
<ConsistencyModule:> ham_path(?Start,?End,+Succ)

   Constrains elements in Succ to form a Hamiltonian path from Start to End.

Arguments
   Start               An integer or (domain) variable (array notation accepted)
   End                 An integer or (domain) variable (array notation accepted)
   Succ                A collection of different (domain) variables or integers

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 path, a path through every node in
  the graph, visiting each node once, with Start giving the first node
  of the path, and End giving the last node of the path. Note that the
  Succ of the last node will be N+1, i.e. a dummy node not in the graph. 

  Note that the Gecode implementation of this constraint has index (node id)
  starting from 0, rather than 1. This constraint is actually posted
  as ham_path_offset_g/3 with an offset of 1. A version of this constraint
  with native Gecode indexing is available as circuit_g/1.

  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 path() constraint, using an offset 
  of 1.



Examples
   [eclipse 5]: ham_path(S,E,[X]).

S = 1
E = 1
X = 2


[eclipse 2]: ham_path(S,E,[A,B]).

S = S{[1, 2]}
E = E{[1, 2]}
A = A{[2, 3]}
B = B{[1, 3]}

[eclipse 3]: ham_path(2,1,[A,B]).

A = 3
B = 1

[eclipse 5]: ham_path(S,E,[2,4,1]).

S = 3
E = 2



See Also
   ham_path_g / 3, ham_path_offset_g / 4
