非对称交换——通过交换最小化列表中的最大/最小差异

Question

Was doing some exercises in CodeChef and came across the Asymmetric Swaps problem:

Problem

Chef has two arrays and of the same size.

In one operation, Chef can:

• Choose two integers and (1 ≤, ≤ ) and swap the elementsand.

Chef came up with a task to find the minimum possible value of ( − ) after performing the swap operation any (possibly zero) number of times.

Since Chef is busy, can you help him solve this task?

Note thatanddenote the maximum and minimum elements of the array respectively.

I have tried the below logic for the solution. But the logic fails for some test cases and I have no access to the failed test cases and where exactly the below code failed to meet the required output.

T = int(input())
for _ in range(T):
    arraySize = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    sortedList = sorted(A+B)
    minLower = sortedList[arraySize-1] - sortedList[0]                # First half of the sortedList
    minUpper = sortedList[(arraySize*2)-1] - sortedList[arraySize]    # Second half of the sortedList
    print(min(minLower,minUpper))

I saw some submitted answers and didn't get the reason or logic why they are doing so. Can someone guide where am I missing?

Answer 1

The approach to sort the input into one list is the right one. But it is not enough to look at the left and the right half of that sorted list.

It could well be that there is another sublist of length that has its extreme values closer to each other.

Take for instance this input:

A = [1,4,5]
B = [6,11,12]

Then the sorted list is [1,4,5,6,11,12] and [4,5,6] is actually the sublist which minimises the difference between its maximum and minimum value.

So implement a loop where you select the minimum among A[i+N-1] - A[i] .