UVALive - 3644：X-Plosives

X-Plosives

来源：UVALive

标签：数据结构、并查集

参考资料：

相似题目：

题目

A secret service developed a new kind of explosive that attain its volatile property only when a specific association of products occurs. Each product is a mix of two different simple compounds, to which we call a binding pair. If N > 2, then mixing N different binding pairs containing N simple compounds creates a powerful explosive. For example, the binding pairs A+B, B+C, A+C (three pairs, three compounds) result in an explosive, while A+B, B+C, A+D (three pairs, four compounds) does not. You are not a secret agent but only a guy in a delivery agency with one dangerous problem: receive
binding pairs in sequential order and place them in a cargo ship. However, you must avoid placing in the same room an explosive association. So, after placing a set of pairs, if you receive one pair that might produce an explosion with some of the pairs already in stock, you must refuse it, otherwise, you must accept it.
An example. Lets assume you receive the following sequence: A+B, G+B, D+F, A+E, E+G, F+H. You would accept the first four pairs but then refuse E+G since it would be possible to make the following explosive with the previous pairs: A+B, G+B, A+E, E+G (4 pairs with 4 simple compounds). Finally, you would accept the last pair, F+H.
Compute the number of refusals given a sequence of binding pairs.

输入

The input will contain several test cases, each of them as described below. Consecutive test cases are separated by a single blank line.
Instead of letters we will use integers to represent compounds. The input contains several lines. Each line (except the last) consists of two integers (each integer lies between 0 and 105) separated by a single space, representing a binding pair.
Each test case ends in a line with the number ‘-1’. You may assume that no repeated binding pairs appears in the input.

输出

For each test case, the output must follow the description below.
A single line with the number of refusals.

输入样例

1 2
3 4
3 5
3 1
2 3
4 1
2 6
6 5
-1

输出样例

3

题目大意

某类简单化合物由2种不同元素组成。现将一批这样的简单化合物装车，如果车上有k个简单化合物它们恰好包含k种元素，那么将发生爆炸。所以每当拿到一个化合物，就应该检查它是否会引起爆炸，如果是则拒绝装车，否则应该装车。求解有多少未装车的化合物。

解题思路

并查集思想。将每个简单化合物想象成一条边，两种元素即为边的两个顶点。将某化合物加入集合中，如果构成了环路，则会发生爆炸。

参考代码

#include
#define MAXN 100005
int pa[MAXN];

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

int main(){
	int a,b;
	while(~scanf("%d",&a)){
		for(int i=0;i<MAXN;i++){
			pa[i]=i;
		}
		
		int cnt=0;
		while(a!=-1){
			scanf("%d",&b);
			int ra=find(a);
			int rb=find(b);
			if(ra==rb) cnt++;
			else pa[rb]=ra;
			scanf("%d",&a);
		}
		
		printf("%d\n",cnt);
	}
	return 0;
}