PAT A1021

题目：https://pintia.cn/problem-sets/994805342720868352/problems/994805482919673856

测试1段错误：没有考虑到n=1的情况

测试3运行超时：我的思路是把每个节点的最大深度找到，然后排序。算法太挫，最后只有23分，没办法了。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
const int maxn = 10010;
bool adj[maxn][maxn] = {false};
bool hashtable[maxn] = {false};
int n, k = 0, maxdepth;
struct Node{
	int id;
	int depth;
}root[maxn];
void DFS(int u, int depth){
	for(int i = 1; i <= n; i++){
		if(hashtable[i] == false && adj[u][i]){
			hashtable[i] = true;
			DFS(i, depth+1);
		}
	}
	if(depth > maxdepth)
		maxdepth = depth;
}
bool judge(){
	for(int i = 1; i <= n; i++){
		if(hashtable[i] == false){
			hashtable[i] = true;
			k++;
			DFS(i, 0);
		}
	}
	memset(hashtable, 0, sizeof(hashtable));
	if(k!=1)
		return false;
	else
		return true;
}
void TravelDFS(){
	for(int i = 1; i <= n; i++){
		hashtable[i] = true;
		maxdepth = 0;
		DFS(i, 0);
		root[i].id = i;
		root[i].depth = maxdepth;
		memset(hashtable, 0, sizeof(hashtable));
	}
}
bool cmp(Node a, Node b){
	return a.depth > b.depth;
}
int main(){
	scanf("%d", &n);
	if(n == 1){
		printf("1");
		return 0;
	}
	for(int i = 0; i < n - 1; i++){
		int id1, id2;
		scanf("%d%d", &id1, &id2);
		adj[id1][id2] = true;
		adj[id2][id1] = true;
	}
	if(judge()){
		TravelDFS();
		sort(root + 1, root + n + 1, cmp);
		for(int i = 1; root[i].depth == root[1].depth; i++)
			printf("%d\n", root[i].id);
	}
	else{
		printf("Error: %d components\n", k);
	}
	return 0;
}

后来看了书，晓得了记录第一次遍历最远的根节点，然后在从任意一个根节点遍历，记录最远的根，就是答案。输出的时候注意重复编码不输出（这种情况出现在1号在正中间，第一次就把所有的节点都保存了。第二次的时候要重复记录）

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;
const int maxn = 10010;
bool adj[maxn][maxn] = {false};
bool hashtable[maxn] = {false};
int n, k = 0, maxdepth = -1, num = 0;
vector<int> ans;
void DFS(int u, int depth){
	for(int i = 1; i <= n; i++){
		if(hashtable[i] == false && adj[u][i]){
			hashtable[i] = true;
			DFS(i, depth+1);
		}
	}
	if(depth > maxdepth){
		while(ans.size() != num){
			ans.pop_back();
		}
		ans.push_back(u);
		maxdepth = depth;
	}
	else if(depth == maxdepth){
		ans.push_back(u);
	}
}
bool judge(){
	for(int i = 1; i <= n; i++){
		if(hashtable[i] == false){
			hashtable[i] = true;
			k++;
			DFS(i, 0);
		}
	}
	memset(hashtable, 0, sizeof(hashtable));
	num = ans.size();
	if(k!=1)
		return false;
	else
		return true;
}
void TravelDFS(){
	hashtable[ans[0]] = true;
	maxdepth = -1;
	DFS(ans[0], 0);
}
int main(){
	scanf("%d", &n);
	if(n == 1){
		printf("1");
		return 0;
	}
	for(int i = 0; i < n - 1; i++){
		int id1, id2;
		scanf("%d%d", &id1, &id2);
		adj[id1][id2] = true;
		adj[id2][id1] = true;
	}
	if(judge()){
		TravelDFS();
		sort(ans.begin(), ans.end());
		for(int i = 0; i < ans.size(); i++){
			if(ans[i]!=ans[i+1])
				printf("%d\n", ans[i]);
		}
	}
	else{
		printf("Error: %d components\n", k);
	}
	return 0;
}