HDU 1102 Constructing Roads （最小生成树 Prim算法）

女爷i 2024-02-18 16:39 51阅读 0赞

## Constructing Roads ##

**Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)  
Total Submission(s): 24869 Accepted Submission(s): 9583**

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

思路：将已经修好了的路的权值设置为0.

AC代码：

#include<cstdio>
    #include<algorithm>
    #include<cstring>
    using namespace std;
    const int INF = 1e7;
    const int maxn = 100 + 10;
    int  w[maxn][maxn];
    int d[maxn];
    int vist[maxn];
    int N;
    
    void Prim(){
      memset(vist,0,sizeof(vist));
      for(int i = 2; i <= N; i++)
      d[i] = w[1][i];
      vist[1] = 1;
      
      int sum = 0;
      for(int i = 2; i <= N; i++){
      int Min = INF , tmp;   	
      	for(int j = 1; j <= N; j++){
      	  if(!vist[j] && Min > d[j]){
      	  	Min = d[j];
      	  	tmp = j;
    		}
    	  }
    	  vist[tmp] = 1;
    	  sum += Min;
    	  
    	  for(int i = 1; i <= N; i++){
    	  	if(tmp != i && d[i] > w[tmp][i]) d[i] = w[tmp][i];
    	  }
      }	
      
      printf("%d\n",sum);
    }
    int main(){
    	while(scanf("%d",&N) == 1){
    		for(int i = 1; i <= N; i++){
    			for(int j = 1; j <= N; j++){
    				scanf("%d",&w[i][j]);
    			}
    		}
    		
        int Q;
        scanf("%d",&Q);
        for(int i = 1; i <= Q; i++){
        	int a,b;
        	scanf("%d%d",&a,&b);
        	w[a][b] = 0;
        	w[b][a] = 0;
    	}
    	
    	Prim();
    	}
    	return 0;
    }