結果
問題 | No.1302 Random Tree Score |
ユーザー |
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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 |
ソースコード
#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";}