Global Constraint Catalog: Clex_alldifferent_except

5.221. lex_alldifferent_except_0

DESCRIPTION

LINKS

Origin

H. Simonis

Constraint

$𝚕𝚎𝚡_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝_𝚎𝚡𝚌𝚎𝚙𝚝_0 (𝚅𝙴𝙲𝚃𝙾𝚁𝚂)$

Synonyms

$𝚕𝚎𝚡_𝚊𝚕𝚕𝚍𝚒𝚏𝚏_𝚎𝚡𝚌𝚎𝚙𝚝_0$ , $𝚕𝚎𝚡_𝚊𝚕𝚕𝚍𝚒𝚜𝚝𝚒𝚗𝚌𝚝_𝚎𝚡𝚌𝚎𝚙𝚝_0$ , $𝚊𝚕𝚕𝚍𝚒𝚏𝚏_𝚘𝚗_𝚝𝚞𝚙𝚕𝚎𝚜_𝚎𝚡𝚌𝚎𝚙𝚝_0$ , $𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝_𝚘𝚗_𝚝𝚞𝚙𝚕𝚎𝚜_𝚎𝚡𝚌𝚎𝚙𝚝_0$ , $𝚊𝚕𝚕𝚍𝚒𝚜𝚝𝚒𝚗𝚌𝚝_𝚘𝚗_𝚝𝚞𝚙𝚕𝚎𝚜_𝚎𝚡𝚌𝚎𝚙𝚝_0$ .

Type

𝚅𝙴𝙲𝚃𝙾𝚁

𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)

Argument

𝚅𝙴𝙲𝚃𝙾𝚁𝚂

𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚎𝚌 - 𝚅𝙴𝙲𝚃𝙾𝚁)

Restrictions

| 𝚅𝙴𝙲𝚃𝙾𝚁 | \geq 1

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙴𝙲𝚃𝙾𝚁, 𝚟𝚊𝚛)

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙴𝙲𝚃𝙾𝚁𝚂, 𝚟𝚎𝚌)

𝚜𝚊𝚖𝚎_𝚜𝚒𝚣𝚎

(𝚅𝙴𝙲𝚃𝙾𝚁𝚂, 𝚟𝚎𝚌)

Purpose

All the non null vectors of the collection $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ are distinct. A vector is null if all its components are equal to zero. Two non null vectors $(u_{1}, u_{2}, \dots, u_{n})$ and $(v_{1}, v_{2}, \dots, v_{n})$ are distinct if and only if there exists $i \in [1, n]$ such that $u_{i} \neq v_{i}$ .

Example

(\begin{matrix} 〈\begin{matrix} 𝚟𝚎𝚌 - 〈0, 0, 0〉, \\ 𝚟𝚎𝚌 - 〈5, 2, 0〉, \\ 𝚟𝚎𝚌 - 〈5, 8, 0〉, \\ 𝚟𝚎𝚌 - 〈0, 0, 0〉 \end{matrix}〉 \end{matrix})

The $𝚕𝚎𝚡_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝_𝚎𝚡𝚌𝚎𝚙𝚝_0$ constraint holds since its two non null vectors, i.e. the second and third vectors are distinct (the vectors $〈 5, 2, 0 〉$ and $〈 5, 8, 0 〉$ differ in their second component.

Typical

| 𝚅𝙴𝙲𝚃𝙾𝚁 | > 1

| 𝚅𝙴𝙲𝚃𝙾𝚁𝚂 | > 1

Arg. properties

Contractible wrt. $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ .

See also

implied by: $𝚕𝚎𝚡_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝$ .

Keywords

characteristic of a constraint: vector, joker value.

modelling: difference between pairs of variables.

Global Constraint Catalog

5. Global Constraint Catalogue

5.221. lex_alldifferent_except_0