18.py

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

triangle = """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"""

triangle = triangle.split('\n')
h = len(triangle) ## height of triangle above

for i in range(h):
    triangle[i] = list(map(int, triangle[i].split(' ')))
## make the triangle traversable

def btdp():
    for i in range(h - 2, -1, -1):
        for j in range(i+1):
            triangle[i][j] += max(triangle[i+1][j], triangle[i+1][j+1])
    print(triangle[0][0])

## above is a bottom-top dynamic programming approach

def tbdp():
    for i in range(1, h):
        for j in range(i+1):
            if j == 0:
                triangle[i][j] += triangle[i-1][j]
            elif j == i:
                triangle[i][j] += triangle[i-1][j-1]
            else:
                triangle[i][j] += max(triangle[i-1][j], triangle[i-1][j-1])
    print(max(triangle[h-1]))
    
btdp()

#########################################################################
# https://stackoverflow.com/questions/8002252/euler-project-18-approach #
#########################################################################