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# cycle(+Edges, ++EdgeWeights, -CycleCost)

A constraint that forces a Hamiltonian cycle in a directed graph
*Edges*
- A list of ic variables
*EdgeWeights*
- A square matrix of integers
*CycleCost*
- The cost of the cycle

## Description

Edges is a list of length VertexCount of ic variables, where VertexCount is the number of
vertices in the graph. Each variable needs to have a domain which is the subset of
[1..VertexCount]. The values in the i-th variable's domain correspond to edges in the
graph, so the domain value j of the i-th variable corresponds to an edge (i,j).
EdgeWeights is a square matrix (array of arrays) of size VertexCount*VertexCount of nonnegative
integers. The value indexed [i,j] corresponds to the cost of the edge (i,j). Values on the diagonal
([i,i]) are unimportant since the correspond to edges (i,i) which are automatically removed by
the constraint.
CycleCost is an ic variable that corresponds to the cost of the cycle.
This version of the constraint uses the maximal propagation level. For more details and
configuration of different propagation levels see cycle/4.

### Modes and Determinism

- cycle(+, ++, -) is semidet

### Fail Conditions

It is impossible to find any Hamiltonian cycle in the graph
### Exceptions

*(1) general error *
- Wrong edge weigh matrix size.
*(1) general error *
- Wrong edge list length.
*(6) out of range *
- Wrong edge domain values.
*(1) general error *
- Wrong weight value.
*(8) bad argument list *
- Unknown options

## See Also

cycle / 4