Swapping Problem
题意翻译
给定 $n$ 和两个长度为 $n$ 的数组 $a,b$,最多交换一次 $b$ 中的两个位置的值(可以不交换)。
最小化 $\sum_{i=1}^{n}|a_i-b_i|$。
$n \le 2\times10^5$;$a_i,b_i\le 10^9$。
题目描述
You are given 2 arrays $ a $ and $ b $ , both of size $ n $ . You can swap two elements in $ b $ at most once (or leave it as it is), and you are required to minimize the value $ $$$\sum_{i}|a_{i}-b_{i}|. $ $$$
Find the minimum possible value of this sum.
输入输出格式
输入格式
The first line contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ).
The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le {10^9} $ ).
The third line contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ 1 \le b_i \le {10^9} $ ).
输出格式
Output the minimum value of $ \sum_{i}|a_{i}-b_{i}| $ .
输入输出样例
输入样例 #1
5
5 4 3 2 1
1 2 3 4 5
输出样例 #1
4
输入样例 #2
2
1 3
4 2
输出样例 #2
2
说明
In the first example, we can swap the first and fifth element in array $ b $ , so that it becomes $ [ 5, 2, 3, 4, 1 ] $ .
Therefore, the minimum possible value of this sum would be $ |5-5| + |4-2| + |3-3| + |2-4| + |1-1| = 4 $ .
In the second example, we can swap the first and second elements. So, our answer would be $ 2 $ .