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.
  
  """
  
    Assignment problem in Google CP Solver.
  
    Winston 'Operations Research', Assignment Problems, page 393f
    (generalized version with added test column)
  
    Compare with the following models:
    * Comet   : http://www.hakank.org/comet/assignment.co
    * ECLiPSE : http://www.hakank.org/eclipse/assignment.ecl
    * Gecode  : http://www.hakank.org/gecode/assignment.cpp
    * MiniZinc: http://www.hakank.org/minizinc/assignment.mzn
    * Tailor/Essence': http://www.hakank.org/tailor/assignment.eprime
    * SICStus: http://hakank.org/sicstus/assignment.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/
  """
  from __future__ import print_function
  from ortools.constraint_solver import pywrapcp
  
  
  def main(cost, rows, cols):
    # Create the solver.
    solver = pywrapcp.Solver("n-queens")
  
    #
    # data
    #
  
    # declare variables
    total_cost = solver.IntVar(0, 100, "total_cost")
    x = []
    for i in range(rows):
      t = []
      for j in range(cols):
        t.append(solver.IntVar(0, 1, "x[%i,%i]" % (i, j)))
      x.append(t)
    x_flat = [x[i][j] for i in range(rows) for j in range(cols)]
  
    #
    # constraints
    #
  
    # total_cost
    solver.Add(
        total_cost == solver.Sum(
            [solver.ScalProd(x_row, cost_row) for (x_row, cost_row) in zip(
                x, cost)]))
  
    # exacly one assignment per row, all rows must be assigned
    [solver.Add(solver.Sum([x[row][j] for j in range(cols)]) == 1)
     for row in range(rows)]
  
    # zero or one assignments per column
    [solver.Add(solver.Sum([x[i][col] for i in range(rows)]) <= 1)
     for col in range(cols)]
  
    objective = solver.Minimize(total_cost, 1)
  
    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add(x_flat)
    solution.Add(total_cost)
  
    # db: DecisionBuilder
    db = solver.Phase(x_flat,
                      solver.INT_VAR_SIMPLE,
                      solver.ASSIGN_MIN_VALUE)
  
    solver.NewSearch(db, [objective])
    num_solutions = 0
    while solver.NextSolution():
      print("total_cost:", total_cost.Value())
      for i in range(rows):
        for j in range(cols):
          print(x[i][j].Value(), end=' ')
        print()
      print()
  
      for i in range(rows):
        print("Task:", i, end=' ')
        for j in range(cols):
          if x[i][j].Value() == 1:
            print(" is done by ", j)
      print()
  
      num_solutions += 1
    solver.EndSearch()
  
    print()
    print("num_solutions:", num_solutions)
    print("failures:", solver.Failures())
    print("branches:", solver.Branches())
    print("WallTime:", solver.WallTime())
  
  
  # Problem instance
  # hakank: I added the fifth column to make it more
  #         interesting
  rows = 4
  cols = 5
  cost = [[14, 5, 8, 7, 15],
          [2, 12, 6, 5, 3],
          [7, 8, 3, 9, 7],
          [2, 4, 6, 10, 1]]
  
  if __name__ == "__main__":
    main(cost, rows, cols)
  