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 operations:
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
题目意思:
初始时,一共有n个元素的组合。
给出三个操作:(k p q)
k==1 p q:合并p, q所在的集合
k==2 p q:把p移动到q所在的集合
k==3 p:输出p所在的集合的元素的个数和元素之和
分析:
所以就需要将删除的这个点的影响降到0,
也就是给删除的点申请一个新的id,
以后都是用这个新的id来表示这个点,
这样原来的那个集合里的点p就没意义,自然影响就为0.
#include <iostream> #include<algorithm> #include <cstdio> #include<cstring> #include<math.h> #include<memory> using namespace std; typedef long long LL; #define max_v 200005 int pa[max_v]; int sum[max_v];//sum[x] x(根结点)所在元素集合所有元素的和 int id[max_v];//id[x]=y 表示x结点现在的编号为y int cnt[max_v];//cnt[x] x(根结点)所在集合元素的个数 int n,m,tot; void make_set(int x) { pa[x]=sum[x]=id[x]=x; cnt[x]=1; } int find_set(int x) { if(x!=pa[x]) pa[x]=find_set(pa[x]); return pa[x]; } void union_set(int x,int y)//x合并到y { x=find_set(x); y=find_set(y); if(x==y) return ; pa[x]=y; sum[y]+=sum[x]; cnt[y]+=cnt[x]; } void del(int x) { int fx=find_set(id[x]); sum[fx]-=x; cnt[fx]--; tot++; id[x]=tot; pa[tot]=tot; sum[tot]=x; cnt[tot]=1; } int main() { int n,m,k; int x,y; while(~scanf("%d %d",&n,&m)) { tot=n; for(int i=0;i<=n;i++) make_set(i); for(int i=0;i<m;i++) { scanf("%d",&k); if(k==1)//x合并到y { scanf("%d %d",&x,&y); union_set(id[x],id[y]); }else if(k==2)//x从原有集合拿出放入到y { scanf("%d %d",&x,&y); int fx=find_set(id[x]); int fy=find_set(id[y]); if(fx!=fy) { del(x); union_set(id[x],id[y]); } }else//输出x所在集合元素个数和所有元素和 { scanf("%d",&x); int fx=find_set(id[x]); printf("%d %d ",cnt[fx],sum[fx]); } } } return 0; }