POJ

Til the Cows Come Home

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 51 2 202 3 303 4 204 5 201 5 100

Sample Output

90

解题思路：最短路的模板题，以这题为例子，介绍各种最短路算法，和图的各种表示。这里介绍了经典Dijkstra算法和，队列优化的Bell算法，即Spfa算法。Dijkstra算法不能解决负环，而Spfa可以，本例中，spfa返回1代表有负环，0代表没有。算法具体解释参考其他博文。

Dijkstra 邻接矩阵表示

#include<iostream>#include<deque>#include<memory.h>#include<stdio.h>#include<map>#include<string>#include<algorithm>#include<vector>#include<math.h>#include<stack>#include<queue>#include<set>#define inf 1<<29#define MAXV 4005using namespace std;//dijkstra 邻接矩阵表示int rect[MAXV][MAXV];int n,m;void dijkstra(int s,int e){    int i,j,min,v;    int d[MAXV];    bool vis[MAXV];    for(i=1;i<=n;i++){        vis[i]=0;        d[i]=rect[s][i];    }    for(i=1;i<=n;i++){        min=inf;        for(j=1;j<=n;j++)            if(!vis[j]&&d[j]<min){                v=j;                min=d[j];            }        vis[v]=1;        for(j=1;j<=n;j++)            if(!vis[j]&&d[j]>rect[v][j]+d[v])                d[j]=rect[v][j]+d[v];    }    printf("%d\n",d[e]);}int main(){    int a,b,c;    while(~scanf("%d%d",&m,&n)){        for(int i=1;i<=n;i++)            for(int j=1;j<=n;j++)                if(i==j)                    rect[i][j]=0;                else                    rect[i][j]=rect[j][i]=inf;        for(int i=1;i<=m;i++){            scanf("%d%d%d",&a,&b,&c);            if(rect[a][b]>c)                rect[a][b]=rect[b][a]=c;        }        dijkstra(n,1);    }    return 0;}


Dijkstra 邻接表
#include<iostream>#include<deque>#include<memory.h>#include<stdio.h>#include<map>#include<string>#include<algorithm>#include<vector>#include<math.h>#include<stack>#include<queue>#include<set>#define inf 1<<29#define MAXV 4005using namespace std;struct edge{    int v1,v2,w,next;}e[MAXV];int n,m,edge_num;int head[MAXV],d[MAXV];bool vis[MAXV];void insert_edge(int v1,int v2,int w){    e[edge_num].v1=v1;    e[edge_num].v2=v2;    e[edge_num].w=w;    e[edge_num].next=head[v1];    head[v1]=edge_num++;    e[edge_num].v1=v2;    e[edge_num].v2=v1;    e[edge_num].w=w;    e[edge_num].next=head[v2];    head[v2]=edge_num++;}void dijkstra(int s,int en){    int i,j,v,min;    memset(vis,0,sizeof(vis));    vis[s]=true;    d[s]=0;    v=s;    for(j=1;j<=n;j++){        for(i=head[v];i!=-1;i=e[i].next){            int u1=e[i].v2;            if(!vis[u1]&&d[v]+e[i].w<d[u1])                d[u1]=d[v]+e[i].w;        }        min=inf;        for(i=0;i<n;i++){            if(!vis[i]&&d[i]<min){                v=i;                min=d[i];            }        }        vis[v]=true;    }    printf("%d\n",d[en]);}int main(){    int a,b,c;    while(~scanf("%d%d",&m,&n)){        edge_num=0;        memset(head,-1,sizeof(head));        for(int i=1;i<=n;i++)            d[i]=inf;        for(int i=1;i<=m;i++){            scanf("%d%d%d",&a,&b,&c);            insert_edge(a,b,c);        }        dijkstra(n,1);    }    return 0;}


Spfa 邻接矩阵
#include<iostream>#include<deque>#include<memory.h>#include<stdio.h>#include<map>#include<string>#include<algorithm>#include<vector>#include<math.h>#include<stack>#include<queue>#include<set>#define inf 1<<29#define MAXV 4005using namespace std;int rect[MAXV][MAXV];int n,m;int time[MAXV];int d[MAXV];int vis[MAXV];bool spfa(int s,int e){    queue<int> que;    memset(time,0,sizeof(time));    for(int i=1;i<=n;i++)d[i]=inf;    memset(vis,0,sizeof(vis));    que.push(e);    d[e]=0;    time[e]++;    vis[e]=1;    while(!que.empty()){        int tp=que.front();        que.pop();        vis[tp]=0;        for(int i=1;i<=n;i++){            if(d[i]>d[tp]+rect[tp][i]){                d[i]=d[tp]+rect[tp][i];                if(!vis[i]){                    que.push(i);                    vis[i]=1;                    if(++time[i]>=n)                        return 1;                }            }        }    }    printf("%d\n",d[s]);    return 0;}int main(){    int a,b,c;    while(~scanf("%d%d",&m,&n)){        for(int i=1;i<=n;i++)            for(int j=1;j<=n;j++)                if(i==j)                    rect[i][j]=0;                else                    rect[i][j]=rect[j][i]=inf;        for(int i=1;i<=m;i++){            scanf("%d%d%d",&a,&b,&c);            if(rect[a][b]>c)                rect[a][b]=rect[b][a]=c;        }        spfa(n,1);    }    return 0;}

Spfa 邻接表
#include<iostream>#include<deque>#include<memory.h>#include<stdio.h>#include<map>#include<string>#include<algorithm>#include<vector>#include<math.h>#include<stack>#include<queue>#include<set>#define inf 1<<29#define MAXV 4005using namespace std;//spfa 邻接表struct edge{    int v1,v2,w,next;}e[MAXV];int n,m,edge_num;int head[MAXV],d[MAXV];bool vis[MAXV];int time[MAXV];void insert_edge(int v1,int v2,int w){    e[edge_num].v1=v1;    e[edge_num].v2=v2;    e[edge_num].w=w;    e[edge_num].next=head[v1];    head[v1]=edge_num++;    e[edge_num].v1=v2;    e[edge_num].v2=v1;    e[edge_num].w=w;    e[edge_num].next=head[v2];    head[v2]=edge_num++;}bool spfa(int s,int en){    queue<int> que;    memset(vis,0,sizeof(vis));    memset(time,0,sizeof(time));    for(int i=1;i<=n;i++)d[i]=inf;    que.push(en);    d[en]=0;    time[en]++;    vis[en]=1;    while(!que.empty()){        int tp=que.front();        que.pop();        vis[tp]=0;        for(int i=head[tp];i!=-1;i=e[i].next)            if(d[tp]+e[i].w<d[e[i].v2]){                d[e[i].v2]=d[tp]+e[i].w;                if(!vis[e[i].v2]){                    vis[e[i].v2]=1;                    que.push(e[i].v2);                    if(++time[e[i].v2]>=n)                        return 1;                }            }    }    printf("%d\n",d[s]);    return 0;}int main(){    int a,b,c;    while(~scanf("%d%d",&m,&n)){        edge_num=0;        memset(head,-1,sizeof(head));        for(int i=1;i<=n;i++)            d[i]=inf;        for(int i=1;i<=m;i++){            scanf("%d%d%d",&a,&b,&c);            insert_edge(a,b,c);        }        spfa(n,1);    }    return 0;}