Idea k: a minimum vector necessarily begins with a minimum sub-sequence in
x,(k-1){.x of length k , itself necessarily begins with the minimal item.On Wed, Feb 13, 2019 at 9:52 AM Roger Hui <[email protected]> wrote: > Yes, well, left as an exercise for the reader. :-) > > Idea: the minimum rotation of a vector necessarily begins with its minimal > item. > > On Wed, Feb 13, 2019 at 9:34 AM Henry Rich <[email protected]> wrote: > >> Yes; but now suppose the lines are very long. Is there a way to find >> the signature (I would call it a canonical form) that doesn't require >> enumerating rotations? (I haven't found a good way yet). >> >> Henry Rich >> >> On 2/13/2019 12:16 PM, Roger Hui wrote: >> > For each row, find a "signature", then find the nub sieve of the >> > signatures. The signature I use here is the minimum of all possible >> > rotations. >> > >> > signature=: {. @ (/:~) @ (i.@# |."0 1 ]) >> > >> > ~: signature"1 a >> > 1 1 1 1 1 0 1 1 1 1 1 0 >> > >> > >> > >> > >> > On Wed, Feb 13, 2019 at 8:55 AM R.E. Boss <[email protected]> wrote: >> > >> >> Let the 12 x 20 matrix be defined by >> >> a=: 0 : 0 >> >> 1 4 4 1 _4 _4 1 1 _4 _1 _1 _4 _4 _1 4 4 _1 _1 4 1 >> >> 1 4 4 1 _4 _4 1 1 _4 _1 _1 _4 _4 _1 4 1 4 _1 _1 4 >> >> 1 4 4 1 _4 _1 _4 1 1 _4 _1 _4 _4 _1 4 1 4 _1 _1 4 >> >> 4 1 1 4 _1 4 1 _4 _4 1 _4 _1 _1 _4 1 _4 _1 4 4 _1 >> >> 4 1 1 4 _1 4 1 _4 _4 1 1 _4 _1 _1 _4 _4 _1 4 4 _1 >> >> _1 4 1 1 4 4 1 _4 _4 1 1 _4 _1 _1 _4 _4 _1 4 4 _1 >> >> _1 4 4 _1 _4 _4 _1 _1 _4 1 1 _4 _4 1 4 4 1 1 4 _1 >> >> _1 4 4 _1 _4 _4 _1 _1 _4 1 1 _4 _4 1 4 _1 4 1 1 4 >> >> _1 4 4 _1 _4 1 _4 _1 _1 _4 1 _4 _4 1 4 _1 4 1 1 4 >> >> 4 _1 _1 4 1 4 _1 _4 _4 _1 _4 1 1 _4 _1 _4 1 4 4 1 >> >> 4 _1 _1 4 1 4 _1 _4 _4 _1 _1 _4 1 1 _4 _4 1 4 4 1 >> >> 1 4 _1 _1 4 4 _1 _4 _4 _1 _1 _4 1 1 _4 _4 1 4 4 1 >> >> ) >> >> >> >> Required is the nubsieve for the items modulo rotation. >> >> So two arrays are considered to be equal if one is a rotation of the >> other. >> >> >> >> The answer I found is >> >> 1 1 1 1 1 0 1 1 1 1 1 0 >> >> >> >> >> >> R.E. Boss >> >> ---------------------------------------------------------------------- >> >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- >> > For information about J forums see http://www.jsoftware.com/forums.htm >> >> >> --- >> This email has been checked for viruses by AVG. >> https://www.avg.com >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
