如何从两个数组中选择元素以使总和最小？

Question

我有两个长度相等的数组，可以选择array1或array2，求和的输出必须是最小的。但是，我从 array1 中选择元素的次数必须与我从 array2 中选择的次数相同。

例子：

array1 = [2, 3, 5, 1]

array2 = [1, 2, 3, 2]

输出将是 8，因为：

At index0: I picked 2 from array1.
At index1: I picked 2 from array2.
At index2: I picked 3 from array2.
At index3: I picked 1 from array1.

我目前的方法：我根据 array1 上的元素对数组进行排序。所以我在 index0 和 index1 处选择了 array1，然后在 index2 和 index3 处选择了 array2。

排序后的示例：

array1 = [1, 2, 3, 5]

array2 = [2, 1, 2, 3]

At index0: I picked 1 from array1.
At index1: I picked 2 from array1.
At index2: I picked 2 from array2.
At index3: I picked 3 from array2.

但是，当数组是这样的时候，我可能会遇到问题：

array1 = [2, 3, 5, 1]

array2 = [1, 7, 6, 2]

根据array1排序后：

array1 = [1, 2, 3, 5]

array2 = [2, 1, 7, 6]

At index0: I picked 1 from array1.
At index1: I picked 2 from array1.
At index2: I picked 7 from array2.
At index3: I picked 6 from array2.

当理想的解决方案是：

At index0: I picked 2 from array2.
At index1: I picked 1 from array2.
At index2: I picked 3 from array1.
At index3: I picked 5 from array1.

有人可以帮我解决这个问题吗？谢谢。

Answer 1

计算差值array1 - array2：

array1 = [2, 3, 5, 1]
array2 = [1, 2, 3, 2]

diff   = [1, 1 ,2, -1]
index  = [0, 1, 2, 3]

排序（并记住索引）：

sorted_diff: [-1, 1, 1, 2]
index2     : [ 3, 0, 1, 2]
            array1 | array2

你必须对数组的一半取反才能得到最小的总和。所以index1，index2来自array2。

示例2：

array1 = [2, 3, 5, 1]
array2 = [1, 7, 6, 2]

diff   = [1, -4 ,-1, -1]
index  = [0, 1, 2, 3]

sorted = [-4, -1, -1, 1]
index2 = [ 1, 2, 3, 0]
        array1 | array2

所以取自array2 index3, index0。