Challenges

challenges.rb

# Where n is a positive integer, the function f(n) satisfies the following:
#
#    f(0) = 0
#    f(1) = 1
#    f(n) = f(n - 1) + f(n - 2)
#
# Create a program to find f(n)

def super_sum(number)
  results = [0, 1]

  (2..number).each { |n| results[n] = results[n - 1] + results[n - 2] }

  return results[number]
end


# Implement a program that lists the nodes of a random binary tree by nodes at the same depth

class Node
  attr_accessor :value
  attr_accessor :node_0
  attr_accessor :node_1

  def initialize(value)
    @value = value
  end
end

def list_nodes_by_depth(node, depth = 0)
  @nodes ||= {}

  return if node.nil?

  @nodes[depth] ||= []
  @nodes[depth] << node.value

  list_nodes_by_depth(node.node_0, depth + 1)
  list_nodes_by_depth(node.node_1, depth + 1)

  return @nodes
end


# Imagine you are playing a board game. You roll a 6-faced dice and move forward the same
# number of spaces that you rolled. If the finishing point is "n" spaces away from the starting
# point, please implement a program that calculates how many possible ways there are to
# arrive exactly at the finishing point

def ultra_sum(number)
  results = [1, 1, 2, 4, 8, 16]

  return results[number] if number < 6

  (6..number).each do |n|
    results[n] = results[n - 1] +
                 results[n - 2] +
                 results[n - 3] +
                 results[n - 4] +
                 results[n - 5] +
                 results[n - 6]
  end

  return results[number]
end

puts ultra_sum(ARGV[0].to_i)