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

Til the Cows Come Home

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 63212		Accepted: 21342

Description

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.

Code

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#define N 2010
#define INF 0x3f3f3f3f

using namespace std;

int map[N][N];
int dis[N];
int vis[N];
int t,n;

void Dijkstra()
{
    int i,j,pos,minn;
    for(i=1; i<=n; i++)
    {
        dis[i] = map[1][i];
        vis[i] = 0;
    }
    vis[1] = 1;
    for(i=1; i<=n-1; i++)
    {
        minn = INF;
        for(j=1; j<=n; j++)
        {
            if(!vis[j] && dis[j] < minn)
            {
                minn = dis[j];
                pos = j;
            }
        }
        vis[pos] = 1;
        for(j=1; j<=n; j++)
        {
            if(!vis[j] && map[j][pos] != INF && dis[j] > dis[pos] + map[pos][j])
            {
                dis[j] = dis[pos] + map[pos][j];
            }
        }
    }
    printf("%d\n",dis[n]);
}

int main()
{
    int i,j,u,v,w;
    scanf("%d %d",&t,&n);
    for(i=1;i<=n;i++)
    {
        for(j=1;j<=n;j++)
        {
            if(i == j)
                map[i][j] = 0;
            else
                map[i][j] = INF;
        }
    }
    for(i=1; i<=t; i++)
    {
        scanf("%d %d %d",&u,&v,&w);
        if(map[u][v] > w)
            map[u][v] = map[v][u] = w;
    }
    Dijkstra();
    return 0;
}

反思：

题目大意：奶牛Bessie想尽快回家，赶在挤奶之前睡个美容觉，因此需要走最短路径~第一行输入t和n，接下来有t行数据，每行三个数据代表两个点和它们的权值（路径长度），n是Bessie的目的地，也是图的大小，Bessie需要从n走到1，求最短路径的长度。最短路模板题，注意要查重边！