Score : $300$ points

问题描述

Takahashi 是一名武术家。武术家中可以学习 $N$ 种招式，分别称为第 $1$、$2$、$\ldots$、第 $N$ 招。对于每种 $1 \leq i \leq N$ 的招式，学习第 $i$ 招需要花费 $T_i$ 分钟的练习时间。另外，在开始练习这一招式时，必须已经学会招式 $A_{i,1}$、$A_{i,2}$、$\ldots$、$A_{i,K_i}$。这里保证对于每个 $1 \leq j \leq K_i$，都有 $A_{i,j} < i$。

在时间 $0$ 时，Takahashi 还未学会任何招式。他不能同时练习超过一种招式，也不能在已经开始练习后中途停止。请找出 Takahashi 学会第 $N$ 招所需的最短分钟数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi is a martial artist. There are $N$ moves that a martial artist can learn, called Move $1$, $2$, $\ldots$, $N$. For each $1 \leq i \leq N$, it takes $T_i$ minutes of practice to learn Move $i$. Additionally, at the beginning of that practice, all of the Moves $A_{i,1}$, $A_{i,2}$, $\ldots$, $A_{i,K_i}$ must be already learned. Here, it is guaranteed that $A_{i,j} < i$ for each $1 \leq j \leq K_i$.

Takahashi has not learned any move at time $0$. He cannot practice for more than one move simultaneously, nor can he stop a practice he has already started. Find the minimum number of minutes needed for Takahashi to learn Move $N$.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq T_i \leq 10^9$
• $0 \leq K_i < i$
• $1 \leq A_{i,j} < i$
• $\sum_{i=1}^N K_i \leq 2\times 10^5$
• $A_{i,1}$, $A_{i,2}$, $\ldots$, $A_{i,K_i}$ are all distinct.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$T_1$ $K_1$ $A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,K_1}$

$T_2$ $K_2$ $A_{2,1}$ $A_{2,2}$ $\ldots$ $A_{2,K_2}$

$\vdots$

$T_N$ $K_N$ $A_{N,1}$ $A_{N,2}$ $\ldots$ $A_{N,K_N}$

Output

Print the minimum number of minutes needed for Takahashi to learn Move $N$.

Sample Input 1

3
3 0
5 1 1
7 1 1

Sample Output 1

10

Here is one possible plan for Takahashi.

• At time $0$, start practicing for Move $1$ to learn Move $1$ at time $3$.
• Then, at time $3$, start practicing for Move $3$ to learn Move $3$ at time $10$.

Here, Takahashi spends $3+7=10$ minutes to learn Move $3$, which is the fastest possible. Note that he does not need to learn Move $2$ to learn Move $3$.

Sample Input 2

5
1000000000 0
1000000000 0
1000000000 0
1000000000 0
1000000000 4 1 2 3 4

Sample Output 2

5000000000

Note that the answer may not fit into a $32$-bit integer.

update @ 2024/3/10 09:55:05