poj 1308 Is It A Tree?

Is It A Tree?

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 22790		Accepted: 7814

Description

A tree is a well-known data structure that is either empty (null, void, nothing) or is a set of one or more nodes connected by directed edges between nodes satisfying the following properties. 

There is exactly one node, called the root, to which no directed edges point. 
Every node except the root has exactly one edge pointing to it. 
There is a unique sequence of directed edges from the root to each node. 
For example, consider the illustrations below, in which nodes are represented by circles and edges are represented by lines with arrowheads. The first two of these are trees, but the last is not. 

In this problem you will be given several descriptions of collections of nodes connected by directed edges. For each of these you are to determine if the collection satisfies the definition of a tree or not.

Input

The input will consist of a sequence of descriptions (test cases) followed by a pair of negative integers. Each test case will consist of a sequence of edge descriptions followed by a pair of zeroes Each edge description will consist of a pair of integers; the first integer identifies the node from which the edge begins, and the second integer identifies the node to which the edge is directed. Node numbers will always be greater than zero.

Output

For each test case display the line "Case k is a tree." or the line "Case k is not a tree.", where k corresponds to the test case number (they are sequentially numbered starting with 1).

Sample Input

6 8  5 3  5 2  6 4
5 6  0 0

8 1  7 3  6 2  8 9  7 5
7 4  7 8  7 6  0 0

3 8  6 8  6 4
5 3  5 6  5 2  0 0
-1 -1

Sample Output

Case 1 is a tree.
Case 2 is a tree.
Case 3 is not a tree.

题意：判断由这些组成的树是不是一棵树；

解题：并查集的应用；

注意：

1.空树也是树；

2.不能有环；

3.不能是森林；

参考代码：

#include <iostream>
#include <stdio.h>
#include <string.h>
using namespace std;
int father[30000+1],rank[30000+1];
bool flag[30000+1];
void init(int n){
	for (int i=0;i<=n;i++){
		father[i]=i;
		rank[i]=1;
		flag[i]=false;
	}
}
int find(int x){
	if (x!=father[x])
		father[x] = find(father[x]);	//路径压缩
	return father[x];
}
void Union(int x,int y){
	int i=find(x);
	int j=find(y);
	if (i==j)
		return;
	if (rank[i]<rank[j])
		father[i]=j;
	else{
		father[j]=i;
		if (rank[i]==rank[j])	//两棵树同高
			rank[i]++;
	}
}
bool same(int i,int j){
	if (find(i)==find(j))
		return true;
	return false;
}
int main(){
	int a,b,t=1;
	while (cin>>a>>b){
		if (a==b&&a==-1)
			break;
		if (a==0&&b==0){
			cout<<"Case "<<t++<<" is a tree."<<endl;
			continue;
		}
		flag[a]=flag[b]=true;
		init(1000);
		bool tree=true;
		if (a==b)
			tree=false;
		else
			Union(a,b);
		int first=a;
		while (cin>>a>>b){
			if (a==0&&b==0)
				break;
			if (find(a)==find(b))
				tree=false;
			flag[a]=flag[b]=true;
			Union(a,b);
		}
		for (int i=1;i<=1000;i++){
			if (flag[i]==true&&find(i)!=find(first)){
				tree=false;
				break;
			}
		}
		if (tree==false)
			cout<<"Case "<<t++<<" is not a tree."<<endl;
		else
			cout<<"Case "<<t++<<" is a tree."<<endl;
	}
	return 0;
}