Highway Project

本文介绍了一个基于图论的算法,用于解决如何构建最优高速公路网络的问题,以确保从首都到其他城市的旅行时间最短且总成本最低。该算法通过两次遍历图的方式找到了每个城市之间的最短路径及相应的最小建设成本。

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注意long long


Edward, the emperor of the Marjar Empire, wants to build some bidirectional highways so that he can reach other cities from the capital as fast as possible. Thus, he proposed the highway project.

The Marjar Empire has N cities (including the capital), indexed from 0 to N - 1 (the capital is 0) and there are M highways can be built. Building the i-th highway costs Ci dollars. It takes Di minutes to travel between city Xi and Yi on the i-th highway.

Edward wants to find a construction plan with minimal total time needed to reach other cities from the capital, i.e. the sum of minimal time needed to travel from the capital to city i (1 ≤ iN). Among all feasible plans, Edward wants to select the plan with minimal cost. Please help him to finish this task.


Input

There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:

The first contains two integers N, M (1 ≤ N, M ≤ 105).

Then followed by M lines, each line contains four integers Xi, Yi, Di, Ci (0 ≤ Xi, Yi < N, 0 < Di, Ci < 105).

Output

For each test case, output two integers indicating the minimal total time and the minimal cost for the highway project when the total time is minimized.

Sample Input
2
4 5
0 3 1 1
0 1 1 1
0 2 10 10
2 1 1 1
2 3 1 2
4 5
0 3 1 1
0 1 1 1
0 2 10 10
2 1 2 1
2 3 1 2
Sample Output
4 3
4 4
#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int N=1e5+10;
#define inf (1ll<<60)

struct AA{
    int y;
    int d;
    int w;
    AA(){}
    AA(int yy,int dd,int ww):y(yy),d(dd),w(ww){}
};

AA aa[N];

vector<AA> v[N];
ll dist[N];
int wei[N];
int vis[N];

void dijkstra(){
    //memset(dist,63,sizeof(dist));
    fill(dist,dist+N,inf);
    memset(vis,0,sizeof(vis));
    dist[0]=0;
    queue<int> q;
    q.push(0);
    vis[0]=true;
    wei[0]=0;
    while(!q.empty()){
        int u=q.front();
        //cout<<u<<endl;
        q.pop();
        //for(auto uu:v[u]){
        for(int i=0;i<v[u].size();i++){
            AA uu=v[u][i];
            if(dist[u]+uu.d<dist[uu.y]){
                dist[uu.y]=dist[u]+uu.d;
              //  cout<<"uu.y:"<<uu.y<<" "<<dist[uu.y]<<endl;
                wei[uu.y]=uu.w;
                if(!vis[uu.y]){
                    q.push(uu.y);
                    vis[uu.y]=true;
                }
            }else if(dist[u]+uu.d==dist[uu.y]){
                wei[uu.y]=min(wei[uu.y],uu.w);
                if(!vis[uu.y]){
                    q.push(uu.y);
                    vis[uu.y]=true;
                }
            }
        }
        vis[u]=false;
    }
}

int main(){
    int n,m;
    //freopen("in.txt","r",stdin);
    int t;
    cin>>t;
    while(t--){
        int n,m;
        cin>>n>>m;
        for(int i=0;i<=n;i++)
        v[i].clear();
        for(int i=0;i<m;i++){
            int x,y,d,w;
            scanf("%d%d%d%d",&x,&y,&d,&w);
            v[x].push_back(AA(y,d,w));
            v[y].push_back(AA(x,d,w));
        }
        dijkstra();
        ll ans=0,anw=0;
        for(int i=1;i<n;i++){
            ans+=dist[i];
            anw+=wei[i];
           // cout<<"i"<<dist[i]<<" "<<wei[i]<<endl;
        }
        cout<<ans<<" "<<anw<<endl;
    }
    //fclose(stdin);
}
#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define pll pair<ll,ll>
#define plll pair<int,pll>
#define infp (1ll<<60)

const int N=1e5+10;
vector<plll> g[N];

bool vis[N];
pll dis[N];
int n,m;
void spfa(){
    queue<int> q;
    for(int i=0;i<n;i++)
    dis[i]=pll(infp,infp),vis[i]=0;
    q.push(0);
    dis[0]=pll(0,0);
    vis[0]=1;
    while(!q.empty()){
        int u=q.front();
        //cout<<u<<endl;
        for(int i=0;i<g[u].size();i++){
            int v=g[u][i].first;
            int d=g[u][i].second.first;
            int c=g[u][i].second.second;
            if(dis[v]>pll(dis[u].first+d,c)){
                dis[v]=pll(dis[u].first+d,c);
                if(!vis[v]){
                    vis[v]=1;
                    q.push(v);
                }
            }
        }
        vis[u]=0;
        q.pop();
    }
}


int main(){
   // freopen("in.txt","r",stdin);
    int t;
    cin>>t;
    while(t--){
        cin>>n>>m;
        for(int i=0;i<n;i++)
        g[i].clear();
        for(int i=0;i<m;i++){
            int x,y,d,c;
            scanf("%d%d%d%d",&x,&y,&d,&c);
            g[x].push_back(plll(y,pll(d,c)));
            g[y].push_back(plll(x,pll(d,c)));
        }
        spfa();
        ll d=0,c=0;
        for(int i=0;i<n;i++){
            d+=dis[i].first;
            c+=dis[i].second;
        }
        cout<<d<<" "<<c<<endl;
    }
    //fclose(stdin);
}


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