POJ - 2387 Til the Cows Come Home（最短路）（Dijkstra模板题）

POJ - 2387  Til the Cows Come Home（Dijkstra模板题）(无向图） 

Problem

Bessie is out in the field and wants to get back to the barn to get as much sleep as possible before Farmer John wakes her for the morning milking. Bessie needs her beauty sleep, so she wants to get back as quickly as possible. 

Farmer John's field has N (2 <= N <= 1000) landmarks in it, uniquely numbered 1..N. Landmark 1 is the barn; the apple tree grove in which Bessie stands all day is landmark N. Cows travel in the field using T (1 <= T <= 2000) bidirectional cow-trails of various lengths between the landmarks. Bessie is not confident of her navigation ability, so she always stays on a trail from its start to its end once she starts it. 

Given the trails between the landmarks, determine the minimum distance Bessie must walk to get back to the barn. It is guaranteed that some such route exists.

 

Input

* Line 1: Two integers: T and N 
* Lines 2..T+1: Each line describes a trail as three space-separated integers. The first two integers are the landmarks between which the trail travels. The third integer is the length of the trail, range 1..100.

 

Output

* Line 1: A single integer, the minimum distance that Bessie must travel to get from landmark N to landmark 1.

 

Sample Input

5 5
1 2 20
2 3 30
3 4 20
4 5 20
1 5 100
 

Sample Output

90

 

Hint

INPUT DETAILS: 
There are five landmarks. 
OUTPUT DETAILS: 
Bessie can get home by following trails 4, 3, 2, and 1.

 

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 题意：

 给出两个整数T,N，然后输入一些点之间的直接距离，求N到1之间的最短距离.。

思路：

标准dijkstra求单源最短路，但是要注意判重。

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
#include<iostream>
#define INF 0x3f3f3f3f
using namespace std;
int vis[1010];//标记该点是否被访问
int dist[1010];//记录每个点到原点的距离
int T,N;
typedef struct GNode
{
    int Nv,Ne;
    int G[1010][1010];
}*Mgraph;
Mgraph Creat_AdjacencyMatrix()//初始化
{
    //cout<<'A'<<endl;
    Mgraph p;
    p=new GNode;
    p->Ne=0;
    p->Nv=N;
    for(int i=1; i<=N; i++)
        for(int j=1; j<=N; j++)
            if(i==j)
                p->G[i][j]=0;
            else
                p->G[i][j]=INF;
    return p;
}
void Insert_Edge(Mgraph &p)//插入边
{
    //cout<<'B'<<endl;
    int v,w,k;
    for(int i=1; i<=T; i++)
    {
        cin>>v>>w>>k;
        if(k<p->G[v][w])//这里是判断是否有重边，应为两点之间的路，未必只有一条。
        {
            p->G[v][w]=k;
            p->G[w][v]=k;
        }
    }

}
void Diskstra(Mgraph p)
{
    int index;
    for(int i=1; i<=N; i++) //初始化原点周围的点到原点的距离
    {
        dist[i]=p->G[1][i];
        //cout<<dist[i]<<endl;
    }
    vis[1]=1;
    while(1)
    {
        int Min=INF;
        //找出所有点中最小的一个
        for(int i=1; i<=N; i++)
        {
            if(vis[i]==0&&Min>dist[i])
            {
                Min=dist[i];
                index=i;
            }
        }

        if(Min==INF)
            break;
        else
            vis[index]=1;
        //更新最小点周围点到原点的距离
        for(int i=1; i<=N; i++)
            if(!vis[i]&&dist[i]>dist[index]+p->G[index][i])
                dist[i]=dist[index]+p->G[index][i];
    }
    cout<<dist[N]<<endl;
}
int main()
{
    Mgraph graph;
    cin>>T>>N;
    memset(vis,0,sizeof(vis));
    memset(dist,INF,sizeof(dist));
    graph=Creat_AdjacencyMatrix();//创建邻接矩阵
    Insert_Edge(graph);
    Diskstra(graph);
    return 0 ;
}