結果
| 問題 |
No.3105 Parallel Connection and Spanning Trees
|
| コンテスト | |
| ユーザー |
 tute7627
|
| 提出日時 | 2025-04-11 23:01:21 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 153 ms / 5,000 ms |
| コード長 | 18,862 bytes |
| コンパイル時間 | 2,865 ms |
| コンパイル使用メモリ | 216,912 KB |
| 実行使用メモリ | 7,848 KB |
| 最終ジャッジ日時 | 2025-04-11 23:01:27 |
| 合計ジャッジ時間 | 5,060 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 32 |
ソースコード
//#define _GLIBCXX_DEBUG
//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug_print.hpp>
#define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define OUT(...) (static_cast<void>(0))
#endif
#define endl '\n'
#define lfs cout<<fixed<<setprecision(15)
#define ALL(a) (a).begin(),(a).end()
#define ALLR(a) (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
namespace template_tute{
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 4.1e18;
using P = pair<ll, ll>;
template<typename T> using PQ = priority_queue<T>;
template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max<ll>({a,b,c})-min<ll>({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}
template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};
template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << "(" << p.first << "," << p.second << ")";}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; return os;}
template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
auto tmp = v;
for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
rearrange(ord, head);
rearrange(ord, tail...);
}
template<typename T> vector<int> ascend(const vector<T>&v){
vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i)<make_pair(v[j],j);});
return ord;
}
template<typename T> vector<int> descend(const vector<T>&v){
vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);});
return ord;
}
template<typename T> vector<T> inv_perm(const vector<T>&ord){
vector<T>inv(ord.size());
for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
return inv;
}
ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
ll modulo(ll n,ll d){return (n%d+d)%d;};
template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
namespace converter{
int dict[500];
const string lower="abcdefghijklmnopqrstuvwxyz";
const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string digit="0123456789";
const string digit1="123456789";
void regi_str(const string &t){
for(int i=0;i<t.size();i++){
dict[t[i]]=i;
}
}
void regi_int(const string &t){
for(int i=0;i<t.size();i++){
dict[i]=t[i];
}
}
vector<int>to_int(const string &s,const string &t){
regi_str(t);
vector<int>ret(s.size());
for(int i=0;i<s.size();i++){
ret[i]=dict[s[i]];
}
return ret;
}
vector<int>to_int(const string &s){
auto t=s;
sort(t.begin(),t.end());
t.erase(unique(t.begin(),t.end()),t.end());
return to_int(s,t);
}
vector<vector<int>>to_int(const vector<string>&s,const string &t){
regi_str(t);
vector<vector<int>>ret(s.size(),vector<int>(s[0].size()));
for(int i=0;i<s.size();i++){
for(int j=0;j<s[0].size();j++){
ret[i][j]=dict[s[i][j]];
}
}
return ret;
}
vector<vector<int>>to_int(const vector<string>&s){
string t;
for(int i=0;i<s.size();i++){
t+=s[i];
}
sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());
return to_int(s,t);
}
string to_str(const vector<int>&s,const string &t){
regi_int(t);
string ret;
for(auto z:s)ret+=dict[z];
return ret;
}
vector<string> to_str(const vector<vector<int>>&s,const string &t){
regi_int(t);
vector<string>ret(s.size());
for(int i=0;i<s.size();i++){
for(auto z:s[i])ret[i]+=dict[z];
}
return ret;
}
}
template< typename T = int >
struct edge {
int to;
T cost;
int id;
edge():to(-1),id(-1){};
edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
operator int() const { return to; }
};
template<typename T>
using Graph = vector<vector<edge<T>>>;
template<typename T>
Graph<T>revgraph(const Graph<T> &g){
Graph<T>ret(g.size());
for(int i=0;i<g.size();i++){
for(auto e:g[i]){
int to = e.to;
e.to = i;
ret[to].push_back(e);
}
}
return ret;
}
template<typename T>
Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
Graph<T> ret(n);
for(int es = 0; es < m; es++){
int u,v;
T w=1;
cin>>u>>v;u-=indexed,v-=indexed;
if(weighted)cin>>w;
ret[u].emplace_back(v,w,es);
if(!directed)ret[v].emplace_back(u,w,es);
}
return ret;
}
template<typename T>
Graph<T> readParent(int n,int indexed=1,bool directed=true){
Graph<T>ret(n);
for(int i=1;i<n;i++){
int p;cin>>p;
p-=indexed;
ret[p].emplace_back(i);
if(!directed)ret[i].emplace_back(p);
}
return ret;
}
}
using namespace template_tute;
template< int mod >
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int) (1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
return ModInt(lhs) += rhs;
}
friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
return ModInt(lhs) -= rhs;
}
friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
return ModInt(lhs) *= rhs;
}
friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
return ModInt(lhs) /= rhs;
}
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
pair<int,int>frac(){
for(int j=1;j<=10000;j++){
auto v=*this*j;
if(v.x<=10000)return make_pair(v.x,j);
else if(v.x>=mod-10000)return make_pair(-(v.x-mod),j);
}
return make_pair(-1,-1);
}
friend ostream &operator<<(ostream &os, const ModInt &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt< mod >(t);
return (is);
}
static constexpr int get_mod() { return mod; }
};
template< typename T >
struct Combination {
vector< T > _fact, _rfact, _inv;
Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
_fact[0] = _rfact[sz] = _inv[0] = 1;
for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
_rfact[sz] /= _fact[sz];
for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
}
inline T fact(ll k) const { return _fact[k]; }
inline T rfact(ll k) const { return _rfact[k]; }
inline T inv(ll k) const { return _inv[k]; }
T P(ll n, ll r) const {
if(r < 0 || n < r) return 0;
return fact(n) * rfact(n - r);
}
T C(ll p, ll q) const {
if(q < 0 || p < q) return 0;
return fact(p) * rfact(q) * rfact(p - q);
}
T RC(ll p, ll q) const {
if(q < 0 || p < q) return 0;
return rfact(p) * fact(q) * fact(p - q);
}
T H(ll n, ll r) const {
if(n < 0 || r < 0) return (0);
return r == 0 ? 1 : C(n + r - 1, r);
}
//+1がm個、-1がn個で prefix sumが常にk以上
T catalan(ll m,ll n,ll k){
if(n>m-k)return 0;
else return C(n+m,m)-C(n+m,n+k-1);
}
};
using modint = ModInt< MOD9 >;modint mpow(ll n, ll x){return modint(n).pow(x);}modint mpow(modint n, ll x){return n.pow(x);}
//using modint=ld;modint mpow(ll n, ll x){return pow(n,x);}modint mpow(modint n, ll x){return pow(n,x);}
using Comb=Combination<modint>;
template< class T >
struct Matrix {
vector< vector< T > > A;
Matrix() {}
Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}
Matrix(size_t n) : A(n, vector< T >(n, 0)) {};
Matrix(vector<vector<T>>v):A(v){};
size_t height() const {
return (A.size());
}
size_t width() const {
return (A[0].size());
}
inline const vector< T > &operator[](int k) const {
return (A.at(k));
}
inline vector< T > &operator[](int k) {
return (A.at(k));
}
static Matrix I(size_t n) {
Matrix mat(n);
for(int i = 0; i < n; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
(*this)[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
size_t n = height(), m = B.width(), p = width();
assert(p == B.height());
vector< vector< T > > C(n, vector< T >(m, 0));
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)
for(int k = 0; k < p; k++)
C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
A.swap(C);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I(height());
while(k > 0) {
if(k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const {
return (Matrix(*this) += B);
}
Matrix operator-(const Matrix &B) const {
return (Matrix(*this) -= B);
}
Matrix operator*(const Matrix &B) const {
return (Matrix(*this) *= B);
}
Matrix operator^(const long long k) const {
return (Matrix(*this) ^= k);
}
friend ostream &operator<<(ostream &os, Matrix p) {
size_t n = p.height(), m = p.width();
for(int i = 0; i < n; i++) {
os << "[";
for(int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "]\n" : ",");
}
}
return (os);
}
T determinant() {
Matrix B(*this);
assert(width() == height());
T ret = 1;
for(int i = 0; i < width(); i++) {
int idx = -1;
for(int j = i; j < width(); j++) {
if(B[j][i] != 0){
idx = j;
break;
}
}
OUT(i,idx);
if(idx == -1) return (0);
if(i != idx) {
ret *= -1;
swap(B[i], B[idx]);
}
ret *= B[i][i];
T vv = B[i][i];
for(int j = 0; j < width(); j++) {
B[i][j] /= vv;
}
for(int j = i + 1; j < width(); j++) {
T a = B[j][i];
for(int k = 0; k < width(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return (ret);
}
};
//掃き出し法を行う
//返り値のrankは線形独立な行ベクトルの最大本数である
//変更される行列aの0~(rank-1)行目までには基底が入る
template<typename T>
int sweep(Matrix<T> &a, bool is_extended){
int h = a.height(), w = a.width();
int rank = 0;
int limit = w - is_extended;
for(int col=0;col<limit;col++){
int pivot = -1;
for(int row=rank;row<h;row++){
if(a[row][col]!=0){
pivot=row;
break;
}
}
if(pivot==-1)continue;
swap(a[pivot],a[rank]);
if(pivot!=rank){
for(ll i=col;i<w;i++){
a[rank][i] *= -1;
}
}
T tmp=a[pivot][col];
T tmpinv=T(1)/tmp;
for(int row=0;row<h;row++){
if(row!=rank&&a[row][col]!=0){
T fac=a[row][col];
for(int i=col;i<w;i++){
a[row][i]-=a[rank][i]*fac*tmpinv;
}
}
}
//OUT(col,a)
rank++;
}
return rank;
}
//拡大係数行列を入れると解の一つを返す
template<typename T>
vector<T>linear_equation(Matrix<T>a){
int h=a.height(),w=a.width();
int rank = sweep(a,true);
vector<T>ret;
for(int row=rank;row<h;row++)if(a[row][w-1]!=0)return ret;
ret.assign(w-1,(T)0);
for(int i=0;i<rank;i++){
for(int j=0;j<w-1;j++){
if(a[i][j]!=0){
ret[j]=a[i][w-1];
break;
}
}
}
return ret;
}
//拡大係数行列を入れると核空間の基底を返す
template<typename T>
vector<vector<T>>kernel(Matrix<T>a){
int h=a.height(),w=a.width();
int rank = sweep(a,true);
vector<int>cols(w-1,0),piv;
for(int i=0;i<h;i++)for(int j=0;j<w-1;j++){
if(a[i][j]==1){
cols[j]=1;
piv.push_back(j);
break;
}
}
vector<vector<T>>ret;
for(int i=0;i<w-1;i++){
if(cols[i])continue;
vector<T>v(w-1);
v[i]=T(-1);
for(int j=0;j<piv.size();j++)v[piv[j]]=a[j][i];
ret.push_back(v);
}
return ret;
}
void solve(){
ll res=0,buf=0;
bool judge = true;
ll k;cin>>k;
modint ret=1;
modint cf=1;
rep(_,0,k){
ll n,m;cin>>n>>m;
Matrix<modint>mat(n+1,n+2);
mat[0][0]=k;mat[0][1]=-cf;mat[1][0]=-1;mat[1][1]=1;
mat[2][2]=1;
mat[0][n+1]=cf;
rep(i,0,m){
ll u,v;cin>>u>>v;
mat[u][u]+=1;
mat[u][v]-=1;
mat[v][u]-=1;
mat[v][v]+=1;
}
OUT(mat);
//ret*=mat.determinant();
//OUT(mat,mat.determinant());
sweep(mat,false);OUT(mat);
rep(i,1,n+1)ret*=mat[i][i];
cf=mat[0][n+1];
}
ret*=k;
cout<<ret<<endl;
}
int main(){
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
ll res=0,buf=0;
bool judge = true;
int T = 1;
//cin>>T;
while(T--){
solve();
}
return 0;
}