题意:求出每个集合的元素个数,及总和,给出三个操作:
1 将含有a元素和b元素的集合合并;2 将a元素放入含有b元素的集合中;3 输出a元素所在集合的元素个数及总和;
思路:正常并查集,与并查集元素的删除
题目:
I hope you know the beautiful Union-Find structure. In this problem, you’re to implement something similar, but not identical. The data structure you need to write is also a collection of disjoint sets, supporting 3 operati
1 p q | Union the sets containing p and q. If p and q are already in the same set, ignore this command. |
2 p q | Move p to the set containing q. If p and q are already in the same set, ignore this command. |
3 p | Return the number of elements and the sum of elements in the set containing p |
Initially, the collection contains n sets: {1}, {2}, {3}, . . . , {n}.
Input
There are several test cases. Each test case begins with a line containing two integers n and m (1 ≤ n, m ≤ 100, 000), the number of integers, and the number of commands. Each of the next m lines contains a command. For every operation, 1 ≤ p, q ≤ n. The input is terminated by end-of-file (EOF).
Output
For each type-3 command, output 2 integers: the number of elements and the sum of elements.
Explanation
Initially: {1}, {2}, {3}, {4}, {5}
Collection after operation 1 1 2: {1,2}, {3}, {4}, {5}
Collection after operation 2 3 4: {1,2}, {3,4}, {5} (we omit the empty set that is produced when taking out 3 from {3})
Collection after operation 1 3 5: {1,2}, {3,4,5}
Collection after operation 2 4 1: {1,2,4}, {3,5}
Sample Input
5 7
1 1 2
2 3 4
1 3 5
3 4
2 4 1
3 4
3 3
Sample Output
3 12
3 7
2 8
/*对于删除操作,在完美的并查集中(所有节点都直接连接在根节点上),理论上只要把要删除的节点的上级重新指向自己就可以了。
但是实际情况中,我们的并查集形成的树的形态都是不可预估形态的,如果直接将一个节点指向自己可能会将他的“下级”和他一起删除,这就和我们的想法违背了。
所以在一个需要删除的并查集中初始化时就要处理一下:
首先可以将每一个点都设立一个虚拟父节点,这样根节点就是我们设立的虚拟节点,类似于将每个节点放到一个盒子中
如果删除某点,那么可以修改当前节点的父节点来导致当前点的孤立,即删除时把这个节点从当前盒子拿出来,放到另一个盒子中。
由于节点之间都是通过盒子来确定关系的,所以盒子中元素是否存在并不影响节点之间的关系。*/
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<queue>
#define Lint long long int
using namespace std;
const int MAXN=200010;
int f[MAXN];/*盒子内的元素链接*/
int sum[MAXN];/*集合内元素之和*/
int p[MAXN];/*盒子*/
int siz[MAXN];/*集合内元素个数,下标为盒子下标*/
int n,m,cnt;
int find(int x)
{return x==f[x] ? f[x] : f[x]=find( f[x] ) ;
}
int main()
{int opt,u,v,x,y;while( scanf("%d%d",&n,&m)!=EOF )//删除节点,就是把原先的节点设置为虚点,然后把点的位置用num数组指向新的位置。{cnt=n;for(int i=1; i<=n; i++) f[i]=p[i]=sum[i]=i,siz[i]=1;for(int i=1; i<=m; i++){scanf("%d",&opt);if( opt==1 ){scanf("%d%d",&u,&v);u=p[u],v=p[v];u=find( u ),v=find( v );if( u==v ) continue ;f[u]=v;siz[v]+=siz[u],sum[v]+=sum[u];}if( opt==2 ){scanf("%d%d",&u,&v);x=find( p[u] ),y=find( p[v] );if( x==y ) continue ;sum[x]-=u,siz[x]--;/*盒子的名称不变,除去该元素*/x=p[u]=++cnt;/*重新申请一个内存,里面只有要操作的元素,改变该元素的祖先*/f[x]=y;sum[y]+=u,siz[y]++;}if( opt==3 ){scanf("%d",&u);u=find( p[u] );printf("%d %d\n",siz[u],sum[u]);}}}return 0;
}