解题思路：

求出树的直径的两个端点。则树上每一个节点到其它点的最远距离一定是到这两个端点的距离中最长的那一个。

#include <iostream>

#include <cstring>

#include <cstdlib>

#include <cstdio>

#include <cmath>

#include <vector>

#include <queue>

#define LL long long

using namespace std;

const int MAXN = 100000 + 10;

struct Edge

{

    int to, next, w;

}edge[2 * MAXN];

int tot;

int head[MAXN];

int dis[MAXN];

int N, M;

int D[MAXN];

void init()

{

    tot = 0;

    memset(head, -1, sizeof(head));

    memset(D, 0, sizeof(D));

}

void addedge(int u, int v, int w)

{

    edge[tot].to = v;

    edge[tot].next = head[u];

    edge[tot].w = w;

    head[u] = tot++;

}

int dfs(int u, int pre = -1)

{

    int ans = u;

    for(int i=head[u];i!=-1;i=edge[i].next)

    {

        int v = edge[i].to;

        if(v == pre) continue;

        dis[v] = dis[u] + edge[i].w;

        int dv = dfs(v, u);

        if(dis[ans] < dis[dv]) ans = dv;

    }

    return ans;

}

int solve(int u)

{

    dis[u] = 0;

    u = dfs(u);

    dis[u] = 0;

    int v = dfs(u);

    for(int i=1;i<=N;i++) D[i] = max(D[i], dis[i]);

    dis[v] = 0;

    dfs(v);

    for(int i=1;i<=N;i++) D[i] = max(D[i], dis[i]);

    for(int i=1;i<=N;i++) cout << D[i] << endl;

}

int main()

{

    while(scanf("%d", &N)!=EOF)

    {

        int v, w;

        init();

        for(int i=2;i<=N;i++)

        {

            scanf("%d%d", &v, &w);

            addedge(i, v, w);

            addedge(v, i, w);

        }

        solve(1);

    }

    return 0;

}