Global Constraint Catalog: Ccompare_and

5.79. compare_and_count

DESCRIPTION

LINKS

Origin

Constraint

$𝚌𝚘𝚖𝚙𝚊𝚛𝚎_𝚊𝚗𝚍_𝚌𝚘𝚞𝚗𝚝 (𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1, 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 2, 𝙲𝙾𝙼𝙿𝙰𝚁𝙴, 𝙲𝙾𝚄𝙽𝚃, 𝙻𝙸𝙼𝙸𝚃)$

Arguments

Restrictions

| 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1 | = | 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 2 |

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1, 𝚟𝚊𝚛)

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 2, 𝚟𝚊𝚛)

𝙲𝙾𝙼𝙿𝙰𝚁𝙴 \in [=, \neq, <, \geq, >, \leq]

𝙲𝙾𝚄𝙽𝚃 \in [=, \neq, <, \geq, >, \leq]

𝙻𝙸𝙼𝙸𝚃 \geq 0

Purpose

Enforce the condition

$(\sum_{i = 1}^{| 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1 |} 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1 [i] . 𝚟𝚊𝚛 𝙲𝙾𝙼𝙿𝙰𝚁𝙴 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 2 [i] . 𝚟𝚊𝚛) 𝙲𝙾𝚄𝙽𝚃 𝙻𝙸𝙼𝙸𝚃$ .

Example

(〈4, 5, 5, 4, 5〉, 〈4, 2, 5, 1, 5〉, =, \leq, 3)

The $𝚌𝚘𝚖𝚙𝚊𝚛𝚎_𝚊𝚗𝚍_𝚌𝚘𝚞𝚗𝚝$ constraint holds since no more than $𝙻𝙸𝙼𝙸𝚃 = 3$ pairs of variables are equal, i.e., the first, third and fifth pairs.

Typical

| 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1 | > 1

𝚛𝚊𝚗𝚐𝚎

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1 . 𝚟𝚊𝚛) > 1

𝚛𝚊𝚗𝚐𝚎

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 2 . 𝚟𝚊𝚛) > 1

𝙲𝙾𝙼𝙿𝙰𝚁𝙴 \in [=]

𝙲𝙾𝚄𝙽𝚃 \in [=, <, \geq, >, \leq]

𝙻𝙸𝙼𝙸𝚃 > 0

𝙻𝙸𝙼𝙸𝚃 < | 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1 |

Arg. properties

Contractible wrt. $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1$ and $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 2$ (remove items from same position) when $𝙲𝙾𝚄𝙽𝚃 \in [<, \leq]$ .
Extensible wrt. $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 1$ and $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 2$ (add items at same position) when $𝙲𝙾𝚄𝙽𝚃 \in [\geq, >]$ .

Keywords

constraint type: predefined constraint, counting constraint.