TOJ 1883 Domino Effect

Description

Did you know that you can use domino bones for other things besides playing Dominoes? Take a number of dominoes and build a row by standing them on end with only a small distance in between. If you do it right, you can tip the first domino and cause all others to fall down in succession (this is where the phrase ``domino effect'' comes from).

While
this is somewhat pointless with only a few dominoes, some people went to
the opposite extreme in the early Eighties. Using millions of dominoes
of different colors and materials to fill whole halls with elaborate
patterns of falling dominoes, they created (short-lived) pieces of art.
In these constructions, usually not only one but several rows of
dominoes were falling at the same time. As you can imagine, timing is an
essential factor here.

It is now your task to write a program
that, given such a system of rows formed by dominoes, computes when and
where the last domino falls. The system consists of several ``key
dominoes'' connected by rows of simple dominoes. When a key domino
falls, all rows connected to the domino will also start falling (except
for the ones that have already fallen). When the falling rows reach
other key dominoes that have not fallen yet, these other key dominoes
will fall as well and set off the rows connected to them. Domino rows
may start collapsing at either end. It is even possible that a row is
collapsing on both ends, in which case the last domino falling in that
row is somewhere between its key dominoes. You can assume that rows fall
at a uniform rate.

Input

The
input file contains descriptions of several domino systems. The first
line of each description contains two integers: the number n of key
dominoes (1 <= n < 500) and the number m of rows between them. The
key dominoes are numbered from 1 to n. There is at most one row between
any pair of key dominoes and the domino graph is connected, i.e. there
is at least one way to get from a domino to any other domino by
following a series of domino rows.

The following m lines each
contain three integers a, b, and l, stating that there is a row between
key dominoes a and b that takes l seconds to fall down from end to end.

Each system is started by tipping over key domino number 1.

The file ends with an empty system (with n = m = 0), which should not be processed.

Output

For
each case output a line stating the number of the case ('System #1',
'System #2', etc.). Then output a line containing the time when the last
domino falls, exact to one digit to the right of the decimal point, and
the location of the last domino falling, which is either at a key
domino or between two key dominoes(in this case, output the two numbers
in ascending order). Adhere to the format shown in the output sample.
The test data will ensure there is only one solution. Output a blank
line after each system.

Sample Input

2 1
1 2 27
3 3
1 2 5
1 3 5
2 3 5
0 0

Sample Output

System #1
The last domino falls after 27.0 seconds, at key domino 2.

System #2
The last domino falls after 7.5 seconds, between key dominoes 2 and 3.

Source

Southwestern Europe 1996

 #include <stdio.h>
 #include <iostream>
 #include <queue>
 #include <vector>
 #define MAXN 600
 #define inf 0x3f3f3f3f
 using namespace std;

 struct Node{
     int end;
     double dis;
 };

 int n,m;
 double dist[MAXN];
 vector<Node> V[MAXN];

 void spfa(){
     for(int i=; i<=n; i++,dist[i]=inf);
     dist[]=;
     queue<Node> Q;
     Node n1;
     n1.end=;
     n1.dis=;
     Q.push(n1);
     while( !Q.empty() ){
         Node now=Q.front();
         Q.pop();
         for(int i=; i<V[now.end].size(); i++){
             Node temp=V[now.end][i];
             double v=temp.dis+now.dis;
             if( v < dist[temp.end]){
                 dist[temp.end]=v;
                 temp.dis=v;
                 Q.push(temp);
             }
         }
     }
 }

 int main()
 {
     int c=;
     while( scanf("%d %d",&n ,&m)!=EOF ){
         if(n== && m==)break;
         for(int i=; i<=n; i++){
             V[i].clear();
         }
         int a,b,l;
         for(int i=; i<m; i++){
             scanf("%d %d %d",&a ,&b ,&l);
             Node n1,n2;
             n1.end=b;
             n1.dis=l;
             V[a].push_back(n1);
             n2.end=a;
             n2.dis=l;
             V[b].push_back(n2);
         }
         spfa();
         double ans=-;
         int k=;
         for(int i=; i<=n; i++){
             if(dist[i]>ans){
                 ans=dist[i];
                 k=i;
             }
         }
         int flag=,t1,t2;
         for(int i=; i<=n; i++){
             for(int j=; j<V[i].size(); j++){
                 int to=V[i][j].end;
                 double dis=V[i][j].dis;
                 if( (dist[i]+dis+dist[to])/>ans ){
                     flag=;
                     ans=(dist[i]+dis+dist[to])/;
                     t1=i;
                     t2=to;
                 }
             }
         }
         printf("System #%d\n",++c);
         if(flag){
             printf("The last domino falls after %.1lf seconds, between key dominoes %d and %d.\n"
                 ,ans ,min(t1,t2) ,max(t1,t2));
         }else{
             printf("The last domino falls after %.1lf seconds, at key domino %d.\n",ans,k);
         }
         puts("");
     }
     return ;
 }