Global Constraint Catalog: Corder

5.305. order

DESCRIPTION

LINKS

Origin

Constraint

$𝚘𝚛𝚍𝚎𝚛 (𝚅𝙴𝙲𝚃𝙾𝚁𝚂, 𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽)$

Type

𝚅𝙴𝙲𝚃𝙾𝚁

𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)

Arguments

$𝚅𝙴𝙲𝚃𝙾𝚁𝚂$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚎𝚌 - 𝚅𝙴𝙲𝚃𝙾𝚁)$
$𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)$

Restrictions

| 𝚅𝙴𝙲𝚃𝙾𝚁 | \geq 1

| 𝚅𝙴𝙲𝚃𝙾𝚁𝚂 | \geq 1

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙴𝙲𝚃𝙾𝚁𝚂, 𝚟𝚎𝚌)

𝚜𝚊𝚖𝚎_𝚜𝚒𝚣𝚎

(𝚅𝙴𝙲𝚃𝙾𝚁𝚂, 𝚟𝚎𝚌)

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽, 𝚟𝚊𝚛)

𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽 . 𝚟𝚊𝚛 \geq 1

𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽 . 𝚟𝚊𝚛 \leq | 𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽 |

| 𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽 | = | 𝚅𝙴𝙲𝚃𝙾𝚁𝚂 |

Purpose

Given a collection of distinct $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ , enforces $𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽 . 𝚟𝚊𝚛 [i]$ to be equal to the position of vector $𝚅𝙴𝙲𝚃𝙾𝚁𝚂 . 𝚟𝚎𝚌 [i]$ within the sorted vectors of the collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ .

Example

(\begin{matrix} 〈\begin{matrix} 𝚟𝚎𝚌 - 〈1, 1, 2, 2〉, \\ 𝚟𝚎𝚌 - 〈2, 1, 2, 1〉, \\ 𝚟𝚎𝚌 - 〈2, 1, 1, 1〉, \\ 𝚟𝚎𝚌 - 〈1, 1, 1, 2〉, \\ 𝚟𝚎𝚌 - 〈1, 2, 2, 1〉, \\ 𝚟𝚎𝚌 - 〈1, 1, 1, 1〉, \\ 𝚟𝚎𝚌 - 〈2, 2, 1, 1〉, \\ 𝚟𝚎𝚌 - 〈2, 1, 1, 2〉 \end{matrix}〉, \\ 〈3, 7, 5, 2, 4, 1, 8, 6〉 \end{matrix})

The $𝚘𝚛𝚍𝚎𝚛$ constraint holds since:

The vector $〈 1, 1, 2, 2 〉$ is in the third position of the sorted collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ ,
The vector $〈 2, 1, 2, 1 〉$ is in the seventh position of the sorted collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ ,
The vector $〈 2, 1, 1, 1 〉$ is in the fifth position of the sorted collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ ,
The vector $〈 1, 1, 1, 2 〉$ is in the second position of the sorted collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ ,
The vector $〈 1, 2, 2, 1 〉$ is in the fourth position of the sorted collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ ,
The vector $〈 1, 1, 1, 1 〉$ is in the first position of the sorted collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ ,
The vector $〈 2, 2, 1, 1 〉$ is in the eigth position of the sorted collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ ,
The vector $〈 2, 1, 1, 2 〉$ is in the sixth position of the sorted collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ .

Typical

| 𝚅𝙴𝙲𝚃𝙾𝚁 | > 1

| 𝚅𝙴𝙲𝚃𝙾𝚁𝚂 | > 1

Arg. properties

Functional dependency: $𝙿𝙴𝚁𝙼𝚄𝚃𝙰𝚃𝙸𝙾𝙽$ determined by $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ .

Keywords

characteristic of a constraint: sort.

combinatorial object: permutation.

modelling: functional dependency.

Global Constraint Catalog

5. Global Constraint Catalogue

5.305. order