Problem Description

Innocent Wu follows Dumb Zhang into a ancient tomb. Innocent Wu’s at the entrance of the tomb while Dumb Zhang’s at the end of it. The tomb is made up of many chambers, the total number is N. And there are M channels connecting the chambers. Innocent Wu wants
to catch up Dumb Zhang to find out the answers of some questions, however, it’s Dumb Zhang’s intention to keep Innocent Wu in the dark, to do which he has to stop Innocent Wu from getting him. Only via the original shortest ways from the entrance to the end
of the tomb costs the minimum time, and that’s the only chance Innocent Wu can catch Dumb Zhang.
Unfortunately, Dumb Zhang masters the art of becoming invisible(奇门遁甲) and tricks devices of this tomb, he can cut off the connections between chambers by using them. Dumb Zhang wanders how many channels at least he has to cut to stop Innocent Wu. And Innocent
Wu wants to know after how many channels at most Dumb Zhang cut off Innocent Wu still has the chance to catch Dumb Zhang.

 

Input

There are multiple test cases. Please process till EOF.
For each case,the first line must includes two integers, N(<=2000), M(<=60000). N is the total number of the chambers, M is the total number of the channels.
In the following M lines, every line must includes three numbers, and use ai、bi、li as channel i connecting chamber ai and bi(1<=ai,bi<=n), it costs li(0<li<=100) minute to pass channel i.
The entrance of the tomb is at the chamber one, the end of tomb is at the chamber N.

 

Output

Output two numbers to stand for the answers of Dumb Zhang and Innocent Wu’s questions.

 

Sample Input

 

Sample Output

 

Author

FZUACM

 

Source

2015 Multi-University Training Contest 1

#include <iostream>

#include<stdio.h>

#include<string.h>

#include<vector>

#include<algorithm>

#include<cmath>

#include<map>

#include<queue>

using namespace std;

const int N=2005;

const int MAXN=(1<<31)-1;

int INF=0x7f7f7f7f;

 int T,n,m,k,tot;

 int cas=1;

 int head[N];

 struct Edge{

    int to,w,next;

 }edge[60005*2];

 void addedge(int u,int v,int w){

    edge[tot].to=v;

    edge[tot].w=w;

    edge[tot].next=head[u];

    head[u]=tot++;

    edge[tot].to=u;

    edge[tot].w=w;

    edge[tot].next=head[v];

    head[v]=tot++;

 }

 int dis[N],vis[N];

 int minb[N];

 int spfa(int s){

    memset(dis,0x3f,sizeof dis);

    memset(vis,0,sizeof vis);

    memset(minb,0x3f,sizeof minb);

    queue<int> q;

    dis[s]=0;

    minb[s]=0;

    vis[s]=1;

    q.push(s);

    while(!q.empty()){

        int u=q.front();q.pop();

        vis[u]=0;

        for(int i=head[u];~i;i=edge[i].next){

           int v=edge[i].to,w=edge[i].w;

           if(dis[v]==dis[u]+w){

                minb[v]=min(minb[v],minb[u]+1);

                if(!vis[v]){

                    vis[v]=1;

                    q.push(v);

                }

           }

           if(dis[v]>dis[u]+w){

                dis[v]=dis[u]+w;

                minb[v]=minb[u]+1;

                if(!vis[v]){

                    vis[v]=1;

                    q.push(v);

                }

           }

        }

    }

 }

 struct Eg{

    int u,cap,rev;

    Eg(int uu,int cc,int rr){

        u=uu;cap=cc;rev=rr;

    }

 };

 vector<Eg> G[N];

 void add(int u,int v,int cap){

    G[u].push_back(Eg(v,cap,G[v].size()));

    G[v].push_back(Eg(u,0,G[u].size()-1));

 }

 void build(){

    for(int i=1;i<=n;i++){

        for(int j=head[i];~j;j=edge[j].next){

            int v=edge[j].to,w=edge[j].w;

            if(dis[v]==dis[i]+w){

                add(i,v,1);

            }

        }

    }

 }

 bool used[N];

 int dfs(int v,int t,int f){

    if(v==t) return f;

    used[v]=true;

    for(int i=0;i<G[v].size();i++){

        Eg &e=G[v][i];

        if(!used[e.u] && e.cap>0){

            int d=dfs(e.u,t,min(f,e.cap));

            if(d>0){

                e.cap-=d;

                G[e.u][e.rev].cap+=d;

                return d;

            }

        }

    }

    return 0;

 }

 int max_flow(int s,int t){

  int flow=0;

  while(1){

    memset(used,0,sizeof used);

    int f=dfs(s,t,INF);

    if(f==0) return flow;

    flow+=f;

  }

 }

  void init(){

    tot=0;

    memset(head,-1,sizeof head);

    for(int i=0;i<N;i++) G[i].clear();

 }

int main()

{

#ifndef  ONLINE_JUDGE

   freopen("aaa","r",stdin);

#endif

    while(~scanf("%d%d",&n,&m)){

        init();

        for(int i=0;i<m;i++){

            int u,v,w;

            scanf("%d %d %d",&u,&v,&w);

            addedge(u,v,w);

        }

        spfa(1);

        build();

        int ans=max_flow(1,n);

        printf("%d %d\n",ans,m-minb[n]);

    }

    return 0;

}