310844: CF1898D. Absolute Beauty
Description
Kirill has two integer arrays $a_1,a_2,\ldots,a_n$ and $b_1,b_2,\ldots,b_n$ 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 $j$ ($1 \leq i < j \leq n$) 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.
InputEach 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 $2\cdot 10^5$.
OutputFor each test case, output one integer — the maximum possible absolute beauty of the array $b$ after no more than one swap.
ExampleInput6 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 59474Output
4 2 2 16 31 419045Note
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 $16$.
Output
输入数据格式:第一行包含一个整数t(\(1 \leq t \leq 10,000\)),表示测试用例的数量。接下来每个测试用例包含三行,第一行是一个整数n(\(2 \leq n \leq 2 \cdot 10^5\)),表示数组a和b的长度。第二行包含n个整数\(a_1, a_2, \ldots, a_n\)(\(1 \leq a_i \leq 10^9\)),表示数组a。第三行包含n个整数\(b_1, b_2, \ldots, b_n\)(\(1 \leq b_i \leq 10^9\)),表示数组b。所有测试用例的n之和不超过\(2 \cdot 10^5\)。
输出数据格式:对于每个测试用例,输出一个整数,表示在进行最多一次交换后,数组b的最大可能“绝对美丽值”。题目大意:Kirill有两个长度为n的整数数组a和b,他定义数组b的“绝对美丽值”为 \(\sum_{i=1}^{n} |a_i - b_i|\),即数组a和b对应元素之差的绝对值之和。Kirill可以进行最多一次以下操作:选择两个索引i和j(\(1 \leq i < j \leq n\))并交换\(b_i\)和\(b_j\)的值。求在进行最多一次交换后,数组b的最大可能“绝对美丽值”。 输入数据格式:第一行包含一个整数t(\(1 \leq t \leq 10,000\)),表示测试用例的数量。接下来每个测试用例包含三行,第一行是一个整数n(\(2 \leq n \leq 2 \cdot 10^5\)),表示数组a和b的长度。第二行包含n个整数\(a_1, a_2, \ldots, a_n\)(\(1 \leq a_i \leq 10^9\)),表示数组a。第三行包含n个整数\(b_1, b_2, \ldots, b_n\)(\(1 \leq b_i \leq 10^9\)),表示数组b。所有测试用例的n之和不超过\(2 \cdot 10^5\)。 输出数据格式:对于每个测试用例,输出一个整数,表示在进行最多一次交换后,数组b的最大可能“绝对美丽值”。