text: # 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.
  
  """
  
    Magic squares in Google CP Solver.
  
    Magic square problem.
  
    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/
  """
  from __future__ import print_function
  import sys
  from ortools.constraint_solver import pywrapcp
  
  
  def main(n=4):
    # Create the solver.
    solver = pywrapcp.Solver("n-queens")
  
    #
    # data
    #
  
    #
    # declare variables
    #
    x = {}
    for i in range(n):
      for j in range(n):
        x[(i, j)] = solver.IntVar(1, n * n, "x(%i,%i)" % (i, j))
    x_flat = [x[(i, j)] for i in range(n) for j in range(n)]
  
    # the sum
    # s = ( n * (n*n + 1)) / 2
    s = solver.IntVar(1, n * n * n, "s")
  
    #
    # constraints
    #
    # solver.Add(s == ( n * (n*n + 1)) / 2)
  
    solver.Add(solver.AllDifferent(x_flat))
  
    [solver.Add(solver.Sum([x[(i, j)] for j in range(n)]) == s) for i in range(n)]
    [solver.Add(solver.Sum([x[(i, j)] for i in range(n)]) == s) for j in range(n)]
  
    solver.Add(solver.Sum([x[(i, i)] for i in range(n)]) == s)  # diag 1
    solver.Add(solver.Sum([x[(i, n - i - 1)] for i in range(n)]) == s)  # diag 2
  
    # symmetry breaking
    # solver.Add(x[(0,0)] == 1)
  
    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add(x_flat)
    solution.Add(s)
  
    # db: DecisionBuilder
    db = solver.Phase(x_flat,
                      # solver.INT_VAR_DEFAULT,
                      solver.CHOOSE_FIRST_UNBOUND,
                      # solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
  
                      # solver.ASSIGN_MIN_VALUE
                      solver.ASSIGN_CENTER_VALUE)
  
    solver.NewSearch(db)
    num_solutions = 0
    while solver.NextSolution():
      print("s:", s.Value())
      for i in range(n):
        for j in range(n):
          print("%2i" % x[(i, j)].Value(), end=' ')
        print()
  
      print()
      num_solutions += 1
    solver.EndSearch()
  
    print()
    print("num_solutions:", num_solutions)
    print("failures:", solver.Failures())
    print("branches:", solver.Branches())
    print("WallTime:", solver.WallTime())
  
  n = 4
  if __name__ == "__main__":
    if len(sys.argv) > 1:
      n = int(sys.argv[1])
    main(n)
  