# Finds the maximum distance (absolute index difference) between two numbers in an array.
#
# @param arr [Array<Integer>] The input array of numbers.
# @param num1 [Integer] The first target number.
# @param num2 [Integer] The second target number.
# @return [Integer, nil] The maximum absolute index difference, or nil if either number is missing.
def max_distance_between_numbers(arr, num1, num2)
# Variables to track the first and last occurrences of both numbers
first1 = last1 = nil
first2 = last2 = nil
# Single pass through the array: O(N) time complexity, O(1) space complexity
arr.each_with_index do |current, i|
if current == num1
first1 = i if first1.nil? # Record the first time num1 appears
last1 = i # Continuously update the last time num1 appears
elsif current == num2
first2 = i if first2.nil? # Record the first time num2 appears
last2 = i # Continuously update the last time num2 appears
end
end
# Edge case: If either number is not present in the array, return nil
return nil if first1.nil? || first2.nil?
# The maximum distance will always be between the outermost boundaries of the two sets:
# 1. Distance between the first occurrence of num1 and the last occurrence of num2
# 2. Distance between the last occurrence of num1 and the first occurrence of num2
[
(first1 - last2).abs,
(last1 - first2).abs
].max
end
# --- Example Usage ---
array = [2, 3, 7, 3, 3, 4, 8, 8, 8, 11, 9, 1, 3]
number1 = 3
number2 = 8
result = max_distance_between_numbers(array, number1, number2)
if result
puts "The maximum distance between #{number1} and #{number2} is: #{result}"
else
puts "One or both numbers were not found in the array."
end
# run:
#
# The maximum distance between 3 and 8 is: 7
#
