A16316. Absolute Beauty
编程题
普及/提高-
知识点
题目描述
Kirill has two integer arrays $a_1,a_2,…,a_n$ and $b_1,b_2,…,b_n$ of length $n$. He defines the _absolute beauty_ of the array $b$ as
$$ \sum_{i=1}^n|a_i-b_i| $$
Here, $|x|$ denotes the absolute value of $x$.
Kirill can perform the following operation **at most once**:
- select two indices $i$ and $j$ ($1≤i<j≤n$) and swap the values of $b_i$ and $b_j$.
Help him find the maximum possible absolute beauty of the array $b$ after performing **at most one** swap.
$$ \sum_{i=1}^n|a_i-b_i| $$
Here, $|x|$ denotes the absolute value of $x$.
Kirill can perform the following operation **at most once**:
- select two indices $i$ and $j$ ($1≤i<j≤n$) and swap the values of $b_i$ and $b_j$.
Help him find the maximum possible absolute beauty of the array $b$ after performing **at most one** swap.
输入格式
Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \leq t \leq 10\,000$ ). The description of test cases follows.
The first line of each test case contains a single integer $n$ ( $2\leq n\leq 2\cdot 10^5$ ) — the length of the arrays $a$ and $b$ .
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1\leq a_i\leq 10^9$ ) — the array $a$ .
The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1\leq b_i\leq 10^9$ ) — the array $b$ .
It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ .
The first line of each test case contains a single integer $n$ ( $2\leq n\leq 2\cdot 10^5$ ) — the length of the arrays $a$ and $b$ .
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1\leq a_i\leq 10^9$ ) — the array $a$ .
The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1\leq b_i\leq 10^9$ ) — the array $b$ .
It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ .
输出格式
For each test case, output one integer — the maximum possible absolute beauty of the array $b$ after no more than one swap.
输入输出样例
输入 #1
6 3 1 3 5 3 3 3 2 1 2 1 2 2 1 2 2 1 4 1 2 3 4 5 6 7 8 10 1 8 2 5 3 5 3 1 1 3 2 9 2 4 8 2 3 5 3 1 3 47326 6958 358653 3587 35863 59474
输出 #1
4 2 2 16 31 419045
说明/提示
In the first test case, each of the possible swaps does not change the array $b$ .
In the second test case, the absolute beauty of the array $b$ without performing the swap is $|1-1| + |2-2| = 0$ . After swapping the first and the second element in the array $b$ , the absolute beauty becomes $|1-2| + |2-1| = 2$ . These are all the possible outcomes, hence the answer is $2$ .
In the third test case, it is optimal for Kirill to not perform the swap. Similarly to the previous test case, the answer is $2$ .
In the fourth test case, no matter what Kirill does, the absolute beauty of $b$ remains equal to $16$ .
In the second test case, the absolute beauty of the array $b$ without performing the swap is $|1-1| + |2-2| = 0$ . After swapping the first and the second element in the array $b$ , the absolute beauty becomes $|1-2| + |2-1| = 2$ . These are all the possible outcomes, hence the answer is $2$ .
In the third test case, it is optimal for Kirill to not perform the swap. Similarly to the previous test case, the answer is $2$ .
In the fourth test case, no matter what Kirill does, the absolute beauty of $b$ remains equal to $16$ .