Constructing Roads

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 11576    Accepted Submission(s): 4353

Problem Description

There are N villages, which are numbered from 1 to N, and you should build some roads such that every two villages can connect to each other. We say two village A and B are connected, if and only if there is a road between A and B, or there exists a village C such that there is a road between A and C, and C and B are connected.

We know that there are already some roads between some villages and your job is the build some roads such that all the villages are connect and the length of all the roads built is minimum.

 

Input

The first line is an integer N (3 <= N <= 100), which is the number of villages. Then come N lines, the i-th of which contains N integers, and the j-th of these N integers is the distance (the distance should be an integer within [1, 1000]) between village i and village j.

Then there is an integer Q (0 <= Q <= N * (N + 1) / 2). Then come Q lines, each line contains two integers a and b (1 <= a < b <= N), which means the road between village a and village b has been built.

 

Output

You should output a line contains an integer, which is the length of all the roads to be built such that all the villages are connected, and this value is minimum.

 

Sample Input

3

0 990 692

990 0 179

692 179 0

1

1 2

 

Sample Output

179

 

Source

 

Recommend

Eddy

 

思路：简单最小生成树，使用Kruskal，不知道为什么使用Prim总是WA

 

代码：

#include 
      
       #include 
       
        #include 
        
         #include 
         
          #include 
          
           #include 
           
            using namespace std;const int MAXN = 100010;int map[110][110];int a,b;int n,q;int USETree[110];int the_last_flag;int the_last_sum;struct Node{ int first,end; int value; bool select;}Edge[MAXN];int find(int x){ while(x != USETree[x]) { x = USETree[x]; } return x;}void Merge(int x,int y){ int p = find(x); int q = find(y); if(p < q) USETree[q] = p; else USETree[p] = q;}bool cmp(Node a,Node b){ if(a.value != b.value) return a.value < b.value; if(a.first != b.first) return a.first < b.first; return a.end < b.end;}void Kruskal(Node *Egde,int n,int m){ the_last_flag = 0; sort(Edge + 1,Edge + m + 1,cmp); for(int i = 1;i <= m;i ++) { if(the_last_flag == n - 1) break ; int x = find(Edge[i].first); int y = find(Edge[i].end); if(x != y) { Merge(x,y); the_last_flag ++; Edge[i].select = true; } }}int main(){ while(~scanf("%d",&n)) { memset(Edge,0,sizeof(Edge)); for(int i = 1;i <= n;i ++) USETree[i] = i; for(int i = 1;i <= n;i ++) for(int j = 1;j <= n;j ++) scanf("%d",&map[i][j]); scanf("%d",&q); while(q --) { scanf("%d%d",&a,&b); map[a][b] = 0; map[b][a] = 0; } int pos = 0; for(int i = 1;i <= n;i ++) for(int j = 1;j <= n;j ++) { if(j > i) { Edge[++ pos].value = map[i][j]; Edge[pos].first = i;Edge[pos].end = j; } } Kruskal(Edge,n,pos); the_last_sum = 0; for(int i = 1;i <= pos;i ++) { if(Edge[i].select == 1) the_last_sum += Edge[i].value; } printf("%d\n",the_last_sum); } return 0;}