310693: CF1872B. The Corridor or There and Back Again
Description
You are in a corridor that extends infinitely to the right, divided into square rooms. You start in room $1$, proceed to room $k$, and then return to room $1$. You can choose the value of $k$. Moving to an adjacent room takes $1$ second.
Additionally, there are $n$ traps in the corridor: the $i$-th trap is located in room $d_i$ and will be activated $s_i$ seconds after you enter the room $\boldsymbol{d_i}$. Once a trap is activated, you cannot enter or exit a room with that trap.
Determine the maximum value of $k$ that allows you to travel from room $1$ to room $k$ and then return to room $1$ safely.
For instance, if $n=1$ and $d_1=2, s_1=2$, you can proceed to room $k=2$ and return safely (the trap will activate at the moment $1+s_1=1+2=3$, it can't prevent you to return back). But if you attempt to reach room $k=3$, the trap will activate at the moment $1+s_1=1+2=3$, preventing your return (you would attempt to enter room $2$ on your way back at second $3$, but the activated trap would block you). Any larger value for $k$ is also not feasible. Thus, the answer is $k=2$.
InputThe first line of the input contains an integer $t$ ($1 \le t \le 1000$) — the number of test cases.
The descriptions of the test cases follow.
The first line of each test case description contains an integer $n$ ($1 \le n \le 100$) — the number of traps.
The following $n$ lines of each test case description present two integers $d_i$ and $s_i$ ($1 \le d_i, s_i \le 200$) — the parameters of a trap (you must leave room $d_i$ strictly before $s_i$ seconds have passed since entering this room). It's possible for multiple traps to occupy a single room (the values of $d_i$ can be repeated).
OutputFor each test case, print the maximum value of $k$ that allows you to travel to room $k$ and return to room $1$ without encountering an active trap.
ExampleInput7 1 2 2 3 2 8 4 3 5 2 1 200 200 4 1 20 5 9 3 179 100 1 2 10 1 1 18 2 1 1 1 2 3 1 3 1 1 1 3Output
2 5 299 9 9 1 1Note
The first test case is explained in the problem statement above.
In the second test case, the second trap prevents you from achieving $k\ge6$. If $k\ge6$, the second trap will activate at the moment $3+s_2=3+3=6$ (the time you enter room $4$ plus $s_2$). In the case of $k\ge6$, you will return to room $4$ at time $7$ or later. The trap will be active at that time. It can be shown that room $k=5$ can be reached without encountering an active trap.
In the third test case, you can make it to room $299$ and then immediately return to room $1$.
Output
你在一个无限延伸的走廊里,从房间1出发,前往房间k,然后返回房间1。你可以选择k的值。移动到相邻的房间需要1秒。
此外,走廊里还有n个陷阱:第i个陷阱位于房间d_i,并且将在你进入房间d_i后的s_i秒被激活。一旦陷阱被激活,你就不能进入或离开有该陷阱的房间。
确定允许你从房间1安全地旅行到房间k然后返回房间1的最大k值。
输入输出数据格式:
输入:
- 第一行包含一个整数t(1≤t≤1000)——测试用例的数量。
- 接下来是t个测试用例的描述。
- 每个测试用例的第一行包含一个整数n(1≤n≤100)——陷阱的数量。
- 接下来的n行,每行包含两个整数d_i和s_i(1≤d_i,s_i≤200)——一个陷阱的参数(你必须在这个房间停留少于s_i秒)。
输出:
- 对于每个测试用例,打印允许你旅行到房间k然后返回房间1而不遇到激活陷阱的最大k值。
示例:
输入:
```
7
1
2 2
3
2 8
4 3
5 2
1
200 200
4
1 20
5 9
3 179
100 1
2
10 1
1 18
2
1 1
1 2
3
1 3
1 1
1 3
```
输出:
```
2
5
299
9
9
1
1
```题目大意: 你在一个无限延伸的走廊里,从房间1出发,前往房间k,然后返回房间1。你可以选择k的值。移动到相邻的房间需要1秒。 此外,走廊里还有n个陷阱:第i个陷阱位于房间d_i,并且将在你进入房间d_i后的s_i秒被激活。一旦陷阱被激活,你就不能进入或离开有该陷阱的房间。 确定允许你从房间1安全地旅行到房间k然后返回房间1的最大k值。 输入输出数据格式: 输入: - 第一行包含一个整数t(1≤t≤1000)——测试用例的数量。 - 接下来是t个测试用例的描述。 - 每个测试用例的第一行包含一个整数n(1≤n≤100)——陷阱的数量。 - 接下来的n行,每行包含两个整数d_i和s_i(1≤d_i,s_i≤200)——一个陷阱的参数(你必须在这个房间停留少于s_i秒)。 输出: - 对于每个测试用例,打印允许你旅行到房间k然后返回房间1而不遇到激活陷阱的最大k值。 示例: 输入: ``` 7 1 2 2 3 2 8 4 3 5 2 1 200 200 4 1 20 5 9 3 179 100 1 2 10 1 1 18 2 1 1 1 2 3 1 3 1 1 1 3 ``` 输出: ``` 2 5 299 9 9 1 1 ```