024: Langford's number problem

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

  Langford's number problem in Google CP Solver.

  Langford's number problem (CSP lib problem 24)
  http://www.csplib.org/prob/prob024/
  '''
  Arrange 2 sets of positive integers 1..k to a sequence,
  such that, following the first occurence of an integer i,
  each subsequent occurrence of i, appears i+1 indices later
  than the last.
  For example, for k=4, a solution would be 41312432
  '''

  * John E. Miller: Langford's Problem
    http://www.lclark.edu/~miller/langford.html

  * Encyclopedia of Integer Sequences for the number of solutions for each k
    http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=014552


  Also, see the following models:
  * MiniZinc: http://www.hakank.org/minizinc/langford2.mzn
  * Gecode/R: http://www.hakank.org/gecode_r/langford.rb
  * ECLiPSe: http://hakank.org/eclipse/langford.ecl
  * SICStus: http://hakank.org/sicstus/langford.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 sys
import string

from constraint_solver import pywrapcp


def main(k=8, num_sol=0):

    # Create the solver.
    solver = pywrapcp.Solver('Langford')

    #
    # data
    #
    print "k:", k
    p = range(2*k)

    #
    # declare variables
    #
    position = [solver.IntVar(0, 2*k-1, "position[%i]" % i) for i in p]
    solution = [solver.IntVar(1, k, "position[%i]" % i) for i in p]

    #
    # constraints
    #
    solver.Add(solver.AllDifferent(position))

    for i in range(1,k+1):
        solver.Add(position[i+k-1] == position[i-1] + i+1)
        solver.Add(solver.Element(solution, position[i-1]) == i)
        solver.Add(solver.Element(solution, position[k+i-1]) == i)

    # symmetry breaking
    solver.Add(solution[0] < solution[2*k-1])


    #
    # search and result
    #
    db = solver.Phase(position,
                 solver.CHOOSE_FIRST_UNBOUND,
                 solver.ASSIGN_MIN_VALUE)

    solver.NewSearch(db)
    num_solutions = 0
    while solver.NextSolution():
        print "solution:", ",".join([str(solution[i].Value()) for i in p])
        num_solutions += 1
        if num_sol > 0 and num_solutions >= num_sol:
            break

    solver.EndSearch()

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

k = 8
num_sol = 0
if __name__ == '__main__':
    if len(sys.argv) > 1:
        k = string.atoi(sys.argv[1])
    if len(sys.argv) > 2:
        num_sol = string.atoi(sys.argv[2])

    main(k, num_sol)