GlobalCardinality{CVT, CVCT, T}(dimension::Int, values::Vector{T})
This set represents the large majority of the variants of the global-cardinality constraint, with the parameters set in CountedValuesType (CVT parameter) and CountedValuesClosureType (CVCT parameter).
Fixed and open
$\{(x, y) \in \mathbb{T}^\mathtt{dimension} \times \mathbb{N}^d : y_i = |\{ j | x_j = \mathtt{values}_i, \forall j \}| \}$
The first dimension variables are an array, the last variables are the number of times that each item of values is present in the first array. Values that are not in values are ignored.
Also called gcc or count.
Example
[x, y, z, v, w] in GlobalCardinality{FIXED_COUNTED_VALUES, OPEN_COUNTED_VALUES}(3, [2.0, 4.0])
+[x, y, z, v, w] in GlobalCardinality{OPEN_COUNTED_VALUES}(3, [2.0, 4.0])
+[x, y, z, v, w] in GlobalCardinality(3, [2.0, 4.0])
+# v == sum([x, y, z] .== 2.0)
+# w == sum([x, y, z] .== 4.0)
Variable and open
$\{(x, y, z) \in \mathbb{T}^\mathtt{dimension} \times \mathbb{N}^\mathtt{n\_values} \times \mathbb{T}^\mathtt{n\_values} : y_i = |\{ j | x_j = z_i, \forall j \}| \}$
The first dimension variables are an array, the next n_values variables are the number of times that each item of the last n_values variables is present in the first array. Values of the first array that are not in the n_values are ignored.
Also called distribute.
Example
[x, y, z, t, u, v, w] in GlobalCardinality{VARIABLE_COUNTED_VALUES, OPEN_COUNTED_VALUES, T}(3, 2)
+[x, y, z, t, u, v, w] in GlobalCardinality{OPEN_COUNTED_VALUES, T}(3, 2)
+[x, y, z, t, u, v, w] in GlobalCardinality{T}(3, 2)
+# t == sum([x, y, z] .== v)
+# u == sum([x, y, z] .== w)
Fixed and closed
$\{(x, y) \in \mathbb{T}^\mathtt{dimension} \times \mathbb{N}^d : y_i = |\{ j | x_j = \mathtt{values}_i, \forall j \}| \}$
The first dimension variables are an array, the last variables are the number of times that each item of values is present in the first array. Each value of the first array must be within values.
Example
[x, y, z, v, w] in GlobalCardinality{FIXED_COUNTED_VALUES, CLOSED_COUNTED_VALUES, T}(3, [2.0, 4.0])
+# v == sum([x, y, z] .== 2.0)
+# w == sum([x, y, z] .== 4.0)
+# x ∈ [2.0, 4.0], y ∈ [2.0, 4.0], z ∈ [2.0, 4.0]
Variable and closed
$\{(x, y, z) \in \mathbb{T}^\mathtt{dimension} \times \mathbb{N}^\mathtt{n\_values} \times \mathbb{T}^\mathtt{n\_values} : y_i = |\{ j | x_j = z_i, \forall j \}| \}$
The first dimension variables are an array, the next n_values variables are the number of times that each item of the last n_values variables is present in the first array. Each value of the first array must be within the next given n_values.
Also called distribute.
Example
[x, y, z, t, u, v, w] in GlobalCardinality{VARIABLE_COUNTED_VALUES, CLOSED_COUNTED_VALUES, T}(3, 2)
+# t == sum([x, y, z] .== v)
+# u == sum([x, y, z] .== w)
+# x ∈ [v, w], y ∈ [v, w], z ∈ [v, w]