PAT1021:Deepest Root

1021. Deepest Root (25)

时间限制

1500 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

思路

二次dfs
1.第一次dfs确定图是否连通，如果连通找到最深的那个点first（多个就取最先被找到的），没有输出题目要求的错误信息。

2.第二次dfs重置所有状态，然后从first开始dfs，找到的所有的最深的点即是题目要求的节点，依次插入一个set容器中（每次插入会自动排序）。

3.输出set中的所有元素就行。

代码

#include<iostream>
#include<vector>
#include<set>
using namespace std;
vector<vector<int>> graph;
vector<int> highestNodes;
vector<bool> visits(10005,false);
int maxheight = 1;
set<int> results;

void dfs(int root,int height)
{
    visits[root] = true;
    if(height >= maxheight)
    {
        if(height > maxheight)
        {
           highestNodes.clear();
           maxheight = height;
        }
        highestNodes.push_back(root);
    }
    for(int i = 0;i < graph[root].size();i++)
    {
        if(!visits[graph[root][i]])
         dfs(graph[root][i],height + 1);
    }
}

inline void resetVisits(const int n)
{
    for(int i = 0;i <= n;i++)
        visits[i] = false;
}

int main()
{
   int N;
   while(cin >> N)
   {
       //input
       graph.resize(N + 1);
       for(int i = 1;i < N;i++)
       {
           int a,b;
           cin >> a >> b;
           graph[b].push_back(a);
           graph[a].push_back(b);
       }

       int cnt = 0;
       //handle
       int first = -1; //最高的节点之一
       for(int i = 1;i <= N;i++)
       {
           if(!visits[i])
           {
               cnt++;
               dfs(i,1);
               if( i == 1)
               {
                   for(int j = 0;j < highestNodes.size();j++)
                   {
                       results.insert(highestNodes[j]);
                       if(j == 0)
                         first = highestNodes[j];
                   }
               }
           }
       }

       if(cnt > 1)
         cout << "Error: "<< cnt <<" components" << endl;
       else
       {
         highestNodes.clear();
         maxheight = 1;
         resetVisits(N);
         dfs(first,1);
         for(int i = 0;i < highestNodes.size();i++ )
            results.insert(highestNodes[i]);
         for(auto it = results.begin();it != results.end();it++)
            cout << *it << endl;
       }
   }
}