Function cp::Span(globalActivity, activityBinding, subActivity)

# cp::Span¶

The function cp::Span(g,i,a_i) returns 1 if activity $$g$$ and activities $$a_i$$ are all not present, or if the begin of present activity $$g$$ is equal to the first present activity $$a_i$$ and the end of activity $$g$$ is equal to the end of the last present activity $$a_i$$. The function cp::Span(g,i,a_i) is equivalent to

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

and

$\begin{split}g\texttt{.Present} = 1 \Leftrightarrow \left\{ \begin{array}{l} \exists i|a_i\texttt{.Present} \\ g\texttt{.Begin} = \min_{i|a_i\texttt{.Present}} a_i\texttt{.Begin} \\ g\texttt{.End} = \max_{i|a_i\texttt{.Present}} a_i\texttt{.End} \end{array} \right.\end{split}$

This function is typically used in scheduling problems to split an activity into sub activities.

cp::Span(
globalActivity,   ! (input) an expression
activityBinding,  ! (input) an index domain
subActivity       ! (input) 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.

## Return Value¶

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