euler-024

def generate_permutation(digits, target_position)
  remaining_digits = digits.clone
  current_position = 0
  result = []

  (digits.length).downto(1) do |n|
    # Calculate the number of permutations for the remaining (n-1) digits
    factorial = (1..n-1).reduce(1, :*)
    index = 0

    # Find the correct digit for the current position in the result
    while current_position + factorial < target_position
      current_position += factorial
      index += 1
    end

    result << remaining_digits.delete_at(index)
  end

  result.join
end

digits = (0..9).to_a
target_position = 1_000_000

# Generate the millionth permutation without creating all permutations
millionth_permutation = generate_permutation(digits, target_position)

puts "The millionth lexicographic permutation of 0-9 is: #{millionth_permutation}"