Queue Data Structure
Elegant permuted sum
You will be given n integers {a[1], a[2], …, a[n]}. Find a permutation of these n integers so that summation of the absolute differences between adjacent elements is maximized. We will call this value the elegant permuted sum.
Consider the sequence {4, 2, 1, 5}. The permutation {2, 5, 1, 4} yields the maximum summation. For this permutation sum = |2 – 5| + |5 – 1| + |1 – 4| = 3 + 4 + 3 = 10. Of all the 24 permutations, you won't get any summation whose value exceeds 10.
Input data
The first line is the number of test cases t (t < 100). Each case consists of a line that starts with n (1 < n < 51) followed by n non-negative integers. None of the elements of the given permutation will exceed 1000.
Output data
For each test case print the case number followed by the elegant permuted sum.
Examples
3 4 4 2 1 5 4 1 1 1 1 2 10 1
Case 1: 10 Case 2: 0 Case 3: 9