POJ-1308 Is It A Tree?-优快云博客

本文介绍了一个名为IsItATree?的问题，该问题是判断一组节点和它们之间的连接是否构成一棵树的数据结构。通过使用并查集算法，文章详细解释了如何验证输入的边集合是否符合树的定义。

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Is It A Tree?

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 27435		Accepted: 9356

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.

和航电上小希的迷宫一样

#include<iostream>
#include<cstring>
#include<cstdio>
#define MAXN 200000
using namespace std;
int per[MAXN];
bool flag;
int vis[MAXN];
void init()
{
    for(int i=0;i<=MAXN;i++)
        per[i]=i;
} 
int find(int x)
{
    if(per[x]==x)  return x;
    else return per[x]=find(per[x]);
}
void join(int x,int y)
{
    int fx=find(x);
    int fy=find(y);
    if(fy!=fx){
        per[fy]=fx;
    }
    else{
        flag=false;
    }
}
int main()
{
    int a,b,mark=0;
    while(cin>>a>>b)
    {
        if(a==-1&&b==-1)   break;
        mark++;
        memset(vis,0,sizeof(vis));
        if(a==0&&b==0){
            printf("Case %d is a tree.\n",mark);
            continue;
        }
        flag=true;
        init();
        vis[a]=1;
        vis[b]=1;
        join(a,b);
        int cut=0;
        while(cin>>a>>b,a&&b)
        {
            vis[a]=1;
            vis[b]=1;
            join(a,b);
        }
        for(int i=0;i<MAXN;i++){
            if(vis[i]==1&&per[i]==i){
                cut++;
            }
            if(cut>1){
                flag=false;
                break;
            }
        }
        if(flag) printf("Case %d is a tree.\n",mark);
        else printf("Case %d is not a tree.\n",mark);
    }
    return 0;
}