Talk:Topological sort

J implementation

These are brief notes, and do not attempt to document the language itself.

<lang J>dependencySort=: monad define

 parsed=. <@;:;._2 y
 names=. {.&>parsed
 depends=. (> =@i.@#) names e.S:1 parsed
 depends=. (+. +./ .*.~)^:_ depends
 assert.-.1 e. (<0 1)|:depends
 (-.&names ~.;parsed),names /: +/"1 depends

)</lang>

parsed is a list of lines. Each line is a list of words. Each word is a list of characters.

names is the first word extracted from each line.

depends is a connection matrix -- rows and columns correspond to names, and the values are bits -- 1 for names which depend on other names, and 0 for names which do not depend on other names.

The phrase (> =@i.@#) means that names are not allowed to depend on themselves (since the specification said self dependencies should be ignored, and this makes detecting circular dependencies trivial).

The phrase (+. +./ .*.~)^:_ performs transitive closure on a connection matrix.

The assert statement checks for names which depend on themselves. Since we no know names depended on themselves before we did our transitive closure, we know we have a problem if we have any such dependencies.

Finally, we sort the names so that names with fewer dependencies are followed by names with more dependencies. And, we prepend any names which we depend on which would otherwise have no dependencies.

This implementation is a bit naive, since a connection matrix is O(n^2) in space and O(n^3) in time for n dependencies. If this matters, I should probably rewrite the code (and these comments) to use the tree structure mentioned at http://www.jsoftware.com/jwiki/Essays/Tree%20Sum#Descendants