# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
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@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
import sys
import string
from ortools.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)