"""
General store problem in cpmpy.

From http://www.comp.nus.edu.sg/~henz/projects/puzzles/digits/index.html
'''
The General Store  from 'Mathematical Puzzles of Sam Loyd', number 30

The owner of a general store, who is something of a puzzlist, has put
up this sign to see if any of his mathematical friends can translate
it properly. Each different letter stands for a different digit. The
words above the horizontal line represent numbers that add to the
total of 'ALL WOOL'. The problem is to change all the letters to the
correct digits.

       C H E S S
 +       C A S H
 +   B O W W O W
 +     C H O P S
 +   A L S O P S
 + P A L E A L E
 +       C O O L
 +       B A S S
 +       H O P S
 +       A L E S
 +       H O E S
 +   A P P L E S
 +       C O W S 
 +   C H E E S E
 +   C H S O A P
 +     S H E E P
 _______________
   A L L W O O L
'''

Model created by Hakan Kjellerstrand, hakank@hakank.com
See also my cpmpy page: http://www.hakank.org/cpmpy/

"""
import sys
import numpy as np
from cpmpy import *
from cpmpy.solvers import *
from cpmpy_hakank import *


def general_store():


  n = 10

  # variables
  x = intvar(0,9,shape=n,name="x")
  C, H, E, S, A, B, O, W, P, L = x

  # constraints
  model = Model([AllDifferent(x),
                            10000*C + 1000*H + 100*E + 10*S + S
   +                                  1000*C + 100*A + 10*S + H
   +             100000*B + 10000*O + 1000*W + 100*W + 10*O + W
   +                        10000*C + 1000*H + 100*O + 10*P + S
   +             100000*A + 10000*L + 1000*S + 100*O + 10*P + S
   + 1000000*P + 100000*A + 10000*L + 1000*E + 100*A + 10*L + E
   +                                  1000*C + 100*O + 10*O + L
   +                                  1000*B + 100*A + 10*S + S
   +                                  1000*H + 100*O + 10*P + S
   +                                  1000*A + 100*L + 10*E + S
   +                                  1000*H + 100*O + 10*E + S
   +             100000*A + 10000*P + 1000*P + 100*L + 10*E + S
   +                                  1000*C + 100*O + 10*W + S
   +             100000*C + 10000*H + 1000*E + 100*E + 10*S + E
   +             100000*C + 10000*H + 1000*S + 100*O + 10*A + P
   +                        10000*S + 1000*H + 100*E + 10*E + P   
  == 1000000*A + 100000*L + 10000*L + 1000*W + 100*O + 10*O + L
                 ]
                )

  ss = CPM_ortools(model)
  num_solutions = ss.solveAll(display=x)
  print("num_solutions:", num_solutions)

general_store()