5.248. max_size_set_of_consecutive_var
| DESCRIPTION | LINKS | GRAPH |
- Origin
N.Β Beldiceanu
- Constraint
- Arguments
- Restrictions
- Purpose
is the size of the largest set of variables of the collection that all take their value in a set of consecutive values.
- Example
-
In the first example, the two sets and take respectively their values in the two following sets of consecutive values and . Consequently, the corresponding constraint holds since the cardinality of the largest set of variables is 6.
- Typical
- Symmetries
Items of are permutable.
All occurrences of two distinct values of can be swapped.
One and the same constant can be added to the attribute of all items of .
- Arg. properties
Functional dependency: determined by .
- Counting
-
Length () 2 3 4 5 6 7 8 Solutions 9 64 625 7776 117649 2097152 43046721 Number of solutions for : domains
Length () 2 3 4 5 6 7 8 Total 9 64 625 7776 117649 2097152 43046721 Parameter value 1 2 - - - - - - 2 7 30 168 720 5220 27720 249480 3 - 34 240 3080 35580 426720 6059760 4 - - 217 2260 36030 683550 12672940 5 - - - 1716 24660 477162 10592848 6 - - - - 16159 305634 7044632 7 - - - - - 176366 4239424 8 - - - - - - 2187637 Solution count for : domains
- See also
- Keywords
characteristic of a constraint: consecutive values, maximum.
constraint arguments: pure functional dependency.
- Arc input(s)
- Arc generator
-
- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph model
Since the arc constraint is symmetric each strongly connected component of the final graph corresponds exactly to one connected component of the final graph.
PartsΒ (A) andΒ (B) of FigureΒ 5.248.1 respectively show the initial and final graph associated with the first example of the Example slot. Since we use the graph property, we show the largest strongly connected component of the final graph.
Figure 5.248.1. Initial and final graph of the constraint
(a) 
(b)