Is It A Tree?
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 22403 Accepted Submission(s): 5088
Problem 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.
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.
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).
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
5 6 0 0
8 1 7 3 6 2 8 9 7 5
7 4 7 8 7 6 0 0
7 4 7 8 7 6 0 0
3 8 6 8 6 4
5 3 5 6 5 2 0 0
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.
Source
题意：
给出若干对单向联通的数，问这些数能否组成一棵树。输入两个负数结束。
代码：
//判断两点，无环，非森林。
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int fat[];
int nod[];
int find(int x)
{
if(fat[x]!=x)
fat[x]=find(fat[x]);
return fat[x];
}
void connect(int x,int y)
{
int xx=find(x),yy=find(y);
if(xx!=yy)
fat[xx]=yy;
}
int main()
{
int a,b;
for(int i=;i<;i++)
fat[i]=i;
int t=,k=,flag=;
memset(nod,,sizeof(nod));
while(scanf("%d%d",&a,&b))
{
if(a<&&b<) break;
if(a==&&b==)
{
if(!flag) //判断是否是森林
{
int tem=;
for(int i=;i<;i++)
{
if(!nod[i]) continue;
if(tem==) tem=find(i);
else if(tem!=&&find(i)!=tem)
{
flag=;
break;
}
}
}
if(flag) printf("Case %d is not a tree.\n",k);
else printf("Case %d is a tree.\n",k);
t=;
flag=;
k++;
for(int i=;i<;i++)
fat[i]=i;
memset(nod,,sizeof(nod));
continue;
}
nod[a]=;nod[b]=;
if(flag) continue;
if(fat[b]!=b||find(a)==b) //不能是环：b之前不能有父亲，a,b不能互相连接
{
flag=;
continue;
}
fat[b]=a;
connect(b,a);
}
return ;
}