結果
| 問題 | No.1303 Inconvenient Kingdom |
| ユーザー |
 hamamu
|
| 提出日時 | 2020-10-23 21:33:20 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 499 ms / 3,000 ms |
| コード長 | 11,638 bytes |
| コンパイル時間 | 3,480 ms |
| コンパイル使用メモリ | 241,748 KB |
| 最終ジャッジ日時 | 2025-01-15 12:56:14 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 34 |
コンパイルメッセージ
main.cpp: In member function ‘bool MatG<T>::invalid() const’:
main.cpp:106:45: warning: no return statement in function returning non-void [-Wreturn-type]
106 | bool invalid() const { mat.empty(); }
| ^
ソースコード
·#include "bits/stdc++.h"using namespace std;using ll=long long;using vll=vector< ll>;using vvll=vector< vll>;using vvvll=vector< vvll>;using vvvvll=vector<vvvll>;using dd=double;using vdd=vector< dd>;using vvdd=vector< vdd>;using pll=pair<ll,ll>; using tll=tuple<ll,ll,ll>; using qll=tuple<ll,ll,ll,ll>;using vpll=vector< pll>;constexpr ll INF = 1LL << 60;struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)#define REP(i, N) REPS(i, 0, (N)-1)#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)#define DEP(i, N) DEPS(i, 0, (N)-1)#define rep(i, S, E) for (ll i = (S); i <= (E); i++)#define dep(i, E, S) for (ll i = (E); i >= (S); i--)#define each(e, v) for (auto&& e : v)#define ALL(v) (v).begin(), (v).end()#define RALL(v) (v).rbegin(), (v).rend()template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }template<class T> inline T MaxE(vector<T>&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmax(m,v[i]); return m; }template<class T> inline T MinE(vector<T>&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmin(m,v[i]); return m; }template<class T> inline T MaxE(vector<T> &v) { return MaxE(v,0,(ll)v.size()-1); }template<class T> inline T MinE(vector<T> &v) { return MinE(v,0,(ll)v.size()-1); }template<class T> inline T Sum(vector<T> &v,ll S,ll E){ T s=T(); rep(i,S,E)s+=v[i]; return s; }template<class T> inline T Sum(vector<T> &v) { return Sum(v,0,v.size()-1); }template<class T> inline ll sz(T &v){ return (ll)v.size(); }inline ll CEIL(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; }inline ll FLOOR(ll a,ll b){ return -CEIL(-a,b); }template<ll MOD> struct mll_{ll val;mll_(ll v = 0): val(v % MOD){ if (val < 0) val += MOD; }mll_ operator - () const { return -val; }mll_ operator + (const mll_ &b) const { return val + b.val; }mll_ operator - (const mll_ &b) const { return val - b.val; }mll_ operator * (const mll_ &b) const { return val * b.val; }mll_ operator / (const mll_ &b) const { return mll_(*this) /= b; }mll_ operator + (ll b) const { return *this + mll_(b); }mll_ operator - (ll b) const { return *this - mll_(b); }mll_ operator * (ll b) const { return *this * mll_(b); }friend mll_ operator + (ll a,const mll_ &b) { return b + a; }friend mll_ operator - (ll a,const mll_ &b) { return -b + a; }friend mll_ operator * (ll a,const mll_ &b) { return b * a; }friend mll_ operator / (ll a,const mll_ &b) { return mll_(a)/b; }mll_ &operator += (const mll_ &b) { val=(val+b.val)%MOD; return *this; }mll_ &operator -= (const mll_ &b) { val=(val+MOD-b.val)%MOD; return *this; }mll_ &operator *= (const mll_ &b) { val=(val*b.val)%MOD; return *this; }mll_ &operator /= (const mll_ &b) {ll c=b.val,d=MOD,u=1,v=0;while (d){ll t = c / d;c -= t * d; swap(c,d);u -= t * v; swap(u,v);}val = val * u % MOD;if (val < 0) val += MOD;return *this;}mll_ &operator += (ll b) { return *this += mll_(b); }mll_ &operator -= (ll b) { return *this -= mll_(b); }mll_ &operator *= (ll b) { return *this *= mll_(b); }mll_ &operator /= (ll b) { return *this /= mll_(b); }bool operator == (const mll_ &b) const { return val == b.val; }bool operator != (const mll_ &b) const { return val != b.val; }bool operator == (ll b) const { return *this == mll_(b); }bool operator != (ll b) const { return *this != mll_(b); }friend bool operator == (ll a,const mll_ &b) { return mll_(a) == b.val; }friend bool operator != (ll a,const mll_ &b) { return mll_(a) != b.val; }friend ostream &operator << (ostream &os,const mll_ &a) { return os << a.val; }friend istream &operator >> (istream &is,mll_ &a) { return is >> a.val; }static mll_ Combination(ll a,ll b){chmin(b,a-b);if (b<0) return mll_(0);mll_ c = 1;rep(i,0,b-1) c *= a-i;rep(i,0,b-1) c /= i+1;return c;}};using mll = mll_<998244353LL>;using vmll = std::vector<mll>;using vvmll = std::vector<vmll>;using vvvmll = std::vector<vvmll>;using vvvvmll = std::vector<vvvmll>;template<class T> struct MatG{ll h=0, w=0; //h行w列vector<vector<T>> mat;MatG(){}MatG(ll h_, ll w_, T x) { init(h_, w_, x); }MatG(ll h_, ll w_) { init(h_, w_); }MatG(ll h_, ll w_, string c) { init(h_, w_, c); }void init(ll h_, ll w_, T x){ h=h_; w=w_; mat.assign(h, vector<T>(w,x)); }void init(ll h_, ll w_){ init(h_,w_,T()); }void init(ll h_, ll w_, string c){ init(h_, w_); if(c=="E")E(); }ll H() const { return h; }ll W() const { return w; }bool invalid() const { mat.empty(); }vector<T> &operator[](ll i) { return mat[i]; }const vector<T> &operator[](ll i) const { return mat[i]; }MatG<T> &operator+=(const MatG<T> &B) {REP(i,h)REP(j,w) mat[i][j]+=B[i][j];return *this;}MatG<T> operator+(const MatG<T> &B) const {return MatG<T>(*this) += B;}MatG<T> operator*(const MatG<T> &B) const {MatG<T> ret(h, B.W());REP(i, h) REP(j, B.W()) REP(k, w) ret[i][j] += mat[i][k] * B[k][j];return move(ret);}vector<T> operator*(const vector<T> &v) const {vector<T> ret(v.size());REP(i, this->h) REP(j, this->w) ret[i] += this->mat[i][j] * v[j];return move(ret);}MatG<T> Pow(ll N) const {MatG<T> ret(*this), a(*this);for (ll n=N-1; n>0; n>>=1, a=a*a){ if (n&1) ret=ret*a; }return move(ret);}MatG<T> t() const {MatG<T> ret(this->w, this->h);REP(i, this->w) REP(j, this->h) ret[i][j] = this->mat[j][i];return move(ret);}void E(){ rep(i, 0, min(h,w)-1) mat[i][i]=1; }#if defined(_DEBUG)void dump() { ::dump(mat); }#endifMatG(MatG<T> &&B){ *this=move(B); } //以下、ムーブ対応MatG(MatG<T> const &B){ *this=B; }MatG<T> &operator=(MatG<T> &&B){ h=B.h; w=B.w; mat.swap(B.mat); return *this; }MatG<T> &operator=(MatG<T> const &B){ h=B.h; w=B.w; mat=B.mat; return *this; }};using Mat = MatG<mll>;#if 0#include <atcoder/all>using namespace atcoder;#endifvvll cinGraph(ll nodeNum,ll edgeNum,bool isDirected){//無向false、有向truevvll to(nodeNum);rep(i,0,edgeNum-1){ll v,u; cin >> v >> u;v--; u--;to[v].push_back(u);if (!isDirected) to[u].push_back(v);}return move(to);}struct ConnectedComponents{vvll &to; ll n; vll ccids;ConnectedComponents(vvll &to):to(to),n((ll)to.size()),ccids(n,-1){}void dfs(ll v){each(u,to[v]){if (ccids[u]!=-1)continue;ccids[u]=ccids[v];dfs(u);}}pair<ll,vll> get(){ll nm=0;rep(v,0,n-1){if (ccids[v]!=-1)continue;ccids[v]=nm++;dfs(v);}return {nm,move(ccids)};}};pair<ll,mll> GaussJordan(Mat &mat, bool isExtended, bool isTriangle){ll H=mat.H(), W=mat.W();mll det=1;ll rank=0;rep(j,0,W-1-isExtended){ll pivot=-1;rep(i,rank,H-1){if (mat[i][j]!=0){pivot=i; break;}}if (pivot==-1){det=0; continue;}if (rank<pivot){swap(mat[rank],mat[pivot]);det=-det;}det*=mat[rank][j];mll inv=mll(1)/mat[rank][j];rep(jj,j,W-1) mat[rank][jj]*=inv;rep(i,isTriangle?rank+1:0,H-1){mll tim=mat[i][j];if (i==rank || tim==0) continue;rep(jj,j,W-1) mat[i][jj]-=mat[rank][jj]*tim;}if (H==++rank) break;}return {rank,det};}pair<Mat,mll> MatInverse(Mat &A){//正方行列限定ll N=A.H();Mat B(N,2*N);rep(i,0,N-1)rep(j,0,N-1) B[i][j]=A[i][j];rep(i,0,N-1) B[i][N+i]=1;mll det; tie(ignore,det)=GaussJordan(B,false,false);if (det==0) return {Mat(),det};Mat ret(N,N);rep(i,0,N-1)rep(j,0,N-1) ret[i][j]=B[i][N+j];return {move(ret),det};}mll countST(ll N,vvll &to,ll id,vll &cids){unordered_map<ll,ll> mp;vll tr;ll idx=0;rep(v,0,N-1){if (cids[v]!=id) continue;mp[v]=idx++;tr.push_back(v);}ll mm=(ll)tr.size();if (mm==1)return mll(1);Mat L(mm-1,mm-1);//ラプラシアン行列の端を削ったものrep(i,0,mm-2){ll v=tr[i];each(u,to[v]){ll idx=mp[u];if (idx==mm-1)continue;L[i][idx]=-1;}L[i][i]=(ll)to[v].size();}return GaussJordan(L,false,true).second;}mll calc(ll N,vvll &to){Mat L(N,N);rep(v,0,N-1){each(u,to[v]) L[v][u]=-1;L[v][v]=(ll)to[v].size();}mll ans=0;rep(v,1,N-1){Mat B=L;B.mat.erase(B.mat.begin()+v);each(e,B.mat) e.erase(e.begin()+v);B.h--; B.w--;Mat C; mll det; tie(C,det)=MatInverse(B);if (v==1) ans+=det; //任意道路不使用分のカウントrep(u,0,v-1){if (L[u][v]!=0) continue;ans+=C[u][u]*det;}}return ans;}pll solve(ll N,ll M,vvll &to){ll cnm; vll cids; tie(cnm,cids)=ConnectedComponents(to).get();if (cnm==1){mll ans = calc(N,to);return {0,ans.val};}vll csz(cnm);each(e,cids) csz[e]++;sort(ALL(csz));ll fuben=0;{ll tmp=csz[cnm-1]+csz[cnm-2];fuben+=(N-tmp)*tmp;dep(i,cnm-3,0) fuben+=(N-csz[i])*csz[i];}ll x=-1,y=-1;ll p=0,q=0;while (!csz.empty()){ll s=csz.back(); csz.pop_back();if (x==-1) x=s;if (x==s){p++; continue;}if (y==-1) y=s;if (y==s){q++; continue;}break;}mll ans=1;rep(id,0,cnm-1) ans*=countST(N,to,id,cids);if (p>=2){ans*=x*x*p*(p-1)/2;}else{ans*=x*y*q;}return {fuben,ans.val};}pll solv2(ll N,ll M,vvll &to){//愚直解vvll w(N,vll(N));rep(v,0,N-1)each(u,to[v]) w[u][v]=1;vpll idxes;map<pll,ll> mp;rep(v,0,N-1)rep(u,v+1,N-1){mp[{v,u}]=(ll)idxes.size();idxes.emplace_back(v,u);}ll mm=(ll)idxes.size();pll fubenRdMin{INF,INF};ll cnt=0;rep(s,0,(1LL<<mm)-1){ll ck=0;dep(i,mm-1,0){if (!(s&(1LL<<i)))continue;ll v,u; tie(v,u) = idxes[i];if (w[v][u]==0) ck++;if (ck==2){s+=(1LL<<i)-1;break;}}if (ck==2) continue;vvll t2(N);rep(i,0,mm-1){if (!(s&(1LL<<i)))continue;ll v,u; tie(v,u) = idxes[i];t2[v].push_back(u);t2[u].push_back(v);}ll cnm; vll cids; tie(cnm,cids)=ConnectedComponents(t2).get();vll csz(cnm);each(e,cids) csz[e]++;ll fuben=0;rep(i,0,cnm-1) fuben+=(N-csz[i])*csz[i];pll fubenRd{fuben,bitset<64>(s).count()};if (chmin(fubenRdMin,fubenRd)) cnt=1;else if (fubenRdMin==fubenRd) cnt++;}return {fubenRdMin.first, cnt};}void solvecomp(ll N,ll M,vvll &to){pll ret=solve(N,M,to);#if 1cout << ret.first << '\n';cout << ret.second << '\n';#elsepll re2=solv2(N,M,to);if (ret!=re2){cout << "\n======= diff ========\n";cout << ret.first << ' ' << ret.second << '\n';cout << re2.first << ' ' << re2.second << '\n';}#endif}void cin2solve(){ll N,M; cin >> N >> M;vvll to = cinGraph(N,M,false);solvecomp(N,M,to);}void gene(){ll N=7;vpll idxes;map<pll,ll> mp;rep(v,0,N-1)rep(u,v+1,N-1){mp[{v,u}]=(ll)idxes.size();idxes.emplace_back(v,u);}ll mm=(ll)idxes.size();rep(s,0,(1LL<<mm)-1){vvll to(N);rep(i,0,mm-1){if (!(s&(1LL<<i)))continue;ll v,u; tie(v,u) = idxes[i];to[v].push_back(u);to[u].push_back(v);}ll M=bitset<64>(s).count();printf("\b\b\b\b\b\b\b\b\b\b%10lld",s);solvecomp(N,M,to);}}int main(){#if 1//solve();cin2solve();//gene();#elsell t; cin >> t;rep(i, 0, t-1){solve();}#endifreturn 0;}