#724147 (C++17) No.1784 Not a star yet...

• 問題: No.1784 Not a star yet...
• ユーザー: sigma425
• 提出日時: 2021-12-14 23:55:31
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 81 ms / 2,000 ms
• コード長: 11,568 bytes
• コンパイル時間: 3,120 ms
• コンパイル使用メモリ: 226,784 KB
• 実行使用メモリ: 13,184 KB
• 最終ジャッジ日時: 2024-07-23 19:44:11
• 合計ジャッジ時間: 7,279 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	3 ms; 6,812 KB
testcase_01	AC	3 ms; 6,816 KB
testcase_02	AC	3 ms; 6,816 KB
testcase_03	AC	3 ms; 6,812 KB
testcase_04	AC	3 ms; 6,940 KB
testcase_05	AC	3 ms; 6,944 KB
testcase_06	AC	3 ms; 6,940 KB
testcase_07	AC	3 ms; 6,944 KB
testcase_08	AC	4 ms; 6,940 KB
testcase_09	AC	3 ms; 6,944 KB
testcase_10	AC	4 ms; 6,940 KB
testcase_11	AC	3 ms; 6,944 KB
testcase_12	AC	3 ms; 6,940 KB
testcase_13	AC	3 ms; 6,940 KB
testcase_14	AC	5 ms; 6,944 KB
testcase_15	AC	5 ms; 6,940 KB
testcase_16	AC	40 ms; 8,576 KB
testcase_17	AC	11 ms; 6,940 KB
testcase_18	AC	70 ms; 12,032 KB
testcase_19	AC	30 ms; 7,424 KB
testcase_20	AC	11 ms; 6,944 KB
testcase_21	AC	4 ms; 6,944 KB
testcase_22	AC	5 ms; 6,940 KB
testcase_23	AC	4 ms; 6,944 KB
testcase_24	AC	49 ms; 9,344 KB
testcase_25	AC	67 ms; 11,392 KB
testcase_26	AC	19 ms; 6,940 KB
testcase_27	AC	47 ms; 9,216 KB
testcase_28	AC	8 ms; 6,940 KB
testcase_29	AC	5 ms; 6,940 KB
testcase_30	AC	55 ms; 9,984 KB
testcase_31	AC	58 ms; 10,496 KB
testcase_32	AC	22 ms; 6,940 KB
testcase_33	AC	3 ms; 6,940 KB
testcase_34	AC	44 ms; 6,944 KB
testcase_35	AC	4 ms; 6,944 KB
testcase_36	AC	3 ms; 6,940 KB
testcase_37	AC	44 ms; 6,940 KB
testcase_38	AC	42 ms; 6,944 KB
testcase_39	AC	28 ms; 6,944 KB
testcase_40	AC	37 ms; 6,944 KB
testcase_41	AC	4 ms; 6,940 KB
testcase_42	AC	3 ms; 6,944 KB
testcase_43	AC	79 ms; 13,184 KB
testcase_44	AC	80 ms; 13,056 KB
testcase_45	AC	79 ms; 12,928 KB
testcase_46	AC	81 ms; 13,056 KB
testcase_47	AC	80 ms; 13,056 KB
testcase_48	AC	80 ms; 13,184 KB
testcase_49	AC	80 ms; 13,056 KB
testcase_50	AC	80 ms; 12,928 KB
testcase_51	AC	80 ms; 13,184 KB
testcase_52	AC	80 ms; 12,928 KB
testcase_53	AC	81 ms; 12,928 KB
testcase_54	AC	79 ms; 13,056 KB
testcase_55	AC	80 ms; 13,056 KB
testcase_56	AC	80 ms; 12,928 KB
testcase_57	AC	80 ms; 12,928 KB
testcase_58	AC	80 ms; 13,056 KB
testcase_59	AC	80 ms; 13,056 KB
testcase_60	AC	80 ms; 13,056 KB
testcase_61	AC	79 ms; 13,056 KB
testcase_62	AC	80 ms; 12,928 KB
testcase_63	AC	3 ms; 6,940 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
	if(x<y){ x=y; return true; }
	return false;
}
template<class T,class U> bool chmin(T& x, U y){
	if(y<x){ x=y; return true; }
	return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
    return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
  return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<class D> D divFloor(D a, D b){
	return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
	return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
template<unsigned int mod_>
struct ModInt{
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll _v):v(normS(_v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ModInt& operator++(int){ return *this=*this+1;}
	ModInt& operator--(int){ return *this=*this-1;}
	template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}
	template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}
	template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}
	template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}
	ModInt pow(ll p) const {
		if(p<0) return inv().pow(-p);
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	ModInt inv() const {		// should be prime
		return pow(mod-2);
	}
	// ll extgcd(ll a,ll b,ll &x,ll &y) const{
	// 	ll p[]={a,1,0},q[]={b,0,1};
	// 	while(*q){
	// 		ll t=*p/ *q;
	// 		rep(i,3) swap(p[i]-=t*q[i],q[i]);
	// 	}
	// 	if(p[0]<0) rep(i,3) p[i]=-p[i];
	// 	x=p[1],y=p[2];
	// 	return p[0];
	// }
	// ModInt inv() const {
	// 	ll x,y;
	// 	extgcd(v,mod,x,y);
	// 	return make(normS(x+mod));
	// }

	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	bool operator<(const ModInt& b) const { return v<b.v;}
	friend istream& operator>>(istream &o,ModInt& x){
		ll tmp;
		o>>tmp;
		x=ModInt(tmp);
		return o;
	}
	friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
};
int bsf(ll x) { return __builtin_ctzll(x); } 
ll gcd(ll a, ll b){
	a = abs(a), b = abs(b);
	if(a==0) return b;
	if(b==0) return a;
	int shift = bsf(a|b);
	a >>= bsf(a);
	do{
		b >>= bsf(b);
		if(a>b) swap(a,b);
		b -= a;
	}while(b);
	return a<<shift;
}

struct Frac{
	ll x,y;		// x/y
	Frac(ll x_ = 0):x(x_),y(1){}
	Frac(ll x_,ll y_){
		ll g = gcd(x_,y_);
		if(y_ < 0) g = -g;
		x = x_ / g;
		y = y_ / g;
	}

	Frac operator-() const { return {-x,y}; }
	Frac operator+(const Frac& r) const { return {x * r.y + y * r.x, y * r.y}; }
	Frac operator-(const Frac& r) const { return *this + (-r); }
	Frac operator*(const Frac& r) const { return {x * r.x, y * r.y}; }
	Frac operator/(const Frac& r) const { return {x * r.y, y * r.x}; }
	Frac& operator+=(const Frac& r) { return *this = *this + r; }
	Frac& operator-=(const Frac& r) { return *this = *this - r; }
	Frac& operator*=(const Frac& r) { return *this = *this * r; }
	Frac& operator/=(const Frac& r) { return *this = *this / r; }
	template<class T> friend Frac operator+(T a, const Frac& b){ return (Frac(a) += b);}
	template<class T> friend Frac operator-(T a, const Frac& b){ return (Frac(a) -= b);}
	template<class T> friend Frac operator*(T a, const Frac& b){ return (Frac(a) *= b);}
	template<class T> friend Frac operator/(T a, const Frac& b){ return (Frac(a) /= b);}
	bool operator<(const Frac& r) const { return x * r.y < y * r.x; }
	bool operator>(const Frac& r) const { return r < *this; }
	bool operator<=(const Frac& r) const { return !(r < *this); }
	bool operator>=(const Frac& r) const { return !(*this < r); }
	bool operator==(const Frac& r) const { return x == r.x && y == r.y; }
	bool operator!=(const Frac& r) const { return !(*this == r); }
	Frac inv() const {
		return Frac(y,x);
	}
	friend ostream& operator<<(ostream &o,const Frac& x){
		return o << x.x << "/" << x.y;
	}
};
using mint = ModInt<998244353>;
// using mint = Frac;

V<mint> operator+(const V<mint>& a, const V<mint>& b){
	V<mint> c = a;
	rep(i,si(b)) c[i] += b[i];
	return c;
}
V<mint> operator*(const V<mint>& a, mint v){
	V<mint> c = a;
	rep(i,si(a)) c[i] *= v;
	return c;
}

template<class T>
struct Matrix{
	int H,W;
	VV<T> a;

	Matrix() : H(0),W(0){}
	Matrix(int H_,int W_) : H(H_),W(W_),a( VV<T>(H,V<T>(W)) ){}
	Matrix(const VV<T>& v) : H(v.size()), W(v[0].size()), a(v){}

	static Matrix E(int n){
		Matrix a(n,n);
		rep(i,n) a[i][i] = 1;
		return a;
	}

	V<T>& operator[](int i){return a[i];}
	const V<T>& operator[](int i) const {return a[i];}

	Matrix operator+(const Matrix& r) const {
		assert(H==r.H && W==r.W);
		VV<T> v(H,V<T>(W));
		rep(i,H) rep(j,W) v[i][j] = a[i][j] + r.a[i][j];
		return Matrix(v);
	}
	Matrix operator-(const Matrix& r) const {
		assert(H==r.H && W==r.W);
		VV<T> v(H,V<T>(W));
		rep(i,H) rep(j,W) v[i][j] = a[i][j] - r.a[i][j];
		return Matrix(v);
	}
	Matrix operator*(const Matrix& r) const {
		assert(W==r.H);
		VV<T> v(H,V<T>(r.W));
		rep(i,H) rep(k,W) rep(j,r.W) v[i][j] += a[i][k] * r.a[k][j];
		return Matrix(v);
	}
	Matrix& operator+=(const Matrix& r){return (*this)=(*this)+r;}
	Matrix& operator-=(const Matrix& r){return (*this)=(*this)-r;}
	Matrix& operator*=(const Matrix& r){return (*this)=(*this)*r;}

	Matrix pow(ll p) const {
		assert(H == W);
		Matrix res = E(H);
		Matrix x = *this;
		while(p){
			if(p&1) res *= x;
			x *= x;
			p >>= 1;
		}
		return res;
	}

	friend ostream& operator<<(ostream &o,const Matrix& A){
		rep(i,A.H){
			rep(j,A.W) o<<A.a[i][j]<<" ";
			o<<endl;
		}
		return o;
	}

	/*
		副作用がある, 基本的に自分でこれを呼ぶことはない
		掃き出し法をする
		左からvar列が掃き出す対象で、それより右は同時に値を変更するだけ(e.g. 逆行列は右に単位行列おいてから掃き出す)
		行swap, 列swap は行わない

		rank を返す
	*/
	int sweep(int var){
		int rank = 0;
		vector<bool> used(H);
		rep(j,var){
			int i=0;
			while(i<H && (used[i]||iszero(a[i][j]))) i++;
			if(i==H) continue;
			used[i] = true;
			rank++;
			T t = a[i][j];
			rep(k,W) a[i][k] = a[i][k]/t;
			rep(k,H) if(k!=i){
				T tt = a[k][j];
				rep(l,W) a[k][l] = a[k][l]-a[i][l]*tt;
			}
		}
		return rank;
	}

};
bool iszero(mint x){return x==0;}
bool isone(mint x){return x==1;}
template<class T>
pair< int, vector<T> > solveLinearEquation(const Matrix<T>& A, vector<T> b){
	assert(A.H==(int)b.size());
	int H = A.H, W = A.W;

	Matrix<T> X(H,W+1);
	rep(i,H) rep(j,W) X[i][j] = A[i][j];
	rep(i,H) X[i][W] = b[i];
	int rank = X.sweep(W);
	rep(i,H){
		bool allzero = true;
		rep(j,W) if(!iszero(X[i][j])) allzero = false;
		if(allzero){
			if(!iszero(X[i][W])){		//0x + 0y + 0z = non0
				return pair<int,vector<T> >(-1,vector<T>());
			}
		}
	}
	vector<bool> done(H);
	vector<T> x(W);
	rep(j,W){
		int c0 = 0, c1 = 0;
		int I = -1;
		rep(i,H){
			if(iszero(X[i][j])) c0++;
			else if(isone(X[i][j])) c1++,I=i;
		}
		if(c0==H-1 && c1==1 && !done[I]){
			x[j] = X[I][W];
			done[I] = true;
		}
	}
	return pair<int,vector<T> >(W-rank,x);
}


int X,Y;
V<mint> f[255][255];
V<mint> F(int x,int y){
	if(0<=x&&x<=X&&0<=y&&y<=Y) return f[x][y];
	return V<mint>(Y+2,0);
}
V<mint> Const(mint v){
	V<mint> res(Y+2); res[Y+1] = v;
	return res;
}

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);

	int N; cin >> N;
	V<int> sx(N),sy(N);
	rep(i,N-1){
		int a,b,c; cin >> a >> b >> c; a--,b--;
		if(c == 1){
			sx[a]++,sx[b]++; X++;
		}else{
			sy[a]++,sy[b]++; Y++;
		}
	}
	int fr = N*(N-1)/2 - (N-2);

	rep(y,Y+1){
		f[0][y] = V<mint>(Y+2); f[0][y][y] = 1;
	}
	auto A = Vec<mint>(Y+1,Y+1);
	V<mint> b(Y+1);

	rep(x,X+1) rep(y,Y+1){
		mint U = x ? mint(x)/(X+2*Y) * (1 - mint(N-x-y)/fr) : 0;
		mint D = x != X ? (mint(X-x)/(X+2*Y)) * (mint(N-1-x-y)/fr) : 0;
		mint L = y ? mint(2*y)/(X+2*Y) * (1 - mint(N-x-y)/fr) : 0;
		mint R = y != Y ? (mint(2*(Y-y))/(X+2*Y)) * (mint(N-1-x-y)/fr) : 0;
		mint M = 1-U-D-L-R;
		show("----------------");
		shows(x,y);
		show(U);show(D);show(L);show(R);show(M);
		show("-----------------");
		// f(x,y) = Uf(x-1,y) + Df(x+1,y) + Lf(x,y-1) + Rf(x,y+1) + Mf(x,y) + 1/N
		if(x != X){
			// compute f(x+1,y)
			f[x+1][y] = ( F(x-1,y) * U + F(x,y-1) * L + F(x,y+1) * R + F(x,y) * (M-1) + Const(mint(N).inv()) ) * (-D).inv();
		}else{
			if(y != Y){
				// this should be 0
				auto exp = F(x-1,y) * U + F(x+1,y) * D + F(x,y-1) * L + F(x,y+1) * R + F(x,y) * (M-1) + Const(mint(N).inv());
				rep(i,Y+1) A[y][i] = exp[i];
				b[y] = -exp[Y+1];
			}else{
				// f[X][Y] = const
				rep(i,Y+1) A[y][i] = f[X][Y][i];
				b[y] = -f[X][Y][Y+1];
			}
		}
	}
	auto p = solveLinearEquation<mint>(A,b);
	show(p.fs);
	auto Eval = [&](V<mint> f){
		mint res = 0;
		rep(i,Y+1) res += f[i] * p.sc[i];
		res += f[Y+1];
		return res;
	};
	if(false){
		shows("f_debug");
		rep(x,X+1){
			rep(y,Y+1) cout << Eval(f[x][y]) << " ";
			cout << endl;
		}
	}
	mint bg = 0, en = 0;
	rep(i,N) bg += Eval(f[sx[i]][sy[i]]);
	en = Eval(f[X][Y]) + Eval(F(1,0)*X) + Eval(F(0,1)*Y);
	cout << bg-en << endl;
}