PAT_A1021#Deepest Root

Source:

PAT A1021 Deepest Root (25 分)

Description:

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 (≤) which is the number of nodes, and hence the nodes are numbered from 1 to N. Then N−1lines 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 componentswhere 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

Keys:

• set（C++ STL）
• vector（C++ STL）
• 深度优先搜索（Depth First Search）
• 图的存储和遍历

Attention:

• 邻接矩阵存储图的规模要小于1e3，否则用邻接表存储

Code:

 /*
 Data: 2019-05-18 19:50:30
 Problem: PAT_A1021#Deepest Root
 AC: 45:38

 题目大意：
 寻找无环图中深度最大的生成树
 输入：
 第一行给出结点数N<1e4（结点从1~N）
 接下来N-1行给出存在边的两结点V1和V2
 输出：
 给出最大深度生成树的根结点，不唯一从小到大依次输出根结点。
 若图不连通则给出连通分量个数

 基本思路：
 从任意顶点开始遍历全图，root记录所能达到的最大深度及其顶点；
 再从root中任选一顶点，再次遍历全图，leaf记录所能达到的最大深度及顶点；
 如果图连通的话，
 生成树的最大深度就是第二次遍历全图所能达到的最大深度；
 the deepest root就是root+leaf的并集
 */

 #include<cstdio>
 #include<algorithm>
 #include<set>
 #include<vector>
 using namespace std;
 const int M=1e4;
 int vis[M],n,depth,f;
 set<int> root,leaf;
 vector<int> grap[M];

 void DFS(int u, int deep)
 {
     vis[u]=;
     if(deep > depth)
     {
         depth=deep;
         if(f)
         {
             root.clear();
             root.insert(u);
         }
         else
         {
             leaf.clear();
             leaf.insert(u);
         }
     }
     else if(deep == depth)
         if(f)   root.insert(u);
         else    leaf.insert(u);

     for(int i=; i<grap[u].size(); i++)
     {
         int v = grap[u][i];
         if(vis[v]==)
             DFS(v,deep+);
     }
 }

 int Travel()
 {
     int block=;
     fill(vis,vis+M,);
     for(int v=; v<=n; v++)
     {
         if(vis[v]==)
         {
             DFS(v,);
             block++;
         }
     }
     return block;
 }

 int main()
 {
 #ifdef  ONLINE_JUDGE
 #else
     freopen("Test.txt", "r", stdin);
 #endif // ONLINE_JUDGE

     scanf("%d", &n);
     for(int i=; i<n; i++)
     {
         int v1,v2;
         scanf("%d%d", &v1,&v2);
         grap[v1].push_back(v2);
         grap[v2].push_back(v1);
     }
     depth=;f=;
     int block = Travel();
     if(block > )
         printf("Error: %d components\n", block);
     else
     {
         fill(vis,vis+M,);f=;
         DFS(*root.begin(),);
         for(auto it=leaf.begin(); it!=leaf.end(); it++)
             root.insert(*it);
         for(auto it=root.begin(); it!=root.end(); it++)
             printf("%d\n", *it);
     }

     return ;
 }