PyPE solution to PE problem 18

    ProjectEuler.net 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 5
    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)

    Solution
    --------

    We begin at the apex (0,0) and work our way down, recursively traversing the
    tree (i.e. depth-first). Each time we calculate the maximum sum at a given
    co-ordinate, we cache the value for future use. This modification reduces
    the execution time from 0.05s to 0.0s (as measurd by time.clock) over the
    brute-force approach of trying all of the paths individually.

    Answer
    ------

    1074