
ZOJ Problem Set  4068
PUBG is a multiplayer online battle royale video game. In the game, up to one hundred players parachute onto an island and scavenge for weapons and equipment to kill others while avoiding getting killed themselves. Airdrop in this game is a key element, as airdrops often carry with them strong weapons or numerous supplies, helping players to survive. Airdrop in the game(?) Consider the battle field of the game to be a twodimensional plane. An airdrop has just landed at point $(x_0, y_0)$ (both $x_0$ and $y_0$ are integers), and all the $n$ players on the battle field, where $(x_i, y_i)$ (both $x_i$ and $y_i$ are integers) indicates the initial position of the $i$th player, start moving towards the airdrop with the following pattern:
But the battle is tough and it's almost impossible for all the players to arrive at the airdrop safely. If two or more players meet at point $(x', y')$ other than $(x_0, y_0)$, where both $x'$ and $y'$ are integers, they will fight and kill each other and none of them survive. BaoBao is a big fan of the game and is interested in the number of players successfully arriving at the position of the airdrop, but he doesn't know the value of $x_0$. Given the value of $y_0$ and the initial position of each player, please help BaoBao calculate the minimum and maximum possible number of players successfully arriving at the position of the airdrop for all $x_0 \in \mathbb{Z}$, where $\mathbb{Z}$ is the set of all integers (note that $x_0$ can be positive, zero or negative). InputThere are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case: The first line contains two integers $n$ and $y_0$ ($1 \le n \le 10^5$, $1 \le y_0 \le 10^5$), indicating the number of players and the $y$ value of the airdrop. For the following $n$ lines, the $i$th line contains two integers $x_i$ and $y_i$ ($1 \le x_i, y_i \le 10^5$), indicating the initial position of the $i$th player. It's guaranteed that the sum of $n$ in all test cases will not exceed $10^6$, and in each test case no two players share the same initial position. OutputFor each test case output one line containing two integers $p_\text{min}$ and $p_\text{max}$ separated by one space. $p_\text{min}$ indicates the minimum possible number of players successfully arriving at the position of the airdrop, while $p_\text{max}$ indicates the maximum possible number. Sample Input3 3 2 1 2 2 1 3 5 3 3 2 1 2 5 4 3 2 3 1 3 4 3 Sample Output1 3 0 3 2 2 HintWe now explain the first sample test case. To obtain the answer of $p_\text{min} = 1$, one should consider $x_0 = 3$. The following table shows the position of each player at the end of each time unit when $x_0 = 3$.
To obtain the answer of $p_\text{max} = 3$, one should consider $x_0 = 2$. The following table shows the position of each player at the end of each time unit when $x_0 = 2$.
Author: WENG, Caizhi Source: The 2018 ACMICPC Asia Qingdao Regional Contest 