/*
All intervals problem in JaCoP/Scala.
CSPLib problem number 7
http://www.cs.st-andrews.ac.uk/~ianm/CSPLib/prob/prob007/index.html
"""
Given the twelve standard pitch-classes (c, c , d, ...), represented by
numbers 0,1,...,11, find a series in which each pitch-class occurs exactly
once and in which the musical intervals between neighbouring notes cover
the full set of intervals from the minor second (1 semitone) to the major
seventh (11 semitones). That is, for each of the intervals, there is a
pair of neigbhouring pitch-classes in the series, between which this
interval appears. The problem of finding such a series can be easily
formulated as an instance of a more general arithmetic problem on Z_n,
the set of integer residues modulo n. Given n in N, find a vector
s = (s_1, ..., s_n), such that (i) s is a permutation of
Z_n = {0,1,...,n-1}; and (ii) the interval vector
v = (|s_2-s_1|, |s_3-s_2|, ... |s_n-s_{n-1}|) is a permutation of
Z_n-{0} = {1,2,...,n-1}. A vector v satisfying these conditions is
called an all-interval series of size n; the problem of finding such
a series is the all-interval series problem of size n. We may also be
interested in finding all possible series of a given size.
"""
This model was written by Hakan Kjellerstrand (hakank@bonetmail.com).
See my JaCoP/Scala page: http://www.hakank.org/jacop/jacop_scala.html
*/
import scalaJaCoP._
object AllIntervals extends App with jacop {
//
// simple decomposition of c #= abs(a,b)
// (Not needed any more...)
def my_abs(a:IntVar, b:IntVar, c:IntVar) {
val b1 = new BoolVar("b1")
b1 <=> (a #> b)
b1 -> (c #= a - b)
~b1 -> (c #= b - a)
}
// data
var n = 11
if (args.length > 0) {
n = args(0).toInt
}
// variables
val x = Array.tabulate(n)(i=> new IntVar("x("+i+")", 1, n))
val diffs = Array.tabulate(n-1)(i=> new IntVar("diffs("+i+")", 1, n-1))
// constraints
alldifferent(x)
alldifferent(diffs)
// rows and columns
for(k <- 0 until n-1) {
// JaCoP/Scala don't have abs
diffs(k) #= abs(x(k+1)-x(k))
// This is not needed any more
// my_abs(x(k), x(k+1), diffs(k))
}
// symmetry breaking
x(0) #< x(n-1)
diffs(0) #< diffs(1)
// search
val result = satisfyAll(search(x ++ diffs, max_regret, indomain_min), printIt)
statistics
def printIt() {
print("\nx: ")
x.foreach(v=>print(v.value + " "))
print(" diffs: ")
diffs.foreach(v=>print(v.value + " "))
println()
}
}