#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e4 + 5;
int n, f1[maxn], f2[maxn], f3[maxn], son[maxn];

struct Edge {
	int v, w;
};
vector<Edge> g[maxn];

void dfs(int u) {
	int& s = son[u];
	for (auto e : g[u]) {
		int v = e.v, w = e.w;
		dfs(v);
		if (f1[v] + w > f1[u]) {
			f1[u] = f1[v] + w;
			son[u] = v;
		}
	}
	for (auto e : g[u]) {
		int v = e.v, w = e.w;
		if (v != s)
			f2[u] = max(f2[u], f1[v] + w);
	}
}

void dfs2(int u, int p, int w) {
	if (u == 1) f3[u] = 0;
	else {
		if (u == son[p])
			f3[u] = w + max(f3[p], f2[p]);
		else 
			f3[u] = w + max(f3[p], f1[p]);
	}
	for (auto e : g[u]) {
		dfs2(e.v, u, e.w);
	}
}

void test() {
	puts("[test]");
	for (int i = 1; i <= n; i++) printf("son[%d] = %d\n", i, son[i]);
}

int main() {
	scanf("%d", &n);
	for (int i = 2; i <= n; i++) {
		int a, b;
		scanf("%d%d", &a, &b);
		g[a].push_back({i, b});
	}
	dfs(1);
	dfs2(1, 0, 0);
    for (int i = 1; i <= n; i++)
    	printf("%d\n", max(f1[i], f3[i]));
    	
//    test();
    	
	return 0;
}

80分代码：

#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e4 + 5;
int n, f1[maxn], f2[maxn], f3[maxn], son[maxn];

struct Edge {
	int v, w;
};
vector<Edge> g[maxn];

void dfs(int u) {
	int& s = son[u];
	for (auto e : g[u]) {
		int v = e.v, w = e.w;
		dfs(v);
		f1[u] = max(f1[u], f1[v] + w);
		if (!s || f1[v] > f1[s])
			s = v;
	}
	for (auto e : g[u]) {
		int v = e.v, w = e.w;
		if (v != s)
			f2[u] = max(f2[u], f1[v] + w);
	}
}

void dfs2(int u, int p, int w) {
	if (u == 1) f3[u] = 0;
	else {
		if (u == son[p])
			f3[u] = w + max(f3[p], f2[p]);
		else 
			f3[u] = w + max(f3[p], f1[p]);
	}
	for (auto e : g[u]) {
		dfs2(e.v, u, e.w);
	}
}

int main() {
	scanf("%d", &n);
	for (int i = 2; i <= n; i++) {
		int a, b;
		scanf("%d%d", &a, &b);
		g[a].push_back({i, b});
	}
	dfs(1);
	dfs2(1, 0, 0);
    for (int i = 1; i <= n; i++)
    	printf("%d\n", max(f1[i], f3[i]));
	return 0;
}

#include <bits/stdc++.h>
using namespace std;
const int maxn = 10010;
int n, p[maxn], son[maxn], f1[maxn], f2[maxn], f3[maxn];
struct Edge {
    int v, w;
    Edge () {};
    Edge (int _v, int _w) { v = _v; w = _w; }
};
vector<Edge> g[maxn];
void dfs1(int u) {
    int sz = g[u].size();
    for (int i = 0; i < sz; i ++) {
        int v = g[u][i].v, w = g[u][i].w;
        dfs1(v);    // 记忆化搜索，先把v的相关信息求出来
    }
    // 求解f1[u]和son[u]
    for (int i = 0; i < sz; i ++) {
        int v = g[u][i].v, w = g[u][i].w;
        if (f1[v] + w > f1[u]) {
            f1[u] = f1[v] + w;
            son[u] = v;
        }
    }
    // 求解f2[u]
    for (int i = 0; i < sz; i ++) {
        int v = g[u][i].v, w = g[u][i].w;
        if (v == son[u]) continue;
        if (f1[v] + w > f2[u]) {
            f2[u] = f1[v] + w;
        }
    }
}
void dfs2(int u, int len) { // u表示当前点，len表示u连向其父节点p的边的长度
    if (u == 1) {
        f3[u] = 0;  // 根节点的f3值为0
    }
    else {
        if (u == son[p[u]])
            f3[u] = len + max(f2[p[u]], f3[p[u]]);
        else
            f3[u] = len + max(f1[p[u]], f3[p[u]]);
    }
    int sz = g[u].size();
    for (int i = 0; i < sz; i ++) {
        int v = g[u][i].v, w = g[u][i].w;
        dfs2(v, w);
    }
}
int main() {
    while (scanf("%d", &n) != EOF) {
        for (int i = 1; i <= n; i ++) { // 初始化，虽然有些不是必要的
            g[i].clear();
            f1[i] = f2[i] = f3[i] = son[i] = p[i] = 0;
        }
        for (int i = 2; i <= n; i ++) {
            int a, b;
            scanf("%d%d", &a, &b);
            p[i] = a;
            g[a].push_back(Edge(i, b));
        }
        dfs1(1);
        dfs2(1, 0);
        for (int i = 1; i <= n; i ++)
            printf("%d\n", max(f1[i], f3[i]));
    }
    return 0;
}