=begin

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

   3
  7 5
 2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:


NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

=end


pyramid = '75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23'.split("\n").collect{|a| a.split(' ') }

class BinaryItem #{{{

  attr_accessor :left, :right, :value

  def initialize(value)
    @value = value.to_i
    @marked = false
    @left = nil
    @right = nil
  end

  def marked?
    return @marked
  end

  def mark
    @marked = true
  end

  def markIf(min)
    mark if min <= @value
    @left.markIf(min) unless @left.nil?
    @right.markIf(min) unless @right.nil?
  end

  def maxSum
    if @right.nil?
      rightmax = 0
    elsif !@right.marked?
      rightmax = nil
    else
      rightmax = @right.maxSum
    end
    if @left.nil?
      leftmax = 0
    elsif !@left.marked?
      leftmax = nil
    else
      leftmax = @left.maxSum
    end
    if leftmax.nil? && rightmax.nil?
      return nil
    elsif leftmax.nil?
      return rightmax + @value
    elsif rightmax.nil?
      return leftmax + @value
    elsif leftmax > rightmax
      return leftmax + @value
    else
      return rightmax + @value
    end
  end

  def findMax
    mark
    @value.downto 0 do |min|
      @right.markIf(min)
      @left.markIf(min)
      max = maxSum
      return max if !max.nil?
    end
  end
end #}}}

previous = []
current = []
pyrStart = nil
pyramid.each do |row|
  row.each do |num|
    current.push BinaryItem.new(num)
  end
  previous.each_index do |prev|
    previous[prev].left = current[prev]
    previous[prev].right = current[prev+1]
  end
  previous = current
  if current.size == 1
    pyrStart = current[0]
  end
  current = []
end

print(pyrStart.findMax)