
<ConsistencyModule:> circuit(+Succ,++CostMatrix,+ArcCosts,?Cost)

   Constrains elements in Succ to form a Hamiltonian circuit with cost Cost.

Arguments
   Succ                A collection of N different (domain) variables or integers
   CostMatrix          A NxN matrix collection of integers
   ArcCosts            A collection of N (domain) variables or integers.
   Cost                A (domain) variable or integer (array notation accepted).

Type
   library(gfd)

Description
  Succ is a collection of N elements presenting a digraph of N nodes, where
  the i'th element of Succ represents the successor to node i. The constraint
  enforces Succ to form a Hamiltonian circuit, a path through every node in
  the graph, visiting each node once and forming a circuit. Additionally,
  CostMatrix specifies the cost for traversing between each pair of nodes:
  CostMatrix[i,j] represents the cost of travelling from node i to j, and 
  Cost is constrained to the total Cost for the circuit. The i'th element of 
  ArcCosts is constrained to the cost of the arc in the circuit from node i.

  Note that the Gecode implementation of this constraint has index (node id)
  starting from 0, rather than 1. This constraint is actually posted
  as circuit_offset_g/5 with an offset of 1. A version of this constraint
  with native Gecode indexing is available as circuit_g/4.

  This constraint can be embedded in a constraint expression in its
  functional form (without the last argument).

  ConsistencyModule is the optional module specification to give the 
  consistency level for the propagation for this constraint: 
  gfd_gac for generalised arc consistency (domain consistency), 
  and gfd_vc for value consistency.

  This constraint is implemented by Gecode's circuit() constraint (variant with 
  cost and arc costs), using an offset of 1.



Examples
   [eclipse 5]: CostM = []([](0,3,5,7),[](4,0,9,6),[](2,1,0,5),[](-7,8,-2,0)),
        circuit([2,3,4,1], CostM,        [C1,C2,C3,C4], C).

CostM = []([](0, 3, 5, 7), [](4, 0, 9, 6), [](2, 1, 0, 5), [](-7, 8, -2, 0))
C1 = 3
C2 = 9
C3 = 5
C4 = -7
C = 10


See Also
   circuit / 1, circuit / 3, circuit_g / 4
