# 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.

"""

  SEND+MORE=MONEY in 'any' base in Google CP Solver.

  Alphametic problem SEND+MORE=MONEY in any base.

  Examples:
  Base 10 has one solution:
     {9, 5, 6, 7, 1, 0, 8, 2}
  Base 11 has three soltutions:
     {10, 5, 6, 8, 1, 0, 9, 2}
     {10, 6, 7, 8, 1, 0, 9, 3}
     {10, 7, 8, 6, 1, 0, 9, 2}

  Also, compare with the following models:
  * Comet   : http://www.hakank.org/comet/send_more_money_any_base.co
  * ECLiPSE : http://www.hakank.org/eclipse/send_more_money_any_base.ecl
  * Essence : http://www.hakank.org/tailor/send_more_money_any_base.eprime
  * Gecode  : http://www.hakank.org/gecode/send_more_money_any_base.cpp
  * Gecode/R: http://www.hakank.org/gecode_r/send_more_money_any_base.rb
  * MiniZinc: http://www.hakank.org/minizinc/send_more_money_any_base.mzn
  * Zinc: http://www.hakank.org/minizinc/send_more_money_any_base.zinc
  * SICStus: http://www.hakank.org/sicstus/send_more_money_any_base.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/

"""

import sys
import string
from ortools.constraint_solver import pywrapcp

def main(base=10):

    # Create the solver.
    solver = pywrapcp.Solver('Send most money')

    # data

    # declare variables
    s = solver.IntVar(0,base-1,'s')
    e = solver.IntVar(0,base-1,'e')
    n = solver.IntVar(0,base-1,'n')
    d = solver.IntVar(0,base-1,'d')
    m = solver.IntVar(0,base-1,'m')
    o = solver.IntVar(0,base-1,'o')
    r = solver.IntVar(0,base-1,'r')
    y = solver.IntVar(0,base-1,'y')

    x = [s,e,n,d,m,o,r,y]

    xx = [s,e,n,d,  m,o,r,e, m,o,n,e,y]


    #
    # constraints
    #
    solver.Add(solver.AllDifferent(x, True))

    coeffs =  [1000, 100, 10, 1,         # S E N D +
               1000, 100, 10, 1,         # M O R E
               -10000,-1000, -100,-10,-1 # == M O N E Y
               ]
    
    solver.Add(0 == solver.ScalProd(xx, coeffs))
    solver.Add(s > 0)
    solver.Add(m > 0)


    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add(x)

    collector = solver.AllSolutionCollector(solution)

    solver.Solve(solver.Phase(x,
                              solver.CHOOSE_FIRST_UNBOUND,
                              solver.ASSIGN_MAX_VALUE),
                              [collector])

    num_solutions = collector.SolutionCount()
    money_val = 0
    for s in range(num_solutions):
        print "x:", [collector.Value(s, x[i]) for i in range(len(x))]

    print
    print "num_solutions:", num_solutions
    print "failures:", solver.Failures()
    print "branches:", solver.Branches()
    print "wall_time:", solver.WallTime()
    print


base = 10
if __name__ == '__main__':
    # for base in range(10,30):
    #    main(base)
    if len(sys.argv) > 1:
        base=string.atoi(sys.argv[1])

    main(base)