Ian Visits Mary
题面翻译
题目描述
\(\textrm{lan}\) 和 \(\textrm{Mary}\) 是生活在笛卡尔坐标系格点上的青蛙，\(\textrm{lan}\) 在 \((0,0)\)，而 \(\textrm{Mary}\) 在 \((a,b)\)。
\(\textrm{lan}\) 想在 笛卡尔坐标系上跳来跳去去访问 \(\textrm{Mary}\)。每一秒，他会从当前位置 \((x_p,y_p)\) 跳到整点 \((x_q,y_q)\)，使得若用一条线段连接 \((x_p,y_p)\) 和 \((x_q,y_q)\)，没有整点在这条线段上。
\(\textrm{lan}\) 想尽快见到 \(\textrm{Mary}\)，所以他想用最多两次跳跃到 \((a,b)\)。不幸的是，\(\textrm{lan}\) 不太会数学，你能帮帮他吗？
整点被定义为 \(x\) 坐标和 \(y\) 坐标都是整数的点。
输入格式
第一行包含一个整数 \(t\) ( \(1\le t\le 500\) )，表示测试数据的数量。
对于每一个数据：
只有一行包含两个正整数 \(a,b\) ( \(1\le a,b\le 10^9\) )，含义如题面所示。
输出格式
对于每一个数据：
第一行是一个正整数 \(n\) ( \(1\le n\le 2\) )，表示 \(\textrm{lan}\) 需要几次跳跃访问 \(\textrm{Mary}\)。注意：你不需要让 \(n\) 最小。
下面是 \(n\) 行，在第 \(i\) 行有用空格分开的两个整数 \(x_i,y_i\) ( \(0\le x_i,y_i\le 10^9\) )，表示 \(\textrm{lan}\) 第 \(i\) 次会跳跃到 \((x_i,y_i)\)。必须满足 \(x_n=a,y_n=b\)。
\(\textrm{lan}\) 每次跳转后的位置不需要是不同的。
如果有多组解，输出任意一个。
题目描述
Ian and Mary are frogs living on lattice points of the Cartesian coordinate plane, with Ian living on $ (0,0) $ and Mary living on $ (a,b) $ .
Ian would like to visit Mary by jumping around the Cartesian coordinate plane. Every second, he jumps from his current position $ (x_p, y_p) $ to another lattice point $ (x_q, y_q) $ , such that no lattice point other than $ (x_p, y_p) $ and $ (x_q, y_q) $ lies on the segment between point $ (x_p, y_p) $ and point $ (x_q, y_q) $ .
As Ian wants to meet Mary as soon as possible, he wants to jump towards point $ (a,b) $ using at most $ 2 $ jumps. Unfortunately, Ian is not good at maths. Can you help him?
A lattice point is defined as a point with both the $ x $ -coordinate and $ y $ -coordinate being integers.
输入格式
The first line contains a single integer $ t $ ( $ 1 \le t \le 500 $ ) — the number of test cases. The description of test cases follows.
The first and only line of each test case contains two integers $ a $ and $ b $ ( $ 1\le a,b\le 10^9 $ ) — the coordinates of the lattice point where Mary lives.
输出格式
For each test case, print an integer $ n $ ( $ 1 \le n \le 2 $ ) on the first line, denoting the number of jumps Ian uses in order to meet Mary. Note that you do not need to minimize the number of jumps.
On the $ i $ -th line of the next $ n $ lines, print two integers $ 0 \le x_i,y_i \le 10^9 $ separated by a space, denoting Ian's location $ (x_i,y_i) $ after the $ i $ -th jump. $ x_n = a $ , $ y_n = b $ must hold.
Ian's initial location and his locations after each of the $ n $ jumps need not be distinct.
If there are multiple solutions, output any.
样例 #1
样例输入 #1
8
3 4
4 4
3 6
2 2
1 1
7 3
2022 2023
1000000000 1000000000
样例输出 #1
1
3 4
2
3 2
4 4
2
5 3
3 6
2
1 0
2 2
1
1 1
1
7 3
1
2022 2023
2
69420420 469696969
1000000000 1000000000
分析
从 (0, 0) 到 (x - 1, 1) 再到 (x, y) 肯定合法
也即是在 长为1, 宽为m 或者 宽为1, 长为m 的矩形内连接对角线, 除了端点, 没有别的点在对角线上
代码太简单不写了