Function cp::AllDifferent(valueBinding, values)

# cp::AllDifferent

This function enforces (a slice of) an indexed variable or expression to be assigned all different values, or to determine whether (a slice of) an indexed identifier or expression contains all different values.

## Mathematical Formulation

The function cp::AllDifferent(i,x_i) is equivalent to

$\forall i, j, i\neq j: x_i \neq x_j$

## Function Prototype

cp::AllDifferent(
valueBinding, ! (input) an index binding
values        ! (input/output) an expression
)


## Arguments

valueBinding

The index binding for which the values argument should have all different values.

values

The expression that should have a different value for each element in valueBinding. This expression may involve variables, but can only contain integral or element values (i.e. no strings, fractional, or unit values).

## Return Value

This function returns 1 if the values in values are all distinct, or 0 otherwise. If valueBinding results in zero or one element, then this function will also return 1, and may issue a warning on non-binding constraints.

Note

The following two constraints are equivalent, but a constraint programming solver handles the single row instantiated by Enforcevalues1 much more efficiently than the many instantiated rows resulting from Enforcevalues2.

Constraint Enforcevalues1 {
Definition   :  cp::AllDifferent( i, x(i) );
}

Constraint Enforcevalues2 {
IndexDomain  :  (i,j) | i < j;
Definition   :  x(i) <> x(j);
}


## Example

ElementParameter TheElementParameter {
IndexDomain  : i
Definition   : {
data{ 1 : A,
2 : B,
3 : C }
}
}


With the above data, cp::AllDifferent(i, TheElementParameter(i)) returns 1, because all elements are different. However, with the data below, it returns 0 (the element ‘A’ appears twice).

ElementParameter TheElementParameter {
IndexDomain  : i;
Definition   : {
data{ 1 : A,
2 : B,
3 : A }
}
}


The following code snippet is extracted from the Sudoku example (in which all rows, columns and blocks should have different values). It illustrates the selection of values; particularly illustrating the use of an index domain condition on the first argument as used in the definition of DifferentValuesPerBlock.

Constraint DifferentValuesPerRow {
IndexDomain  :  i;
Definition   :  cp::AllDifferent( j, x(i,j) );
}
Constraint DifferentValuesPerColumn {
IndexDomain  :  j;
Definition   :  cp::AllDifferent( i, x(i,j) );
}
Constraint DifferentValuesPerBlock {
IndexDomain  :  k;
Definition   :  cp::AllDifferent( (i,j) | Blck(i,j) = k, x(i,j) );
}