HDU 3371 Connect the Cities（prim算法）

Posted 2020-11-06 Reqaw’s Blog

题目链接：

http://acm.hdu.edu.cn/showproblem.php?pid=3371

Problem Description

In 2100, since the sea level rise, most of the cities disappear. Though some survived cities are still connected with others, but most of them become disconnected. The government wants to build some roads to connect all of these cities again, but they don’t want to take too much money.  

 

 

Input

The first line contains the number of test cases.
Each test case starts with three integers: n, m and k. n (3 <= n <=500) stands for the number of survived cities, m (0 <= m <= 25000) stands for the number of roads you can choose to connect the cities and k (0 <= k <= 100) stands for the number of still connected cities.
To make it easy, the cities are signed from 1 to n.
Then follow m lines, each contains three integers p, q and c (0 <= c <= 1000), means it takes c to connect p and q.
Then follow k lines, each line starts with an integer t (2 <= t <= n) stands for the number of this connected cities. Then t integers follow stands for the id of these cities.

 

 

Output

For each case, output the least money you need to take, if it’s impossible, just output -1.

 

 

Sample Input

1

6 4 3

1 4 2

2 6 1

2 3 5

3 4 33

2 1 2

2 1 3

3 4 5 6

 

 

Sample Output

1

 

 

Author

dandelion

 

 

Source

HDOJ Monthly Contest – 2010.04.04

 1 /*
 2 问题
 3 输入已经存在的图以及将要增加的边及其花费，计算并输出最小生成树还需要的最小花费
 4 
 5 解题思路
 6 将现在的图连起来使得它们的花费为0，再加入将要建设的边，直接跑一边prim即可，注意不能构成最小生成树
 7 的情况说出-1，代码中的u == -1 结束很关键。 
 8 */ 
 9 #include<cstdio>
10 #include<cstring>
11 
12 const int N=550;
13 const int INF=99999999;
14 int e[N+10][N+10],a[N],dis[N],bk[N];
15 int prim();
16 int n,m,k;
17 
18 int main(){
19     int T,i,j,q,t1,t2,t3,t;
20     scanf("%d",&T);
21     while(T--){
22         for(i=1;i<=N;i++){
23             for(j=1;j<=N;j++){
24                 e[i][j] = i==j?0:INF;
25             }
26         }
27         scanf("%d%d%d",&n,&m,&k);
28         for(i=1;i<=m;i++){
29             scanf("%d%d%d",&t1,&t2,&t3);
30             if(e[t1][t2] > t3){
31                 e[t1][t2] = t3;
32                 e[t2][t1] = t3;
33             }    
34         }
35         for(i=1;i<=k;i++){
36             scanf("%d",&t);
37             for(j=1;j<=t;j++){
38                 scanf("%d",&a[j]);
39             }
40             for(j=1;j<=t-1;j++){
41                 for(q=j+1;q<=t;q++){
42                     e[ a[j] ][ a[q] ]=0;
43                     e[ a[q] ][ a[j] ]=0;
44                 }
45             }
46         }
47         
48         /*for(i=1;i<=n;i++){
49             for(j=1;j<=n;j++){
50                 printf("%9d",e[i][j]);
51             }
52             printf("\n");
53         }*/
54         int ans=prim();
55         if(ans == -1)
56             printf("-1\n");
57         else
58             printf("%d\n",ans);
59     }
60     return 0;
61 } 
62 
63 int prim()
64 {
65     int i;
66     for(i=1;i<=n;i++)
67         dis[i]=e[1][i];
68     memset(bk,0,sizeof(bk));
69     bk[1]=1;
70     int c=1,sum=0,mina,u;
71     
72     while(c < n){
73         mina=INF;
74         u=-1;
75         for(i=1;i<=n;i++){
76             if(!bk[i] && dis[i] < mina){
77                 mina=dis[i];
78                 u=i;
79             }
80         }
81         //printf("u==%d\n",u);
82         if(u == -1)
83             break;
84         bk[u]=1;
85         c++;
86         sum += dis[u];
87         for(i=1;i<=n;i++){
88             if(!bk[i] && dis[i] > e[u][i])
89                 dis[i] = e[u][i];
90         }
91     }
92     if(u == -1)
93         return -1;
94     return sum;    
95 }