[HDU 1856] More is better

并查集解决最大朋友圈问题

最新推荐文章于 2025-09-11 23:50:21 发布

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原文链接：http://www.cnblogs.com/TonyNeal/p/hdu1856.html

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#java

本文探讨如何使用并查集解决求解最大朋友圈数量的问题，包括算法优化、特判处理及实例分析。

More is better

Time Limit: 5000/1000 MS (Java/Others)

Memory Limit: 327680/102400 K (Java/Others)

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

1 2

3 4

5 6

1 6

1 2

3 4

5 6

7 8

Sample Output

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.

【题解】并查集问题：求最大rank

我加入了路径压缩和按秩合并。

然后轻松AC了= =

注意的是有一个特判，n==0时，输出1.

注意不需要开始就全部初始化，那样复杂度为O(10000005*T) T为数据组数，那么肯定受不了。

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 int pre[10000005],r[10000005],n,maxx;
 4 bool vis[10000005];
 5 int find(int x) {
 6     int r=x;
 7     while(pre[r]!=r) r=pre[r];
 8     int i=x,j;
 9     while(i!=r) {
10         j=pre[i];
11         pre[i]=r;
12         i=j;
13     }
14     return r;
15 }
16 void join(int a,int b) {
17     int a1=find(a),b1=find(b);
18     if (a1!=b1) {
19         pre[a1]=b1;
20         r[b1]+=r[a1];
21         if (r[b1]>maxx) maxx=r[b1];
22     }
23 }
24 
25 int main() {
26     while(scanf("%d",&n)!=EOF) {
27         maxx=-1;memset(vis,0,sizeof(vis));
28         if(n==0) {printf("1\n"); continue;}
29         for (int i=1;i<=n;++i) {
30             int a,b;
31             scanf("%d%d",&a,&b);
32             if(!vis[a]) {
33                 vis[a]=1;
34                 pre[a]=a;
35                 r[a]=1;
36             }
37             if(!vis[b]) {
38                 vis[b]=1;
39                 pre[b]=b;
40                 r[b]=1;
41             }
42             join(a,b);
43         }
44         printf("%d\n",maxx);
45     }
46     return 0;
47 }