All Tracks Algorithms Sorting Merge Sort Problem

Fredo and Sums
Tag(s):

Algorithms, Arrays, Easy-Medium, Greedy algorithm, Merge sort, Sorting

Problem
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Fredo has an array A consisting of N elements. He wants to divide the array into \(N/2\) pairs where each array element comes in exactly one pair. Say that pair i has elements \(X_i\) and \(Y_i\), he defines S as :

\(S = \sum_{i=1}^{N/2} abs(X_i-Y_i) \)

He asks you to find the minimum and maximum value of S.

Input Format:

First line consists of an integer T denoting the number of test cases.
Each test case:
First line consists of an integer N denoting the number of elements in the array.
Second line consists of N space separated integers denoting the array elements.

Output Format:
For each test case, print the minimum and maximum sum (space separated). Answer for each test case should come in a new line.

Input Constraints:

\(1 \le T \le 10\)
\(1 \le N \le 10^5\)
\(-10^9 \le A[i] \le 10^9\)
\(N \ is \ even\)

SAMPLE INPUT
1
4
10 20 -10 0
SAMPLE OUTPUT
20 40
Explanation

For minimum sum, we take pairs \((10,20)\) and \((-10,0)\).
For maximum sum, we take pairs \((20,0)\) and \((10,-10)\).

Time Limit: 1,0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, TypeScript, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

July Circuits '17

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