結果

問題 No.1507 Road Blocked
コンテスト
ユーザー mugen_1337
提出日時 2021-05-14 22:58:38
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 780 ms / 2,000 ms
コード長 6,239 bytes
コンパイル時間 3,083 ms
コンパイル使用メモリ 225,756 KB
最終ジャッジ日時 2025-01-21 11:59:25
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;

template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

template<ll Mod>
struct ModInt{
    long long x;
    ModInt():x(0){}
    ModInt(long long 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);}
    ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;}
    ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;}
    ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;}
    ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;}
    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(long long n)const{
        ModInt ret(1),mul(x);
        while(n>0){
            if(n&1) ret*=mul;
            mul*=mul;n>>=1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os,const ModInt &p){return os<<p.x;}
    friend istream &operator>>(istream &is,ModInt &a){long long t;is>>t;a=ModInt<Mod>(t);return (is);}
    static int get_mod(){return Mod;}
};

// 経路圧縮なし，マージテクでunite，クエリ毎O(logN)
struct UnionFindUndo{
    int con;
    vector<int> data;
    stack<tuple<int,int,bool>> history;
    UnionFindUndo(int sz){
        con=sz;
        data.assign(sz,-1);
    }
    bool unite(int x,int y){
        x=root(x),y=root(y);
        
        if(x==y){
            history.push(make_tuple(x,data[x],false));
            history.push(make_tuple(y,data[y],false));
            return false;
        }
        con--;
        history.push(make_tuple(x,data[x],true));
        history.push(make_tuple(y,data[y],false));
        if(data[x]>data[y]) swap(x,y);
        data[x]+=data[y];
        data[y]=x;
        return true;
    }
    int root(int k){return (data[k]<0?k:(root(data[k])));}
    int size(int k){return (-data[root(k)]);}
    bool sameroot(int x,int y){return root(x)==root(y);}
    void undo(){
        {
            auto [fs,sc,con_flag]=history.top();history.pop();
            if(con_flag) con++;
            data[fs]=sc;
        }
        {
            auto [fs,sc,con_flag]=history.top();history.pop();
            if(con_flag) con++;
            data[fs]=sc;
        }
    }
    void snapshot(){while(!history.empty())history.pop();}
    void rollback(){while(!history.empty())undo();}
};

// verified https://codeforces.com/gym/100551/submission/103148848
// ref https://ei1333.hateblo.jp/entry/2017/12/14/000000
struct DynamicConnectivityOffline{
    private:
    int sz;
    using P=pair<int,int>;
    vector<vector<P>> seg;
    vector<pair<P,P>> es;// {{start idx, end idx}, {u, v}}
    map<P,int> cnt,prev;

    void add_seg(int a,int b,P &e,int k,int l,int r){
        if(r<=a or b<=l) return ;
        if(a<=l and r<=b){
            seg[k].push_back(e);
            return ;
        }
        add_seg(a,b,e,2*k,l,(l+r)/2);
        add_seg(a,b,e,2*k+1,(l+r)/2,r);
    }
    

    public:
    int n,q;
    UnionFindUndo uf;

    DynamicConnectivityOffline(int n,int q):n(n),q(q),uf(n){
        sz=1;while(sz<q)sz<<=1;
        seg.resize(sz*2);
    }

    // queryのindex順に追加
    void add_edge(int query_idx,int u,int v){
        if(u>v) swap(u,v);
        if(cnt[P(u,v)]==0) prev[P(u,v)]=query_idx;
        cnt[P(u,v)]++;
    }
    void delete_edge(int query_idx,int u,int v){
        if(u>v) swap(u,v);
        assert(cnt[P(u,v)]>0);
        cnt[P(u,v)]--;
        if(cnt[P(u,v)]==0) es.emplace_back(P(prev[P(u,v)],query_idx),P(u,v));
    }
    void build(){
        for(auto [e,c]:cnt)if(c>0) es.emplace_back(P(prev[e],sz),e);
        for(auto [t,e]:es) add_seg(t.first,t.second,e,1,0,sz);
    }
    // dfs -> segment tree
    // f(query_idx)
    void execute(const function<void(int)> &f,int k=1){
        for(auto [u,v]:seg[k]) uf.unite(u,v);
        if(k<sz){
            execute(f,2*k);
            execute(f,2*k+1);
        }
        else if(k-sz<q) f(k-sz);// query
        for(auto [u,v]:seg[k]) uf.undo();
    }
};

using mint=ModInt<998244353>;

mint i2=mint(2).inverse();

signed main(){

    int N;cin>>N;

    DynamicConnectivityOffline daicon(N,3*N-3);

    vector<pair<int,int>> E;
    rep(i,N-1){
        int u,v;cin>>u>>v;
        E.emplace_back(u,v);
        daicon.add_edge(i,u,v);
    }
    rep(i,N-1){
        auto [u,v]=E[i];
        daicon.delete_edge(N-1+2*i,u,v);
        daicon.add_edge(N-1+2*i+1,u,v);
    }

    daicon.build();

    mint num=0;
    auto f=[&](int k){
        if(k<N-1) return ;
        if((k-N+1)%2) return ;
        int A=daicon.uf.size(0);
        int B=N-A;

        num+=mint(A)*mint(A-1)*i2;
        num+=mint(B)*mint(B-1)*i2;
        return ;
    };

    daicon.execute(f);

    mint den=mint(N)*mint(N-1)*mint(N-1)*i2;
    cout<<num/den<<endl;
    return 0;
}
0