Minimum Absolute Difference in an Array

Problem Description

Given an array of integers, find the minimum absolute difference between any two of its elements.

The absolute difference between two values a and b is written as:

						$|a - b|$

It represents the positive difference between the two numbers.

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Example

Consider the array:

arr = [3, -7, 0]

The possible pairs of elements are:

Pair	$\Vert a-b\Vert$
(3, -7)	10
(3, 0)	3
(-7, 0)	7

The smallest absolute difference among these is:

						$\text{min} = 3$

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Function Description

Write the function minimumAbsoluteDifference with the following signature:

def minimumAbsoluteDifference(arr: list[int]) -> int:

Use to compute the absolute value the following Python function:

abs()

The function should:

• Receive an array of integers arr.

• Return a single integer: the minimum absolute difference between any two elements in the array.

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Input Format

• n integers, representing the array elements.

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Output Format

Print a single integer — the minimum absolute difference.

Sample Input 1

[3,-7, 0]

Sample Output 1

3

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Sample Input 2

 [-59, -36, -13, 1, -53, -92, -2, -96, -54, 75]

Sample Output 2

1

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Sample Input 3

[1, -3, 71, 68, 17]

Sample Output 3

3

Guided steps

• Compute absolute differences.
  Given two numbers a and b, compute their absolute difference check if that is correct with python function abs(a - b).
  Try this on a few pairs from the input array to understand what we are trying to minimize.

• Write pseudocode.
  Before writing the code, write the pseudocode implementing the following logic:

  • Start with a variable to store the smallest difference found so far. Think carefully about how to initialize it — it should be a value larger than any possible difference (for instance, a very large number).

  • Compare every possible pair of elements.

  • Each time you find a smaller absolute difference, update your variable.

  • After all comparisons, return that smallest value.

• Implement and test.
  Translate your pseudocode into Python, then test it on the sample inputs.