Stairs Challenge_Ruby

stair_challenge.rb

puts "Stairs Challenge"
  # Given
  # x = the number of steps to the top of a stair
  # and
  # n = is the maximum stride to be taken
  # Solve for the total number of ways to reach the top step.

  # Assumptions
  # There will always be at least one way.
  # 0 is not a valid stride.

def ways(top_step, stride)
  stair = (1..top_step)
  arr = [1]

  stair.each do |step|
    arr.push(arr.reduce(:+))
    arr.shift if arr.length > stride
  end

  arr[-1]
end

puts ways(3, 3) == 4
puts ways(5, 3) == 13
puts ways(8, 3) == 81
puts ways(6, 4) == 29
puts ways(5, 5) == 16
puts ways(10, 5) == 464
puts ways(42, 10) == 2163721825536
puts ways(1765, 23) == 1039602300720182949531290166735978963919254872540498389861689268819873787659903275891016947657827704312413119114251022853135423993607616893994932325611731804159556097350124510528972587480084537728338077697792780337510887693066344283593811293503921936884013646257847864345096282056840310793188819726663155676582613070220100469550542883893298739091317146652816585042727521424577561376926579159495635578786368512865680619639826539672721693182234770208133052035383723399343718433609037709851685140183430843762289204200541279141793210368