#67 - Maximum path sum II

in Project Euler on 5%

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 in triangle.txt (right click and ‘Save Link/Target As…’) a 15K text file containing a triangle with one-hundred rows.

This is a much more difficult version #18 - Maximum path sum I. It is not possible to try every route to solve this problem, as there are $2^{99}$ altogether! If you could check one trillion $\left(10^{12}\right)$ routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it ;o)

My answer post on #18 - Maximum path sum I{:.heading.flip-title} has the efficient algorithm in question, so please refer to that post for the algorithm. After replacing the file in the code and running again, our output is

7273
0.004878615356596403 seconds.

Thus, the max total from top to bottom is 7273.