007: All-Interval Series

# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
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"""

  All interval problem in Google CP Solver.

  CSPLib problem number 7
  http://www.csplib.org/Problems/prob007
  '''
  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.
  '''

 Compare with the following models:
  * MiniZinc: http://www.hakank.org/minizinc/all_interval.mzn
  * Comet   : http://www.hakank.org/comet/all_interval.co
  * Gecode/R: http://www.hakank.org/gecode_r/all_interval.rb
  * ECLiPSe : http://www.hakank.org/eclipse/all_interval.ecl
  * SICStus : http://www.hakank.org/sicstus/all_interval.pl


  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

"""
import string, sys

from constraint_solver import pywrapcp

def main(n=12):

    # Create the solver.
    solver = pywrapcp.Solver('All interval')

    #
    # data
    #
    print "n:", n

    #
    # declare variables
    #
    x = [solver.IntVar(1, n, 'x[%i]' % i) for i in range(n)]
    diffs = [solver.IntVar(1, n-1, 'diffs[%i]' % i) for i in range(n-1)]

    #
    # constraints
    #
    solver.Add(solver.AllDifferent(x))
    solver.Add(solver.AllDifferent(diffs))

    for k in range(n-1):
        solver.Add(diffs[k] == abs(x[k+1]-x[k]))

    # symmetry breaking
    solver.Add(x[0] < x[n-1])
    solver.Add(diffs[0] < diffs[1])

    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add(x)
    solution.Add(diffs)

    db = solver.Phase(x,
                      solver.CHOOSE_FIRST_UNBOUND,
                      solver.ASSIGN_MIN_VALUE)

    solver.NewSearch(db)
    num_solutions = 0
    while solver.NextSolution():
        print "x:", [x[i].Value() for i in range(n)]
        print "diffs:", [diffs[i].Value() for i in range(n-1)]
        num_solutions += 1
        print

    print "num_solutions:", num_solutions
    print "failures:", solver.Failures()
    print "branches:", solver.Branches()
    print "WallTime:", solver.WallTime()

n=12
if __name__ == '__main__':
    if len(sys.argv) > 1:
        n = string.atoi(sys.argv[1])
    main(n)