hdu1325is it a tree?&&poj1308 is it a tree?(并查集)

题目链接：

huangjing||huangjing

建议做hdu上的这个题，因为poj上面的数据很弱，就是因为只做了poj上面的导致我在一次比赛中一直wa到比赛结束，因为比赛的那次挂的是hdu上的题。。。

题意：
判断由给出的数据得到的是否是一棵树。。。
思路：
这个题有几个要注意的地方。
【1】首先一棵树只能有一个入度为0的点即根节点。。所以根节点唯一。。
【2】除根节点外其他点的入度均为1。

题目：

Language:Default

Is It A Tree?

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 22135 Accepted: 7555

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 45 6  0 08 1  7 3  6 2  8 9  7 57 4  7 8  7 6  0 03 8  6 8  6 45 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.

Source

North Central North America 1997

代码：

#include<cstdio>#include<iostream>#include<algorithm>#include<cstring>using namespace std;int cnt;const int maxn=100000+10;int root[maxn],in[maxn];struct edge{    int u,v;}e[maxn];void init(){    for(int i=1;i<maxn;i++)    {        root[i]=i;        in[i]=0;    }}int findroot(int x){    if(root[x]!=x)        root[x]=findroot(root[x]);    return root[x];}int judge(){    int boss=findroot(e[1].u);//是否存在几棵树    for(int i=1;i<cnt;i++)    {        int fx=findroot(e[i].u);        int fy=findroot(e[i].v);        if(fx==fy&&boss==fx)            continue;        else            return 0;    }    return 1;}int main(){    int a,b,cas=1;    int ans1,ans2;    while(1)    {        ans2=1;        cnt=1;        init();        while(scanf("%d%d",&a,&b)!=EOF)        {           if(a<0&&b<0)               return 0;           if(a==0&&b==0)           {               ans1=judge();               if(ans1&&ans2)                   printf("Case %d is a tree.\n",cas);               else                   printf("Case %d is not a tree.\n",cas);               cas++;               break;           }           e[cnt].u=a;           e[cnt].v=b;           in[b]++;           int fx=findroot(a);           int fy=findroot(b);           if(fx==fy||in[b]>=2)//判断是否有入度为大于2的点 if(fx==fy||b!=fy)这样判断也可以              ans2=0;           else           {               root[fy]=fx;               cnt++;           }        }    }    return 0;}