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# <ConsistencyModule:> circuit_offset(+Succ,+Offset,++CostMatrix,+ArcCosts,?Cost)

Constrains elements in Succ (offset by Offset) to form a Hamiltonian circuit with cost Cost.

Succ
  A collection of N different (domain) variables or integers
Offset
  Offset for Succ (An integer)
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).

## Description

Succ is a collection of N elements presenting a digraph of N nodes, where the value of the i'th element of Succ - Offset 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. The value of Offset is incremented by 1 when the constraint is posted to Gecode. A version of this constraint with native Gecode indexing, i.e. without adjusting Offset, is available as circuit_offset_g/5.

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 Offset + 1.

## See Also

circuit_offset / 2, circuit_offset / 4, circuit_offset_g / 5