# Copyright 2010-2017 Google
# 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.

"""OR-tools solution to the N-queens problem."""
from __future__ import print_function
import time
import sys
from ortools.sat.python import cp_model

class NQueenSolutionPrinter(cp_model.CpSolverSolutionCallback):
  """Print intermediate solutions."""

  def __init__(self, queens):
    self.__queens = queens
    self.__solution_count = 0
    self.__start_time = time.time()

  def SolutionCount(self):
    return self.__solution_count

  def NewSolution(self):
    current_time = time.time()
    print('Solution %i, time = %f s' %
          (self.__solution_count, current_time - self.__start_time))
    self.__solution_count += 1

    all_queens = range(len(self.__queens))
    for i in all_queens:
      for j in all_queens:
        if self.Value(self.__queens[j]) == i:
          # There is a queen in column j, row i.
          print('Q', end = ' ')
        else:
          print('_', end = ' ')
      print()
    print()


def main(board_size):
  # Creates the solver.
  model = cp_model.CpModel()
  # Creates the variables.
  # The array index is the column, and the value is the row.
  queens = [model.NewIntVar(0, board_size - 1, 'x%i' % i)
            for i in range(board_size)]
  # Creates the constraints.

  # All rows must be different.
  model.AddAllDifferent(queens)

  # All columns must be different because the indices of queens are all
  # different.

  # No two queens can be on the same diagonal.
  diag1 = []
  diag2 = []
  for i in range(board_size):
    q1 = model.NewIntVar(0, 2 * board_size, 'diag1_%i' % i)
    q2 = model.NewIntVar(-board_size, board_size, 'diag2_%i' % i)
    diag1.append(q1)
    diag2.append(q2)
    model.Add(q1 == queens[i] + i)
    model.Add(q2 == queens[i] - i)
  model.AddAllDifferent(diag1)
  model.AddAllDifferent(diag2)

  ### Solve model.
  solver = cp_model.CpSolver()
  solution_printer = NQueenSolutionPrinter(queens)
  status = solver.SearchForAllSolutions(model, solution_printer)

  print()
  print('Statistics')
  print('  - conflicts       : %i' % solver.NumConflicts())
  print('  - branches        : %i' % solver.NumBranches())
  print('  - wall time       : %f ms' % solver.WallTime())
  print('  - solutions found : %i' % solution_printer.SolutionCount())


# By default, solve the 8x8 problem.
board_size = 8


if __name__ == '__main__':
  if len(sys.argv) > 1:
    board_size = int(sys.argv[1])
  main(board_size)