Computer

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1232    Accepted Submission(s): 597

Problem Description A school bought the first computer some time ago(so this computer’s id is 1). During the recent years the school bought N-1 new computers. Each new computer was connected to one of settled earlier. Managers of school are anxious about slow functioning of the net and want to know the maximum distance Si for which i-th computer needs to send signal (i.e. length of cable to the most distant computer). You need to provide this information.

Hint: the example input is corresponding to this graph. And from the graph, you can see that the computer 4 is farthest one from 1, so S1 = 3. Computer 4 and 5 are the farthest ones from 2, so S2 = 2. Computer 5 is the farthest one from 3, so S3 = 3. we also get S4 = 4, S5 = 4.  

Input Input file contains multiple test cases.In each case there is natural number N (N<=10000) in the first line, followed by (N-1) lines with descriptions of computers. i-th line contains two natural numbers – number of computer, to which i-th computer is connected and length of cable used for connection. Total length of cable does not exceed 10^9. Numbers in lines of input are separated by a space.  

Output For each case output N lines. i-th line must contain number Si for i-th computer (1<=i<=N).  

Sample Input 5 1 1 2 1 3 1 1 1  

Sample Output 3 2 3 4 4  

Author scnu  

Recommend lcy     经典的树形DP题。 题意是求树中每个点到所有叶子节点的距离的最大值是多少。

由于对于一个节点来说，可能得到的距离最大的值的路径来自他的子树，或者从他的父节点过来，所以用两次DFS。

第一次DFS求出所有节点在他的子树范围内到叶子节点距离的最大值和第二大的值，第二次DFS更新从父节点过来的情况就可以了。

因为如果只存最大值的话，判断一个点的从父节点过来的最大值，那么如果他的父节点存的最大值正好是从该点过来的，那么就失去了从父节点过来的状态，所以要记录最大的两个值。  

/*
HDU 2196
G++ 46ms  916K

*/

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<string.h>
using namespace std;
const int MAXN=10010;
struct Node
{
    int to;
    int next;
    int len;
}edge[MAXN*2];//因为存无向边，所以需要2倍
int head[MAXN];//头结点
int tol;
int maxn[MAXN];//该节点往下到叶子的最大距离
int smaxn[MAXN];//次大距离
int maxid[MAXN];//最大距离对应的序号
int smaxid[MAXN];//次大的序号

void init()
{
    tol=0;
    memset(head,-1,sizeof(head));
}

void add(int a,int b,int len)
{
    edge[tol].to=b;
    edge[tol].len=len;
    edge[tol].next=head[a];
    head[a]=tol++;
    edge[tol].to=a;
    edge[tol].len=len;
    edge[tol].next=head[b];
    head[b]=tol++;
}

//求结点v往下到叶子结点的最大距离
//p是v的父亲结点
void dfs1(int u,int p)
{
    maxn[u]=0;
    smaxn[u]=0;
    for(int i=head[u];i!=-1;i=edge[i].next)
    {
        int v=edge[i].to;
        if(v==p)continue;//不能往上找父亲结点
        dfs1(v,u);
        if(smaxn[u]<maxn[v]+edge[i].len)
        {
            smaxn[u]=maxn[v]+edge[i].len;
            smaxid[u]=v;
            if(smaxn[u]>maxn[u])
            {
                swap(smaxn[u],maxn[u]);
                swap(smaxid[u],maxid[u]);
            }
        }
    }
}
//p是u的父亲结点，len是p到u的长度
void dfs2(int u,int p)
{
    for(int i=head[u];i!=-1;i=edge[i].next)
    {
        int v=edge[i].to;
        if(v==p)continue;
        if(v==maxid[u])
        {
            if(edge[i].len+smaxn[u]>smaxn[v])
            {

                smaxn[v]=edge[i].len+smaxn[u];
                smaxid[v]=u;
                if(smaxn[v]>maxn[v])
                {
                    swap(smaxn[v],maxn[v]);
                    swap(smaxid[v],maxid[v]);
                }
            }
        }
        else
        {
            if(edge[i].len+maxn[u]>smaxn[v])
            {
                smaxn[v]=edge[i].len+maxn[u];
                smaxid[v]=u;
                if(smaxn[v]>maxn[v])
                {
                    swap(smaxn[v],maxn[v]);
                    swap(maxid[v],smaxid[v]);
                }
            }
        }
        dfs2(v,u);
    }
}
int main()
{
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    int n;
    int v,len;
    while(scanf("%d",&n)!=EOF)
    {
        init();
        for(int i=2;i<=n;i++)
        {
            scanf("%d%d",&v,&len);
            add(i,v,len);
        }
        dfs1(1,-1);


        dfs2(1,-1);
        for(int i=1;i<=n;i++)
          printf("%d\n",maxn[i]);
    }
    return 0;
}