Work in progress --- inductive vs deductive
How many layers does an onion have?
For the sake of my fragile ego I decided to improve the time and space performance of my onion solution.
NB. The code below was created by the contributions to
NB. and collaboration on the JForums.
onion0 =: [: ({.&.> #~ 0 ~: */@:$&>) |.@:|:@:}.&.>^:a: @: < @: i.
onion1 =: +/\@(,@(] {. |:@((1 0 + i.@-@|.)@[)) # +:@] $ (, -)@(1 , {:@[)) {.
s =: 1 : '| $ /:@;@u f.'
spiral =: onion0 s
involute =: onion1 sThe problem was harder than I thought. The fundamental trouble spiral is that it is structural, rather than mathematical. That is, involute invents (or defines) onion order, whereas spiral discovers it. In other words: involute is deductive' (it tells the data how to behave), and spiral is inductive (the data tells is how to behave). This approach makes the solution easier to invent, understand, and maintain, and was more inline with the solutions to the zigzag puzzle, but at the cost of time and space (and, hence, my ego). I doubt a structural solution can ever compete with a mathematical one (it uses boxes, it's contains a lot of redundant information, etc), but perhaps we can close the gap a bit. Examining spiral : Each line here represents a different action in spiral. In English, this algorithm might read something like "Grow an onion (line 0), peel layers (line 2) until there's nothing left (line 3), and sweep the floor (line 1)." The Two things make this algorithm slow. First, the boxing (represented by the < >s in the code). This is fundamental to a structural solution in Lines 2 3 are the heart of the solution. The heart of the structural solution could be read as "Here's an ontion" One obvious place to start is the ^:a:, which could be read as "until you're done". Well, clearly, the size (and shape) of the onion holds some relation to the nu The problem was harder than I thought it was. 0 [: ( ) ( )@: <@:i.
1 {.&.> #~ 0 ~: */@:$&> ( )
2 |.@:|:@:}.&.> ( )
3 ^:a: