UPD: Thanks for all the help guys! I threw away my recursive solution and solved it with loops. (DP?) :>

Hello all,

While going through the USACO training pages problem "Number Triangles", I used a recursive function to calculate the answer. You can see the problem statement here: http://train.usaco.org/usacoprob2?a=nOEpHRAhtUw&S=numtri

I used recursion to try and solve it, but ran into a timeout on test case 6:

> Run 6: Execution error: Your program (`numtri') used more than the allotted runtime of 1 seconds (it ended or was stopped at 1.715 seconds) when presented with test case 6. It used 4312 KB of memory.

I realized that with the test data at hand, it made sense that my program would timeout.

Data:

199 
    1 
    0 1 
    0 1 0 
    0 1 0 1 
    0 1 0 1 0 
    0 1 0 1 0 1 
    0 1 0 1 0 1 0 
    0 1 0 1 0 1 0 1 
    0 1 0 1 0 1 0 1 0 
    0 1 0 1 0 1 0 1 0 1 
    0 1 0 1 0 1 0 1 0 1 0 
    ... [and more] ...

My question is, is it possible for me to optimize my recursive solution, or should I try to use a loop instead of recursion? All hints and advice would be appreciated. (No full solutions please.)

My code below (C++11):