A14963. Yet Another Minimization Problem
编程题
普及/提高-
知识点
题目描述
You are given two arrays $a$ and $b$ , both of length $n$ .
You can perform the following operation any number of times (possibly zero): select an index $i$ ( $1 \leq i \leq n$ ) and swap $a_i$ and $b_i$ .
Let's define the cost of the array $a$ as $\sum_{i=1}^{n} \sum_{j=i + 1}^{n} (a_i + a_j)^2$ . Similarly, the cost of the array $b$ is $\sum_{i=1}^{n} \sum_{j=i + 1}^{n} (b_i + b_j)^2$ .
Your task is to minimize the total cost of two arrays.
You can perform the following operation any number of times (possibly zero): select an index $i$ ( $1 \leq i \leq n$ ) and swap $a_i$ and $b_i$ .
Let's define the cost of the array $a$ as $\sum_{i=1}^{n} \sum_{j=i + 1}^{n} (a_i + a_j)^2$ . Similarly, the cost of the array $b$ is $\sum_{i=1}^{n} \sum_{j=i + 1}^{n} (b_i + b_j)^2$ .
Your task is to minimize the total cost of two arrays.
输入格式
Each test case consists of several test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 40$ ) — the number of test cases. The following is a description of the input data sets.
The first line of each test case contains an integer $n$ ( $1 \leq n \leq 100$ ) — the length of both arrays.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 100$ ) — elements of the first array.
The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \leq b_i \leq 100$ ) — elements of the second array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $100$ .
The first line of each test case contains an integer $n$ ( $1 \leq n \leq 100$ ) — the length of both arrays.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 100$ ) — elements of the first array.
The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \leq b_i \leq 100$ ) — elements of the second array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $100$ .
输出格式
For each test case, print the minimum possible total cost.
输入输出样例
输入 #1
3 1 3 6 4 3 6 6 6 2 7 4 1 4 6 7 2 4 2 5 3 5
输出 #1
0 987 914
说明/提示
In the second test case, in one of the optimal answers after all operations $a = [2, 6, 4, 6]$ , $b = [3, 7, 6, 1]$ .
The cost of the array $a$ equals to $(2 + 6)^2 + (2 + 4)^2 + (2 + 6)^2 + (6 + 4)^2 + (6 + 6)^2 + (4 + 6)^2 = 508$ .
The cost of the array $b$ equals to $(3 + 7)^2 + (3 + 6)^2 + (3 + 1)^2 + (7 + 6)^2 + (7 + 1)^2 + (6 + 1)^2 = 479$ .
The total cost of two arrays equals to $508 + 479 = 987$ .
The cost of the array $a$ equals to $(2 + 6)^2 + (2 + 4)^2 + (2 + 6)^2 + (6 + 4)^2 + (6 + 6)^2 + (4 + 6)^2 = 508$ .
The cost of the array $b$ equals to $(3 + 7)^2 + (3 + 6)^2 + (3 + 1)^2 + (7 + 6)^2 + (7 + 1)^2 + (6 + 1)^2 = 479$ .
The total cost of two arrays equals to $508 + 479 = 987$ .