Sorry, yes that is a leap. (x * (x + 1)) * 0.5 is the number of ways to choose two horizontal lines to make 2 sides of the rectangle. (y * (y + 1)) * 0.5 is the number of ways to choose two vertical lines to make the other 2 sides of the rectangle ((x * (x + 1)) * 0.5) * ((y * (y + 1)) * 0.5) is the number of ways to choose the lines to make a rectangle refactoring: 4 %~ x * (x+1) * y * (y+1) 4 %~ */ x,(x+1),y,(y+1) 4 %~ */ x,y,(x+1),(y+1) 4 %~ */ (, >:) x,y
HTH On Wed, Oct 8, 2014 at 4:30 AM, Devon McCormick <[email protected]> wrote: > Hi - > > "countRects" seems like a bit of a leap. I think I understand "4 %~" > because you're overcounting by 4 rotations, but I don't comprehend the > magic behind "*/@(,>:)". > > I see that "(,>:)" concatenates the shape to its increment, e.g. 2 3 3 4 > for the input 2 3, but what's the rationale behind this? > > Thanks, > > Devon > > On Tue, Oct 7, 2014 at 7:41 AM, Tikkanz <[email protected]> wrote: > > > Note that 200 x 200 is a bit of an overkill given 3x2 = 2x3 > > The following choses the lower triangular of a matrix of the different > > sized rectangles to investigate. > > getSizes=: ,@(>:/~) # [: ,/ ,"0/~ > > getSizes >: i. 5 > > > > Given the sides of a rectangle you can count the number of rectangles as > > follows: > > countRects=: 4 %~ */@(, >:) > > countRects 2 3 > > > > Now get the index of the rectangle size with a count closest to 2million > > > > idxClosest=: (i. <./)@(2e6 |@:- ]) > > > > > > Putting it together > > > > */@({~ idxClosest@:(countRects"1)) getSizes >: i.200 > > > > > > > > On Tue, Oct 7, 2014 at 5:37 PM, Jon Hough <[email protected]> wrote: > > > > > Project Euler 85: https://projecteuler.net/problem=85 > > > This problem is not really conceptually hard, but I am struggling with > a > > J > > > solution.I have solved it in Python: > > > ============================================= > > > def pe85(larg, rarg): count = 0 llist = range(1, larg+1) > > > rlist = range(1, rarg+1) > > > for l in llist: for r in rlist: count > += > > > l*r > > > return count > > > > > > if __name__ == "__main__": # test for 2x3 grid, as in question. > k > > > = pe85(2,3) print "Test value: "+str(k) l1 = > range(1,200) # > > > 200 lucky guess l2 = range(1,200) bestfit = 10000 # just a > big > > > number area = 0 for i in l1: for j in l2: > > > diff = abs(2000000 - pe85(i,j)) if > diff > > < > > > bestfit: area = i*j > > > bestfit = diff > > > print "AREA is "+str(area) > > > > > > > > > ================================================The above script will > > give > > > the final area of the closest fit to 2 million. (The python code may > not > > be > > > the best). Also I tested all possibilities up to 200x200, which was > > chosen > > > arbitrarily(~ish). > > > Next my J. I go the inner calculation ok (i.e. see the function pe85 > > > above). In J I have: > > > pe85 =: +/@:+/@:((>:@:i.@:[) *"(0 _) (>:@:i.@:])) > > > NB. I know, too brackety. Any tips for improvement appreciated. > > > > > > > > > But from here things get tricky. If I do the calculation over 200x200 > > > possibilities I end up with a big matrix, of which I have to find the > > > closest value to 2 million, of which then I have to somehow get the > (x,y) > > > values of and then find the area by x*y. > > > > > > The main issue is getting the (x,y) from the best fit value of the > array. > > > > > > i.e. If I do pe85"(0)/~ 200, I get a big array, and I know I can get > the > > > closest absolute value to 2 million but then I need to get the original > > > values to multiply together to give the best fit area. Actually I have > > > bumped into this issue many times. It is easy enough in a 1-d > array,just > > do: > > > (I. somefunc ) { ]) > > > > > > or similar to get the index. But for two indices the problem is beyond > me > > > at the moment. Any help appreciated.Regards,Jon > > > > > > > > > > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > -- > Devon McCormick, CFA > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
