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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.
"""

  Generic alphametic solver in Google CP Solver.

  This is a generic alphametic solver.

  Usage:
     python alphametic.py
                         ->  solves SEND+MORE=MONEY in base 10

     python alphametic.py  'SEND+MOST=MONEY' 11
                         -> solver SEND+MOST=MONEY in base 11

     python alphametic.py TEST <base>
                         -> solve some test problems in base <base>
                            (defined in test_problems())

  Assumptions:
  - we only solves problems of the form
           NUMBER<1>+NUMBER<2>...+NUMBER<N-1> = NUMBER<N>
    i.e. the last number is the sum
  - the only nonletter characters are: +, =, \d (which are splitted upon)


  Compare with the following model:
  * Zinc: http://www.hakank.org/minizinc/alphametic.zinc

  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
import re

from ortools.constraint_solver import pywrapcp



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

# data
print("\nproblem:", problem_str)

# convert to array.
problem = re.split("[\s+=]", problem_str)

p_len = len(problem)
print("base:", base)

# create the lookup table: list of (digit : ix)
a = sorted(set("".join(problem)))
n = len(a)
lookup = dict(list(zip(a, list(range(n)))))

# length of each number
lens = list(map(len, problem))

#
# declare variables
#

# the digits
x = [solver.IntVar(0, base - 1, "x[%i]" % i) for i in range(n)]
# the sums of each number (e.g. the three numbers SEND, MORE, MONEY)
sums = [solver.IntVar(1, 10**(lens[i]) - 1) for i in range(p_len)]

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

ix = 0
for prob in problem:
  this_len = len(prob)

  # sum all the digits with proper exponents to a number
  solver.Add(
      sums[ix] == solver.Sum([(base**i) * x[lookup[prob[this_len - i - 1]]]
                              for i in range(this_len)[::-1]]))
  # leading digits must be > 0
  solver.Add(x[lookup[prob[0]]] > 0)
  ix += 1

# the last number is the sum of the previous numbers
solver.Add(solver.Sum([sums[i] for i in range(p_len - 1)]) == sums[-1])

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

db = solver.Phase(x, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)

solver.NewSearch(db)

num_solutions = 0
while solver.NextSolution():
  num_solutions += 1
  print("\nsolution #%i" % num_solutions)
  for i in range(n):
    print(a[i], "=", x[i].Value())
  print()
  for prob in problem:
    for p in prob:
      print(p, end=" ")
    print()
  print()
  for prob in problem:
    for p in prob:
      print(x[lookup[p]].Value(), end=" ")
    print()

  print("sums:", [sums[i].Value() for i in range(p_len)])
  print()

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

def test_problems(base=10):
  problems = [
      "SEND+MORE=MONEY", "SEND+MOST=MONEY", "VINGT+CINQ+CINQ=TRENTE",
      "EIN+EIN+EIN+EIN=VIER", "DONALD+GERALD=ROBERT",
      "SATURN+URANUS+NEPTUNE+PLUTO+PLANETS", "WRONG+WRONG=RIGHT"
  ]

  for p in problems:
    main(p, base)


problem = "SEND+MORE=MONEY"
base = 10