【并查集模板】 【洛谷P2978】 【USACO10JAN】下午茶时间

P2978 [USACO10JAN]下午茶时间Tea Time

题目描述

N (1 <= N <= 1000) cows, conveniently numbered 1..N all attend a tea time every day. M (1 <= M <= 2,000) unique pairs of those cows have already met before the first tea time. Pair i of these cows who have met is specified by two differing integers A_i and B_i (1 <= A_i <= N; 1 <= B_i <= N). The input never indicates that cows have met each other more than once.

At tea time, any cow i and cow j who have met a mutual friend cow k will meet sometime during that tea time and thus expand their circle of known cows.

Determine whether Q (1 <= Q <= 100) pairs of cows have met after tea times are held for long enough that no new cow meetings are occurring. Query j consists of a pair of different cows X_j and Y_j (1 <= X_j <= N; 1 <= Y_j <= N).

For example, suppose that out of cows 1 through 5, we know that 2 has met 5, 2 has met 3, and 4 has met 5; see (a) below.

   2---3           2---3            2---3
                  |  |            | /|
1         -->  1  |  |    -->  1  | X |
                  |  |            |/ |
   4---5           4---5            4---5
    (a)             (b)              (c)

In the first tea time, cow 2 meets cow 4, and cow 3 meets cow 5; see (b) above. In the second tea time, cow 3 meets cow 4; see (c) above.

N(1 <= N <= 1000)头奶牛，编号为1..N，在参加一个喝茶时间活动。在喝茶时间活动开始之前，已经有M(1 <= M <= 2,000)对奶牛彼此认识（是朋友）。第i对彼此认识的奶牛通过两个不相同的整数Ai和Bi给定(1<= Ai <= N; 1 <= Bi <= N)。输入数据保证一对奶牛不会出现多次。 在喝茶时间活动中，如果奶牛i和奶牛j有一个相同的朋友奶牛k，那么他们会在某次的喝茶活动中去认识对方（成为朋友），从而扩大他们的社交圈。 请判断，在喝茶活动举办很久以后（直到没有新的奶牛彼此认识），Q(1 <= Q <= 100)对奶牛是否已经彼此认识。询问j包含一对不同的奶牛编号Xj和Yj(1 <= Xj <= N; 1 <= Yj <= N)。 例如，假设共有1..5头奶牛，我们知道2号认识5号，2号认识3号，而且4号认识5号；如下图(a)。

   2---3           2---3            2---3
                  |  |            | /|
1         -->  1  |  |    -->  1  | X |
                  |  |            |/ |
   4---5           4---5            4---5
    (a)             (b)              (c)

在某次的喝茶活动中，2号认识4号，3号认识5号；如上图(b)所示。接下来的喝茶活动中，3号认识4号，如上图(c)所示。

输入输出格式

输入格式：

• Line 1: Three space-separated integers: N, M, and Q

• Lines 2..M+1: Line i+1 contains two space-separated integers: A_i and B_i

• Lines M+2..M+Q+1: Line j+M+1 contains query j as two space-separated integers: X_j and Y_j

行1：三个空格隔开的整数：N，M，和Q

行2..M+1：第i+1行包含两个空格隔开的整数Ai和Bi

行M+2..M+Q+1：第j+M+1行包含两个空格隔开的整数Xj和Yj，表示询问j

输出格式：

• Lines 1..Q: Line j should be 'Y' if the cows in the jth query have met and 'N' if they have not met.

行1..Q：如果第j个询问的两头奶牛认识， 第j行输出“Y”。如果不认识，第j行输出“N”

输入输出样例

输入样例#1：

5 3 3 
2 5 
2 3 
4 5 
2 3 
3 5 
1 5 

输出样例#1：

Y 
Y 
N 

说明

感谢@蒟蒻orz神犇 提供翻译。

并查集模板题。不多加赘述，包括了路径压缩、寻找代表元素、集合合并，其他的操作都很好想。看懂这道题并查集就会了（会不会做题还请移步另一道题：小胖的奇偶）。

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstdlib>

const int INF = 9999999;
const int MAXN = 2000 + 10;
const int MAXM = 1000 + 10;

int m,n,q;
int fa[MAXN];

int find(int x)
{
	return fa[x] == x? fa[x] : fa[x] = find(fa[x]);
}


int main()
{
	scanf("%d%d%d", &n, &m, &q);
	for(int i = 1;i <= n; i++)
	{
		fa[i] = i;
	}
	for(int i = 1;i <= m;i++)
	{
		int a,b;
		scanf("%d%d", &a, &b);
		fa[find(a)] = find(b);
	}
	for(int i = 1;i <= q; i++)
	{
		int a,b;
		scanf("%d%d", &a, &b);
		if(find(a) == find(b))
		{
			printf("Y
");
		}
		else
		{
			printf("N
");
		}
	}
	return 0;
}