E - More is better

最新推荐文章于 2025-05-27 07:43:34 发布

原创最新推荐文章于 2025-05-27 07:43:34 发布 · 260 阅读

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本文介绍了一种使用并查集算法解决复杂社交网络中最大朋友圈规模的问题，通过输入直接朋友对来计算最大可能保留的朋友数量。

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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

4
1 2
3 4
5 6
1 6#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
using namespace std;
#define maxn 100010
int par[maxn],num[maxn],sum[maxn];
void init()
{
	for(int i=1;i<=maxn;i++)
	{
	par[i]=i;
	num[i]=1;
    }
}
int find(int x)
{ if(x!=par[x])
 par[x]=find(par[x]);  
    return par[x];  
}
void unite(int a,int b)
{
	int fa=find(a);
	int fb=find(b);
	if(fa!=fb)
    {
	par[fa]=fb;
  }
}
int main()
{int n,a,b;
while(scanf("%d",&n)!=EOF)
{
if(n==0)
printf("%d\n",1);
else{
	init();
	int max=0;
	while(n--)
	{
	scanf("%d%d",&a,&b);
	if(a>max)
	max=a;
	if(b>max)
	max=b;
	unite(a,b);
   }
   memset(sum,0,sizeof(sum));
   for(int i=1;i<=max;i++)
   sum[find(i)]++; 
int max1=0;
for(int i=1;i<=max;i++)
{
	if(sum[find(i)]>max1)
	max1=sum[find(i)];
}
printf("%d\n",max1);
}
}
	return 0;
}

41 23 45 67 8

Sample Output

4
2

Hint

A and B are friends(direct or indirect), B and C are friends(direct or indirect), 
then A and C are also friends(indirect).

 In the first sample {1,2,5,6} is the result.
In the second sample {1,2},{3,4},{5,6},{7,8} are four kinds of answers.

分析：平时有时候会让求集合（畅通工程题），而本题用并查集求得每个集合的元素的个数，最后输出最大的集合的元素个数；

代码：

#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
using namespace std;
#define maxn 100010
int par[maxn],num[maxn],sum[maxn];
void init()
{
	for(int i=1;i<=maxn;i++)
	{
	par[i]=i;
	num[i]=1;
    }
}
int find(int x)
{ if(x!=par[x])
 par[x]=find(par[x]);  
    return par[x];  
}
void unite(int a,int b)
{
	int fa=find(a);
	int fb=find(b);
	if(fa!=fb)
    {
	par[fa]=fb;
  }
}
int main()
{int n,a,b;
while(scanf("%d",&n)!=EOF)
{
if(n==0)
printf("%d\n",1);
else{
	init();
	int max=0;
	while(n--)
	{
	scanf("%d%d",&a,&b);
	if(a>max)
	max=a;
	if(b>max)
	max=b;
	unite(a,b);
   }
   memset(sum,0,sizeof(sum));
   for(int i=1;i<=max;i++)//统计各个集合的个数
   sum[find(i)]++; 
int max1=0;
for(int i=1;i<=max;i++)
{
	if(sum[find(i)]>max1)
	max1=sum[find(i)];
}
printf("%d\n",max1);
}
}
	return 0;
}