pat 1118. Birds in Forest (25) 并查集

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本文介绍了一种算法，用于解决科学家们拍摄的大量森林鸟类照片中的鸟类计数问题。该算法能确定照片中鸟类的最大可能树数量，并判断任意两只鸟是否位于同一棵树上。

1118. Birds in Forest (25)

时间限制

150 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

Some scientists took pictures of thousands of birds in a forest. Assume that all the birds appear in the same picture belong to the same tree. You are supposed to help the scientists to count the maximum number of trees in the forest, and for any pair of birds, tell if they are on the same tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive number N (<= 10⁴) which is the number of pictures. Then N lines follow, each describes a picture in the format:
K B1 B2 ... BK
where K is the number of birds in this picture, and Bi's are the indices of birds. It is guaranteed that the birds in all the pictures are numbered continuously from 1 to some number that is no more than 10⁴.

After the pictures there is a positive number Q (<= 10⁴) which is the number of queries. Then Q lines follow, each contains the indices of two birds.

Output Specification:

For each test case, first output in a line the maximum possible number of trees and the number of birds. Then for each query, print in a line "Yes" if the two birds belong to the same tree, or "No" if not.

Sample Input:

Sample Output:

2 10
Yes
No

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <iostream>
#include <map>
#include <set>

using namespace std;

int N, Q;
int f[10005], a[10005];
int maxn, minn;
set<int> s;

int getf(int x) {
	return f[x] == x ? x : f[x] = getf(f[x]);
}

int main()
{
	cin >> N;
	for (int i = 1; i <= 10003; i++) {
		f[i] = i;
	}
	maxn = -1;
	for (int i = 0; i < N; i++) {
		int K;
		scanf("%d", &K);
		minn = 99999;
		for (int j = 0; j < K; j++) {
			scanf("%d", &a[j]);
			maxn = max(maxn, a[j]);
			minn = min(minn, a[j]);
		}
		for (int j = 0; j < K; j++) {
			f[getf(a[j])] = getf(minn);  //debug f[a[j]] -> f[getf(a[j])]
		}
	}
	for (int i = 1; i <= maxn; i++) {
		s.insert(getf(i));
	}
	printf("%d %d\n", s.size(), maxn);
	cin >> Q;
	while (Q--) {
		int x, y;
		scanf("%d%d", &x, &y);
		if (getf(x) == getf(y)) {
			puts("Yes");
		}
		else {
			puts("No");
		}
	}
	return 0;
}