5.267. multi_global_contiguity

DESCRIPTIONLINKS
Origin

Derived from πšπš•πš˜πš‹πšŠπš•_πšŒπš˜πš—πšπš’πšπšžπš’πšπš’.

Constraint

πš–πšžπš•πšπš’_πšπš•πš˜πš‹πšŠπš•_πšŒπš˜πš—πšπš’πšπšžπš’πšπš’(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚)

Synonym

πš–πšžπš•πšπš’_πšŒπš˜πš—πšπš’πšπšžπš’πšπš’.

Argument
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšŸπšŠπš›-πšπšŸπšŠπš›)
Restrictions
πš›πšŽπššπšžπš’πš›πšŽπš(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšŸπšŠπš›)
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš›β‰₯0
Purpose

Enforce all variables of the πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ collection to be assigned a value greater than or equal to 0. In addition, each value v strictly greater than 0 should appear contiguously.

Example
(0,2,2,1,1,0,0,5)

The πš–πšžπš•πšπš’_πšπš•πš˜πš‹πšŠπš•_πšŒπš˜πš—πšπš’πšπšžπš’πšπš’ constraint holds since the sequence 0 2 2 1 1 0 0 5 contains no more than one group of contiguous 1, no more than one group of contiguous 2, and no more than one group of contiguous 5.

Typical
|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|>3
Symmetry

Items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ can be reversed.

Arg. properties

Contractible wrt. πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.

Counting
Length (n)2345678
Solutions9554133656371474250695400481

Number of solutions for πš–πšžπš•πšπš’_πšπš•πš˜πš‹πšŠπš•_πšŒπš˜πš—πšπš’πšπšžπš’πšπš’: domains 0..n

ctrs/multi_global_contiguity-1-tikz

ctrs/multi_global_contiguity-2-tikz

See also

common keyword: πšπš›πš˜πšžπš™Β (sequence).

implied by: πšŠπš•πš•_πšŽπššπšžπšŠπš•, πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš, πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš_πšŽπš‘πšŒπšŽπš™πš_0, πšπšŽπšŒπš›πšŽπšŠπšœπš’πš—πš, πšπš•πš˜πš‹πšŠπš•_πšŒπš˜πš—πšπš’πšπšžπš’πšπš’, πš’πš—πšŒπš›πšŽπšŠπšœπš’πš—πš.

Keywords

combinatorial object: sequence.

constraint type: predefined constraint.