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


# 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
#         interestingrows = 4
cols = 5
cost = [[14, 5, 8, 7, 15], [2, 12, 6, 5, 3], [7, 8, 3, 9, 7], [2, 4, 6, 10, 1]]