Neat little programming puzzle

[sohcahtoa82 at gmail.com]

On Monday, December 15, 2014 9:52:58 PM UTC-8, Jason Swails wrote:
> This was a problem posed to me, which I solved in Python.  I thought it was neat and enjoyed the exercise of working through it; feel free to ignore.  For people looking for little projects to practice their skills with (or a simple distraction), read on.
> 
> 
> You have a triangle of numbers such that each row has 1 more number than the row before it, like so:
> 
> 
>         1
>      3    2
>    8    6    1
> 5    10   15  2
> 
> 
> The task is to find the maximum possible sum through the triangle that you can compute by adding numbers that are adjacent to the value chosen in the row above.  In this simple example, the solution is 1+3+6+15=25.  As the number of rows increases, the possible paths through the triangle grows exponentially (and it's not enough to just look at the max value in each row, since they may not be part of the optimum pathway, like the '8' in row 3 of the above example).
> 
> 
> The challenge is to write a program to compute the sum of https://gist.github.com/swails/17ef52f3084df708816d.
> 
> 
> I liked this problem because naive solutions scale as O(2^N), begging for a more efficient approach.
> 
> 
> Have fun,
> Jason

If you really like these kinds of problems, you should really check out Project Euler.  Many of them are easy to solve via brute force, but some, while you could easily produce a brute force program, would take millions of years to solve and so require you to be clever.

https://projecteuler.net/

As someone else mentioned, this is similar to problems 18 and 67.  You could probably solve it with a path-finding algorithm, but there are probably even more clever methods than that.