The problem is to find and count all of the unique sets of three positive integers that sum to 1,000,000. For example, one of the triples is:
+/333332 333333 333335 1000000 Another one: +/333331 333333 333336 1000000 Yet another: +/999998 1 1 1000000 Now just find all the other unique ones & count them. Skip On Sat, May 19, 2018 at 8:58 PM 'Jon Hough' via Programming < programm...@jsoftware.com> wrote: > If I understand the problem correctly, you want to find the number of > partitions of 1,000,000 which have size 3. > e.g. > Partitions of 10 of size 3 are: > 1 1 8, 1 2 7, 1 3 6, 1 4 5, 2 2 6, 2 3 5, 2 4 4, 3 3 4 > So there are 8. > > In general a recursive function to find all partitions of y of size x is: > > nparts=:4 :0 > if. (x =1) *. y =1 do. > 1 > elseif. y =1 do. 0 > elseif. x >y do. 0 > elseif. (x <: 0) +. y <:0 do. 0 > elseif. 1 do. > ((x-1) nparts (y-1)) + x nparts y- x > end. > ) > > 3 nparts 10 > 8 > > This, unfortunately blows up the stack for large y (e.g. 1,000,000). I > don't have time to modify it into > an iterative approach, but will try later. > > > -------------------------------------------- > On Sun, 5/20/18, Skip Cave <s...@caveconsulting.com> wrote: > > Subject: [Jprogramming] Quora Problem > To: "programm...@jsoftware.com" <programm...@jsoftware.com> > Date: Sunday, May 20, 2018, 5:43 AM > > Another interesting quora problem: > > How many distinct triplets have a sum > of 1,000,000 (provided all numbers > are integers and are positive)? > < > https://www.quora.com/qemail/track_click?al_imp=eyJ0eXBlIjogMzUsICJoYXNoIjogMTcxMDQ0NjU4Mn0%3D&al_pri=QuestionLinkClickthrough&aoid=oMo937UDzj8&aoty=2&aty=4&click_pos=1&ct=1526747413834671&et=103&id=62216bf7b30d40aea1d79bf4401c8317&request_id=289&src=1&st=1526747413838426&stories=2518686273&uid=bqluVqSeN78&v=0 > > > > The obvious straightforward solution > would be to use the odometer verb: > > odo=: #: i.@(*/) > > 1e6=+/"1 odo 3#1e6 > > |limit error: odo > > | 1000000=+/"1 odo 3#1000000 > > > Ooops. Unfortunately, I don't have near > enough memory to use this approach. > > Any suggestions? > > > Skip > > > > Skip Cave > Cave Consulting LLC > ---------------------------------------------------------------------- > 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
