problem 18

"""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 4 82 47 65
19 1 23 75 3 34
88 2 77 73 7 63 67
99 65 4 28 6 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 4 68 89 53 67 30 73 16 69 87 40 31
4 62 98 27 23 09 70 98 73 93 38 53 60 4 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 con(allnum):
  
  for row in  range (13,-1,-1):
   for col in range(14 - 1):
     if allnum[row + 1][col] > allnum[row + 1][col + 1]:
       allnum[row][col] = allnum[row][col] +  allnum[row + 1][col]
     else:
       allnum[row][col] = allnum[row][col] +  allnum[row + 1][col + 1]  
  return (allnum[0][0])
all_num =[
[75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[95, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[17, 47, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[18, 35, 87, 10, 0 ,0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[20, 4, 82, 47, 65, 0 ,0, 0, 0, 0, 0, 0, 0, 0, 0],
[19, 1, 23, 75, 3 ,34, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[88, 2, 77, 73, 7, 63, 67, 0, 0, 0, 0, 0, 0, 0, 0],
[99, 65, 4, 28, 6, 16, 70, 92, 0, 0, 0, 0, 0, 0, 0],
[41, 41, 26, 56, 83, 40, 80, 70, 33, 0, 0, 0, 0, 0, 0],
[41, 48, 72, 33, 47, 32, 37, 16, 94, 29, 0, 0, 0, 0, 0],
[53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14, 0, 0, 0, 0],
[70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57, 0, 0, 0],
[91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48, 0, 0],
[63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31, 0],
[4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]
]

print(con(all_num))