最小生成树 Kruskal算法 HDU　1102 Constructing Roads

Problem A

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 13   Accepted Submission(s) : 5

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. <br><br>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.<br>

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.<br><br>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.<br>

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. <br>

Sample Input

3 0 990 692 990 0 179 692 179 0 1 1 2

Sample Output

179

算法分析：

很简单的最小生成树，但接触到快排，很不错。

代码实现：

#include<bits/stdc++.h>
using namespace std;
struct node
{
      int x,y,v;
}a[100010];
int fa[100005];
int find(int x)
{
    return x==fa[x]?x:fa[x]=find(fa[x]);
}
int cmp(const void *c,const void *b)//快排比较函数
{
    return (*(struct node *)c).v-(*(struct node *)b).v;
}
int main()
{

  int n;
  while(scanf("%d",&n)!=EOF)
 {
     int m=0;//一开始没想这m循环输出，所以m在外面清0，教训
     for(int i=0;i<=n;i++)
        fa[i]=i;
     for(int i=1;i<=n;i++)
    for(int j=1;j<=n;j++)//转化
   {
       int x;
       scanf("%d",&x);
       if(x!=0)
       {
           a[m].x=i;
           a[m].y=j;
           a[m].v=x;m++;
       }
   }
   int q;
   scanf("%d",&q);
   int k=0;
   for(int i=1;i<=q;i++)//已经修好的路。
   {
       int x,y;
       scanf("%d%d",&x,&y);

      int r1=find(x);
      int r2=find(y);
      if(r1!=r2)
      {
          fa[r1]=r2;
          k++;
      }
   }
   qsort(a,m,sizeof(a[0]),cmp);//必须要快排，不然会挂掉
   int tot=0;
   for(int i=0;i<m;i++)
   {
       int r1=find(a[i].x);
       int r2=find(a[i].y);
       if(r1!=r2)
       {
           fa[r1]=r2;
           tot+=a[i].v;
           k++;
       }
       if(k==n-1) break;
   }
   printf("%d\n",tot);
 }
  return 0;
}