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Eulerian circuit - working with lists

Description
A Eulerian circuit is a closed circuit that uses every given arc exactly once. The algorithm is implemented using the data structure 'list', making use of list operators and list handling routines (splitting off list head or tail, first occurrence of an element).

Further explanation of this example: 'Mosel User Guide', Section 8.5 Working with lists


Source Files

Data Files





euler.mos

(!******************************************************
   Mosel User Guide Example Problems
   ================================= 

   file euler.mos
   ``````````````
   Constructing a Eulerian circuit (a closed circuit 
   that uses every given arc exactly once).
   - Working with lists -
   
   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, Oct. 2006
*******************************************************!)

model "Eulerian circuit"

 declarations
  NODES = 1..12                        ! Set of nodes
  UNUSED: array(NODES) of list of integer
  TOUR: list of integer
  NEWT, TAIL: list of integer
 end-declarations

 initializations from 'euler.dat'
  UNUSED
 end-initializations
 
 ct:=sum(i in NODES) getsize(UNUSED(i))

 TOUR:=[1]                            ! Choose node 1 as start point

 while(ct>0) do                       ! While there are unused arcs:
     ! Find first node in TOUR with unused outgoing arc(s)
  node:=0
  forall(i in TOUR)
   if UNUSED(i) <> [] then
    node:=i
    break
   end-if

     ! Insertion position (first occurrence of 'node' in TOUR)
  pos:= findfirst(TOUR, node) 

     ! Construct a new subtour starting from 'node'
  cur:=node                           ! Start with current node
  NEWT:=[]
  while(UNUSED(cur) <> []) do
   NEWT+=splithead(UNUSED(cur),1)     ! Take first unused arc
   cur:=getlast(NEWT)                 ! End point of arc is new current node
  end-do
  
     ! Stop if the subtour is not a closed loop (=> no Eulerian circuit)
  if cur<>node then                   ! Compare start and end of subtour
   writeln("Tour cannot be closed")
   exit(1)
  end-if 

     ! Add the new subtour to the main journey
  TAIL:=splittail(TOUR, -pos)         ! Split off the tail from main tour
  TOUR += NEWT + TAIL                 ! Attach subtour and tail to main tour
  ct -= getsize(NEWT)
 end-do
 
 writeln("Tour: ", TOUR)              ! Print the result
 
end-model

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