Deepest Root (并查集+DFS树的深度)

 

 

 

 

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

 

  1 #include <iostream>

  2 

  3 #include <vector>

  4 

  5 #include <queue>

  6 

  7 using namespace std;

  8 

  9 vector<int> adj[10001];

 10 int visit[10001];

 11 int Tree[10001];

 12 int root[10001];

 13 int MM[10001];

 14 int num;

 15 int getroot(int x)

 16 

 17 {

 18 

 19     if(Tree[x]==-1)  return x;

 20 

 21     else

 22 

 23     {

 24         int tem=getroot(Tree[x]);

 25         Tree[x]=tem;

 26         return tem;

 27     }

 28 

 29 }

 30 

 31 

 32 

 33 

 34 

 35 void DFS(int x,int d)

 36 

 37 {

 38     visit[x]=1;

 39     int i;

 40     for(i=0;i<adj[x].size();i++)

 41     {

 42 

 43         if(visit[adj[x][i]]==0) 

 44             DFS(adj[x][i],d+1);

 45     }

 46     root[num++]=d;

 47 }

 48 

 49 

 50 

 51 

 52 

 53 

 54 

 55 

 56 

 57 int main()

 58 

 59 {

 60     int n,a,b,i,j;

 61     while(cin>>n)

 62     {

 63         for(i=1;i<=n;i++)//初始化

 64         {

 65             Tree[i]=-1;

 66             adj[i].clear();

 67         }

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

 69         {

 70             cin>>a>>b;

 71             adj[a].push_back(b);

 72             adj[b].push_back(a);

 73             a=getroot(a);//并查集

 74             b=getroot(b);

 75             if(a!=b)

 76             {

 77                 Tree[a]=b;

 78             }

 79         }

 80         int count=0;//极大连通图个数

 81         for(i=1;i<=n;i++)

 82         {

 83             if(Tree[i]==-1) count++;

 84         }

 85         if(count!=1)

 86         {

 87             cout<<"Error: "<<count<<" components"<<endl;//不是树

 88         }

 89         else

 90         {

 91             for(i=1;i<=n;i++)

 92             {

 93                 for(j=1;j<=n;j++)//每次查找都要初始化

 94                     visit[j]=0;

 95                 num=0;

 96                 DFS(i,1);

 97                 MM[i]=0;

 98                 for(j=0;j<num;j++)

 99                 {

100                     if(MM[i]<root[j])

101                         MM[i]=root[j];

102                 }

103             }

104             int max=0;

105             for(i=1;i<=n;i++)

106             {

107                 if(max<MM[i])

108                     max=MM[i];

109             }

110             for(i=1;i<=n;i++)

111             {

112                 if(max==MM[i])

113                     cout<<i<<endl;

114             }

115         }

116     }

117     return 0;

118 }