結果
問題 | No.1302 Random Tree Score |
ユーザー |
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提出日時 | 2020-12-02 22:37:34 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2,382 ms / 3,000 ms |
コード長 | 8,356 bytes |
コンパイル時間 | 2,865 ms |
コンパイル使用メモリ | 213,016 KB |
最終ジャッジ日時 | 2025-01-16 13:38:33 |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
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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;using ll = long long;template <class T> using vec = vector<T>;template <class T> using vvec = vector<vec<T>>;template<class T> bool chmin(T& a,T b){if(a>b) {a = b; return true;} return false;}template<class T> bool chmax(T& a,T b){if(a<b) {a = b; return true;} return false;}#define rep(i,n) for(int i=0;i<(n);i++)#define drep(i,n) for(int i=(n)-1;i>=0;i--)#define all(x) (x).begin(),(x).end()#define debug(x) cerr << #x << " = " << (x) << endl;constexpr ll mod = 998244353;struct mint {ll x;mint(ll x=0):x((x%mod+mod)%mod){}friend ostream &operator<<(ostream& os,const mint& a){return os << a.x;}friend istream &operator>>(istream& is,mint& a){ll t;is >> t;a = mint(t);return (is);}mint& operator+=(const mint a) {if ((x += a.x) >= mod) x -= mod;return *this;}mint& operator-=(const mint a) {if ((x += mod-a.x) >= mod) x -= mod;return *this;}mint& operator*=(const mint a) {(x *= a.x) %= mod;return *this;}mint operator+(const mint a) const {mint res(*this);return res+=a;}mint operator-(const mint a) const {mint res(*this);return res-=a;}mint operator*(const mint a) const {mint res(*this);return res*=a;}mint pow(ll t) const {if (!t) return 1;mint a = pow(t>>1);a *= a;if (t&1) a *= *this;return a;}// for prime modmint inv() const {return pow(mod-2);}mint& operator/=(const mint a) {return (*this) *= a.inv();}mint operator/(const mint a) const {mint res(*this);return res/=a;}bool operator==(const mint& r)const{return x==r.x;}};class combination{public:vector<mint> fact,inv,finv;combination(int N){fact = inv = finv = vector<mint>(N+1);fact[0] = fact[1] = 1;inv[0] = inv[1] = 1;finv[0] = finv[1] = 1;for(ll i=2;i<=N;i++){fact[i] = fact[i-1]*i;inv[i] = (mint) mod - inv[mod%i]*(mod/i);finv[i] = finv[i-1]*inv[i];}}mint f(int i){return fact[i];}mint comb(int n,int k){if(n<k) return 0;if(n<0 || k<0) return 0;return fact[n]*finv[k]*finv[n-k];}mint hcomb(int n,int k){if(n==0 && k==0) return 1;return comb(n+k-1,k);}};namespace FastFourierTransform {using real = double;struct C {real x, y;C() : x(0), y(0) {}C(real x, real y) : x(x), y(y) {}inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }inline C conj() const { return C(x, -y); }};const real PI = acosl(-1);int base = 1;vector< C > rts = { {0, 0},{1, 0} };vector< int > rev = {0, 1};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));}while(base < nbase) {real angle = PI * 2.0 / (1 << (base + 1));for(int i = 1 << (base - 1); i < (1 << base); i++) {rts[i << 1] = rts[i];real angle_i = angle * (2 * i + 1 - (1 << base));rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));}++base;}}void fft(vector< C > &a, int n) {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++) {C z = a[i + j + k] * rts[j + k];a[i + j + k] = a[i + j] - z;a[i + j] = a[i + j] + z;}}}}vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {int need = (int) a.size() + (int) b.size() - 1;int nbase = 1;while((1 << nbase) < need) nbase++;ensure_base(nbase);int sz = 1 << nbase;vector< C > fa(sz);for(int i = 0; i < sz; i++) {int x = (i < (int) a.size() ? a[i] : 0);int y = (i < (int) b.size() ? b[i] : 0);fa[i] = C(x, y);}fft(fa, sz);C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);for(int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;fa[i] = z;}for(int i = 0; i < (sz >> 1); i++) {C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];fa[i] = A0 + A1 * s;}fft(fa, sz >> 1);vector< int64_t > ret(need);for(int i = 0; i < need; i++) {ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);}return ret;}};template< typename T >struct ArbitraryModConvolution {using real = FastFourierTransform::real;using C = FastFourierTransform::C;ArbitraryModConvolution() = default;vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {if(need == -1) need = a.size() + b.size() - 1;int nbase = 0;while((1 << nbase) < need) nbase++;FastFourierTransform::ensure_base(nbase);int sz = 1 << nbase;vector< C > fa(sz);for(int i = 0; i < a.size(); i++) {fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);}fft(fa, sz);vector< C > fb(sz);if(a == b) {fb = fa;}else{for(int i = 0; i < b.size(); i++) {fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);}fft(fb, sz);}real ratio = 0.25 / sz;C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);for(int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);C a1 = (fa[i] + fa[j].conj());C a2 = (fa[i] - fa[j].conj()) * r2;C b1 = (fb[i] + fb[j].conj()) * r3;C b2 = (fb[i] - fb[j].conj()) * r4;if(i != j) {C c1 = (fa[j] + fa[i].conj());C c2 = (fa[j] - fa[i].conj()) * r2;C d1 = (fb[j] + fb[i].conj()) * r3;C d2 = (fb[j] - fb[i].conj()) * r4;fa[i] = c1 * d1 + c2 * d2 * r5;fb[i] = c1 * d2 + c2 * d1;}fa[j] = a1 * b1 + a2 * b2 * r5;fb[j] = a1 * b2 + a2 * b1;}fft(fa, sz);fft(fb, sz);vector< T > ret(need);for(int i = 0; i < need; i++) {int64_t aa = llround(fa[i].x);int64_t bb = llround(fb[i].x);int64_t cc = llround(fa[i].y);aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;ret[i] = aa + (bb << 15) + (cc << 30);}return ret;}};ArbitraryModConvolution<mint> NTT;vec<mint> pow(vec<mint>& pol,int n,int N){if(n==1) return pol;auto res = pow(pol,n>>1,N);res = NTT.multiply(res,res);if(n&1) res = NTT.multiply(res,pol);res.resize(N);return res;}int main(){cin.tie(0);ios::sync_with_stdio(false);int N;cin >> N;vec<mint> pol(N);vec<mint> fact(N,1);for(int i=1;i<N;i++){fact[i] = fact[i-1]*i;pol[i] =((mint) i)/fact[i-1];}auto res = pow(pol,N,2*(N-1)+1);cout << res[2*(N-1)]*fact[N-2]/((mint) N).pow(N-2) << "\n";}