Neat little programming puzzle

[neng.zhou at gmail.com]

On Tuesday, December 16, 2014 12:52:58 AM UTC-5, 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

Here is a program in Picat, which has a built-in tabling mechanism for dynamic programming solutions:

http://picat-lang.org/euler/p18.pi

Cheers,
NF