When you feel the urge to go one step beyond, don't forget to deliver. ------------------------------------------------------------------------ |\/| Randy A MacDonald | APL: If you can say it, it's done.. (ram) |/\| [EMAIL PROTECTED] | |\ | | The only real problem with APL is that BSc(Math) UNBF'83 | it is "still ahead of its time." Sapere Aude | - Morten Kromberg Natural Born APL'er | Demo website: http://156.34.82.188/ -----------------------------------------------------(INTP)----{ gnat }-
----- Original Message ----- From: "June Kim" <[EMAIL PROTECTED]> To: "Programming forum" <programming@jsoftware.com> Sent: Saturday, February 03, 2007 8:33 PM Subject: Re: [Jprogramming] Collatz Problem again > Thank you, Roger, for your insightful solution! Your new solution runs > in about 9 secs, compared to 36 secs. > > 2007/2/4, Roger Hui <[EMAIL PROTECTED]>: > > Even if a program is going to be run just once or > > a problem is already solved there is satisfaction > > in doing it well for oneself. The pursuit of Truth > > and Beauty makes life worth living. Better than > > watching the Super Bowl, for instance. > > > > > > Yes, indeed. > > In the process I may find some paradigms of programming, as Robert Floyd did[0]: > > <quote> > In my own experience of designing difficult algorithms, I find a > certain technique most helpfult in expanding my own capabilities. > After solving a challenging problem, I solve it again from scratch, > retracing only the insight of the earlier solution. I repeat this > until the solution is as clear and direct as I can hope for. Then I > look for a general rule for attacking similar problems, that would > have led me to approach the given problem in the most efficient way > the first time. Often, such a rule is of permanent value. ...... The > rules of Fortran can be learned within a few hours; the associated > paradigms take much longer, both to learn and to unlearn. --Robert W. > Floyd > </quote> > > And as George Polya, from his excellent book How to Solve It, said: > > <quote> > Even fairly good students, when they have obtained the solution of the > problem and written down neatly the argument, shut their books and > look for something else. Doing so, they miss an important and > instructive phase of the work. ... A good teacher should understand > and impress on his students the view that no problem whatever is > completely exhausted. --George Polya > </quote> > > Dijkstra always said he seeks beauty, and we should do so[1]. Donald > Knuth explicitly said "a programmer who subconsciously views himself > as an artist will enjoy what he does and will do it better."[2] > > [0] http://www.iisc.ernet.in/academy/resonance/May2005/pdf/May2005Classics.pdf > (Robert Floyd's Turing Award Lecture) > [1] http://www.amazon.com/exec/obidos/ISBN=0387972994/ (Beauty is Our Business) > [2] http://fresh.homeunix.net/~luke/misc/knuth-turingaward.pdf (Don > Knuth's Turing Award Lecture) > > > > > > > ----- Original Message ----- > > From: Devon McCormick <[EMAIL PROTECTED]> > > Date: Saturday, February 3, 2007 11:22 am > > Subject: Re: [Jprogramming] Collatz Problem again > > > > > June - > > > > > > how many times do you plan to solve the problem or do you plan to > > > extend the search? > > > > > > I'm asking because I just wrote "collatz" myself for the > > > projectEuler math > > > challenge. My version, which I wrote in less than 5 minutes, took > > > about1350 seconds to complete for the first million integers. > > > Obviously,Roger's version is far faster. > > > > > > However, I may never run this code again. > > > > > > I looked at one of the discussion groups on the math challenge site > > > and, typically, much of the talk was about shaving seconds off an > > > implementation of code to solve one of the problems. > > > > > > I still fail to grasp the economics of spending hours of one's own, > > > irreplaceable time to save seconds of processing time, especially > > > for one-shot solutions and especially since I can do other things > > > in the 1300 seconds I "waste" by not running faster code. > > > > > > Apologies to long-time readers of this forum for this re-iteration > > > of my standard rant, number one on the list, but it continues to be > > > relevant. > > > > > > Just to point out the benefits of coding quickly and > > > inefficiently, in the > > > few days since I got interested in this math challenge, I've > > > gotten my > > > ranking up to around 380 out of 2089, so I've passed about 1700 > > > people. > > > Not to brag: I owe it to J and a little of it to advance peeks at > > > some of the problems people have asked about on the forum. > > > > > > I probably should really be embarrassed that I'm gaining on people > > > in a race where most of them are crawling, wearing boxes on their > > > heads and dragging chains. > > > > > > So, I'm unwilling to spend more than a few minutes to improve on a > > > solution, especially one that Roger wrote. However, his essay on the > > > solution is worthwhile, especially for the notion of caching > > > results, as > > > this has general applicability and may be a time-saver in the future. > > > > > > Good luck, > > > > > > Devon > > > > > > On 2/3/07, June Kim <[EMAIL PROTECTED]> wrote: > > > > > > > > Have a look at this problem: > > > > > > > > http://www.programming- > > > challenges.com/pg.php?page=downloadproblem&probid=110101&format=html> > > > > In short, you need to calculate the maximum cycle length in a > > > given range. > > > > > > > > Roger wrote an essay which is related to this problem. > > > > http://www.jsoftware.com/jwiki/Essays/Collatz_Conjecture > > > > > > > > Suppose we want to calculate the maximum cycle length of collatz > > > > sequences for 1, ..., 1e6. > > > > > > > > It would be defined, using Roger's definition, as >./ cn 1e6 > > > > > > > > It currently takes around 40 secs on the computer I'm using. > > > Could you > > > > improve its efficiency? > > ---------------------------------------------------------------------- > > 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
