procon

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:x: test/yuki5436.test.cpp

Depends on

Code

#define PROBLEM "https://yukicoder.me/problems/5436"

#include "../template.hpp"

#include "../Graph2/Rerooting.hpp"

#include "../type/modint.hpp"

using mint=ModInt<1000000007>;

signed main(){
    int n;cin>>n;
    Graph<mint> g(n);
    g.read(n-1,-1,true,false);

    using T=tuple<mint,mint,mint>;
    function<T(T,Edge<mint>)> f=[&](T dpch,Edge<mint> e){
        auto [a2,a1,cnt]=dpch;
        return T(a1*2*e.w+a2+e.w*e.w*(cnt+1),a1+e.w*(cnt+1),cnt+1);
    };
    function<T(T,T)> merge=[&](T l,T r){
        return T(get<0>(l)+get<0>(r),get<1>(l)+get<1>(r),get<2>(l)+get<2>(r));
    };

    Rerooting<T,mint> R(g,f,merge,T(0,0,0));
    R.build();
    mint res=0;
    rep(i,n) res+=get<0>(R.ans[i]);
    cout<<res/2<<endl;
    return 0;
}
#line 1 "test/yuki5436.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/5436"

#line 1 "template.hpp"
#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;
}

#line 4 "test/yuki5436.test.cpp"

#line 1 "Graph2/GraphTemplate.hpp"



// graph template
// ref : https://ei1333.github.io/library/graph/graph-template.hpp
template<typename T=int>
struct Edge{
    int from,to;
    T w;
    int idx;
    Edge()=default;
    Edge(int from,int to,T w=1,int idx=-1):from(from),to(to),w(w),idx(idx){}
    operator int() const{return to;}
};

template<typename T=int>
struct Graph{
    vector<vector<Edge<T>>> g;
    int V,E;
    Graph()=default;
    Graph(int n):g(n),V(n),E(0){}

    int size(){
        return (int)g.size();
    }
    void resize(int k){
        g.resize(k);
        V=k;
    }
    inline const vector<Edge<T>> &operator[](int k)const{
        return (g.at(k));
    }
    inline vector<Edge<T>> &operator[](int k){
        return (g.at(k));
    }
    void add_directed_edge(int from,int to,T cost=1){
        g[from].emplace_back(from,to,cost,E++);
    }
    void add_edge(int from,int to,T cost=1){
        g[from].emplace_back(from,to,cost,E);
        g[to].emplace_back(to,from,cost,E++);
    }
    void read(int m,int pad=-1,bool weighted=false,bool directed=false){
        for(int i=0;i<m;i++){
            int u,v;cin>>u>>v;
            u+=pad,v+=pad;
            T w=T(1);
            if(weighted) cin>>w;
            if(directed) add_directed_edge(u,v,w);
            else         add_edge(u,v,w);
        }
    }
};


#line 2 "Graph2/Rerooting.hpp"

template<typename T,typename GT=int>
struct Rerooting{
    using E=function<T(T,Edge<GT>)>;//集合，頂点番号
    using M=function<T(T,T)>;
    using F=function<T(T,int)>;
    
    Graph<GT> g;
    // dp_v = fix(merge(f(dp_c1,edge(v,c1)),...,f(dp_ck,edge(v,ck))),v)
    E f;    // f(T,Edge)->T  辺情報を考慮し，merge前の形
    M merge;// TxT->T，子を集約する関数，モノイド
    T e;    // mergeの単位元
    F fix;  // TxN->T  補正
    vector<vector<T>> dp;
    vector<T> ans;
    
    Rerooting(Graph<GT> &g,E f,M merge,T e,F fix=[](T a,int b){return a;}):
    g(g),f(f),merge(merge),e(e),fix(fix),dp(g.size()),ans(g.size(),e){}

    T dfs1(int pre,int now){
        T ret=e;
        for(int i=0;i<(int)g[now].size();i++)if(g[now][i]!=pre){
            dp[now][i]=dfs1(now,g[now][i]);
            ret=merge(ret,f(dp[now][i],g[now][i]));
        }
        return fix(ret,now);
    }
    void dfs2(int pre,int now,T frompar){
        for(int i=0;i<(int)g[now].size();i++){
            if(g[now][i]==pre){
                dp[now][i]=frompar;
                break;
            }
        }
        vector<T> lsum(g[now].size()+1),rsum(g[now].size()+1);//親も混ぜて累積
        lsum[0]=e;rsum[g[now].size()]=e;
        for(int i=0;i<(int)g[now].size();i++) lsum[i+1]=merge(lsum[i],f(dp[now][i],g[now][i]));
        for(int i=(int)g[now].size();i>0;i--) rsum[i-1]=merge(rsum[i],f(dp[now][i-1],g[now][i-1]));
        for(int i=0;i<(int)g[now].size();i++)if(g[now][i]!=pre){
            T fromme=merge(lsum[i],rsum[i+1]);
            dfs2(now,g[now][i],fix(fromme,now));
        }
    }
    void build(int root=0){
        for(int i=0;i<(int)g.size();i++) dp[i].resize(g[i].size());
        dfs1(-1,root);
        dfs2(-1,root,e);
        for(int i=0;i<(int)g.size();i++){
            for(int j=0;j<(int)g[i].size();j++) ans[i]=merge(ans[i],f(dp[i][j],g[i][j]));
            ans[i]=fix(ans[i],i);
        }
    }
};
#line 6 "test/yuki5436.test.cpp"

#line 1 "type/modint.hpp"
template<int Mod>
struct ModInt{
    int x;
    ModInt():x(0){}
    ModInt(int y): x (y >= 0 ? y % Mod : (Mod - (-y) % Mod) % Mod){}
    ModInt(long long y){
        if (y >= 0)
        {
            x = (int)(y % (ll)(Mod));
        }
        else
        {
            int tmp = (int)((-y) % (ll)Mod);
            x = (Mod - tmp) % 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;}
};
#line 8 "test/yuki5436.test.cpp"

using mint=ModInt<1000000007>;

signed main(){
    int n;cin>>n;
    Graph<mint> g(n);
    g.read(n-1,-1,true,false);

    using T=tuple<mint,mint,mint>;
    function<T(T,Edge<mint>)> f=[&](T dpch,Edge<mint> e){
        auto [a2,a1,cnt]=dpch;
        return T(a1*2*e.w+a2+e.w*e.w*(cnt+1),a1+e.w*(cnt+1),cnt+1);
    };
    function<T(T,T)> merge=[&](T l,T r){
        return T(get<0>(l)+get<0>(r),get<1>(l)+get<1>(r),get<2>(l)+get<2>(r));
    };

    Rerooting<T,mint> R(g,f,merge,T(0,0,0));
    R.build();
    mint res=0;
    rep(i,n) res+=get<0>(R.ans[i]);
    cout<<res/2<<endl;
    return 0;
}
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