<filename>projecteuler.net/problem_018.py
# Maximum path sum I
# 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)

#
# Dijkstra's algorithm
#
#

def solve(problem):
    problem = problem
    traversal = []
    for row in problem:
        traversal.append(tuple([int(node), int(node)] for node in row))

    size = len(traversal)
    for row, nodes in enumerate(traversal):
        row_size = len(nodes)
        # update connected nodes
        next_row = row + 1
        if next_row == size:
            break

        for col, node in enumerate(nodes):
            for c in (col, col +1):
                connected_node = traversal[next_row][c]
                distance = node[1] + connected_node[0]
                if  distance > connected_node[1]:
                    connected_node[1] = distance

    return max(node[1] for node in traversal[-1])

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'))

if __name__ == '__main__':
    print(__file__, ': ', solve(triangle))
