Couldn't sleep. Turns out it soesn't take too long to brute force it by pencil and paper. Given z is 28..1, y is 27..1 and x is 26..1, you start with z at 28 and y at 27 and x at 2. It took me 15 minutes to enumerate the list of 61 solutions. Certainly not near J's speed, but I would have thought longer than 15 minutes.
Good night. Rob On Mon, May 27, 2013 at 2:54 AM, Robert Herman <[email protected]> wrote: > My reference to Perl's output was of the solutions printed on the count > lines such as this: > > 1: 2 27 28 > 2: 3 26 28 > 3: 4 25 28 > ..... > > 60: 17 19 21 > 61: 18 19 20 > Total 61 > > Raul, thank you so much for your other pointers on inspecting the arrays. > I will have two more days after work going over all of that. It's amazing > how working through this seemingly simple problem with your help has taught > me more about J than the hours I spent just doing single bits from the J > dictionary. What would be the best J book to go through the vocabulary in > problem sets such as this? Rosetta code? J for C programmers? > > My son said that one of the students arrived at the correct answer of 61 > without a computer. I can't believe this given the time it would require to > go through the answer space via pencil and paper (28^3). Is there a closed > form solution, or algebraic solution? > > Good night, it's almost 3 am here in Macau. > > Thanks, > > Rob > > > > > On Mon, May 27, 2013 at 2:19 AM, Raul Miller <[email protected]>wrote: > >> On Sun, May 26, 2013 at 2:01 PM, Robert Herman <[email protected]> >> wrote: >> > I have worked through the solution arrived at by a few of you to better >> > learn J, namely this one: >> > >> > +/,(57=x+/y+/z)*x</y*y</z >> > >> > In order to fully understand the way the matrix operations are carried >> out, >> > I minimized the answer space by making P = 13, and worked through the >> > output (not shown for brevity's sake) of the following input lines I >> placed >> > in a project file (learning the IDE with this problem too): >> > >> > P =: 13 >> > x =: >:i.4 >> > y =: >:x >> > z =: >:y >> > >> > 3 4 $ x,y,z >> > >> > (13=x+/y+/z)*x</y*y</z >> > +/,(13=x+/y+/z)*x</y*y</z >> > >> > +/,((13=[+/+/)*[</]*</)~i.7 >> >> Since this is a rank 3 bit array, we can ask J to display it more >> compactly. >> >> <"2 '.*'{~((13=[+/+/)*[</]*</)~i.7 >> >> We can also use this prefix to inspect some of the intermediate results: >> <"2 '.*'{~([</]*</)~i.7 >> <"2 '.*'{~(</)~i.7 >> >> That said, some interemdiate results are not bit arrays and are >> perhaps best inspected directly: >> (]*</)~i.7 >> >> >> > Anyway, I was tempted to try and make the J program look like the Perl >> > oneby using >> > for. but I realized I was lapsing into old habits. My minimal >> programming >> > experience is all with imperative languages or some Lisp too. My next >> > question is how do you get the J program to print the solutions as in >> the >> > Perl program? >> >> That's an open-ended question, since "as in" has a contextual and case >> specific meaning. >> >> Personally, I usually try and understand intermediate results (usually >> there is only one and I can just extract an expression which computes >> it and see what it does with sample data. >> >> > In my 3 x 4 matrices of the reduced problem set, I could see >> > how the 1's in the solution selection matrix set related to the >> original 3 >> > x 4 matrix of x, y and z rows. Without re-writing it, is there a way to >> > index the solution? >> >> I am not sure what you mean by this. >> >> I mean, of course you can index the solution, but the solution has >> only a single number. You can also rewrite the expression which >> creates that solution and index from those results. But I feel like I >> am not understanding your question. >> >> > One question that is on my mind is the tacit vs. explicit style. I am in >> > love with the way you all distill the solution down to a tacit >> one-liner, >> > just as a maths formula is simplified, however, I am starting to think >> that >> > if and when I revisit this problem in the future, it will take a bit of >> > jarring to read it, translate it if you will. I am guessing for. loops >> are >> > very expensive cycle-wise and it would be just as easy to make words for >> > phrases if I wish to preserve future readability. I am getting addicted >> to >> > the fast way of working in the J environment, and I am grateful to all >> on this >> > list for sharing their wisdom. >> >> I think that any time we delve into some area of computation that >> leaving and coming back after an extended absence can leave us in a >> jarring situation where we need to reacquaint ourselves with the >> original topic. I do not know of any general cure for this, finding >> good names for things, and good examples, can be fruitful. >> >> Thanks, >> >> -- >> Raul >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
