Project Euler Problem 18

Many of you may know project Euler. It is a website posing interesting programming tasks, varying in difficulty. About a year ago I had a first look at it, but for lack of time I did not solve too many of the problems. Today I felt in the mood to get hands on that again and I had not solved problem 18 up till now:

http://projecteuler.net/problem=18

You are given a triangle of numbers and your task is to calculate the maximum sum going from top to bottom, while you can go either on step to the left or one step to the right on your way down.
The first, naive approach is to use brute force and calculate every possible sum. However, as stated at project Euler, for larger triangles computation time will soon be too long.

So here is the approach I was following:

At each point in the triangle (except for the top and edges) the maximum possible sum is the number at that point plus the maximum of the sum at the two predecssing points, i.e. left and right predecessors.

Using this you avoid brute force and can solve larger the same problem for larger triangles, such as given in problem 67, in a reasonable amount of time.

http://projecteuler.net/problem=67

Based on what I wrote you can use any language you like to implement your solution.
If you feel the need to look at my implementation, go to my git my git repository.
It gave me the correct answers for both problem 18 and problem 67.

Remark: This algorithm might remind you of message passing algorithms such as max-product that are used for inference in graphical models.