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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.
"""

  Pandigital numbers in Google CP Solver.

  From Albert H. Beiler 'Recreations in the Theory of Numbers',
  quoted from http://www.worldofnumbers.com/ninedig1.htm
  '''
  Chapter VIII : Digits - and the magic of 9

  The following curious table shows how to arrange the 9 digits so that
  the product of 2 groups is equal to a number represented by the
  remaining digits.

     12 x 483 = 5796
     42 x 138 = 5796
     18 x 297 = 5346
     27 x 198 = 5346
     39 x 186 = 7254
     48 x 159 = 7632
     28 x 157 = 4396
     4 x 1738 = 6952
     4 x 1963 = 7852
  '''

  See also MathWorld http://mathworld.wolfram.com/PandigitalNumber.html
  '''
  A number is said to be pandigital if it contains each of the digits
  from 0 to 9 (and whose leading digit must be nonzero). However,
  'zeroless' pandigital quantities contain the digits 1 through 9.
  Sometimes exclusivity is also required so that each digit is
  restricted to appear exactly once.
  '''

  * Wikipedia http://en.wikipedia.org/wiki/Pandigital_number


  Compare with the the following models:
  * MiniZinc: http://www.hakank.org/minizinc/pandigital_numbers.mzn
  * Comet   : http://www.hakank.org/comet/pandigital_numbers.co
  * ECLiPSe : http://www.hakank.org/eclipse/pandigital_numbers.ecl
  * Gecode/R: http://www.hakank.org/gecoder/pandigital_numbers.rb
  * ECLiPSe : http://hakank.org/eclipse/pandigital_numbers.ecl
  * SICStus : http://hakank.org/sicstus/pandigital_numbers.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
import sys

from ortools.constraint_solver import pywrapcp

#
# converts a number (s) <-> an array of integers (t) in the specific base.
#


def toNum(solver, t, s, base):
  tlen = len(t)
  solver.Add(
      s == solver.Sum([(base**(tlen - i - 1)) * t[i] for i in range(tlen)]))



# Create the solver.
solver = pywrapcp.Solver("Pandigital numbers")

#
# data
#
max_d = base - 1
x_len = max_d + 1 - start
max_num = base**4 - 1

#
# declare variables
#
num1 = solver.IntVar(0, max_num, "num1")
num2 = solver.IntVar(0, max_num, "num2")
res = solver.IntVar(0, max_num, "res")

x = [solver.IntVar(start, max_d, "x[%i]" % i) for i in range(x_len)]

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

toNum(solver, [x[i] for i in range(len1)], num1, base)
toNum(solver, [x[i] for i in range(len1, len1 + len2)], num2, base)
toNum(solver, [x[i] for i in range(len1 + len2, x_len)], res, base)

solver.Add(num1 * num2 == res)

# no number must start with 0
solver.Add(x[0] > 0)
solver.Add(x[len1] > 0)
solver.Add(x[len1 + len2] > 0)

# symmetry breaking
solver.Add(num1 < num2)

#
# solution and search
#
solution = solver.Assignment()
solution.Add(x)
solution.Add(num1)
solution.Add(num2)
solution.Add(res)

db = solver.Phase(x, solver.INT_VAR_SIMPLE, solver.INT_VALUE_DEFAULT)

solver.NewSearch(db)
num_solutions = 0
solutions = []
while solver.NextSolution():
  print_solution([x[i].Value() for i in range(x_len)], len1, len2, x_len)
  num_solutions += 1

solver.EndSearch()

if 0 and num_solutions > 0:
  print()
  print("num_solutions:", num_solutions)
  print("failures:", solver.Failures())
  print("branches:", solver.Branches())
  print("WallTime:", solver.WallTime())
  print()

def print_solution(x, len1, len2, x_len):
  print("".join([str(x[i]) for i in range(len1)]), "*", end=" ")
  print("".join([str(x[i]) for i in range(len1, len1 + len2)]), "=", end=" ")
  print("".join([str(x[i]) for i in range(len1 + len2, x_len)]))


base = 10
start = 1