This is our solution and implementation to problem #67 on Project Euler.
Note: the code and contents here might be slightly different than what is in the video. We've made some improvements to some of the code since recording.
If you would like to view the original problem and solve it, please visit: Maximum Path Sum II on Project Euler. If you're having trouble solving this problem, or are just curious to see how others have solved it, feel free to take a look, but please put solid effort into solving this before viewing the actual solution to the problem.
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.
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.
NOTE: This is a much more difficult version of Problem 18. It is not possible to try every route to solve this problem, as there are 299 altogether! If you could check one trillion (1012) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)
Our solution is given in the TypeScript code below:
This implementation found the solution in 5ms.
If you would like to view the answer, click below to reveal. Please consider reviewing the implementation and trying to code your own solution before viewing the answer.
The answer is 7273.
All of our solutions are hosted on GitHub. The code on this page was pulled from the repo and the solution and execution time were calculated based on that code.