1021 Deepest Root (25)（25 point(s)）

problem

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

tip

answer

#include <cassert>
#include <set>
#include <iostream>
#include <vector>
#include <cstring>

#define Max 10010
#define fi first
#define se second
using namespace std;

int N;
int Root[Max], V[Max];
vector<int > E[Max];
set<int > S, Last;
set<int>::iterator it;

void Init(){
	for(int i = 1; i <= N; i++){
		Root[i] = i;
	}
}

int Find(int i){
	if(Root[i] != i) Root[i] = Find(Root[i]);
	return Root[i];
}

void Union(int a, int b){
	int ra = Find(a);
	int rb = Find(b);
	if(ra == rb) return ;
	Root[ra] = Find(Root[rb]);
}

int TreeNum() {
	int num = 0;
	for(int i = 1; i <= N; i++){
		if(Root[i] == i) num++;
	}
	return num;
}

int DFS(int t, int deep, int &maxD){
	if(deep > maxD){
		maxD = deep;
		S.clear();
		S.insert(t);
	}
	if(deep == maxD){
		S.insert(t);
	}
	V[t] = 1;
	for(int i = 0; i < E[t].size(); i ++){
		if(!V[E[t][i]]){
			DFS(E[t][i], deep+1, maxD);
		}
	}
}

void InitV(){
	memset(V, 0, sizeof(V));
}

void PrintStatus(){
	for(it = S.begin(); it != S.end(); it++){
		cout<<*it<<" ";
	}
	cout<<endl;
}
int main(){
//	freopen("test.txt", "r", stdin) ;
	ios::sync_with_stdio(false);
	//N<= 10000
	cin>>N;
	if(N == 0){
		assert(false);
		cout<<"0"<<endl;
	}
	Init();
	int a, b;
	for(int i = 0; i < N-1; i++) {
		cin>>a>>b;
		E[a].push_back(b);
		E[b].push_back(a);
		Union(a, b);
	}
	if(TreeNum() > 1) {
		cout<<"Error: "<<TreeNum()<<" components";
	}else{
		int maxD = 0, deepN;
		DFS(1, 0, maxD);
//		PrintStatus(); 
		for(it = S.begin(); it != S.end(); it++){
			Last.insert(*it);
			deepN = *it;
		}
		maxD = 0;
//		cout<<deepN<<endl;
		InitV();
		DFS(deepN, 0, maxD);
//		PrintStatus();
		for(it = S.begin(); it != S.end(); it++){
			Last.insert(*it);
		}
		for(it = Last.begin(); it != Last.end(); it++){
			cout<<*it<<endl;
		}
	}
	return 0; 
}

exprience

• acyclic 无环的