'''
Problem 18
31 May 2002

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)
'''

def dfs_max(i, j):
  key = str(i) + ':' + str(j)
  if key in sums: return sums[key]
  if (i >= len(tree) or (j >= len(tree[i]))): return 0
  sums[key] = int(tree[i][j]) + max(dfs_max(i+1, j), dfs_max(i+1, j+1))
  return sums[key]
file = open('018.txt', 'r')
tree, sums = [], {}
for line in file:
  tree.append(line.rstrip('\n').split(' '))
print dfs_max(0, 0)

'''
Problem 18
31 May 2002

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)
'''

tree, sums = [], {}
file = open('018.txt', 'r')
for line in file:
  tree.append(map(int, line.rstrip('\n').split(' ')))

def dfs_max(i=0, j=0):
  if (i >= len(tree) or (j >= len(tree[i]))):
    return 0
  key = str(i) + ':' + str(j)
  if key in sums:
    return sums[key]
  sums[key] = tree[i][j] + max(dfs_max(i+1, j), dfs_max(i+1, j+1))
  return sums[key]

print dfs_max()

Add Problem 18 solution.