6 apr 2009
- Reflected upper triangle
Question is how to generate most efficiently the following triangle (for n=5 ):
0 0 0 0 0 1 5 0 0 0 2 6 9 0 0 3 7 10 12 0 4 8 11 13 14
Here is one solution:
rut0=: 3 : '|:(-y) [\ (i.-:y * >:y) #^:_1~ ,<:/~i.y' NB. spaces around dyadic verbs only
Both execution time and space seem to be quadratic:
ts'rut0 1000' 0.04063091 16785664 ts'rut0 2000' 0.191562 67121408 ts'rut0 3000' 0.41281229 2.6845619e8
Another solution is slower:
rut1=: 3 : '|:(-y) [\ ( * <:@:(+/\)) y ( <.@%~ <: | ) i.*:y' ts'rut1 1000' 0.11202145 17830016 ts'rut0 1000' 0.066635274 16785664 ts'rut1 2000' 0.53065204 71307392 ts'rut0 2000' 0.19167078 67121408 ts'rut1 3000' 1.2301193 2.852169e8 ts'rut0 3000' 0.48619975 2.6845619e8
7 apr 2009
In private communication, Groeneveld showed his fluency in J by his superb solution:
rut287=: +/\@(# , ])@}:\@i.@- rnkng scores 'rut0 3000';'rut287 3000' 1 8.7909662 3.0829519 2.8514769 0 1 1 1 (rut0 -:rut287) 3000 1