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respectable
Find the minimal absolute value of a sum of two elements.
Programming 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:

A[0] = 1 A[1] = 4 A[2] = -3

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:

class Solution { public int solution(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:

A[0] = 1 A[1] = 4 A[2] = -3

the function should return 1, as explained above.

Given array A:

A[0] = -8 A[1] = 4 A[2] = 5 A[3] =-10 A[4] = 3

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].
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