## 5.178. in_interval

 DESCRIPTION LINKS GRAPH AUTOMATON
Origin

Domain definition.

Constraint

$\mathrm{\pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi  \pi °\pi },\mathrm{\pi »\pi Ύ\pi },\mathrm{\pi \pi Ώ}\right)$

Synonyms

$\mathrm{\pi \pi \pi }$, $\mathrm{\pi \pi }$.

Arguments
 $\mathrm{\pi  \pi °\pi }$ $\mathrm{\pi \pi \pi \pi }$ $\mathrm{\pi »\pi Ύ\pi }$ $\mathrm{\pi \pi \pi }$ $\mathrm{\pi \pi Ώ}$ $\mathrm{\pi \pi \pi }$
Restriction
$\mathrm{\pi »\pi Ύ\pi }\beta €\mathrm{\pi \pi Ώ}$
Purpose

Enforce the domain variable $\mathrm{\pi  \pi °\pi }$ to take a value within the interval $\left[\mathrm{\pi »\pi Ύ\pi },\mathrm{\pi \pi Ώ}\right]$.

Example
$\left(3,2,5\right)$

The $\mathrm{\pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$ constraint holds since its first argument $\mathrm{\pi  \pi °\pi }=3$ is greater than or equal to its second argument $\mathrm{\pi »\pi Ύ\pi }=2$ and less than or equal to its third argument $\mathrm{\pi \pi Ώ}=5$.

Typical
 $\mathrm{\pi »\pi Ύ\pi }<\mathrm{\pi \pi Ώ}$ $\mathrm{\pi  \pi °\pi }>\mathrm{\pi »\pi Ύ\pi }$ $\mathrm{\pi  \pi °\pi }<\mathrm{\pi \pi Ώ}$
Symmetries
• $\mathrm{\pi »\pi Ύ\pi }$ can be decreased.

• $\mathrm{\pi \pi Ώ}$ can be increased.

• An occurrence of a value of $\mathrm{\pi  \pi °\pi }$ can be replaced by any other value in $\left[\mathrm{\pi »\pi Ύ\pi },\mathrm{\pi \pi Ώ}\right]$.

• One and the same constant can be added to $\mathrm{\pi  \pi °\pi }$, $\mathrm{\pi »\pi Ύ\pi }$ and $\mathrm{\pi \pi Ώ}$.

Remark

Entailment occurs immediately after posting this constraint.

The $\mathrm{\pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$ constraint is referenced under the name $\mathrm{\pi \pi \pi }$ inΒ

Systems

member in Choco, dom in Gecode, in in JaCoP, in in SICStus.

See also

generalisation: $\mathrm{\pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi }$Β (reified version), $\mathrm{\pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi }$Β (single interval replaced by a set of intervals), $\mathrm{\pi \pi }_\mathrm{\pi \pi \pi }$Β (interval replaced by set variable).

Keywords
Derived Collections
 $\mathrm{\pi \pi \pi }\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄}-\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi }-\mathrm{\pi \pi \pi \pi }\right),\left[\mathrm{\pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi }-\mathrm{\pi  \pi °\pi }\right)\right]\right)$
Arc input(s)

$\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄}$ $\mathrm{\pi Έ\pi ½\pi \pi ΄\pi \pi  \pi °\pi »}$

Arc generator
$\mathrm{\pi \pi  \pi \pi ·\pi \pi Ά\pi }$$\beta ¦\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi },\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }\right)$

Arc arity
Arc constraint(s)
 $\beta ’\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }.\mathrm{\pi \pi \pi }\beta €\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }.\mathrm{\pi \pi }$
Graph property(ies)
$\mathrm{\pi \pi \pi \pi }$$=1$

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.178.1 respectively show the initial and final graph associated with the Example slot. Since we use the $\mathrm{\pi \pi \pi \pi }$ graph property, the unique arc of the final graph is stressed in bold.

Automaton

FigureΒ 5.178.2 depicts the automaton associated with the $\mathrm{\pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$ constraint. We have a single 0-1 signature variable $S$ as well as the following signature constraint: $\mathrm{\pi  \pi °\pi }\beta ₯\mathrm{\pi »\pi Ύ\pi }\beta §\mathrm{\pi  \pi °\pi }\beta €\mathrm{\pi \pi Ώ}\beta S$.