7.4 Exercises

Exercise 7.1 (See solution)

Magic Sequence
A magic sequence of length is a sequence
$x_0,\;x_1,\;\ldots\;,\;x_{n-1}$
of integers such that for every $i=0,\ldots,n-1$
is an integer between 0 and .
the number occurs exactly times in the sequence.

Write a parameterized script that, given , can enumerate all magic sequences of length .
The script should use the procedure
{FD.exactly K S I}
that creates a propagator for the constraint saying that exactly K fields of the record S are equal to the integer I.
You can drastically reduce the search space of the script by having propagators for the redundant constraints
$x_0\;+\;\ldots\;+\;x_{n-1}\;=\;n$
and
$(-1)\cdot x_0\;+\;\ldots\;+\;(n-2)\cdot x_{n-1}\;=\;0$
Explain why these constraints are redundant.