Global Constraint Catalog: Csum

5.392. sum_set

DESCRIPTION

LINKS

GRAPH

Origin

H. Cambazard

Constraint

$𝚜𝚞𝚖_𝚜𝚎𝚝 (𝚂𝚅, 𝚅𝙰𝙻𝚄𝙴𝚂, 𝙲𝚃𝚁, 𝚅𝙰𝚁)$

Arguments

$𝚂𝚅$	$𝚜𝚟𝚊𝚛$
$𝚅𝙰𝙻𝚄𝙴𝚂$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚕 - 𝚒𝚗𝚝, 𝚌𝚘𝚎𝚏 - 𝚒𝚗𝚝)$
$𝙲𝚃𝚁$	$𝚊𝚝𝚘𝚖$
$𝚅𝙰𝚁$	$𝚍𝚟𝚊𝚛$

Restrictions

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙰𝙻𝚄𝙴𝚂, [𝚟𝚊𝚕, 𝚌𝚘𝚎𝚏])

𝚍𝚒𝚜𝚝𝚒𝚗𝚌𝚝

(𝚅𝙰𝙻𝚄𝙴𝚂, 𝚟𝚊𝚕)

𝚅𝙰𝙻𝚄𝙴𝚂 . 𝚌𝚘𝚎𝚏 \geq 0

𝙲𝚃𝚁 \in [=, \neq, <, \geq, >, \leq]

Purpose

Let $𝚂𝚄𝙼$ denote the sum of the $𝚌𝚘𝚎𝚏$ attributes of the $𝚅𝙰𝙻𝚄𝙴𝚂$ collection for which the corresponding values $𝚟𝚊𝚕$ occur in the set $𝚂𝚅$ . Enforce the following constraint to hold: $𝚂𝚄𝙼 𝙲𝚃𝚁 𝚅𝙰𝚁$ .

Example

(\begin{matrix} {2, 3, 6}, \\ 〈\begin{matrix} 𝚟𝚊𝚕 - 2 & 𝚌𝚘𝚎𝚏 - 7, \\ 𝚟𝚊𝚕 - 9 & 𝚌𝚘𝚎𝚏 - 1, \\ 𝚟𝚊𝚕 - 5 & 𝚌𝚘𝚎𝚏 - 7, \\ 𝚟𝚊𝚕 - 6 & 𝚌𝚘𝚎𝚏 - 2 \end{matrix}〉, =, 9 \end{matrix})

The $𝚜𝚞𝚖_𝚜𝚎𝚝$ constraint holds since the sum of the $𝚌𝚘𝚎𝚏$ attributes $7 + 2$ for which the corresponding $𝚟𝚊𝚕$ attribute belongs to the first argument $𝚂𝚅 = {2, 3, 6}$ is equal (i.e., since $𝙲𝚃𝚁$ is set to $=$ ) to its last argument $𝚅𝙰𝚁 = 9$ .

Typical