1021 Deepest Root（DFS，连通分量）

A graph which is connected and acyclic can be considered a tree. The hight of the tree depends on the selected root. Now you are supposed to find the root that results in a highest tree. Such a root is called the deepest root.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤10​4​​) which is the number of nodes, and hence the nodes are numbered from 1 to N. Then N−1 lines follow, each describes an edge by given the two adjacent nodes' numbers.

Output Specification:

For each test case, print each of the deepest roots in a line. If such a root is not unique, print them in increasing order of their numbers. In case that the given graph is not a tree, print Error: K components where K is the number of connected components in the graph.

Sample Input 1:

5
1 2
1 3
1 4
2 5

Sample Output 1:

3
4
5

Sample Input 2:

5
1 3
1 4
2 5
3 4

Sample Output 2:

Error: 2 components

Analyze:

    We can list the number of connected components to judge whether these nodes can be considered a tree. If the number is greater than 2, we're suppose to print 'Error'. Then we need to use dfs for the second time to record those nodes that are deepest. Actually, we can find some nodes that are deepest at the first time, but we still ignore some nodes. A leaf can be a root.

    For example, 1 - 2 - 3: At the first dfs, you maybe start with node 1, so node 3 will be recorded. In fact, 1 can also be the deepest root. That's why we need secondly dfs.

#include<iostream>
#include<vector>
#include<set>
#include<algorithm>

using namespace std;

int n, max_height;
vector<vector<int>> v;
vector<int> temp;
set<int> s;
bool visited[10001];

void Dfs(int node, int height){
	if(height > max_height){
		temp.clear();
		temp.push_back(node);
		max_height = height;
	}else if(height == max_height){
		temp.push_back(node);
	}
	visited[node] = true;
	for(int i = 0; i < v[node].size(); i++){
		if(visited[v[node][i]] == false)
			Dfs(v[node][i], height + 1);
	}
}

int main(){
	int n1, n2, cnt = 0;
	scanf("%d", &n);
	v.resize(n + 1);
	for(int i = 0; i < n - 1; i++){
		scanf("%d %d", &n1, &n2);
		v[n1].push_back(n2);
		v[n2].push_back(n1);
	}
	for(int i = 1; i <= n; i++){
		if(visited[i] == false){
			Dfs(i, 1);
			if(i == 1){
				if(temp.size() > 0) n1 = temp[0];
				for(int j = 0; j < temp.size(); j++)
					s.insert(temp[j]);
			}
			cnt++;
		}
	}
	if(cnt > 1){
		printf("Error: %d components", cnt);
	}else{
		fill(visited, visited + 10001, false);
		temp.clear();
		Dfs(n1, 1);
		for(int i = 0; i < temp.size(); i++)
			s.insert(temp[i]);
		for(auto it = s.begin(); it != s.end(); it++)
			printf("%d\n", *it);
	}
	return 0;
}