【图论05】并查集 1003 Is It A Tree?

算法思路：并查集，判断连通并且无环，只有一个0入度顶点。

无环条件：边数 + 1 = 顶点数。

连通条件：只有1个或者0个（回路）顶点满足 next_node[j] == j && flag[j] != 0。

//模板开始
#include <string>   
#include <vector>   
#include <algorithm>   
#include <iostream>   
#include <sstream>   
#include <fstream>   
#include <map>   
#include <set>   
#include <cstdio>   
#include <cmath>   
#include <cstdlib>   
#include <ctime>
#include<iomanip>
#include<string.h>
#define SZ(x) (int(x.size()))
using namespace std;

int toInt(string s){
	istringstream sin(s); 
	int t; 
	sin>>t; 
	return t;
}
template<class T> string toString(T x){
	ostringstream sout; 
	sout<<x; 
	return sout.str();
}
typedef long long int64;
int64 toInt64(string s){
	istringstream sin(s); 
	int64 t; 
	sin>>t;
	return t;
}
template<class T> T gcd(T a, T b){ 
	if(a<0) 
		return gcd(-a, b);
	if(b<0) 
		return gcd(a, -b);
	return (b == 0)? a : gcd(b, a % b);
}
//模板结束（通用部分）

#define ifs cin


int findset(int x, int pa[])
{
	return pa[x] != x ? pa[x] = findset(pa[x], pa) : x;
}

//【图论05】并查集 1003 Is It A Tree?
#define MAX_SIZE 100005
int next_node[MAX_SIZE];		//存储有向图的边
int in[MAX_SIZE];		//存储节点的入度
int out[MAX_SIZE];		//存储节点的出度
int flag[MAX_SIZE];		//标记节点是否存在

void init()		//初始化
{
	for(int i = 0; i < MAX_SIZE; i++)
	{
		next_node[i] = i;
	}
	memset(in, 0, sizeof(in));
	memset(out, 0, sizeof(out));
	memset(flag, 0, sizeof(flag));
}

int findset(int a)		//找元素所在集合的代表元(因为用了路径压缩，路径压缩的主要目的是为了尽快的确定元素所在的集合）
{
	while(next_node[a] != a)
	{
		a = next_node[a];
	}
	return a;
}

void union_nodes(int a, int b)		//集合合并
{
	int a1 = findset(a);
	int b1 = findset(b);
	next_node[a1] = b1;
}

int main()
{
	//ifstream ifs("shuju.txt", ios::in);
	int m, n;
	int cases = 0;
	while(ifs>>m>>n && !(m < 0 && n < 0))
	{
		cases++;
		if(m == 0 && n == 0)
		{
			cout<<"Case "<<cases<<" is a tree."<<endl;

			continue;
		}

		int bianshu = 0;
		init();
		bianshu++;
		union_nodes(m, n);
		out[m]++;
		in[n]++;
		flag[m]++;
		flag[n]++;

		while(ifs>>m>>n && !(m == 0 && n == 0))		//输入数据，建立有向图，并合并相关集合
		{
			//int a = data[0] - 'a';
			//int b = data[strlen(data) - 1] - 'a';
			bianshu++;
			union_nodes(m, n);
			out[m]++;
			in[n]++;
			flag[m]++;
			flag[n]++;
		}

		int count = 0;
		for(int j = 0; j < MAX_SIZE; j++)		//计算有向图中连通分支的个数
		{
			if(next_node[j] == j && flag[j] != 0)
			{
				count++;
			}
		}

		int root = 0;
		for(int j = 0; j < MAX_SIZE; j++)
		{
			if(in[j] == 0 && flag[j] != 0)
			{
				root++;
			}
		}

		if(root >= 2)
		{
			cout<<"Case "<<cases<<" is not a tree."<<endl;
			continue;
		}

		int jiedianshu = 0;
		for(int j = 0; j < MAX_SIZE; j++)
		{
			if(flag[j] != 0)
			{
				jiedianshu++;
			}
		}

		if(jiedianshu == 1)
		{
			cout<<"Case "<<cases<<" is not a tree."<<endl;

		}

		if(count == 1 && jiedianshu == bianshu + 1)
		{
			cout<<"Case "<<cases<<" is a tree."<<endl;

		}
		else
		{
			cout<<"Case "<<cases<<" is not a tree."<<endl;

		}
	}

	return 0;
}