feat: add minimum absolute difference pairs algorithm

data_structures/arrays/minimum_absolute_difference_pairs.py

@@ -0,0 +1,47 @@
+def minimum_absolute_difference_pairs(arr: list[int]) -> list[list[int]]:
+    """
+    Given an array of distinct integers, return all pairs of elements
+    with the minimum absolute difference.
+
+    Args:
+        arr: list of integers
+
+    Returns:
+        list of pairs (as lists) with the minimum absolute difference
+
+    Examples:
+        >>> minimum_absolute_difference_pairs([4, 2, 1, 3])
+        [[1, 2], [2, 3], [3, 4]]
+        >>> minimum_absolute_difference_pairs([1, 3, 6, 10, 15])
+        [[1, 3]]
+        >>> minimum_absolute_difference_pairs([3, 8, -10, 23, 19, -4, -14, 27])
+        [[-14, -10], [19, 23], [23, 27]]
+        >>> minimum_absolute_difference_pairs([])
+        []
+        >>> minimum_absolute_difference_pairs([5])
+        []
+    """
+    if len(arr) < 2:
+        return []
+
+    # Sort array for adjacent difference comparison
+    arr.sort()
+
+    # Find minimum difference
+    min_diff = float("inf")
+    for i in range(1, len(arr)):
+        min_diff = min(min_diff, arr[i] - arr[i - 1])
+
+    # Collect all pairs with minimum difference
+    result = []
+    for i in range(1, len(arr)):
+        if arr[i] - arr[i - 1] == min_diff:
+            result.append([arr[i - 1], arr[i]])
+
+    return result
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()