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AVAILABLE LESSONS:

Lesson 1

Iterations

Lesson 2

Arrays

Lesson 3

Time Complexity

Lesson 4

Counting Elements

Lesson 5

Prefix Sums

Lesson 6

Sorting

Lesson 7

Stacks and Queues

Lesson 8

Leader

Lesson 9

Maximum slice problem

Lesson 10

Prime and composite numbers

Lesson 11

Sieve of Eratosthenes

Lesson 12

Euclidean algorithm

Lesson 13

Fibonacci numbers

Lesson 14

Binary search algorithm

Lesson 15

Caterpillar method

Lesson 16

Greedy algorithms

Lesson 17

Dynamic programming

Find the minimal absolute value of a sum of two elements.

Spoken language:

Let A be a non-empty array consisting of N integers.

The *abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

has pairs of indices (0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (2, 2).

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

int solution(int A[], int N);

that, given a non-empty array A consisting of N integers, returns the minimal abs sum of two for any pair of indices in this array.

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Copyright 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

Let A be a non-empty array consisting of N integers.

The *abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

has pairs of indices (0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (2, 2).

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

int solution(vector<int> &A);

that, given a non-empty array A consisting of N integers, returns the minimal abs sum of two for any pair of indices in this array.

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Copyright 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

Let A be a non-empty array consisting of N integers.

The *abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

has pairs of indices (0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (2, 2).

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

int solution(vector<int> &A);

that, given a non-empty array A consisting of N integers, returns the minimal abs sum of two for any pair of indices in this array.

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Copyright 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

class Solution { public int solution(int[] A); }

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

int solution(List<int> A);

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

func Solution(A []int) int

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

class Solution { public int solution(int[] A); }

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

class Solution { public int solution(int[] A); }

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

function solution(A);

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

fun solution(A: IntArray): Int

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

function solution(A)

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use `#A` to get the length of the array A.

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

int solution(NSMutableArray *A);

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

function solution(A: array of longint; N: longint): longint;

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

function solution($A);

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

sub solution { my (@A) = @_; ... }

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

def solution(A)

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

def solution(a)

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

object Solution { def solution(a: Array[Int]): Int }

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

public func solution(_ A : inout [Int]) -> Int

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

public func solution(_ A : inout [Int]) -> Int

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

function solution(A: number[]): number;

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Let A be a non-empty array consisting of N integers.

*abs sum of two* for a pair of indices (P, Q) is the absolute value |A[P] + A[Q]|, for 0 ≤ P ≤ Q < N.

For example, the following array A:

The abs sum of two for the pair (0, 0) is A[0] + A[0] = |1 + 1| = 2.

The abs sum of two for the pair (0, 1) is A[0] + A[1] = |1 + 4| = 5.

The abs sum of two for the pair (0, 2) is A[0] + A[2] = |1 + (−3)| = 2.

The abs sum of two for the pair (1, 1) is A[1] + A[1] = |4 + 4| = 8.

The abs sum of two for the pair (1, 2) is A[1] + A[2] = |4 + (−3)| = 1.

The abs sum of two for the pair (2, 2) is A[2] + A[2] = |(−3) + (−3)| = 6.

Write a function:

Private Function solution(A As Integer()) As Integer

For example, given the following array A:

the function should return 1, as explained above.

Given array A:

the function should return |(−8) + 5| = 3.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].