# 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 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):
        for j in range(cols):
            x[(i, j)] = solver.IntVar(0, 1, 'x(%i,%i)' % (i, j))
    x_flat = [x[(i[j] for i in range(rows) for j in range(cols)]    

    #
    # constraints
    #
    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
    for row in range(rows):
        r = [x[row][j] for j in range(cols)]
        solver.Add(solver.Sum(r) == 1)

    # zero or one assignments per column
    for col in range(cols):
        c = [x[i][col] for i in range(rows)]        
        solver.Add(solver.Sum(c) <= 1)
    

    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()
        xval = [x[i][j].Value() for i in range(rows) for j in range(cols)]
        print "x:", xval
        for i in range(rows):
            for j in range(cols):
                print xval[i*cols+j],
            print
        print
        num_solutions += 1        
    solver.EndSearch()
    
    print
    print "num_solutions:", num_solutions
    print "failures:", solver.failures()
    print "branches:", solver.branches()
    print "wall_time:", solver.wall_time()


# 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)