Euler_Problem-044.b93

>v%%% %%%%       >    v
v06p09:/2*-1*3:p06::+1<vg07g09                         <<  <
g$ >:70p:3*1   v #      >0v>vv p03+g03*2:p04-\g04+g03:<
v                      <3 pp2# v/4    <   >:30g+40g`! |     
1#  >            4**1+:0^ 40>0g>:40g`#^_>:|:/4p03/2g03< $   
>-:|^6-p08:/2*-< #        >^ >30g2/30p4/^ >$30g:*-30g\  |   
 8 >$$           ^v030:+1**46+g09g08             ># !#  # _^
 >::**::**8*20p1 ^v>vv p03+g03*2:p04-\g04+g03:<@.-g08g0 9<
                  pp2# v/4    <   >:30g+40g`! |  ^5%6   <$
                  40>0g>:40g`#^_>:|:/4p03/2g03< >$     ^ 
                  >^ >30g2/30p4/^ >$30g:*-30g\ #^_6%5-#^_^



[20] 2^30 const  (muss vorher gesetzt sein)
[30] res
[40] op

[60] i
[70] j
[80] m
[90] n


integer-square: (see http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29)

 >0v>vv p03+g03*2:p01-\g01+g03:<
 3 pp2# v/4    <   >:30g+10g`! |
0^ 10>0g>:10g`#^_>:|:/4p03/2g03<
   >^ >30g2/30p4/^ >$30g        

isPentagonal:

        >0v>vv p03+g03*2:p01-\g01+g03:<
        3 pp2# v/4    <   >:30g+10g`! |
64**1+:0^ 10>0g>:10g`#^_>:|:/4p03/2g03< >$     >    // NO PENT
          >^ >30g2/30p4/^ >$30g:*-30g\ #^_6%5-#^_   // PENT

-------------------------------------------------------------------------------

My first attempt at this problem took over 5 hours to compute and had a complexity of O(n^3). 

The problem is that you need a square root to inverse the pentagonal formula and Befunge has no square root function.
So I needed to implement my own version of integer square roots in Befunge (see [wikipedia](http://en.wikipedia.org/wiki/Methods_of_computing_square_roots)).
The program is still not really fast but it's good that I managed to speed it up to a time where you can execute it without waiting the whole night.

Also this program is nicely compact, by the time I'm writing this my Befunge interpreter [BefunExec](http://www.mikescher.de/programs/view/BefunGen) has gotten a display of all possible paths a program can take.
And if you look at the graph of this program, it looks pretty interesting...