<reponame>schwanberger/projectEuler
# Maximum path sum I: https://projecteuler.net/problem=18
# 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 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)
# data = [ 
# [3],
# [7, 4],
# [2, 4, 6],
# [8, 5, 9, 3]
# ]

data = [
[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, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23],
    ]

currentMax = 0


def brutus(i, j, result):
    global currentMax
        
    if i == len(data) - 1:
        if result > currentMax:
            currentMax = result
        return 0
    return brutus(i + 1, j, result + data[i + 1][j]) + brutus(i + 1, j + 1, result + data[i + 1][j + 1])


brutus(0, 0, data[0][0])
print currentMax


# Maximum path sum I: https://projecteuler.net/problem=18
# 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 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)
# data = [ 
# [3],
# [7, 4],
# [2, 4, 6],
# [8, 5, 9, 3]
# ]

data = [
[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, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23],
    ]

currentMax = 0


def brutus(i, j, result):
    global currentMax
        
    if i == len(data) - 1:
        if result > currentMax:
            currentMax = result
        return 0
    return brutus(i + 1, j, result + data[i + 1][j]) + brutus(i + 1, j + 1, result + data[i + 1][j + 1])


brutus(0, 0, data[0][0])
print currentMax
# Maximum path sum I: https://projecteuler.net/problem=18 # 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 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) # data = [ # [3], # [7, 4], # [2, 4, 6], # [8, 5, 9, 3] # ]