A15270 | $Meeting on the Line$

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题目描述

$n$ people live on the coordinate line, the $i$ -th one lives at the point $x_i$ ( $1 \le i \le n$ ). They want to choose a position $x_0$ to meet. The $i$ -th person will spend $|x_i - x_0|$ minutes to get to the meeting place. Also, the $i$ -th person needs $t_i$ minutes to get dressed, so in total he or she needs $t_i + |x_i - x_0|$ minutes. Here $|y|$ denotes the absolute value of $y$ . These people ask you to find a position $x_0$ that minimizes the time in which all $n$ people can gather at the meeting place.

The first line contains a single integer $t$ ( $1 \le t \le 10^3$ ) — the number of test cases. Then the test cases follow. Each test case consists of three lines. The first line contains a single integer $n$ ( $1 \le n \le 10^5$ ) — the number of people. The second line contains $n$ integers $x_1, x_2, \dots, x_n$ ( $0 \le x_i \le 10^{8}$ ) — the positions of the people. The third line contains $n$ integers $t_1, t_2, \dots, t_n$ ( $0 \le t_i \le 10^{8}$ ), where $t_i$ is the time $i$ -th person needs to get dressed. It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, print a single real number — the optimum position $x_0$ . It can be shown that the optimal position $x_0$ is unique. Your answer will be considered correct if its absolute or relative error does not exceed $10^{−6}$ . Formally, let your answer be $a$ , the jury's answer be $b$ . Your answer will be considered correct if $\frac{|a−b|}{max(1,|b|)} \le 10^{−6}$ .

输入 #1

7
1
0
3
2
3 1
0 0
2
1 4
0 0
3
1 2 3
0 0 0
3
1 2 3
4 1 2
3
3 3 3
5 3 3
6
5 4 7 2 10 4
3 2 5 1 4 6

输出 #1

C++ 编辑器

输入

输出