hdu 2066 ( 最短路) Floyd & Dijkstra & Spfa

http://acm.hdu.edu.cn/showproblem.php?pid=2066

今天复习了一下最短路和最小生成树,发现居然闹了个大笑话-----我居然一直写的是Floyd,但我自己一直以为这是Dijkstra---我居然一直把两个算法

记的是混的,还居然一直没有被别人发现,真是个大乌龙

好了,看看这道题,赤裸裸的最短路水题,首先来个Floyd的,把城市看成点,将连通的的点赋值为给定的时间,未连通的赋值为很大,这是个无向的关系

然后就是三个循环,以一个点为媒介,把每个点遍历一遍,比较找出点连通的最小值就行,稍微优化一点点就不会超时了

code

 #include<cstdio>
 #include<algorithm>
 #define inf 1000000005
 using namespace std;
 int mp[][],q[];
 void jjc()
 {
     int i,j;
     for (i=;i<=;i++){
        for (j=;j<=;j++){
            if (i==j) mp[i][j]=;
            else mp[i][j]=inf;
        }
     }
 }
 int min(int x,int y){
     if (x<y) return x;
     else return y;
 }
 int main()
 {
     int t,s,d,c,i,j,k,w,mx,a,b,mn;
     while (~scanf("%d %d %d",&t,&s,&d))
     {
         jjc();
         mx=;mn=inf;
         while (t--)
         {
             scanf("%d %d %d",&a,&b,&c);
             if (mp[a][b]>c)
                  mp[a][b]=mp[b][a]=c;
             if (a>mx) mx=a;  没有给定范围,所以找范围
             if (b>mx) mx=b;
             if (a<mn) mn=a;
             if (b<mn) mn=b;
         }
         for (k=mn;k<=mx;k++){
             for (i=mn;i<=mx;i++){
                 if (mp[i][k]>=inf) continue; //稍微优化一点点
                for (j=mn;j<=mx;j++){
                    mp[i][j]=min(mp[i][j],mp[i][k]+mp[k][j]);
                }
             }
         }
         for (i=;i<=s;i++)
           scanf("%d",&q[i]);
         int ans=inf;
         while (d--)
         {
             scanf("%d",&w);
             for (i=;i<=s;i++)
             {
                if (mp[q[i]][w]<ans)
                    ans=mp[q[i]][w];
             }
         }
         printf("%d\n",ans);
     }
     return ;
 }

然后是Dijkstra的, Floyd是把任意两点的最短距离都求了出来,而Dijkstra只是求了特定的起点与所有点之间的最短路,一般情况而言,后者要快于前者,具体用哪种根据题目而定

按照距离从小到大的顺序,找出从给定起点能够到达的下一点,每找到一个这样的点,然后更新其余点之间的距离

code

 #include<cstdio>
 #define inf 100000005
 using namespace std;
 int map[][],vis[],dis[];
 int st[],sr[];
 int mn,mx;
 int min(int x,int y)
 {
     if (x<y) return x;
     else return y;
 }
 void jjc()
 {
     int i,j;
     for (i=;i<=;i++){
         for (j=;j<=;j++){
             if (i==j) map[i][j]=;
             else map[i][j]=inf;
         }
     }
 }
 void dijkstra(int x)
 {
     int i,pos,j,q;
     for (i=mn;i<=mx;i++)
     {
         dis[i]=map[x][i];
         vis[i]=;
     }
     vis[x]=;
     for (i=mn;i<=mx;i++)
     {
         q=inf;pos=x;
         for (j=mn;j<=mx;j++)
             if (!vis[j]&&dis[j]<q)
             {
                 pos=j;
                 q=dis[j];
             }
         vis[pos]=;
         for (j=mn;j<=mx;j++)
              dis[j]=min(dis[j],dis[pos]+map[pos][j]);
     }
 }
 int main()
 {
     int t,s,d,a,b,c,i,j;
     while (~scanf("%d %d %d",&t,&s,&d))
     {
         jjc();
         mx=,mn=inf;
         while (t--)
         {
             scanf("%d %d %d",&a,&b,&c);
             if (map[a][b]>c)
                map[a][b]=map[b][a]=c;
             if (a>mx) mx=a;
             if (b>mx) mx=b;
             if (a<mn) mn=a;
             if (b<mn) mn=b;
         }
         for (i=;i<=s;i++)
            scanf("%d",&st[i]);
         for (i=;i<=d;i++)
             scanf("%d",&sr[i]);
         int ans=inf;
         for (i=;i<=s;i++)
         {
             dijkstra(st[i]);
             for (j=;j<=d;j++)
                if (dis[sr[j]]<ans)
                   ans=dis[sr[j]];
         }
         printf("%d\n",ans);
     }
     return ;
 }

队列储存,广搜版的spfa

code

 #include<cstdio>
 #include<cstring>
 #include<queue>
 #define inf 0x3fffffff
 using namespace std;
 int map[][],vis[],dis[];
 int st[],sr[];
 int mn,mx,s,d;
 void jjc()
 {
     int i,j;
     for (i=;i<=;i++){
         for (j=;j<=;j++){
             if (i==j) map[i][j]=;
             else map[i][j]=inf;
         }
     }
 }
 int spfa()
 {
    int num,i;
    memset(vis,,sizeof(vis));
    for (i=mn;i<=mx;i++)
        dis[i]=inf;
    queue<int> q;
    for (i=;i<=s;i++)
    {
        dis[st[i]]=;
        q.push(st[i]);
    }
    while(!q.empty())
    {
        num=q.front();
        q.pop();
        vis[num]=;
        for (i=mn;i<=mx;i++)
        {
            if (dis[i]>dis[num]+map[num][i])
            {
                dis[i]=dis[num]+map[num][i];
                if (vis[i]==)
                {
                    vis[i]=;
                    q.push(i);
                }
            }
        }
    }
    int p=inf;
    for (i=;i<=d;i++)
    {
        if (p>dis[sr[i]]) p=dis[sr[i]];
    }
    return p;
 }
 int main()
 {
     int t,a,b,c,i,j;
     while (~scanf("%d %d %d",&t,&s,&d))
     {
         jjc();
         mx=,mn=inf;
         while (t--)
         {
             scanf("%d %d %d",&a,&b,&c);
             if (map[a][b]>c)
                map[a][b]=map[b][a]=c;
             if (a>mx) mx=a;
             if (b>mx) mx=b;
             if (a<mn) mn=a;
             if (b<mn) mn=b;
         }
         for (i=;i<=s;i++)
            scanf("%d",&st[i]);
         for (i=;i<=d;i++)
             scanf("%d",&sr[i]);
         int ans=spfa();
         printf("%d\n",ans);
     }
     return ;
 }