4.2.4.2. Additional Gecode constraints

In this section: among_seq, circuit_cost, circuit_cost_array, gecode_array_set_element_intersect, gecode_array_set_element_intersect_in, gecode_array_set_element_partition.

among_seq

predicate among_seq(array [int] of var int: x,
                    set of int: S,
                    int: l,
                    int: m,
                    int: n)
predicate among_seq(array [int] of var bool: x,
                    bool: b,
                    int: l,
                    int: m,
                    int: n)
Every subsequence of x of length l has at least m and at most n occurrences of the values in S

circuit_cost

predicate circuit_cost(array [int] of int: c,
                       array [int] of var int: x,
                       var int: z)
Constrains the elements of x to define a circuit where x[i] = j means that j is the successor of i. Additionally, constrain z to be the cost of the circuit. Each edge cost is defined by array c.

circuit_cost_array

predicate circuit_cost_array(array [int] of int: c,
                             array [int] of var int: x,
                             array [int] of var int: y,
                             var int: z)
Constrains the elements of x to define a circuit where x[i] = j means that j is the successor of i. Additionally, constrain z to be the cost of the circuit. Each edge cost is defined by array c. The variables y[i] are constrained to be the edge cost of the node x[i].

gecode_array_set_element_intersect

predicate gecode_array_set_element_intersect(var set of int: x,
                                             array [int] of var set of int: y,
                                             var set of int: z)
Constrain z to be the intersection of all sets in y that are selected by x: \(i \in {\bf z} \leftrightarrow \forall j \in {\bf x}: (i \in {\bf y}[j])\)

gecode_array_set_element_intersect_in

predicate gecode_array_set_element_intersect_in(var set of int: x,
                                                array [int] of var set of int: y,
                                                var set of int: z,
                                                set of int: u)
Constrain z to be a subset of u, and z to be the intersection of all sets in y that are selected by x: \(i \in {\bf z} \leftrightarrow \forall j \in {\bf x}: (i \in {\bf y}[j])\)

gecode_array_set_element_partition

predicate gecode_array_set_element_partition(var set of int: x,
                                             array [int] of var set of int: y,
                                             var set of int: z)
Constrain z to be the disjoint union of all sets in y that are selected by x: \(i \in {\bf z} \leftrightarrow \exists j \in {\bf x}: (i \in {\bf y}[j])\) and \(i \in {\bf x} \land j \in {\bf x} \land i\neq j \rightarrow {\bf y}[i] \cap {\bf y}[j]=\emptyset\)