Poj 2599 Godfather(树的重心)

最新推荐文章于 2020-11-18 22:52:28 发布

nancheng58

最新推荐文章于 2020-11-18 22:52:28 发布

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分类专栏：点分治

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本文介绍了一个基于树结构的问题，即如何找到树中的重心节点。通过分析警察试图找出芝加哥黑手党头目的背景故事，文章详细解释了算法实现过程，包括输入输出格式、核心数据结构与算法步骤。

Godfather
Time Limit: 2000MS Memory Limit: 65536K
Description
Last years Chicago was full of gangster fights and strange murders. The chief of the police got really tired of all these crimes, and decided to arrest the mafia leaders.
Unfortunately, the structure of Chicago mafia is rather complicated. There are n persons known to be related to mafia. The police have traced their activity for some time, and know that some of them are communicating with each other. Based on the data collected, the chief of the police suggests that the mafia hierarchy can be represented as a tree. The head of the mafia, Godfather, is the root of the tree, and if some person is represented by a node in the tree, its direct subordinates are represented by the children of that node. For the purpose of conspiracy the gangsters only communicate with their direct subordinates and their direct master.
Unfortunately, though the police know gangsters’ communications, they do not know who is a master in any pair of communicating persons. Thus they only have an undirected tree of communications, and do not know who Godfather is
Based on the idea that Godfather wants to have the most possible control over mafia, the chief of the police has made a suggestion that Godfather is such a person that after deleting it from the communications tree the size of the largest remaining connected component is as small as possible. Help the police to find all potential Godfathers and they will arrest them.
Input
The first line of the input file contains n — the number of persons suspected to belong to mafia (2 ≤ n ≤ 50 000). Let them be numbered from 1 to n.
The following n − 1 lines contain two integer numbers each. The pair ai, bi means that the gangster ai has communicated with the gangster bi. It is guaranteed that the gangsters’ communications form a tree.
Output
Print the numbers of all persons that are suspected to be Godfather. The numbers must be printed in the increasing order, separated by spaces.
Sample Input
6
1 2
2 3
2 5
3 4
3 6
Sample Output
2 3
Source
Northeastern Europe 2005, Northern Subregion

/*
找树的重心们.
*/
#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#define MAXN 50001
using namespace std;
int n,m,rt,f[MAXN],ans[MAXN],tot,sum,cut,head[MAXN],size[MAXN];
struct edge{int v,next;}e[MAXN*2];
int read()
{
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9') x=x*10+ch-48,ch=getchar();
    return x*f;
}
void add(int u,int v)
{
    e[++cut].v=v;e[cut].next=head[u];head[u]=cut;
}
void Clear()
{
    memset(size,0,sizeof size);
    memset(head,0,sizeof head);
    memset(f,0,sizeof f);
    cut=rt=tot=0;
}
void slove(int u,int fa)
{
    size[u]=1;
    for(int i=head[u];i;i=e[i].next)
    {
        if(e[i].v==fa) continue;
        slove(e[i].v,u);
        size[u]+=size[e[i].v];
        f[u]=max(f[u],size[e[i].v]);
    }
    f[u]=max(f[u],sum-size[u]);
    if(f[rt]>f[u]) rt=u,ans[tot=1]=u;
    else if(f[rt]==f[u]) ans[++tot]=u;
}
int main()
{
    int t,x,y;
    n=read();
    Clear();
    for(int i=1;i<=n-1;i++)
    {
        x=read(),y=read();
        add(x,y),add(y,x);
    }
    sum=n;f[0]=1e9;
    slove(1,rt);
    sort(ans+1,ans+tot+1);
    for(int i=1;i<=tot;i++) printf("%d ",ans[i]);
    printf("\n");
    return 0;
}