Score : $600$ points

问题描述

有 $N$ 个编号为 $1$ 到 $N$ 的点，以及 $M$ 条道路。第 $i$ 条（$1 \leq i \leq M$）道路在点 $a_i$ 和点 $b_i$ 之间双向连接，并且需要 $c_i$ 分钟通过。使用一些数量的道路可以从任意一个点到达另一个点。在点 $1,\ldots, K$ 上有房子。

对于 $i=1,\ldots,Q$，解决以下问题：

高桥当前位于编号为 $x_i$ 的房子处，他想要前往编号为 $y_i$ 的房子处。
自从他上次睡觉后经过了 $t_i$ 分钟，他就无法再继续移动。
他只能在有房子的点上睡觉，但可以任意次数地进行休息。
如果他可以从点 $x_i$ 到达点 $y_i$，则输出 Yes；否则，输出 No。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are $N$ points numbered $1$ through $N$, and $M$ roads. The $i$-th ($1 \leq i \leq M$) road connects Point $a_i$ and Point $b_i$ bidirectionally and requires $c_i$ minutes to pass through. One can travel from any point to any other point using some number of roads. There is a house on Points $1,\ldots, K$.

For $i=1,\ldots,Q$, solve the following problem.

Takahashi is currently at the house at Point $x_i$ and wants to travel to the house at Point $y_i$.
Once $t_i$ minutes have passed since his last sleep, he cannot continue moving anymore.
He can get sleep only at a point with a house, but he may do so any number of times.
If he can travel from Point $x_i$ to Point $y_i$, print Yes; otherwise, print No.

Constraints

• $2 \leq K \leq N \leq 2 \times 10^5$
• $N-1 \leq M \leq \min (2 \times 10^5, \frac{N(N-1)}{2})$
• $1 \leq a_i \lt b_i \leq N$
• If $i \neq j$, then $(a_i,b_i) \neq (a_j,b_j)$.
• $1 \leq c_i \leq 10^9$
• One can travel from any point to any other point using some number of roads.
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq x_i \lt y_i \leq K$
• $1 \leq t_1 \leq \ldots \leq t_Q \leq 10^{15}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $K$

$a_1$ $b_1$ $c_1$

$\vdots$

$a_M$ $b_M$ $c_M$

$Q$

$x_1$ $y_1$ $t_1$

$\vdots$

$x_Q$ $y_Q$ $t_Q$

Output

Print $Q$ lines. The $i$-th line should contain the answer for the $i$-th problem.

Sample Input 1

6 6 3
1 4 1
4 6 4
2 5 2
3 5 3
5 6 5
1 2 15
3
2 3 4
2 3 5
1 3 12

Sample Output 1

No
Yes
Yes

In the $3$-rd problem, it takes no less than $13$ minutes from Point $1$ to reach Point $3$ directly. However, he can first travel to Point $2$ in $12$ minutes, get sleep in the house there, and then travel to Point $3$. Thus, the answer is Yes.

update @ 2024/3/10 10:42:13