# P3018 [USACO11MAR]树装饰Tree Decoration

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• 题目提供者 FarmerJohn2
• 评测方式 云端评测
• 标签 USACO 2011
• 难度 提高+/省选-
• 时空限制 1000ms / 128MB
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## 题意翻译

题目描述

约翰正在装饰他家的圣诞树。圣诞树上有个 N 个结点，第一个结点是根，其余结点都有唯一的

父亲结点，第 i 个结点的父亲是 P i 。由于根没有父亲，所以记 P 1 = −1。

约翰可以在每个结点上挂载装饰物，但费用是变化。在第 i 个结点上挂载一个装饰物需要花费 C i

元钱。奶牛对这个圣诞树上每个结点都有特殊的装饰需求，对于第 i 个结点，奶牛要求以它为根的子

树上必须有 D i 个装饰物。请问约翰在哪些结点上挂载装饰物，才能满足奶牛的要求，并且使得装饰

费用最少？

输入 • 第一行：单个整数 N，1 ≤ N ≤ 10 5

• 第二行到 N 行：第 i+1 行有三个整数：P i ，D i 和 C i ，1 ≤ P i ≤ N, 0 ≤ D i ≤ 10 6 , 1 ≤ C i ≤ 100

输出 • 单个整数，表示完成所有装饰要求的最少费用

样例输入

5 -1 9 3 1 2 2 5 3 2 5 1 4 2 3 3 样例输出

20 提示 在第四个结点上放一个，花 4 元；在第三个

结点上放五个，花 10 元；在第二个结点上放三

个，花 6 元；

感谢@lushangyin 提供的翻译

## 题目背景

征求翻译。如果你能提供翻译或者题意简述，请直接发讨论，感谢你的贡献。

## 题目描述

Farmer John is decorating his Spring Equinox Tree (like a Christmas tree but popular about three months later). It can be modeled as a rooted mathematical tree with N (1 <= N <= 100,000) elements, labeled 1...N, with element 1 as the root of the tree. Each tree element e > 1 has a parent, P_e (1 <= P_e <= N). Element 1 has no parent (denoted '-1' in the input), of course, because it is the root of the tree.

Each element i has a corresponding subtree (potentially of size 1) rooted there. FJ would like to make sure that the subtree corresponding to element i has a total of at least C_i (0 <= C_i <= 10,000,000) ornaments scattered among its members. He would also like to minimize the total amount of time it takes him to place all the ornaments (it takes time K*T_i to place K ornaments at element i (1 <= T_i <= 100)).

Help FJ determine the minimum amount of time it takes to place ornaments that satisfy the constraints. Note that this answer might not fit into a 32-bit integer, but it will fit into a signed 64-bit integer.

For example, consider the tree below where nodes located higher on the display are parents of connected lower nodes (1 is the root):

For example, consider the tree below where nodes located higher on
the display are parents of connected lower nodes (1 is the root):

1
|
2
|
5
/ \
4   3

Suppose that FJ has the following subtree constraints:

Minimum ornaments the subtree requires
|     Time to install an ornament
Subtree      |       |
root   |   C_i  |  T_i
--------+--------+-------
1    |    9   |   3
2    |    2   |   2
3    |    3   |   2
4    |    1   |   4
5    |    3   |   3

Then FJ can place all the ornaments as shown below, for a total
cost of 20:

1 [0/9(0)]     legend: element# [ornaments here/
|                      total ornaments in subtree(node install time)]
2 [3/9(6)]
|
5 [0/6(0)]
/ \
[1/1(4)] 4   3 [5/5(10)]

## 输入输出格式

输入格式：

* Line 1: A single integer: N

* Lines 2..N+1: Line i+1 contains three space-separated integers: P_i, C_i, and T_i

输出格式：

* Line 1: A single integer: The minimum time to place all the

ornaments

## 输入输出样例

输入样例#1： 复制
5
-1 9 3
1 2 2
5 3 2
5 1 4
2 3 3

输出样例#1： 复制
20

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