【杭电1856】More is better找最大集合

最大朋友圈数量算法

最新推荐文章于 2022-09-29 16:49:08 发布

原创最新推荐文章于 2022-09-29 16:49:08 发布 · 391 阅读

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本文介绍了一个寻找最大朋友圈数量的算法实现，通过输入一系列直接朋友对，利用并查集的方法找到最大的朋友圈规模。讨论了基本的并查集实现，并尝试加入按秩合并优化。

More is better

Time Limit:1000MS Memory Limit:102400KB 64bit IO Format:%I64d & %I64u

Submit Status

Description

Mr Wang wants some boys to help him with a project. Because the project is rather complex, the more boys come, the better it will be. Of course there are certain requirements.

Mr Wang selected a room big enough to hold the boys. The boy who are not been chosen has to leave the room immediately. There are 10000000 boys in the room numbered from 1 to 10000000 at the very beginning. After Mr Wang's selection any two of them who are still in this room should be friends (direct or indirect), or there is only one boy left. Given all the direct friend-pairs, you should decide the best way.

Input

The first line of the input contains an integer n (0 ≤ n ≤ 100 000) - the number of direct friend-pairs. The following n lines each contains a pair of numbers A and B separated by a single space that suggests A and B are direct friends. (A ≠ B, 1 ≤ A, B ≤ 10000000)

Output

The output in one line contains exactly one integer equals to the maximum number of boys Mr Wang may keep.

Sample Input

Sample Output

4
2

找出最大集合，有直接或间接朋友关系的为一个集合

#include<cstdio>
 #include<algorithm>
 using namespace std; 
  int n,a,b,max0,max1,i,num[10000000],f[10000000];
  int find(int a)
  {
      if(a==f[a])
         return a;
     else
         return f[a]=find(f[a]);
 }
 void f1(int x,int y)
 {
     int nx,ny;
     nx=find(x);
     ny=find(y);
     if(nx!= ny) 
     {  
         	f[ny]=nx;
         num[nx]+=num[ny];
		 }		 	    
 }
 int main()
 {
     while(~scanf("%d",&n))
     {
         for(i = 1 ; i <= 1e7 ; i++)
         {
             f[i]=i;
            
             num[i]=1;        
         }
         if(n == 0)
         {
             printf("1\n");
             continue;
         }
         max0=0;
         for(i = 0 ; i < n ; i++)
         {
             scanf("%d %d",&a,&b);
             max0=max(max0,max(a,b));       
             f1(a,b);
         }
         max1=0;
         for(i = 1 ; i <= max0 ; i++)                                 
                 max1=max(max1,num[i]);        
         printf("%d\n",max1);
     }
  } 

下面代码为啥加上按秩合并就compilation error了╮(╯_╰)╭

#include<cstdio>
 #include<algorithm>
 using namespace std; 
  int n,a,b,max0,max1,i,num[10000000],f[10000000],rank[100000000]；
  int find(int a)
  {
      if(a==f[a])
         return a;
     else
         return f[a]=find(f[a]);
 }
 void f1(int x,int y)
 {
     int nx,ny;
     nx=find(x);
     ny=find(y);
     if(nx== ny) return;
     if(rank[nx]>rank[ny])
     {  
         	f[ny]=nx;
         num[nx]+=num[ny];
		 }
		 else
		 {
		 	f[nx]=ny;
		 	if(rank[nx]=rank[ny])
		 	rank[y]++;
		 	num[ny]+=num[nx];	
			 
						  }		 	    
 }
 int main()
 {
     while(~scanf("%d",&n))
     {
         for(i = 1 ; i <= 1e7 ; i++)
         {
             f[i]=i;
            rank[i]=0;
             num[i]=1;        
         }
         if(n == 0)
         {
             printf("1\n");
             continue;
         }
         max0=0;
         for(i = 0 ; i < n ; i++)
         {
             scanf("%d %d",&a,&b);
             max0=max(max0,max(a,b));       
             f1(a,b);
         }
         max1=0;
         for(i = 1 ; i <= max0 ; i++)                                 
                 max1=max(max1,num[i]);        
         printf("%d\n",max1);
     }
  }