Topological sort/Extracted top item

Topological sort/Extracted top item is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Given a mapping between items, and items they depend on, a topological sort orders items so that no item precedes an item it depends upon.

The compiling of a design in the VHDL language has the constraint that a file must be compiled after any file containing definitions it depends on. A tool exists that extracts file dependencies.

• Assume the file names are single words, given without their file extensions.
• Files mentioned as only dependants, have no dependants of their own, but their order of compiling must be given.
• Any self dependencies should be ignored.

A top level file is defined as a file that:

1. Has dependents.
2. Is not itself the dependent of another file

Task Description

Given the following file dependencies as an example:

FILE    FILE DEPENDENCIES
====    =================
top1    des1 ip1 ip2
top2    des1 ip2 ip3
ip1     extra1 ip1a ipcommon
ip2     ip2a ip2b ip2c ipcommon
des1    des1a des1b des1c
des1a   des1a1 des1a2
des1c   des1c1 extra1

The task is to create a program that given a graph of the dependency:

1. Determines the top levels from the dependencies and show them.
2. Extracts a compile order of files to compile any given (usually top level) file.
3. Give a compile order for file top1.
4. Give a compile order for file top2.

You may show how to compile multiple top levels as a stretch goal

Note: this task differs from task Topological sort in that the order for compiling any file might not include all files; and that checks for dependency cycles are not mandated.

C.f. Topological sort

J

Derived from the topological sort implementation:

<lang j>compileOrder=: dyad define

 targets=. ;: x
 parsed=. <@;:;._2 y
 names=. ~.({.&>parsed),targets,;parsed
 depends=. (> =@i.@#) names e.S:1 (#names){.parsed
 depends=. (+. +./ .*.~)^:_ depends
 keep=. +./depends (] , #~) names e. targets
 r=.0 0$
 while.#names=. keep#names do.
   depends=. keep#keep#"1 depends
   keep=. 0<+/"1 depends
   r=.r,;:inv (-.keep)#names
 end.

)

topLevel=: [: ({.&> -. [:;}.&.>) <@;:;._2 </lang>

The changes are:

1. Added an argument for the target(s) we wish to find dependencies for
2. Make sure that these targets are included in our dependency structures
3. Make sure that things we can depend on are included in our dependency structures
4. Select these targets, and the things they depend on, once we know what depends on what
5. When ordering names by dependencies:
   1. only consider names and dependencies we want to keep
   2. repeat: extract names with no remaining dependencies

Example:

<lang j>dependencies=: noun define

 top1    des1 ip1 ip2
 top2    des1 ip2 ip3
 ip1     extra1 ip1a ipcommon
 ip2     ip2a ip2b ip2c ipcommon
 des1    des1a des1b des1c
 des1a   des1a1 des1a2
 des1c   des1c1 extra1

)

  >topLevel dependencies

top1 top2

  'top1' compileOrder dependencies

extra1 ip1a ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1 ip1 ip2 des1a des1c des1 top1

  'top2' compileOrder dependencies

ip3 extra1 ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1 ip2 des1a des1c des1 top2

  'top1 top2' compileOrder dependencies

ip3 extra1 ip1a ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1 ip1 ip2 des1a des1c des1 top1 top2 </lang>

Python

Where the compile order between a subset of files is arbitraary, they are shown on the same line. <lang python>try:

   from functools import reduce

except: pass

1. Python 3.x: def topx(data:'dict', tops:'set'=None) -> 'list':

def topx(data, tops=None):

   'Extract the set of top-level(s) in topological order'
   for k, v in data.items():
       v.discard(k) # Ignore self dependencies
   if tops is None:
       tops = toplevels(data)
   return _topx(data, tops, [], set())

def _topx(data, tops, _sofar, _sofar_set):

   'Recursive topological extractor'
   _sofar += [tops] # Accumulates order in reverse
   _sofar_set.union(tops)
   depends = reduce(set.union, (data.get(top, set()) for top in tops))
   if depends:
       _topx(data, depends, _sofar, _sofar_set)
   ordered, accum = [], set()
   for s in _sofar[::-1]:
       ordered += [sorted(s - accum)]
       accum |= s
   return ordered

def printorder(order):

   'Prettyprint topological ordering'
   if order:
       print("First: " + ', '.join(str(s) for s in order[0]))
   for o in order[1:]:
       print(" Then: " + ', '.join(str(s) for s in o))

def toplevels(data):

   \
   Extract all top levels from dependency data
   Top levels are never dependents
   
   for k, v in data.items():
       v.discard(k) # Ignore self dependencies
   dependents = reduce(set.union, data.values())
   return  set(data.keys()) - dependents

if __name__ == '__main__':

   data = dict(
       top1  = set('ip1 des1 ip2'.split()),
       top2  = set('ip2 des1 ip3'.split()),
       des1  = set('des1a des1b des1c'.split()),
       des1a = set('des1a1 des1a2'.split()),
       des1c = set('des1c1 extra1'.split()),
       ip2   = set('ip2a ip2b ip2c ipcommon'.split()),
       ip1   = set('ip1a ipcommon extra1'.split()),
       )

   tops = toplevels(data)
   print("The top levels of the dependency graph are: " + ' '.join(tops))

   for t in sorted(tops):
       print("\nThe compile order for top level: %s is..." % t)
       printorder(topx(data, set([t])))
   if len(tops) > 1:
       print("\nThe compile order for top levels: %s is..."
             % ' and '.join(str(s) for s in sorted(tops)) )
       printorder(topx(data, tops))</lang>

Sample Output

The top levels of the dependency graph are: top2 top1

The compile order for top level: top1 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip1a, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip1, ip2
 Then: top1

The compile order for top level: top2 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip2, ip3
 Then: top2

The compile order for top levels: top1 and top2 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip1a, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip1, ip2, ip3
 Then: top1, top2