More is better(并查集)

最新推荐文章于 2021-10-25 19:11:05 发布

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最新推荐文章于 2021-10-25 19:11:05 发布

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分类专栏： ACM训练+实训+大学编程练习文章标签：并查集

本文链接：https://blog.youkuaiyun.com/FEATHER2016/article/details/76602515

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本文介绍了一个寻找最大朋友圈数量的问题及解决方法。通过并查集算法处理大量直接朋友关系，找到可以保持联系的最大人数。

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More is better

Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 327680/102400 K (Java/Others)
Total Submission(s): 29034 Accepted Submission(s): 10321

Problem 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
4
1 2
3 4
5 6
1 6
4
1 2
3 4
5 6
7 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.

Author
lxlcrystal@TJU

Source
HDU 2007 Programming Contest - Final

大意：寻找有联系的个数最多的人。
注意当n==0时，输出1；

#include <stdio.h>
#define MAXN 10000000
int pre[MAXN], num[MAXN];
int find(int a)
{
    if(pre[a]!=a)
        pre[a] = find(pre[a]);
    return pre[a];
}
void merge(int a, int b)
{
    int p = find(a);
    int q = find(b);
    if(p!=q)
    {
        pre[p] = q;
        num[q] += num[p];
    }
}
/*
我不太理解为什么这里不对，明明就是一样的啊~
将上面的函数改成下述，Wrong Answer！
void merge(int a, int b)
{
     if(find(a)!=find(b))
       {
          pre[find(a)] = find(b);
          num[find(b)] += num[find(a)];
       }
}
*/
int main()
{
    int n, a, b;
    while(~scanf("%d", &n))
    {
        if(n==0)
        {
            printf("1\n");
            continue;
        }
        int max = 0;
        for(int i=0;i<=MAXN;i++)
        {
            pre[i] = i;
            num[i] = 1;
        }
        for(int i=0;i<n;i++)
        {
            scanf("%d %d", &a, &b);
            if(max<a)
                max = a;
            if(max<b)
                max = b;
            merge(a, b);
        }
        int MAX = 0;
        for(int i=1;i<=max;i++)
        {
            if(num[i]>MAX)
                MAX = num[i];
        }
        printf("%d\n", MAX);
    }
    return 0;
}