PAT_A1021#Deepest Root
Source:
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 components
whereK
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 ;
}
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