On Nov 25, 2006, at 7:34 AM, Oleg Kobchenko wrote:
I found a problem that is said to an assignment for introductory C
course but it
turned to be not so trivial. It can be rephrased in J as: for a
positive integer
m find the array v or equivalently (m,m)$v so that result is a
matrix with atoms
of i.*:m filling in zig-zag order. (restricted to square matrix
for time being)
example
4 4$0 1 5 6 2 4 7 12 3 8 11 13 9 10 14 15
0 1 5 6
2 4 7 12
3 8 11 13
9 10 14 15
I tackled the problem by noticing the sum of cell index pair for
each layer is
constant but run into trouble when need to eliminate extra pairs
after passing
the middle layer.
All suggestions welcome.
PS. zig-zag order is used in jpeg encoding http://en.wikipedia.org/
wiki/JPEG
--
IN APL V Fifth International APL Users' Conference May 15-18, 1973,
Toronto, is my paper "The Variety of Definitions of a Simple
Function", giving 17 ways to solve this problem, not limiting it to
square solutions. It discusses algebraic solutions and structural
solutions. The solvers, besides myself, are Phil Abrams, Larry Breed,
Graham Driscoll, Adin Falkoff, Michael Halpern, Ken Iverson, Howard
Smith, Lou Solheim, Roy Sykes and S. Tsao. The solutions are not
zigzag, however, but zigzag can be obtained by judicious use of
reverse. It was written while the APL group was in Philadelphia, and
where I was next to Ken when he stopped and calmed a runaway horse
and held it until it was claimed.
Eugene
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
