At the moment, I'm rooting for 54 by 54 as the answer! ff=: 13 :'(>:i.x) */>:i.y' f=: 13 :'*/~ >:i.y' (7 ff 7)-:f 7 good=: 13 :'}:1,x>+/\,y' sum=: 13 :'+/(x good y)#, y'
400 < 400 sum 5 ff 5 400 < 400 sum 6 ff 6 400 < 400 sum 7 ff 7 400 sum f 6 400 sum f 7 400 sum f 8 6 ff 6 400 sum 6 ff 6 2e6 < 2e6 sum 52 ff 52 2e6 < 2e6 sum 53 ff 53 2e6 < 2e6 sum 54 ff 54 2e6 sum f 53 2e6 sum f 54 2e6 sum f 55 2e6 sum 54 ff 54 This stays in 2 dimensions. Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Raul Miller Sent: Saturday, October 11, 2014 6:10 PM To: Programming forum Subject: Re: [Jprogramming] Project Euler 85, Python and J I understand that boxed index lists can be used to index multi-dimensioned arrays. And that can be a convenient abstraction. However, I have been dealing with very large datasets recently, and boxed data on the critical path, at least for some operations, becomes prohibitively slow. When I can use regular numeric structures to replace irregular boxed structures, the overall speedup from the representation change usually more than makes up for the cost of changing representation. Thanks, -- Raul On Sat, Oct 11, 2014 at 11:48 AM, Devon McCormick <devon...@gmail.com> wrote: > I think what you may be missing is that boxed items can be used to index an > array of dimensions higher than 1: > > ]rr=. 10 10?@$1000 > 590 147 158 729 522 732 355 5 955 673 > 858 350 740 105 669 546 334 840 546 184 > 629 608 375 697 224 240 921 182 477 509 > 463 692 151 192 639 115 543 589 636 769 > 240 916 823 902 529 591 757 343 755 622 > 589 665 484 430 849 430 460 987 769 628 > 731 581 107 42 23 145 195 820 223 487 > 725 362 263 376 945 883 760 897 675 188 > 89 884 484 790 793 178 131 324 291 199 > 527 52 725 187 867 297 411 495 985 478 > ]whprm=. rr e. p: i.>./,rr NB. Which are prime? > 0 0 0 0 0 0 0 1 0 1 > 0 0 0 0 0 0 0 0 0 0 > 0 0 0 0 0 0 0 0 0 1 > 1 0 1 0 0 0 0 0 0 1 > 0 0 1 0 0 0 1 0 0 0 > 0 0 0 0 0 0 0 0 1 0 > 0 0 1 0 1 0 0 0 1 1 > 0 0 1 0 0 1 0 0 0 0 > 1 0 0 0 0 0 1 0 0 1 > 0 0 0 0 0 0 0 0 0 0 > > Say we want to replace all primes by 1: > > whprm+rr*-.whprm NB. Arithmetical way > 590 147 158 729 522 732 355 1 955 1 > 858 350 740 105 669 546 334 840 546 184 > 629 608 375 697 224 240 921 182 477 1 > 1 692 1 192 639 115 543 589 636 1 > 240 916 1 902 529 591 1 343 755 622 > 589 665 484 430 849 430 460 987 1 628 > 731 581 1 42 1 145 195 820 1 1 > 725 362 1 376 945 1 760 897 675 188 > 1 884 484 790 793 178 1 324 291 1 > 527 52 725 187 867 297 411 495 985 478 > > or, since > ($ #: I.@:,) whprm > 0 7 > 0 9 > 2 9 > 3 0 > 3 2 > 3 9 > 4 2 > 4 6 > 5 8 > 6 2 > 6 4 > 6 8 > 6 9 > 7 2 > 7 5 > 8 0 > 8 6 > 8 9 > (1) (<"1 ($ #: I.@:,) whprm) } rr NB. Using indexes > 590 147 158 729 522 732 355 1 955 1 > 858 350 740 105 669 546 334 840 546 184 > 629 608 375 697 224 240 921 182 477 1 > 1 692 1 192 639 115 543 589 636 1 > 240 916 1 902 529 591 1 343 755 622 > 589 665 484 430 849 430 460 987 1 628 > 731 581 1 42 1 145 195 820 1 1 > 725 362 1 376 945 1 760 897 675 188 > 1 884 484 790 793 178 1 324 291 1 > 527 52 725 187 867 297 411 495 985 478 > > > > On Sat, Oct 11, 2014 at 4:02 AM, Raul Miller <rauldmil...@gmail.com> > wrote: > > > Yes: > > > > This mechanism, and the insight behind it, is the heart of the > > multi-dimensional array mechanism. > > > > As a simple example, if you have a 10x10x10 array, and you want the value > > at index 6,7,3 that value is at index 673 of the ravel of that array. > > > > It's about which representation is most convenient for the operation you > > are performing. > > > > Thanks, > > > > -- > > Raul > > > > On Sat, Oct 11, 2014 at 1:43 AM, Jon Hough <jgho...@outlook.com> wrote: > > > > > Also, regarding Ben Gorte's > > > > > > Idot =: $ #: I.@:, > > > > > > This is an equivalent of I. for higher dimensions. > > > > > > I'm having trouble understanding how this works. > > > > > > Here is my understanding. > > > > > > 1. ravel the matrix and index elements (I.@:,) > > > 2. Next is a fork of $ #: I.@:, > > > > > > Right "prong" is the aforementioned element indices. > > > > > > Left "prong" is the shape of the original array/matrix. > > > > > > middle "prong" is the antibase of the right prong w.r.t. the left. > > > > > > This seems to work for matrices of any size or dimension. > > > > > > Is this the standard way to index multidimensional arrays? > > > > > > > > > > > > > From: jgho...@outlook.com > > > > To: programm...@jsoftware.com > > > > Date: Sat, 11 Oct 2014 06:33:45 +0100 > > > > Subject: Re: [Jprogramming] Project Euler 85, Python and J > > > > > > > > Using (2 ! >:) is clearly better than doing my double for-loop. I'm > > > embarrassed I missed that. > > > > > > > > The real meat of my confusion with multidimensional arrays is in not > > > just finding the indices but doing something with the elements at the > > > indices. > > > > > > > > e.g. For a single dimension array, there could be a function to fund > > the > > > primes less than 100. > > > > > > > > > > > > primelist =: (I.@:(1&=)@:(1&p:)) { ] > > > > > > > > > > > > and primelist >: i. 100 > > > > > > > > > > > > should spit out > > > > > > > > > > > > 2 3 5 ... ...97 > > > > > > > > > > > > But what if instead of having >: i. 100 > > > > > > > > I had ( for some reason ) > > > > > > > > arr =: 10 10 $ >: i. 100 > > > > > > > > > > > > So I have a 10 by 10 matrix of all positive ints up to 100. > > > > > > > > > > > > primelist clearly will not work on arr. But if I want to return the > > list > > > of primes, as a single dimensional list I'm not sure how to do that. > > > > > > > > > > > > Or, for example, if I want to change the elements of arr to 1 if and > > > only if the sum of the (i, j) indices are prime (just a random > example). > > > > > > > > > > > > In procedural python this could be quickly done with a double > for-loop > > > and a prime test. In J this type of problem still escapes me. > > > > > > > > > > > > > > > > > Date: Fri, 10 Oct 2014 19:35:26 -0400 > > > > > From: devon...@gmail.com > > > > > To: programm...@jsoftware.com > > > > > Subject: Re: [Jprogramming] Project Euler 85, Python and J > > > > > > > > > > countRects=: */@(2 ! >:) NB. How many pairs each of > > > vertical > > > > > * horizontal lines > > > > > getSizes=: ,@(>:/~) # [: ,/ ,"0/~ NB. All pairs of i. y > > > > > idxClosest=: 4 : '(i. <./)@(x |@:- ])y'"(0 2) NB. Index of > mat y > > > to > > > > > value x > > > > > ({~ *2e6*&idxClosest@:(countRects"1)) getSizes >: i.200 NB. > > > Closest > > > > > to 2e6 > > > > > 77 36 > > > > > ({~ *1e6*&idxClosest@:(countRects"1)) getSizes >: i.200 NB. > > > Closest > > > > > to 1e6 > > > > > 63 31 > > > > > countRects"1 ] 63 31,:77 36 NB. How close is each? > > > > > 999936 1999998 > > > > > > > > > > > > > > > On Fri, Oct 10, 2014 at 1:14 PM, Linda Alvord < > > lindaalv...@verizon.net > > > > > > > > > wrote: > > > > > > > > > > > What is the correct answerfor this problem? > > > > > > > > > > > > Linda > > > > > > > > > > > > -----Original Message----- > > > > > > From: programming-boun...@forums.jsoftware.com > > > > > > [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of > > > Stefano > > > > > > Lanzavecchia > > > > > > Sent: Friday, October 10, 2014 11:47 AM > > > > > > To: programm...@jsoftware.com > > > > > > Subject: Re: [Jprogramming] Project Euler 85, Python and J > > > > > > > > > > > > Actuary the use of ravel and antibase is common practice to solve > > > > > > certain problems in APL and isn't considered cheating. So I > > wouldn't > > > > > > say it's "not nice" but I would definitely go for antibase > instead > > of > > > > > > a combination of floored-divide and modulus. As a bonus, a > solution > > > > > > based on antibase would scale to problems of any rank and not > just > > 2d > > > > > > matrices. > > > > > > > > > > > > Have fun! > > > > > > -- > > > > > > Stefano > > > > > > > > > > > > > On 10/ott/2014, at 17:35, Sebastiano Tronto < > > > sebastiano.tro...@gmail.com > > > > > > > > > > > > > wrote: > > > > > > > > > > > > > > Hi, > > > > > > > A dirty trick to get the job done would be to ravel the matrix > ( > > , > > > ), > > > > > > solve > > > > > > > the 1d version of the problem and then get the "true" indexes > > with > > > > > > > something like (<.@%&200 , 200&|). > > > > > > > For example, if you needed to just find the max: > > > > > > > (<.@%&200 , 200&|) (i. >./) , m > > > > > > > where m is your matrix. > > > > > > > > > > > > > > I know this isn't a nice way to solve the problem, but it > should > > > work. > > > > > > > > > > > > > > Sebastiano > > > > > > > > > > > > > > 2014-10-07 6:37 GMT+02:00 Jon Hough <jgho...@outlook.com>: > > > > > > > > > > > > > >> 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 > > > > > > > > > ---------------------------------------------------------------------- > > > > > > 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 > > > > > > ---------------------------------------------------------------------- > > > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
