Too Min Too Max (Codeforces 1934A)
Tags: Greedy, math

Given an array $$$a$$$ of $$$n$$$ elements, find the maximum value of the expression:$$$$$$|a_i - a_j| + |a_j - a_k| + |a_k - a_l| + |a_l - a_i|$$$$$$where $$$i$$$, $$$j$$$, $$$k$$$, and $$$l$$$ are four distinct indices of the array $$$a$$$, with $$$1 \le i, j, k, l \le n$$$.Here $$$|x|$$$ denotes the absolute value of $$$x$$$.

Input: The first line contains one integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer $$$n$$$ ($$$4 \le n \le 100$$$) — the length of the given array.The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^6 \le a_i \le 10^6$$$).

Output: For each test case, print a single integer — the maximum value.

Note: In the first test case, for any selection of $$$i$$$, $$$j$$$, $$$k$$$, $$$l$$$, the answer will be $$$0$$$. For example, $$$|a_1 - a_2| + |a_2 - a_3| + |a_3 - a_4| + |a_4 - a_1| = |1 - 1| + |1 - 1| + |1 - 1| + |1 - 1| = 0 + 0 + 0 + 0 = 0$$$.In the second test case, for $$$i = 1$$$, $$$j = 3$$$, $$$k = 2$$$, and $$$l = 5$$$, the answer will be $$$6$$$. $$$|a_1 - a_3| + |a_3 - a_2| + |a_2 - a_5| + |a_5 - a_1| = |1 - 2| + |2 - 1| + |1 - 3| + |3 - 1| = 1 + 1 + 2 + 2 = 6$$$.

Sample Inputs:
5
4
1 1 1 1
5
1 1 2 2 3
8
5 1 3 2 -3 -1 10 3
4
3 3 1 1
4
1 2 2 -1

Sample Outputs:
0
6
38
8
8

Solution (Python):
for _ in range(int(input())):
    (_, a) = (input(), sorted(map(int, input().split())))
    print(a[-1] - a[0] + a[-1] - a[1] + a[-2] - a[0] + a[-2] - a[1])

Solution (Python):
for s in [*open(0)][2::2]:
    (a, b, *_, c, d) = sorted(map(int, s.split()))
    print(c + d - a - b << 1)

Solution (Python):
def solution2():
    n: int = int(input())
    nums = sorted(list(map(int, input().split())))
    return abs(nums[-1] - nums[0]) + abs(nums[-1] - nums[1]) + abs(nums[-2] - nums[0]) + abs(nums[-2] - nums[1])
n: int = int(input())
for i in range(n):
    print(solution2())