Function cp::Alternative(globalActivity, activityBinding, subActivity, noSelected)

# cp::Alternative

The function cp::Alternative(g,i,a_i,n), returns

• if activity $$g$$ is not present, the value 1 if none of the activities $$a_i$$ are present and 0 otherwise.

• if activity $$g$$ is present, the value 1 if precisely $$n$$ activities $$a_i$$ are present and these present activities match the activity $$g$$.

The function cp::Alternative(g,i,a_i,n) is equivalent to

$g\texttt{.Present} = 0 \Leftrightarrow \forall i: a_i\texttt{.Present} = 0$

and

$\begin{split}g\texttt{.Present} = 1 \Leftrightarrow \left\{ \begin{array}{l} \sum_i a_i\texttt{.Present} = n \\ \forall i: a_i\texttt{.Present} \Rightarrow \left\{ \begin{array}{l} g\texttt{.Begin} = a_i\texttt{.Begin} \\ g\texttt{.End} = a_i\texttt{.End} \end{array} \right. \end{array} \right.\end{split}$

This function is typically used in scheduling problems to denote selected (matching) activities.

cp::Alternative(
globalActivity,   ! (input) an expression
activityBinding,  ! (input) an activity binding
subActivity,      ! (input) an expression
noSelected        ! (optional) an expression
)


## Arguments

globalActivity

An expression resulting in an activity.

activityBinding

An index domain that specifies and possibly limits the scope of indices. This argument follows the syntax of the index domain argument of iterative operators.

subActivity

An expression resulting in an activity. The result is a vector with an element for each possible value of the indices in index domain activityBinding.

noSelected

The number of alternatives, the default being 1. This expression may involve variables.

## Return Value

This function returns 1 if the above condition is satisfied, or otherwise 0. When the index domain activityBinding is empty this function will return an error.

## Example

In the example below we require precisely one of the activities altAct(i) to match the activity chosenAct(i).

Constraint PreciselyOneAlternativeMatches {
Definition   :  cp::Alternative( chosenAct, i, altAct(i) );
}


We could change the above example to allow multiple matches as follows:

Variable noMatches {
Range        :  {
{ 1 .. n }
}
}
Constraint AtLeastOneAlternativeMatches {
Definition   :  cp::Alternative( chosenAct, i, altAct(i), noMatches );
}


Here, the number of matches is counted in the integer variable noMatches.