Global Constraint Catalog: Cin

5.180. in_intervals

DESCRIPTION

LINKS

Origin

Domain definition.

Constraint

$𝚒𝚗_𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕𝚜 (𝚅𝙰𝚁, 𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂)$

Synonym

$𝚒𝚗$ .

Arguments

$𝚅𝙰𝚁$	$𝚍𝚟𝚊𝚛$
$𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚕𝚘𝚠 - 𝚒𝚗𝚝, 𝚞𝚙 - 𝚒𝚗𝚝)$

Restrictions

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂, [𝚕𝚘𝚠, 𝚞𝚙])

𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂 . 𝚕𝚘𝚠 \leq 𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂 . 𝚞𝚙

| 𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂 | > 0

Purpose

Enforce the domain variable $𝚅𝙰𝚁$ to take a value within one of the intervals specified by the collection of intervals $𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂$ .

Example

(5, 〈𝚕𝚘𝚠 - 1 𝚞𝚙 - 1, 𝚕𝚘𝚠 - 3 𝚞𝚙 - 5, 𝚕𝚘𝚠 - 8 𝚞𝚙 - 8〉)

The $𝚒𝚗_𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕𝚜$ constraint holds since its first argument $𝚅𝙰𝚁 = 5$ belongs to the second intervals of the collection of intervals $𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂$ .

Typical

| 𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂 | > 1

Symmetries

Items of $𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂$ are permutable.
$𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂 . 𝚕𝚘𝚠$ can be decreased.
$𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂 . 𝚞𝚙$ can be increased.
One and the same constant can be added to $𝚅𝙰𝚁$ as well as to the $𝚕𝚘𝚠$ and $𝚞𝚙$ attributes of all items of $𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂$ .

Arg. properties

Extensible wrt. $𝙸𝙽𝚃𝙴𝚁𝚅𝙰𝙻𝚂$ .

Remark

Entailment occurs immediately after posting this constraint.

Systems

dom in Gecode, in in JaCoP, in in SICStus.

See also

specialisation: $𝚒𝚗_𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕$ (set of intervals replaced by single interval).

Keywords

constraint arguments: unary constraint.

constraint type: value constraint, predefined constraint.

filtering: arc-consistency.

modelling: interval, domain definition.