text: """http://projecteuler.net/problem=018
  
  Maximum path sum I
  
  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 4
  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:
  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
  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)
  
  Solution by jontsai <hello@jontsai.com>
  """
  from utils import *
  
  EXPECTED_ANSWER = 1074
  
  input = '''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'''
  
  pyramid = [int(n) for n in input.split()]
  num_rows = int(quadratic(1, 1, -2 * len(pyramid)))
  
  def get_pyramid_cell(row, col):
      """Get a cell from the pyramid
      row 0 = top row
      col 0 = left-most column
      """
      row_offset = (row * (row + 1)) / 2
      index = row_offset + col
      cell = pyramid[index]
      return cell
  
  MAX_PATH_CACHE = {}
  
  def max_path(row, col):
      key = (row, col,)
      if key in MAX_PATH_CACHE:
          value = MAX_PATH_CACHE[key]
      else:
          if row + 1 == num_rows:
              # last row
              value = get_pyramid_cell(row, col)
          else:
              # not the last row
              subpaths = []
              # left path
              subpaths.append(max_path(row + 1, col))
              # right path
              subpaths.append(max_path(row + 1, col + 1))
              value = get_pyramid_cell(row, col) + max(subpaths)
          MAX_PATH_CACHE[key] = value
      return value
  
  answer = max_path(0, 0)
  
  print 'Expected: %s, Answer: %s' % (EXPECTED_ANSWER, answer)
  
  