problem_18.py

"""
Problem 18: Maximum path sum I¶

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)
"""

RAW = """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"""

def longest_path(rows: list) -> list:
    for i in reversed(range(len(rows))):
        if i == len(rows)-1:  # last row base case
            longest = dict(zip(range(len(rows[i])), [[entry] for entry in rows[i]]))

        else:
            new_longest = {}
            for position, value in enumerate(rows[i]):
                left = [value] + longest[position]
                right = [value] + longest[position+1]
                new_longest[position] = left if sum(left) > sum(right) else right

            longest = new_longest
    
    return longest[0]


if __name__ == '__main__':

    baby_rows = [list(map(int, row.split(' '))) for row in list(RAW.split('\n'))]
    
    print(sum(longest_path(baby_rows)))