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

巴特西

1021 Deepest Root (25)（25 point(s)）

problem

tip

answer

exprience

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