UVA - 11987
Time Limit: 1000MS | Memory Limit: Unknown | 64bit IO Format: %lld & %llu |
Description
Problem A
Almost Union-Find
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). The size of input file does not exceed 5MB.
Output
For each type-3 command, output 2 integers: the number of elements and the sum of elements.
Sample Input
5 7 1 1 2 2 3 4 1 3 5 3 4 2 4 1 3 4 3 3
Output for the Sample Input
3 12 3 7 2 8
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}
Rujia Liu‘s Present 3: A Data Structure Contest Celebrating the 100th Anniversary of Tsinghua University
Special Thanks: Yiming Li
Note: Please make sure to test your program with the gift I/O files before submitting!
Source
Root :: AOAPC I: Beginning Algorithm Contests -- Training Guide (Rujia Liu) :: Chapter 3. Data Structures :: Fundamental Data Structures :: Exercises:
Intermediate
Root :: Prominent Problemsetters :: Rujia Liu
Root :: Rujia Liu‘s Presents :: Present 3: A Data Structure Contest
思路:1,3比较好实现,2则有点麻烦,2属于并查集的删除操作,需要另设一组real[]数组来确定元素的实际地址,每删除一个元素,就把这个元素放在最后面。。我本来以为直接把p指向q的根就行了,但发现这是错的。如果p是叶子结点,那可以,但如果是某个集合的根呢。我们只是要把这一个元素移掉,如果直接把p指向q的根,它的叶子节点们也过去啦。。。而如果另设一组real数组的话就可以将影响降为0啦。。
AC代码:
#include <cstdio> #include <cstring> #include <algorithm> #define LL long long using namespace std; const int maxn = 200005; int pa[maxn], real[maxn], cnt[maxn]; int n, m, vnum; LL sum[maxn]; int find(int x) { return pa[x] != x ? pa[x] = find(pa[x]) : x; } void Union(int a, int b) { int a1 = find(real[a]), b1 = find(real[b]); pa[a1] = b1; sum[b1] += sum[a1]; cnt[b1] += cnt[a1]; } void Move(int a) { int t = find(real[a]); sum[t] -= a, cnt[t]--; real[a] = ++vnum; //并查集的这里到n了,所以要先++,之前后++的样例没过,检查半天=_=|| sum[real[a]] = a, cnt[real[a]] = 1, pa[real[a]] = real[a]; } int main() { while(scanf("%d %d", &n, &m) != EOF) { for(int i = 0; i <= n; i++) { pa[i] = real[i] = sum[i] = i; cnt[i] = 1; } vnum = n; int ord, p, q; while(m--) { scanf("%d", &ord); if(ord == 1) { scanf("%d %d", &p, &q); if(find(real[p]) != find(real[q])) Union(p, q); } else if(ord == 2) { scanf("%d %d", &p, &q); if(find(real[p]) != find(real[q])) Move(p), Union(p, q); } else if(ord == 3) { scanf("%d", &p); int tmp = find(real[p]); printf("%d %lld\n", cnt[tmp], sum[tmp]); } } } return 0; }