1021. Deepest Root (25)

Posted 2020-10-17 给杰瑞一块奶酪~

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


先随便找个点找出离这个点最远的点，首先这些点是符合的，然后从中拿一点做同样操作。
可以这样考虑，最深的根至少存在两个，至少是两端一端一个，中间的点必定离其中一个或多个端点最远所以随便找个点a，找出的离这个点最远的点bi,bi一定符合，然后只需要再从这些点里拿出一个端点bk做同样操作就可以找出剩下满足的点ci。因为其他没找出来的点ci肯定是离第一次选的点a近一些，也就是离第一次找出的点bi远。所以只需要再用一个点bk就课可以找出来。
用了邻接表和深搜。
代码：

#include <iostream>
#include <cstring>
#include <algorithm>
#define Max 10005
using namespace std;
int fir[Max*2],nex[Max*2],u[Max*2],v[Max*2];//双向邻接表
int vis[Max],vi[Max];//vis标记是否访问，vi标记是否已经被认定为满足条件的点 不重复记录
int maxd[Max],no,maxv,last;//last最初为1 maxd为空，方便更新整个数组 no为下标，第一次找完后  last更新为no  方便之后的查找对no进行更新 ，不影响之前找到的点
int n,cunion;//cunion记录连通分量
void dfs(int k,int height)
{
    if(height > maxv)
    {
        maxv = height;
        no = last;
        if(!vi[k])vi[k] = 1,maxd[no ++] = k;
    }
    else if(height == maxv && !vi[k])vi[k] = 1,maxd[no ++] = k;
    int p = fir[k];
    while(p != -1)
    {
        if(!vis[v[p]])
        {
            vis[v[p]] = 1;
            dfs(v[p],height + 1);
        }
        p = nex[p];
    }
}
int main()
{
    cin>>n;
    memset(fir,-1,sizeof(nex));
    for(int i = 0;i < n - 1;i ++)
    {
        cin>>u[i]>>v[i];
        u[i+n-1] = v[i];
        v[i+n-1] = u[i];
        nex[i] = fir[u[i]];
        fir[u[i]] = i;
        nex[i+n-1] = fir[u[i+n-1]];
        fir[u[i+n-1]] = i+n-1;
    }
    for(int i = 1;i <= n;i ++)
    {
        if(!vis[i])
        {
            cunion ++;
            vis[i] = 1;
            dfs(i,1);
        }
    }
    if(cunion != 1)cout<<"Error: "<<cunion<<" components"<<endl;
    else
    {
        last = no;
        memset(vis,0,sizeof(vis));
        memset(vi,0,sizeof(vi));
        for(int i = 0;i < last;i ++)
        vi[maxd[i]] = 1;
        dfs(maxd[0],1);
        sort(maxd,maxd+no);
        for(int i = 0;i < no;i ++)
            cout<<maxd[i]<<endl;
    }
}