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

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

Succ
  A collection of N different (domain) variables or integers
CostMatrix
  A NxN matrix collection of 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 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.

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

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/4 with an offset of 1. A version of this constraint with native Gecode indexing is available as circuit_g/3.

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), using an offset of 1.

## Examples

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

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

## See Also

circuit_offset_g / 4, circuit / 1, circuit / 4, circuit_g / 3