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hdu-1325 & poj-1308 Is It A Tree?

2024-11-15 15:41:39   204人阅读

http://acm.hdu.edu.cn/showproblem.php?pid=1325

题意：

判断一个图是不是说树

 只有树的根入度为 0 ，其余结点入度均为 1;

Is It A Tree?

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 15503    Accepted Submission(s): 3443


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. 

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.

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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.
 

Source
North Central North America 1997
 

#include <iostream>  
#include <cstdio>  
#include <string>  
#include <cstring>  
#include <cstdlib>  
#include <algorithm>  
#include <vector>  
#include <set>  
#include <map>  

using namespace std;

#define N 100010

bool used[N*10];
int queue[N];
int in[N];
int fa[N];

int findd(int x)
{
	if (fa[x] == -1)
		return x;
	else
		return fa[x] = findd(fa[x]);
}

void un(int n,int m)
{
	int fx = findd(n);
	int fy = findd(m);
	if (fx != fy)
		fa[fy] = fx;
}

int main()
{
	int n, m, cases = 1;
	memset(used,false,sizeof(used));
	memset(in,0,sizeof(in));
	memset(fa,-1,sizeof(fa));
	bool ok = true; int num = 0;

	while (scanf("%d %d", &n, &m) != EOF)
	{
		if (n == -1 && m == -1)
			break;
		else if (n == 0 && m == 0)
		{
			int num1 = 0;
			for (int i = 0; i < num; i++)
			{
				if (findd(queue[i]) != findd(queue[0]))
				{
					ok = false;
					break;
				}
				if (in[queue[i]] == 0)
					num1++;
				if (in[queue[i]] > 1)
				{
					ok = false;
					break;
				}
			}

			if (num1 != 1)
				ok = false;
			if (num == 0)
				ok = true;

			if (ok)
				printf("Case %d is a tree.\n",cases++);
			else
				printf("Case %d is not a tree.\n", cases++);

			memset(used, false, sizeof(used));
			memset(in, 0, sizeof(in));
			memset(fa, -1, sizeof(fa));
			ok = true, num = 0;
		}
		else
		{
			if (!used[n])
			{
				used[n] = true;
				queue[num++] = n;
			}
			if (!used[m])
			{
				used[m] = true;
				queue[num++] = m;
			}
			if (findd(n) == findd(m))
				ok = false;
			else
			{
				in[m]++;
				un(n,m);
			}
		}
	}
	return 0;
}





hdu-1325 & poj-1308 Is It A Tree?


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