(x >= mod) x -= mod;
return x;
}
inline unsigned mul(unsigned a, unsigned b) {
return 1ull * a * b % (unsigned long long) mod;
}
void ensure_base(int nbase) {
if(nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for(int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
assert(nbase <= max_base);
while(base < nbase) {
int z = mod_pow(root, 1 << (max_base - 1 - base));
for(int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
rts[(i << 1) + 1] = mul(rts[i], z);
}
++base;
}
}
void ntt(vector< int > &a) {
const int n = (int) a.size();
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for(int i = 0; i < n; i++) {
if(i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for(int k = 1; k < n; k <<= 1) {
for(int i = 0; i < n; i += 2 * k) {
for(int j = 0; j < k; j++) {
int z = mul(a[i + j + k], rts[j + k]);
a[i + j + k] = add(a[i + j], mod - z);
a[i + j] = add(a[i + j], z);
}
}
}
}
vector< int > multiply(vector< int > a, vector< int > b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
int inv_sz = inverse(sz);
for(int i = 0; i < sz; i++) {
a[i] = mul(a[i], mul(b[i], inv_sz));
}
reverse(a.begin() + 1, a.end());
ntt(a);
a.resize(need);
return a;
}
};
long long fac[200005], finv[200005], inv[200005];
void COMinit() {
fac[0] = fac[1] = finv[0] = finv[1] = inv[1] = 1;
for (int i = 2; i < 200005; i++) {
fac[i] = fac[i - 1] * i % mod;
inv[i] = mod - inv[mod % i] * (mod / i) % mod;
finv[i] = finv[i - 1] * inv[i] % mod;
}
}
long long COM(int n, int k){
if (n < k) return 0;
if (n < 0 || k < 0) return 0;
return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
}
long long choose(int n,int k) {
if(n < 0 || k < 0) return 0;
if(n == 0) return 1;
return COM(n+k-1,k-1);
}
vector<int> modpow(int L,vector<int>a,long long b) {
vector<int>ans(1,1);
NumberTheoreticTransform<mod>ntt;
while(b) {
if(b & 1) {
ans = ntt.multiply(ans,a);
ans.resize(L);
}
a = ntt.multiply(a,a);
a.resize(L);
b /= 2;
}
return ans;
}
long long modpow2(long long a,long long b) {
long long ans = 1;
while(b) {
if(b & 1) {
(ans *= a) %= mod;
}
(a *= a) %= mod;
b /= 2;
}
return ans;
}
int main() {
COMinit();
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N;
cin >> N;
vector<int>tmp(N);
for(int i = 1; i < N; i++) {
tmp[i] = i*finv[i-1]%mod;
}
tmp = modpow(2*N-1,tmp,N);
cout << fac[N-2]*tmp[2*N-2]%mod*modpow2(modpow2(N,N-2),mod-2)%mod << "\n";
}
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