https://vjudge.net/contest/363991#problem/A

超妙的树形dp
一个递归，一个递推
f[i]表示i结点往下走的最远距离，g[i]表示往上走的最远距离
f[i]=max(f[j])+i->v;
g[i]=max(g[pa],f[e[pa]->n]+e[pa]->v)+i->v;

 

#include <iostream>
#include <cstdio>
#include <queue>
#include <algorithm>
#include <cmath>
#include <cstring>
#define inf 2147483647
#define N 100010
#define p(a) putchar(a)
#define For(i,a,b) for(long long i=a;i<=b;++i)

using namespace std;
long long n,x,y;
long long d[N];
long long f[N],g[N];//f[]表示当前的节点到其叶子结点的最短距离，g[]表示这个点往上走的最大距离
struct node{
    long long n;
    long long v;
    node *next;
}*e[N];

void in(long long &x){
    long long y=1;char c=getchar();x=0;
    while(c<'0'||c>'9'){if(c=='-')y=-1;c=getchar();}
    while(c<='9'&&c>='0'){ x=(x<<1)+(x<<3)+c-'0';c=getchar();}
    x*=y;
}
void o(long long x){
    if(x<0){p('-');x=-x;}
    if(x>9)o(x/10);
    p(x%10+'0');
}

void clear(){
    memset(f,0,sizeof(f));
    memset(g,0,sizeof(g));
    memset(e,0,sizeof(e));
}

void push(long long x,long long y,long long v){
    node *p;
    p=new node();
    p->n=y;
    p->v=v;
    if(e[x]==0)
        e[x]=p;
    else{
        p->next=e[x]->next;
        e[x]->next=p;
    }
}

long long dfs(long long x,long long fa){
    for(node *i=e[x];i;i=i->next){
        if(i->n!=fa)
            f[x]=max(f[x],dfs(i->n,x)+i->v);
    }
    return f[x];
}

void bfs(long long x,long long fa,long long F){
    long long temp=0;
    for(node *i=e[fa];i;i=i->next){
        if(i->n!=F&&i->n!=x)
            g[x]=max(g[x],f[i->n]+i->v);
        else if(i->n==x)
            temp=i->v;
    }
    if(fa!=F) g[x]=max(g[fa],g[x])+temp;
    for(node *i=e[x];i;i=i->next){
        if(i->n!=fa) bfs(i->n,x,fa);
    }
}

signed main(){
    while(cin>>n){
        clear();
        For(i,2,n){
            in(x);in(y);
            push(i,x,y);
            push(x,i,y);
        }
        dfs(1,1);
        bfs(1,0,0);
        For(i,1,n) o(max(f[i],g[i])),p('\n');
    }
    return 0;
}