1021. Deepest Root (25)-PAT甲级真题（图的遍历，dfs，连通分量的个数）

A graph which is connected and acyclic can be considered a tree. The height 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 (<=10000) 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
题目大意：给出n个结点（1~n）之间的n条边，问是否能构成一棵树，如果不能构成则输出它有的连通分量个数，如果能构成一棵树，输出能构成最深的树的高度时，树的根结点。如果有多个，按照从小到大输出。
分析：首先深度优先搜索判断它有几个连通分量。如果有多个，那就输出Error: x components，如果只有一个，就两次深度优先搜索，先从一个结点dfs后保留最高高度拥有的结点们，然后从这些结点中的其中任意一个开始dfs得到最高高度的结点们，这两个结点集合的并集就是所求

#include <iostream>
#include <vector>
#include <set>
#include <algorithm>
using namespace std;
int n, maxheight = 0;
vector<vector<int>> v;
bool visit[10010];
set<int> s;
vector<int> temp;
void dfs(int node, int height) {
    if(height > maxheight) {
        temp.clear();
        temp.push_back(node);
        maxheight = height;
    } else if(height == maxheight){
        temp.push_back(node);
    }
    visit[node] = true;
    for(int i = 0; i < v[node].size(); i++) {
        if(visit[v[node][i]] == false)
            dfs(v[node][i], height + 1);
    }
}
int main() {
    scanf("%d", &n);
    v.resize(n + 1);
    int a, b, cnt = 0, s1 = 0;
    for(int i = 0; i < n - 1; i++) {
        scanf("%d%d", &a, &b);
        v[a].push_back(b);
        v[b].push_back(a);
    }
    for(int i = 1; i <= n; i++) {
        if(visit[i] == false) {
            dfs(i, 1);
            if(i == 1) {
                if (temp.size() != 0) s1 = temp[0];
                for(int j = 0; j < temp.size(); j++)
                    s.insert(temp[j]);
            }
            cnt++;
        }
    }
    if(cnt >= 2) {
        printf("Error: %d components", cnt);
    } else {
        temp.clear();
        maxheight = 0;
        fill(visit, visit + 10010, false);
        dfs(s1, 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;
}

#include <iostream>

#include <vector>

#include <set>

#include <algorithm>

using namespace std;

int n, maxheight = 0;

vector<vector<int>> v;

bool visit[10010];

set<int> s;

vector<int> temp;

void dfs(int node, int height) {

if(height > maxheight) {

temp.clear();

temp.push_back(node);

maxheight = height;

} else if(height == maxheight){

temp.push_back(node);

}

visit[node] = true;

for(int i = 0; i < v[node].size(); i++) {

if(visit[v[node][i]] == false)

dfs(v[node][i], height + 1);

}

int main() {

scanf("%d", &n);

v.resize(n + 1);

int a, b, cnt = 0, s1 = 0;

for(int i = 0; i < n - 1; i++) {

scanf("%d%d", &a, &b);

v[a].push_back(b);

v[b].push_back(a);

}

for(int i = 1; i <= n; i++) {

if(visit[i] == false) {

dfs(i, 1);

if(i == 1) {

if (temp.size() != 0) s1 = temp[0];

for(int j = 0; j < temp.size(); j++)

s.insert(temp[j]);

}

cnt++;

}

if(cnt >= 2) {

printf("Error: %d components", cnt);

} else {

temp.clear();

maxheight = 0;

fill(visit, visit + 10010, false);

dfs(s1, 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;

}

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